MEF - PARAMETRII DE DISCRETIZARE A STRUCTURILOR · 2016. 10. 12. · finite element modeling, higher Von Mises stresses can be achieved in the case of convex fillet welding A as compared

Fiabilitate si Durabilitate - Fiability & Durability No 2/ 2015 Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X

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CONTENTS

Pag.

1. Claudiu BABIS; Oana CHIVU; Zoia APOSTOLESCU; Dan NITOI - THE

INFLUENCE OF WELD SEAM SHAPE AND THE FATIGUE IN CASE OF THE

FILLET WELDS..............................................................................................................

3

2. Claudiu BABIS; Oana CHIVU; Zoia APOSTOLESCU; Catalin AMZA - RAISING THE DURABILLITY CURVES IN CASE OF WELDING ELEMENTS........

8

3. Constantin BREZEANU, Ioana POPESCU, Păun ANTONESCU -

TOPOLOGICAL STRUCTURE OF CONNECTING MECHANISMS IN THE

ELECTRIC GRID……………………………………………………………………………

15

4. Ştefan GHIMISI - EXPERIMENTAL INVESTIGTION OF THE FRETTING

PHENOMENON..............................................................................................................

23

5. Ovidiu ANTONESCU, Cătălina ROBU, Paun ANTONESCU - LINKAGES FOR

QUADRUPED BIO-ROBOT WALKING…………………………………………………

28

6. Ioana POPESCU, Ovidiu ANTONESCU, Păun ANTONESCU - STRUCTURAL

AND GEOMETRICAL ANALYSIS OF THE LIFTING MANIPULATORS FOR A

GREEN ENVIRONMENT………………………………………………………………….

36

7. Păun ANTONESCU, Ovidiu ANTONESCU, Constantin BREZEANU - THE

GEOMETRY OF THE SPATIAL FOUR-BAR MECHANISMAND OF ITS

PARTICULAR FORMS………………………………………………………………………

44

8. Ovidiu ANTONESCU, Viorica VELISCU, Daniela ANTONESCU - PLANAR

MECHANISMS USED FOR GENERATING CURVE LINE TRANSLATION MOTION

52

9. Ovidiu ANTONESCU, Viorica VELIȘCU, Constantin BREZEANU - MAIN

TYPES OF MECHANISMS USED AS WINDSHIELD WIPER …………………………

59

10. Marian G. POP, Ioan BADIU, Marcel S. POPA - PROCESSING ELECTRICAL

EROSION TO ROTATE WITEH TEETH TILTED.............................

67

11. Marcel S.POPA, Ioan BADIU - GEAR WHEELS THE PROCESSED BY

ELECTRICAL EROSION. ............................................................................................

86


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3

THE INFLUENCE OF WELD SEAM SHAPE AND THE FATIGUE IN

CASE OF THE FILLET WELDS

Claudiu BABIS; Oana CHIVU; Zoia APOSTOLESCU; Dan NITOI

Abstract:

The stress concentrators at MA/MB welding joint will increase by the cross sectional convexity of the

fillet weld. Therefore, for variable loaded structures, based on a satisfactory fatigue life, concave fillet welds

are preferred likely to ensure low stress concentrators at the MA/MB welding joint due to a smooth passing

from the fillet weld to the basic material. The present paper aims is analyse the fatigue life duration raising

durability curves based on experimental determination and using the Finite Element Analysis Method.

Keywords: stress concentrators, fillet welds, FEM.

1. Introduction

In the case of corner welding, the theoretically thickness of the welded row is equal

with the high of the isoscel triangle inscribed in the weld transversal section (figure 1).

a b c d

Fig. 1 Possible shapes of the welded corner rows

a-plane; b – convex, c – concave, d – sharp concav

According to the figure 1, depending of the fraction k/a, the welded rows could be:

-plane, when k/a ≈ 2 ( figure 1.a ), convex, when k/a > 2 ( figure 1.b ), concave,

when k/a < 2 ( figure 1 c and d ). Because the weld convex shape, favorize concentration

of the stresses in the deposed metal it is recomended to used the concave shape mostly to

structures that works in oscillating conditions. It has to be mentioned that in the case of

concave rows an optimally angle has to be define because when the concavity increases the

residual stresses also increases. Some norms provides the α angle to be larger than 70o.

The convex cross sectional shape of fillet welds has a negative impact on the level of

stress concentrators [6], leading to its growth as compared to the concave case. There are

various rehabilitation techniques used in order to decrease stress concentrators and increase

fatigue life: milling of the weld toe; hammer peening; WIG re -melting of the weld toe [7].


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2. Research methodology

In view of determining the fatigue life, two types of samples have been used: cross joint

welds, marked as A – the wire based MAG welding, providing convex fillet welds and D –

the MAG tubular wire welding providing concave fillet welds, respectively.

In order to test fatigue life, 9 samples have been extracted by means of mechanical

cutting, similar to the one shown in Figure 1, and classified into three sample batches so as to

apply rehabilitation techniques as follows: the first batch A1;A2; A3 and B1;B2;B3,

respectively – without rehabilitation; the second batch: A3;A4;A5 and B3;B4;B5,

respectively – based on the milling of the weld toe and the third batch A6;A7;A8 and

B6;B7;B8 , respectively- based on WIG re-melting.

Fig. 2. Shape and dimensions of samples for fatigue life

The samples have been tested for fatigue, according to symmetrical stress cycles such as

stretch and compression, 10 Hz, frequency. Each batch took into account three values as

provided by the ±14 KN; ±9KN and ±7,5KN forces, thus, obtaining the corresponding

fatigue frames. The number of cycles till the breaking point has been determined for each

sample and then, durability curves have been outlined. Comparison of the fatigue life

durations has been conducted in the case of convex and concave fillet welds, with or without

the rehabilitation techniques applied. On space grounds, only some of the results obtained will

be presented.

The next step of the research tackled a comparative finite element based analysis of the

stress level for both concave and convex fillet welds. Moreover, fatigue tests and durability

curves have been dealt with.

For each sample batch, with or without applied rehabilitation techniques, a durability curve

has been achieved followed by comparisons. To mark durability curves, three force variations

have been applied to each batch, as follows: for batch 1: A1/D1 →±14 KN; A2/D2 →F2= ±9

KN; A3/D3 → ±7,5 KN; for batch 2: A5/D5 → ±14 KN; A6/D6 →±7,5 KN; for batch 3:

A8/D8→±14 KN; A9/D9 →±7,5KN.


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Fatigue life results are presented in table 1.

Table 1 Fatigue Life Test Results for Sample A

No.

Technical

Shape

Marking f [Hz] +/-Fi [KN] t [s] N=t*f

1

convex

without

A1

10

±F1=±14 594 5940

2 A2 ±F2=±9 1488 14880

3 A3 ±F3=±7,5 7384 73840

4 Milling of

weld toe

A5 ±F1=±14 843 8430

5 A6 ±F3=±7,5 10706 107060

6 WIG re-

melting

A8 ±F1=±14 1752 17520

7 A9 ±F3=±7,5 22152 221520

Table 2. Fatigue Life Test Results for Sample D

No.

Technical

Shape Marking f [Hz] +/-Fi [KN] t [s] N=t*f

1

convex

without

D1

10

±F1=±14 1850 18500

2 D2 ±F2=±9 4612.8 46128

3 D3 ±F3=±7,5 22890 228904

4 Milling of weld

toe

D5 ±F1=±14 2682 26820

5 D6 ±F3=±7,5 33189 331896

6 WIG re-melting

D8 ±F1=±14 5457 54570

7 D9 ±F3=±7,5 68672 686720

The holistic picture of the stresses exerting upon the welded structure focuses on the Von

Mises type of stress as shown in Figure 3.

a b

Fig. 3. Von Mises type of stress by a Ftot = 14 KN force

a- Convex fillet welding A- σmax = 0.24·109 N/m

2; b- concave fillet welding D σmax = 0.19·10

9N/m

2.


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3. Conclusions

The durability curves for samples A and D, respectively are revealed in Figure 4 and 5.

σ1a(n) Without rehabilitation; p=2 ; r=6.3

σ2a(n); milling; p=2 ; r= 6,4

σ3a(n)WIG re-melting; p=2 ; r= 6,6

Fig. 4. Durability curves for sample A

σ1a(n) Without rehabilitation; p=2 ; r=6.3

σ2a(n); milling; p=2 ; r= 6,4

σ3a(n)WIG re-melting; p=2 ; r= 6,6

Fig. 5. Durability curves for sample D


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As shown in Figure 4 and 5, there is no durability curve asymptotic to the horizontal

axis and hence, there is no resistance to fatigue σ0 .

As illustrated in Tables 1 and 2 as well as in Figures 4 and 5, there is a growth by

almost 40% in the number of fatigue cycles as a result of milling the weld toe (A5; A6 and

D5; D6, respectively) and by up to 195% as a result of WIG re-melting of the weld toe (A8;

A9 and D8; D9, respectively),as compared to the situation in which no rehabilitation

technique is applied (A1; A2; A3 and D1; D2; D3, respectively).

Figure 4 indicates a growth of 210 % in the fatigue life for sample D as compared to

similar A samples, according to the similar loads and rehabilitation techniques.

A key observation drawn from Figure 2 a and b highlights the fact that, by means of

finite element modeling, higher Von Mises stresses can be achieved in the case of convex

fillet welding A as compared to concave fillet welding D.

4. References

[1] A. Ohta, T. Mawari (1990). Fatigue strength of butt welded Al-Mg aluminium alloy: tests

with maximum stress at yield strength. Fatigue & Fracture of Engineering Materials &

Structures, 13, 53-58.

[2] B. Chang, Y. Shi, L. Lu (2001). Studies on the stress distribution and fatigue behavior of

welded-bonded lap shear joints. Journal of Materials Processing Technology, 108, 307-313.

[3] C. Lindgren, J.O. Sperle, M. Jonsson (1996). Fatigue strength of spot welded beams in

ligh strength steels. Welding in the World, 37, 90-104.

[4] C-H. Lee, K-H. Chang, G-C. Jang, C-Y Lee (2009). Effect of welded geometry on the

fatigue life of non-load-carrying fillet welded cruciform joints. Engineering Failure Analysis,

16 849-855.

[5] D. P. Kihl, S. Sarkani (1999). Mean stress effects in fatigue of welded steel joints.

Probabilistic Engineering Mechanics, 14, 97-104.

[6] D. Zivkovic, B. Anzulovic (2005). The fatigue of 5083 aluminium alloy welds with the

shot-peened crater hot cracks. Materials & Design, 26, 247-250.

[7] F. Lefebvre, S. Ganguly, I. Sinclair (2005). Micromechanical aspects of fatigue in a MIG

welded aliminium airframe alloy. Part 1. Microstructural Characterization, Material Science

and Engineering, 397, 338-445.


8

RAISING THE DURABILLITY CURVES IN CASE OF WELDING

ELEMENTS

Claudiu BABIS; Oana CHIVU; Zoia APOSTOLESCU; Catalin AMZA

[email protected]; [email protected]; [email protected];

[email protected]

Abstract: Raising the durabillity curves is very important, being a useful tool in assessing the duration of the

fatigue life of an item or welded structure. Determination of life duration up to fail, indicate us the right time

for the rehabilitation of welded structure leading to labor savings and avoiding catastrophic failurewe that

would endanger people's lives.

The paper will present for three welded specimens experimental determinations of variable load cycles

until failure, then will rise durabillity curves using a mathematical program.

Key words: variable stresses; fatigue life; durability curves

1. Introduction

The present paper is based on the opinion that dynamically exposed weld elements,

contain cracks of different sizes and that is why rehabilitation is required after a period of

time given by the durabillity curves.

There are numerous welded structures likely to be exposed to stress in the course of

time (bridges, power installations, etc.). Research has proved that such structures crack under

stress concentrations lower than the tear resistance of the static materials they are made up of;

the higher the stress concentration the sooner the fracture. The functioning time, that is the

number of stress variation cycles a component is resistant to depend on its maximum stress

level. This is graphically shown by an experimentally fixed curve (Wohler’s curve)-figure 1.

Fig. 1. Wohler’s curve

Such a curve in N-σ ( N-τ) system shows that the higher the number of cycles N any

component is resistant to, the lower the stress σ. For a certain value σ0 of overall stress, the

component resists to numerous, countless reinitializing cycles.

mailto:[email protected]





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This value σ0 stands for fatigue resistance. Research has shown that ferrous metals

resistant to 10 7

variation cycles of the overall stress never crack. Hence, for such materials,

fatigue resistance is defined according to NB=10 7. Fatigue resistance of welded joints is

much lower than that of the material due to the overall welding stress concentration. Internal

and external concentrators differ from the structure itself. Unlike the material, that may

display lamination defects, the weld displays defects typical of molded materials. Internal

concentrators are the result of pores of gases, the roots of the welds and joints of electrodes

change, in the case of manual welding. External concentrators can be seen at the ends of the

welding line as well as in the junction point of the welding and base material. The

concentrators impact can be lowered or even eliminated by appropriate welding of the

respective junctions. The concentration coefficient value is influenced by various factors

typical of welded joints: the base material, additional material, the welding procedure used,

internal and external welding defects, the junction form, the welding bead form, recurring

stress concentrations, etc. The weld may bring about the lower fatigue resistance of the

component even if the welding is of high quality and does not modify the strength lines flow

of the respective component.

2. Research methodology

The research conducted, consists in an analysis of the fatigue life of three identical

welded samples marked with I1; I2 and I3, using three values of the apllied forces.

3. Shape and dimensions of samples

Figure 2 illustrates the shape and dimensions of the samples to be subject to fatigue

tests.

Fig.2 Shape and dimensions of weld

deposited samples

Fig. 3 Shape and dimensions of

sampleswith seam weld deposit

dynamically stressed


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The sample is obtained from a 7 mm thick, 30 mm wide and 390 mm long wideplate

and is made of common steel S235JR according to NF EN 10028-2.

The sample presented in Figure 2 will bring about three samples I1; I2 and I3, of

approximately 130 mm long and 5 mm wide, the width is obtained by previous mechanical

grinding on both sides of the wideplate width.

Once samples 1; 2 and 3 have been extracted, one set of samples will be obtained as

follows: set 1: I1; I2 and I3 corresponding to sample I;

A stress variation ΔF1=±10 KN; ΔF2=±8 KN and ΔF3=± 6,5 KN respectively will be

applied to samples 1; 2 and 3 corresponding to each sample/set in order to obtain a durability

curve for each of the sample/set. The stress cycle will be alternating and symmetric and the

stress factor is a tensile-pressure type. Figure 3 shows the shape and dimensions of samples

1; 2 and 3, as resulted from samples I.

The samples I are obtained, as follows: the sample set I1; I2 and I3 respectively,

corresponding to the first sample I is obtained from a 7 X 30 X 390 mm wideplate with

cycling weld deposition, by means of a manual welding SMEI covered electrode procedure, a

3 mm thick, 15 mm wide and 390 long weld bead, the resulting dimension of the samples

obtained being 10 X 5 X 130 mm. A 10 mm tickness is achieved since 3 more mm are added

to the initial 7 mm tickness of the wideplate.

4. The Welding Parameters

In the case of welding deposits as applied to samples I, SUPERBAZ E 7018 electrodes

were used, in conformity with AWS A5.1, with a 3.25 mm electrode wire diameter. Tabel 1

indicates the weld deposit parameters corresponding to samples I.

Table 1

The parameters of the weld deposit

No.crt. Parameter Sample I

1 Is [A] 180…190

2 Ua [V] 21-22

3 ts [s] 165

4 Lc [cm] 39

5 vs [cm/s] 0.23

6 El [KJ/cm] 10.656

5. Fatigue tests

Fatigue tests were based on the LVF 100 HM type of fatigue test installation,

belonging to the laboratory of materials research within the Department of Materials and

Welding Technology.

For all three samples I1; I2; I3, the stress cycle applied was alternating and

symmetric, more precisely σmax= - σmin. Hence, σmed= 0 and the asymmetry coefficient R=

σmin/σmax= -1.


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The tests were conducted at a 10 Hz frequency.

In order to elevate the durability curves for all three sample sets I; II and III, three

variation values of the loading forces are required: ±ΔF1=±10 KN for sample I1; ±ΔF2 = ±8

KN for sample I2 and ±ΔF3 = ±6,5 KN for sample I3.

Fatigue tests followed several phases:

-fixing samples between the blades of the machine and tightening them with the

dynamometric key;

- selection of the loading variation program, of the loading stress cycle and work

frequency. Stress variations as above mentioned: ±ΔF1=±10 KN; ±ΔF2 = ±8 KN and ±ΔF3 =

±6,5 KN, the stress cycle was alternative and symmetric and the frequency was 10 Hz;

- extraction of frames during trials that show the number of cycle left until the

cracking moment;

Then, the data were collected and the durability curves were processed by means of

“Math Cad” program.

Figures 4a and 4b show the crack of sample I1 fixed between the blades of the

machine as well as a frame obtained due to the data analysis program, during the fatigue test,

which reveals that the stress variation as applied to sample I1 was ±10 KN and the sample

cracked after 640 seconds, more precisely, after 6400 stress cycles, based on a 10 Hz

frequency.

a b Fig. 4 Phases of fatigue test for sample I1

Figures 5a and 5b illustrate the cracking moment of sample I2 fixed between the

blades of the machine as well as a frame obtained due to the data analysis program, during the

fatigue test, which reveals that the stress variation as applied to sample I2 was ±8 KN and the

sample cracked after 1120 seconds, more precisely, after 11200 stress cycles, based on a 10

Hz frequency. It is worth mentioning an increase in the number of cycles left until the crack

moment as compared to sample I1, by approximately 75%.


12

a b

Fig. 5 Phases of fatigue test for sample I2

Similarly, figures 6a and 6b illustrate the cracking moment of sample I3 fixed

between the blades of the machine as well as a frame obtained due to the data analysis

program, during the fatigue test, which reveals that the stress variation as applied to sample I3

was ±6.5 KN and the sample cracked after 1877 seconds, more precisely, after 18770 stress

cycles, based on a 10 Hz frequency. It is worth mentioning an increase in the number of

cycles left until the crack moment as compared to sample I2, by approximately 68%.

a b

Fig. 6 Phases of fatigue test for sample I3

In the case of the sample set I1; I2 and I3, with rough seam weld deposit, the increase

in the number of cycles left until the cracking moment from 6400 cycles for I1 until 18770

for I3 accounts for a decrease in stress variation as applied to the samples, from ±10 KN to

±6,5 KN.


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6. Research results

Table 2 presents all data collected during fatigue tests for all the three seam welded

based samples I1; I2 and I3. Table 2

Fatigue tests data

No. Sample status Reference F [Hz] ±ΔF Duration

[s] N

1 seam welded

based

I1

10

±ΔF1=±10 640 6400

2 I2 ±ΔF2=±8 1120 11200

3 I3 ±ΔF3=±6,5 1877 18770

References in Tabel 2 indicate: F-frequency; ±ΔF variation of stress applied; N-

number of cycles left until cracking moment.

6. Marking durability curves

The durability curve ( - Wohler’s curve) for steels can be approximated

according to logarithmic scales (lg-lg), in the form of a logarithmic regression expressed as

[2]:

(1)

where: lg A is the junction point between the curve and the vertical axis; 1/p – inclination of

the straight line; - variation of stress due to variation of force exerted between a maximum

and a minimum; n- number of cycles.

Equation (4) can be also depicted as:

(2)

If lgA ha a certain value r, then, equation (5 ) becomes ( 6 ).

(3)

(4)

Equation (7) represents the variation of the durability curve based on linear

coordinates.

By means of Mathcad program, for samples I1; I2 and I3, we have obtained the values

p=2 and r=5.83, for which the graph of the function reaches the test points of the type

I samples, aI= ( 6400; 11200; 18770) and f1=( 10; 8 6). The graph is shown in Figure 7 as

follows:


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Fig.7 Durability curve in linear coordinates for samples I1; I2 and I3; material

S235JR; symmetric cycle- σmed= 0; σmax= - σmin; R= -1; frequency=10 Hz

7. Conclusions

We can observe from figure 7 that the durabillity curve is not asymptotic to the

horizontal. This means that in case of welded elements does not exist a fatigue resistance that

in case of unwelded elements.

It becomes noteworthy the fact that the existence of a weld bead on a machine part

exerts a negative effect on the number of cycles until cracking, reduced to almost 40% as

compared to the situation in which the machine part is not seam welded based. This reduction

of fatigue life when welding is applied occurs even if the welding is of high quality and does

not modify the forces within the respective machine part. This is due to the fact that, during

welding, the thin layer of the melted material drips over the original material, cools off

quickly and it is not hot enough to melt the original material. Hence, there is no proper

welding, the melted layer hardens quickly, gases and pollutants are not entirely exhausted and

they transform into stress concentrators highly visible in the faying surface of the weld

deposits but invisible from the exterior and lead to fatigue resistance. Furthermore, welding

residual stresses also reduce resistance to fatigue, when a weld bead is applied. By processing

both the machine part and the welded bead, cutting off a few millimiters, most of these

defects are eliminated (representing the stress concentrators), thus, the machine part becomes

more resistant to fatigue. In conclusion, the grinding process can be considered a highly

efficient technique likely to improve resistance to fatigue of some welded structures.

8. References

[1] Tom Lassen, Fatigue life analyses of welded structures, ISTE Ltd, 2006

[2] A. Almar Næss, Fatigue Handbook, Trondheim, Tapir, 1985

[3] A. Almar Næss, Fatigue Handbook, Trondheim, Tapir, 1985

[4] Claudiu Babis, Gheorghe Solomon, Dan Nitoi, Dumitru Titi Cicic - Cercetări privind

rezistenta la oboseală a sudurilor de colt ( Researches regarding Fatigue Strength of

Fillet Welds ) - ASR International Conference, 13- 14 octombrie 2011, Chisinău,

Republic of Moldova

[5] *** EUROCODE 3: Design of steel structures, 1993. Part 1–9: Fatigue strength of

steel structures, European Norm EN 1993-1–9.


15

TOPOLOGICAL STRUCTURE OF CONNECTING MECHANISMS

IN THE ELECTRIC GRID

Constantin BREZEANU, Silcotub S. A. (grup Tenaris) Călărași, [email protected]

Ioana POPESCU, Iuliu Maniu Highschool of Bucharest, [email protected]

Dr. Păun ANTONESCU, Politehnica University of Bucharest, [email protected]

Abstract: The paper presents the main types of mechanisms used within the connecting systems from the

high- and low-voltage electric grid. The purpose is the accurate construction of the kinematic diagrams of

the mechanisms of electrical connection. For the low voltage connecting systems the topological structure

of three kinematic schemes of articulated plane mechanisms is analysed. The structural-topological

analysis is extended to other three kinematic schemes of simple plane mechanisms used as high voltage

connecting systems. The structural-topological study is then applied to the complex plane mechanisms

used as high voltage separators.

Keywords: topological structure, kinematic scheme, mobility, connecting mechanism, electric grid.

1. Articulated planar mechanisms used for low voltage connecting systems

Connecting systems normally use plane mechanisms with articulated bars [1,3,6,7], or in

the simplest form of a single equalizing bar articulated frame (fig. 1.1) or in the shape of an

articulated quadrangle (fig. 1.2, 1.3).

Fig. 1.1. Balanced mech. B; Fig. 1.2. Quadrilateral mechanism; Fig. 1.3. Quadrilateral mech. B-B

The equalizing bar mechanism (fig. 1.1) shows the a1 arc as the resistance force, opposing

to the electromagnetic force Fm of EM, and it is one of the oldest solutions of electromagnetic

relay switch [20] for small nominal currents. The quadrangle mechanism (fig. 1.2) is

mechanically driven by the coupling Mm, by means of the crank 1, till the bars 1 and 2 are

placed one continuing the other, which corresponds to the extreme position of the equalizing

bar 3, when connection C is made.

1

A0

A

B0

B

0

EM

a1

Fm

1

A0

A

B0

B

0

C

2

3

Mm

A0

B0

A

B

C

D D0

1 2

3

a1

0

EM

Fm


16

The quadrangle type mechanism (fig. 1.3) is driven by the electromagnet EM till the bars

1 and 2 are one continuing the other, and the connection in point C is obtained in the extreme

position of the equalizing bar 3. The arc a1 acts as the resistance force and can open

connection C if electric power is no longer supplied into the EM.

The mobility of the equalizing bar mechanism (fig. 1.1) shall be determined with the

formula for plane mechanisms [5]:

453 23 CCnM (1)

From the kinematic scheme the following values stand out: 0,1,1 45 CCn .

Replacing these numbers in the formula (1) we obtain: 1012133 M

The mobility corresponds to the rotation motion of the bar 1 (the equalizing bar) around

the axis of the fixed articulation A0. The connection in point A results from the rotation of bar

1, which can be obtained with the attraction driving force Fm. Interrupting the power supply

into the EM results in breaking the connection in A assisted by the arc in tension a1.

The mobility of the crank – equalizing bar mechanism (fig. 1.2) or of the equalizing bar

- equalizing bar mechanism (fig. 1.3) is determined with the formula (1), where the numerical

values are introduced: 0,4,3 45 CCn .

The following mobility results from replacement: 1042333 M

The only independent motion is the rotation of bar 1 by means of the driving torque Mm

(fig. 1.2) or by means of the driving force Fm (fig. 1.3), which leads to the connection in C.

2. Simple planar mechanisms used for high voltage connecting systems

We consider the kinematic scheme (fig. 2.1) related to the mechanism of a low oil power

switch, for really high voltage with breaking arcs [1,3].

Fig. 2.1. Quadrangle mechanism. Fig. 2.2. Slipper mechanism. Fig. 2.3. Roller mechanism.

0

A0

A

B0

C

B

1

2

3

3

Mm

Fm

1

D’

A0

B0

B

a1

C0

D0

A

D

1

1 2 3

3

E

E’

0

0

A’

A0’

C

A

B

B0

C’ 1 2

3

4 5

0

A0

C0

Fm

C

B’


17

The mobile connection 3 has a rotating motion in an upper horizontal plane, and a part of

it, DE, gets into the fixed connection. The articulated quadrangle B0BCC0 (fig. 2.1) receives

the motion in the A0A arm that is rotating in a lower horizontal plane of force Fm.

Disconnection is obtained by means of the arc a1 that is tensioned in the D’E’ position.

The mobility of the mechanism is determined by means of the formula (1) in which we

introduce the structural numerical parameters: 0,4,3 45 CCn . 104233 M .

This value verifies the unambiguous determined motion of the mechanism with a single

leading element 1. With regard to the slipper mechanism (fig. 2.2), guiding in the oscillating

crank lever 3, the topological structure is the same as for the previous mechanism (fig. 2.1).

The difference consists in the existence of a translational coupling between the slipper 2

and the crank lever 3. The mechanism is actuated by means of the Mm coupling, and the

connection position C must be reached in the extreme position of the bar 3, which

corresponds to the angle (A0AB0) of 900.

The roller mechanism (fig. 2.3) is driven by a translational piston 1 actuated by the force

Fm of the compressed air. We should notice that the rollers 2 and 4 (articulated by the

equalizing bar 3) are connected to the upper part with the corresponding guide on the rod 1

respectively on the oscillating crank lever 5.

The mobility of the mechanism is determined by means of the formula (1) where we

introduce the numerical values identified on the kinematic diagram (fig. 2.3):

2,5,5 45 CCn . Thus, we obtain for the mobility the value 325253 M .

One of the three mobilities corresponds to the translational motion of the leading piston 1.

The other two mobilities are represented by the independent rotary motions of the rollers 2

and 4. The connection in point C is obtaine din the left position of the piston 1, where the

angle B0BC0 is 900, or in the right position of piston 1, where the angle B0B’C0 is equal to

900. The position of the connecting point C changes, and it can be placed in point C’ in the

right part of the figure (fig. 2.3).

3. Complex planar mechanisms used as automated pneumatic switches

These planar mechanisms with a complex structure are used as separators (switches) for

three-phase high voltage power lines [1,2,3]. We consider the kinematic scheme (fig. 3.1) of

an automated switch of 35 KW [3], which is pneumatically driven by means of a double

piston with a rack bar, or by a roller guided in a crank lever.


18

Fig. 3.1. Kinematic scheme of the three-phase connecting complex mechanism

From piston 1, driven by force Fm, by means of the rack bar gear (1) – geared sector (2),

motion is transmitted to the articulated quadrangle (2, 3, 4). Thus, by means of the

reciprocating rod 3, the rotation of bar 2 is transmitted to the equalizing bar 4, through the

articulation D.

Following the kinematic chain, from the equalizing bar 4, through the reciprocating rod 5

with the articulations E and F, motion is transmitted to the translating rod 6 at the end of

which there is the mobile connecting point K1 of the first phase of electric power.

Together with reaching the final position of rod 6, we obtain the synchronous

displacement of rods 10 and 14, corresponding to the mobile connecting points K2 and K3 of

the other two phases of the high voltage electric power.

From the equalizing bar 4, through the double articulation G, motion is transmitted to

the articulated bars 7 and 11, and then to the equalizing bars 8 and 12.

On the way to the mobile connecting point K2 we identify the articulated quadrangle

D0GG’D’0 or through the component elements (0,4,7,8). Also, the kinematic way to the

mobile connecting point K3 contains the anti-quadrangle D0GG’’D0’’ (0, 4, 11, 12). The

equalizing bar 12 is linked to a buffer made up of the kinematic elements 15 (piston rod) and

16 (cylinder). On the kinematic scheme (fig. 3.1) we identify the following numerical values

of the parameters in the formula (1): 1,23,16 45 CCn ; 11232163 M .

Mobility shows that the mechanism can be driven by a single leading element, piston 1.

A

Fm

B0

C

D

D0

E

F

G

D’0

G’ E’

F’ F’’

E’’

G’’

D0’’ H

I

I0

1

2

3

4

5

6

0

7

8

9

10

1

1

1

2

13

14

0 0

15

16

0

B

2

K1 K2 K3


19

The motion flow can be traced by means of the structural – topological formula of the

drive mechanism motor MM for each contact K1, K2 and K3, starting from the actuator

mechanism MA(0,1). Thus, the structural – topological formula for the contact K1 is

)6,5()4,3()2,()1,0( 12 LDLDeLDMAMM (2)

In the second phase of the contact K2, the structural – topological formula becomes

)10.9()8,7()4,3()2,()1,0( 12 LDLDLDeLDMAMM (3)

For the third contact K3, the structural – topological formula is written

)16,15()14.13()12,11()4,3()2,()1,0( 12 LDLDLDLDeLDMAMM (4)

In formulas (2, 3, 4) we noted as e12 the imaginary kinematic element equivalent to the

superior kinematic joint made by the gear formed of the rack 1 and the geared sector 2. We

should mention that the dyadic chain LD(15,16) of the RTR type is a sort of hydraulic buffer.

4. Mechanism of the high voltage three-pole separator

We take into consideration the kinematic scheme (fig. 4.1) of the mechanism of a

separator for voltages higher than 60 kV.

Actuation of the contact bars in points K1, K2 and K3 is carried out by means of the

mechanism of a quadrangle of the equalizing bar – lever type (A0ABB0) through lever 1.

The three contacts are obtained in the extreme position of the equalizing bar 3, when lever

1 and the reciprocating rod 2 are one following the other.

From the equalizing bar 3, through the articulation C, the rotary motion of the former

(clockwise) is transmitted through the reciprocating rod 4 to the equalizing bar 5 that is

rotating, trigonometrically, until the bars b3 and b5 reach a vertical position (in contact K2).

From the equalizing bar 3 the motion is transmitted, to the left and to the right, by means

of articulated quadrangles to the equalizing bars 3’ and 3’’ with the fixed articulations B0’ and

B0’’. Between the upper and lower axes of the fixed articulation B0 and D0 respectively B0’,

D0’ and B0’’, D0’’ we mount insulators. Following the kinematic scheme of the separator

mechanism (fig. 4.1) we infer the numerical values 0,23,15 45 CCn that we introduce in

the formula (1), resulting in 10232153 M

This result corresponds to a rigid structure, so that the mechanism should be an

undetermined static system. In reality, the mechanism operates on the basis of only one

leading element 1, and the result above is due to the double link between the equalizing bars

3, 3’ respectively 3 and 3’’. Thus, the reciprocating rods 7 and 7’ are mounted parallel to the

reciprocating rods 6 and 6’, which does not introduce additional geometric conditions.

From a geometrical point of view, the mechanism can operate without bars 7 and 7’, case

in which the structural parameters are: 0,19,13 45 CCn . Introducing the numerical

values in the formula (1) we obtain 10192133 M

Indeed the mechanism transmits the unambiguous determined motion from the leading

element 1 to the led elements 3, 5 respectively 3’, 5’ and 3’’, 5’’. The structural-topological

formula of the drive mechanism is


20

)''5,''4()''3,'6()'5,'4()'3,6()5,4()3,2()1,0( LDLDLDLDLDLDMAMM (5)

Fig. 4.1. Kinematic scheme of the three-pole separator mechanism

5. The mechanism of the single-column separator (with roller and crank levers)

The kinematic scheme of the mechanism (fig. 5.1) shows that the drive uses a pneumatic

actuator p with a double piston 1 [3].

a) b) c)

Fig. 5.1. Kinematic scheme of the single-column mechanism

2

1

3

3

4

’

4

5

3’ 3’’

A0

A

E

B0

C

D

D0

4’ 4’’

4’’

4’

C’ C’’ 6 6’

B0’’ B0

’

E’ E’’

7 7’

5’ 5’’ D’ D’’

D0’ D0’’

K1 K2 K3

F F’ F’’

0 0 0

0 0 0

B

b3

b5

2

3 5

4 1

0

0

A

B

B0 C0

C

K

3 5

2

3 5

4 1

0

0

A

B

B0 C0

C

3 5

2

3 5

4 1

0

0

A

B

B0 C0

C

K

3 5


21

We notice that the mechanism with a symmetrical structure has two rollers 2 and 4

guided in the corresponding crank levers 3 and 5. Is identified 5n mobile kinematic

elements; 55 C class kinematic couplings (mono-mobile) out of which a translational

coupling A(0,1) and 4 rotary couplings B(1,2), C(1,4), B0(3,0) and C0(5,0); 24 C are 4 class

kinematic couplings (bi-mobile) of plane rotary translation. Introducing these numerical

values in the formula (1) we obtain

21325253 M

We should notice that two of the three independent motions of the mechanism are

passive mobilities, represented by the rotation of each of the rollers 2 and 4 around their

centre.The available independent motion is the translational motion of the double piston 1 in

the fixed pneumatic cylinder, vertically mounted.

The structural – topological formula of the drive mechanism analysed above is

)5,4()3,2()1,0( LDLDMAMM (6)

The kinematic scheme in the position of closed contact K (fig. 5.1a) corresponds to the

up-and-down displacement of piston 1, and the separating position of the two bars b3 and b5

(fig. 5.1b) corresponds to the up-and-down displacement of piston 1.

By replacing the plane upper kinematic couplings (2,3) and (4,5) with one equivalent

element e23(2) respectively e45(4), we obtain the equivalent kinematic diagram (fig. 5.1c).

In this equivalent kinematic diagram all the kinematic couplings are class 5, or

translational (0,1), (2,3), (4,5), or rotary (1,2), (3,0) and (1,4), (5,0).

We should mention that, for the constructive diagram of the pneumatic separating

mechanism, we shall provide locking bolts for the two equalizing bars 3 and 5 especially due

to the weight of the double piston 1.

6. Conclusions

The mechanisms related to electric switch systems are plane mechanisms with articulated

bars, having a simple topological structure in the case of low electric voltages. The mobility

of these mechanisms is usually carried out by means of electromagnets.

For high electric voltages, the plane mechanisms used are based on kinematic diagrams

with single contour lines articulated bars, driven by spiral arcs.

For three-phase power lines, the mechanisms used are carried out as complex plane

structures with parallel kinematic chains. These mechanisms are pneumatically driven, and

are provided with a pneumatic buffer for one of the three phases.

We carried out an equivalent kinematic scheme, both for the pneumatic actuator and for

the parallel final kinematic chains. The structural topological analysis of the mechanism of a

three-phase separator shows that the kinematic diagram uses serial quadrangle mechanisms.


22

Bibliography 1. Hortopan, G., Electric Devices, The Didactic and Ped. Publ. House, Bucharest, 1972;

2. Hortopan, G., Low Voltage Electric Devices, The Technical Publ. House, Bucharest, 1969;

3. Macsymiuk, J., Mechanisms of Connecting Electric Devices, The Technical Publ. House,

Bucharest, 1970.

4. Antonescu, P., Mechanisms, Printech Publishing House, Bucharest, 2003;

5. Antonescu, O., Antonescu, P., Mechanisms and Manipulators, Printech Publishing House,

Bucharest, 2007;

6. Nedela, N., Antonescu, O., Mechanisms used for medium voltage power switches, Journal

Mechanisms and Manipulators, Vol. 8, No 1, 2009, p. 43-50;

7. Nedela, N., Geonea, I., Mechanisms used for high voltage switching devices, Journal Mechanisms

and Manipulators, Vol. 9, No 1, 2010, p. 51-58.


23

EXPERIMENTAL INVESTIGTION OF THE FRETTING

PHENOMENON

Ştefan GHIMISI, Constantin Brâncuși University of Targu Jiu,

[email protected]

Abstract. Fretting is now fully identified as a small amplitude oscilatory motion which induces a

harmonic tangential force between two surfaces in contact.It is related to three main loadings, i.e.

fretting-wear, fretting-fatigue and fretting corrosion.Fretting regimes were first mapped by

Vingsbo. In a similar way, three fretting regimes will be considered: stick regime,slip regime and

mixed regime. The mixed regime was made up of initial gross slip followed by partial slip

condition after a few hundred cycles. Obviously the partial slip transition develops the highest

stress levels which can induce fatigue crack nucleation depending on the fatigue properties of the

two contacting first bodies. Therefore prediction of the frontier between partial slip and gross slip

is required.

Keywords: fretting, wear, experiment

1.Introducțion

Fretting is now fully identified as a small amplitude oscilatory motion which induces a

harmonic tangential force between two surfaces in contact. It is related to three main

loadings,i.e. fretting-wear,fretting-fatigue and fretting corrosion.

The main parameters were reported to be amplitude displasement, normal load ,

frequency,surface roughness and morphology, and residual stresses. More recently fretting

has been discussed using the third-body concept and using the means of the velocity

accommodation mechanisms introduced by Godet et al.[1,2]

Fretting regimes were first mapped by Vingsbo. In a similar way,three fretting regimes

will be considered: stick regime,slip regime and mixed regime. The mixed regime was made

up of initial gross slip followed by partial slip condition after a few hundred cycles. Obviously

the partial slip transition develops the highest stress levels which can induce fatigue crack

nucleation depending on the fatigue properties of the two contacting first bodies. Therefore

prediction of the frontier between partial slip and gross slip is required.

The type of surface damage that occurs in fretting contact depends on the magnitude

of the surface normal and tangential tractions. In existing fretting models the relative

displacement is assumed to be accommodated mainly microslip in the contact surface[3].

The present paper argues that adhesion forces and elastic deformation in the contact

zone may contribute significantly to the relative displacement during fretting of metals. A

simultaneously applied tangential force and normal into contact appears a adhesion force. A

tangential force whose magnitude is less equal on greater than the force of limiting friction

will not give rise on give rise to a sliding motion.It is determined the energy loss dissipated

per fretting cycle.


24

2.Experimental means

For the study of the fretting phenomen in case of elastics assemblages spring slides

with multiple sheets,I used the experimental stall from fig.1.[4]

The stall permits testing for one slide and for spring slides with multiple sheets, too.

2.1. Description of the stall

On the rigid support the elastic lamella (6) is assembling through the agency of the

superior plate (4) and of the screws (1).

The assemblage is made through the agency of 8 balls ( 4 balls inferior and 4 superior balls)

who assure a point contact between the ball and the lamella.

The elastic lamella (6) oscillates because of the rod crank mechanism with eccentric (8).This

mechanism is actioned with the electrical engine assuring the necessary conditions for

producing the fretting phenomenon.

The contact is charged with the assistance of 4 screws (1) through the agency of some

helicoidal springs(2) and through the agency of some radial-axial bearings with conic rolls.

The helicoidal springs beforehand standarded permit a charge with a normal and known force,

the presence of the radial-axial bearings assuring the eliminate of friction between the screw

and the superior plate.

Fig.1. Experimental stall

The stall can be used for the testing at fretting of some couples by different materials.

This stall can be adapted for study of the lamellar springs with many sheets.

The lamellas used in experiments have the dimensions 560x56x2 mm and are realised

by spring steel having hardness 55 HRC.

The balls are spring balls and have 19 mm in diameter.The lamella is suported in

inferior side on 4 balls in superior side the charge of the contact is made through the agency


25

of 4 balls. The rod-crank mechanism permits a displace at the end (extremity) of the 20 mm

lamella and can modify this displace by changing of the system excentricity. The system is

actioned through the agency of electrical enging having revolution of 750 rot/min.

Helping with this experimental stall we can made fretting tries for normales and

different forces for different numbers of solicitation cycles.

We obtained different wear traces corresponding fretting wear. So, we find the dependence of

the normal charcing force, and we can compare the different fretting traces by comparing of

different fretting zones for certains conditions of contact.

Therewith we can compare the theoretical results previously presented with the

experimental results. Traces wear obtained was assumed with a video camera and processing

on the computer . The displacement at the contact level was determined, like we shown

previously helping with the video camera and computer.

The determination of displacement was made for the two renges of balls.

In the table 1. are the traces wear obtained for a normal charcing of 200 N on the each

screw.

Table 1. Fretting wear

Number

of cycles

Pozition of balls

face back

30000

40000

50000


26

For comparing the traces wear obtained with the theoretical results obtained for the

fretting phenomenon we determined the central area and the annular adjacent area, and the

results are in the table 2 for the front balls and in the table 3, for the back balls.

Table 2

Nr.

crt.

Loading

[N]

Number of

cycles

Area

central

[mm2]

Radius

central

[mm]

Area

ext.

[mm2]

Radius

ext.

[mm]

Area

annular

[mm2]

1 200 30000 0.15300 0.22070 0.63278 0.4488 0.47978

2 200 40000 0.22219 0.26596 0.99215 0.5622 0.76996

3 200 50000 0.28807 0.30281 1.27996 0.6383 0.99189

Table 3

Nr.

crt.

Loading

[N]

Number of

cycles

Area

central

[mm2]

Radius

central

[mm]

Area

ext.

[mm2]

Radius

ext.

[mm]

Area

annular

[mm2]

1 200 30000 0.19752 0.25075 0.77363 0.4962 0.57611

2 200 40000 0.24173 0.27739 1.40647 0.6691 1.16474

3 200 50000 0.37215 0.34418 1.70178 0.7360 1.32963

In fig.2. and 3 are the dependence of the wear traces by the cycles numbers for a normal

force by 200 N and for the two position of the balls in front and back.

Fig.2. The dependence of the wear traces by

the numbers of cycles for F= 200N; in front


27

Fig.3. The dependence of the wear traces by

the numbers of cycles for F= 200N;back

3.Conclusion

The experimental stall permits realization of the experimental tries for the study of

fretting. We can determine the different size of the fretting areas and we can compare these

with the theoretical results.

Can be made considerations for existence of one friction coefficient who is variable between

the surfaces coresponding by one fretting contact.

4.References

[1]P.Blanchard,Ch.Colombier,V.Pellerin,S.Fayeulle and L.Vincent, Material effects in

fretting wear: application to iron ,titanium and aluminium alloys, Met. Trans. A,22(1991)

1535-1544

[2] O.Vingsbo and M.Soderberg,On fretting maps,Wear, 126 (1988) 131-147

[3]K.L.Johnson,Contact Mechanics,Cambridge University Press,Cambridge,1985,pp.202-233

[4] St. Ghimisi, Fenomenul de Fretting, Editura Sitech, Craiova, ISBN 973-746-422-2, ISBN

978-973-746-422-4, 2006, pag. 331


28

LINKAGES FOR QUADRUPED BIO-ROBOT WALKING

Ovidiu ANTONESCU, Politehnica University Bucharest, [email protected]

Cătălina ROBU, Tudor Vianu Hight School, Giurgiu, [email protected]

Paun ANTONESCU, Politehnica University Bucharest, [email protected]

Abstract: This paper analyses the Jansen mechanism. It then presents a few pictures of a mobile

quadruped robot, which will help to describe how the robot moves. We take into consideration the

kinematic scheme of the spatial mechanism with bars (spatial linkage), which is used for each of the

four robot legs. Each leg mechanism is driven by two rotate brushless actuators that include a spur

gear low-ratio transmission. By means of analyzing the kinematic scheme, the spatial mechanism

mobility that operates in both horizontal and vertical plane is calculated.

Keywords: bio-robot walking, quadruped robot, spatial mechanism, spur gear, mobility

1. INTRODUCTION

Research in the field of walking robots is extremely active. Robots of different sizes, from

the size of an insect to that of a van, have been built. There are many websites presenting a

considerable number of walking robots [4]. It is amazing how many ways of copying what

animals easily do exist, and how creative they are (fig. 1).

Even if the structures of walking robots can be innovative, it is the structure of their legs

that usually receives the highest degree of attention from researchers [2].

Analysing the mechanics of walking robots, one will notice that the main majority of

robots equipped with more than two legs use the planar mechanism [1] of the pantograph

type with 2 mobile joints for walking (fig. 2).

Fig. 1. The bi-mobile pantograph Fig. 2. The kinematic scheme of

mechanism used in the walking robot bi-mobile pantograph mechanism


29

In spite of the large variety of walking robots, the mechanical principles used for

designing the legs are quite limited. We should notice that in nature, muscles / ligaments can

be considered as extendible links, which corresponds to the pantograph mechanism.

Pantograph mechanisms are so frequent in the structure of walking robots because they

are extremely simple and versatile.

Even if this property of the pantograph mechanism is used for creating a suitable leg

trajectory, there are other ways in which a pantograph operates. In figure 2, the trajectory of

point E is determined by the horizontal motion of point A and the vertical motion of point O.

Obviously, this mechanism can be used effectively [5, 6] as it has already been used

successfully in the Vehicle with Adaptable Suspensions (fig. 2).

This operation requires two drive sources, which is regarded as a disadvantage since it

increases the complexity and the energy consumption. This double mobility is common for

most walking mechanisms that use pantographs.

Another disadvantage of this mechanism is that it requires a system to control the leg

kinematics in order to determine the trajectory of the fulcrum.

This system usually incorporates sensors for detecting the soil, and maintaining the

position of the frame as to the soil, which requires a permanent control of the mechanism

kinematics.

Some electric robots can carry their own power source as batteries. The range of power

sources used for robots is limited by the same factors that limit wheeled vehicles. The weight

of the fuel or of the energy stored in the batteries, as well as the weight of its structure and

control systems must be reduced as much as possible since carrying its own weight stands for

the main power consumption.

One of the greatest disadvantages of walking robots is their inefficient power

consumption. Due to the combination between their relatively large weight, numerous

actuators, conversion losses, the power consumption of the control systems and of the sensors,

these machines are a whole lot less efficient than wheeled vehicles or biological walkers.

Although it is difficult to reach the efficiency of animals, it is still possible to build

walking robots (fig. 3) whose power consumption for the distance travelled is similar to that

of wheeled vehicles off-road.

Fig. 3. Raibet’s quadruped walking robot (left) and

the one made by the University of Boston (right)


30

2. THE MOBILE WALKING THEO JANSEN TYPE ROBOT

A new mechanism was invented by the Dutch Theo Jansen. His later activity focused on

this mechanism that can be found in many kinetic sculptures [3, 7].

The kinematic scheme of the Jansen mechanism (fig. 4 left) points out 7 mobile kinematic

elements. The geometrical scheme (fig. 4 right) shows, in the lower part, the closed curve

representing the trajectory of the fulcrum M represented by node 5.

Therefore, the mechanism is made up of seven mobile kinematic elements [1, 2], and the

crank is the driving kinematic element (actuator).

Fig. 4. Kinematic scheme (left) and geometrical scheme (right) of

the Theo Jansen mechanism

We should notice that, in the scheme used (fig. 4 right), the bars were noted as bar type

elements. We should also keep in mind the fact that elements 4, 5, 7 and 2, 9, 10 each

determine a rigid triangle, representing distinct kinematic elements [1]. Thus, the Jansen

mechanism results from a kinematic chain with 8 kinematic elements, of which one is the

fulcrum (fig. 4).

The mechanism is constrained to a single position of the component kinematic elements

for each position of the crank, therefore there is a single degree of mobility [1]. The position

of all the elements can be calculated on the basis of the known position of the crank.

By examining the mechanism, we find out that it can meet the criteria of a walking robot,

its legs are driven by a single central crank (fig. 5).

B0

A

A0

2

1

B

3

C

D E

M

x

y

4 5

6

7

3

7


31

Fig. 5. Building scheme of the quadruped robot (left) and

kinematic scheme (right) of the Jansen mechanism

The legs move longitudinally against each other while the robot is moving, and they

cannot stay firmly against the surface on which they walk. At least one leg must move in

order to compensate for the force of the mechanism.

The Jansen mechanism is worth being studied as a viable alternative for a walking robot if

it is assessed from the point of view of its design criteria. For a constant crank rotation speed,

the necessary time to move between each angular position is also constant.

The four Jansen mechanisms with articulated bars have been pointed out in the building

scheme of the quadruped walking robot (fig. 5 left).

Two Jansen mechanisms were mounted on the frame. They are actuated by an electric

engine, each from the same crank. We can see the left one (fig. 5 left).

3. THE SPATIAL MECHANISM OF THE LEG OF A QUADRUPED BIO-ROBOT

The mechanism of the leg of a quadruped robot (fig. 6, 7) includes in its structure a

plate 6 that rotates in a horizontal plane.


32

Fig. 6. Pictures of the leg (left) and of the supporting frame (right)

of the quadruped robot

Three articulations have been provided on the vertical plate 6 (fig. 7): A0, B0 and D0

represented in the kinematic scheme by using the symbol of a fixed articulation in the rotation

plane.

Fig. 7. Kinematic scheme of the spatial mechanism of the quadruped leg

The mobility of the spatial mechanism shall be checked by using the general formula

6

2

5

1

)()(r

rm

mb rNmCM (1)

In the first part of the formula (1), we noted the mobility of a kinematic coupling as m

(liberty), and Cm stands for the number of class m kinematic couplings.

Also, in the second part of the formula (1), we noted r the rank of the space associated to a

closed kinematic contour (the number of the independent elementary movements).


33

Consequently, Nr stands for the number of independent r rank closed contours.

The numerical values of these structural parameters are deduced from the kinematic

scheme of the mechanism (fig. 7) and are presented as a matrix:

00020

00008

65432

54321

NNNNN

CCCCC (2)

Introducing these numerical values in the (1) formula, we obtain

22381 bM (3)

The two mobile joints correspond to the independent rotation motions of crank 1 and

pivoting plate 6 (fig. 7).

The mechanism includes two actuator kinematic couplings also called actuator

mechanisms MA(0,6) and MA(6,1).

The structural – topological formula of the bi-mobile driving mechanism is

)5,4()3,2()1,6()6,0( LDLDMAMAMM (4)

Considering the fact that the quadrangle B0CDD0 is a parallelogram (fig. 7), the trajectory

of point M in the plane of the kinematic element 4 is a circle arc in the plane of the vertical

plate 6. The rotation motion in a horizontal plane of the articulated planar mechanism is

carried out while point M leaves the surface on which the walking robot is moving.

The supporting frame of the four robot legs is shaped as the letter I (fig. 8 left) in a

horizontal projection.

The plates containing the electronic circuits are mounted on this supporting frame (fig. 8

right), controlling the 8 electric motors, two actuators for each leg.

Fig. 8. The supporting frame of the quadruped robot, diagram (left) and photo (right)

The electric motor that rotates the pivoting plate 6 is mounted on the supporting frame

(fig. 8), and the electric motor that drives crank 1 is mounted on the rotating plate 6. The two

pivot bushings of plate 6 are provided with ball roller axial radial bearings.

The position of the supporting frame is set by means of the second electric motor

MA(6,1), where crank 1 directly rotates, so that its height is minimum (fig. 9).

175

E0

F0

215


34

We should notice that, for lifting the robot frame – the frame of the walking robot, crank

1(A0A) rotates clockwise (fig. 9 right). The M1 point of the leg corresponds to the lower

position of the robot frame, and in this case, the kinematic scheme of the mechanism is

represented by a thick continuous line (fig. 9 left).

Fig. 9. The extreme positions of the mechanism M1, M2 (left)

and the rotation of crank 1 (right)

Point M2 corresponds to the upper position of the robot frame, and the dotted line was

used to draw the kinematic scheme of the planar articulated mechanism (fig. 9).

The step taken by each leg, through point M, is obtained by means of the first electric

motor MA(0,6), in which the supporting plate 6 together with the whole linkage rotates in a

horizontal plane at a certain angle.

During the rotation in a horizontal plane, the driving electric motor MA(6,1) rotates crank

1 counter-clockwise, so that point M no longer touches the horizontal plane of the ground.

A program is used to control the command that actuates the eight electric motors, so that

the legs placed diagonally to the supporting frame touch the ground.

4. CONCLUSIONS

The paper has presented the correct kinematic scheme of the Jansen mechanism as

compared to some geometrical representations of the mechanism as a beam, where joints are

called nodes and bars are called elements.

We have pointed out that three linked rigid bars create a rigid body, called a kinematic

element. As compared to the planar mono-mobile Jansen type mechanism, which enables a

constant movement of the quadruped robots, spatial mechanisms with a double mobility

(actuators) enable variable steps, smaller or larger. The kinematic scheme of the spatial

mechanism that was analysed in the paper can meet the requirements of a walking leg.

A0

B1

A1

C1

D1

D0

M1

E0

F0

1

3

4

5

6

0

0

B'

x0

y0

B0

2

x

y

6

M2

C2

D2

h12

B0

2

x

A0

A1

B1

B2

A2

C2

D0

D2

M2

y

1

3

4

5

3

2


35

REFERENCES

[1] Antonescu, P., Mechanisms, Printech Publishing House, Bucharest, 2003

[2] Antonescu, P., Antonescu, O., Methods of determining the mobility (D.O.F.) of complex

structure manipulators, Journal Mech. and Manip., Vol. 3, No. 1, 2004, pp.49-54;

[3] www.mechanicalspider.com; www.strandbeest.com

[4] MIT Leg Lab-Milestones in the Development of Legged Robots

http://www.ai.mit.edu/projects/leglab/background/milestones.html [5] The Adaptive Suspension Vehicle

http://www.ieeecss.org/CSM/library/1986/dec1986/w07-12.pdf [6] Walking Truck http://cyberneticzoo.com/?p=2032

[7] Theo Jansen Mechanism http://www.google.ro/search?

http://www.ai.mit.edu/projects/leglab/background/milestones.html

http://www.ieeecss.org/CSM/library/1986/dec1986/w07-12.pdf

http://cyberneticzoo.com/?p=2032


36

STRUCTURAL AND GEOMETRICAL ANALYSIS OF THE LIFTING

MANIPULATORS FOR A GREEN ENVIRONMENT

Ioana POPESCU, Iuliu Maniu Highschool, Bucharest, e-mail: [email protected]

Dr. Ovidiu ANTONESCU, Univ. Politehnica of Bucharest, e-mail: [email protected]

Dr. Păun ANTONESCU, Univ. Politehnica of Bucharest, e-mail: [email protected]

Abstract: The lifting and getting off the bins, to and from the body of special waste trucks, by some

planar linkage – manipulators are studied. These lifting manipulators are equipped with gripper systems

in order to load and unload the bins. Several kinematical schemas of type mono– and bi-mobile

manipulators are analyzed, these being driven by one or two linear actuators. The kinematical geometry

of these planar manipulators by means of scale drawing of the kinematical schema is displayed. Two

solutions for a better efficiency and a green environment have been proposed. Finally, a modeling and

simulation case of the lifting manipulator is presented.

Keywords: lifting manipulator, mobility, simulation

1. Introduction

The development of lifting manipulators for loading and unloading the waste freight into

and from specialized trucks has not been treated so much in literature [2].

One of the best reference titles on bin lifting automotive history is “The photographic

archive of waste trucks” by John B. Montville [4] that presents the development of garbage

gathering vehicles since First World War to nowadays.

The first waste vehicles had an open top part of the body to collect the garbage though

they were not specially designed to perform this task. By 1920 about twenty garbage trucks

with closed carriage were accomplished in Great Britain. The advantage of this type was a

bigger quantity of garbage that can be loaded in cleaner conditions into a greater carriage.

First truck carriage with outer bunker had been made in 1929 and the rear loading body

with waste compactor in 1938. This principle of rear loading compactor carriage is the most

used in present, even if at that time the waste bins were manually lifted and unloaded. Other

models of waste trucks are with side (1947) or front (1955) loading.

2. Waste bins and loading mechanisms

The waste is collected in special containers or bins [3], [4] of diverse sizes being made of

steel (for larger dimensions) or plastic.


37

Fig. 1. Waste loading process Fig. 2. Mechanical bin lifting

After the mechanical loading of the waste (fig. 2) from bin into the receiving bunker of

truck, the garbage is pushed into the main compartment of carriage (fig. 1).

These bin lifting mechanisms (fig. 1) represent mono-mobile or bi-mobile manipulators

[1] that grasp the bin, lift it until the receiving bunker level and lean it until the waste begin to

fall into bunker. Ones the bin is rotated by over 90 degrees from initial position, the bin opens

by itself maintaining the lid in vertical position (fig. 1 or 2) and the waste is unloaded.

3. Mono-mobile lifting manipulators

Let’s consider a mono-mobile lifting mechanism for heavy containers (fig. 3). This

manipulator is a planar mechanism [1] that consists of one closed kinematical contour with

hydraulic cylinder and another kinematical contour which is alternatively open in lifting phase

or closed in waste unloading phase.

Fig. 3. Mono-mobile lifting manipulator for heavy containers


38

Initially, the rotate cylinder 1 of manipulator is in vertical position (thick line - fig. 3)

having the piston 2 at top of it so that the rocker 3 has segment BB0 in horizontal position. Bar

4 is linked to the container 5 by a hook which allows an easy hanging of it and, also, a

rotation of it in unloading phase (thin line - fig. 3).

In final position (thin line – fig. 3) the piston 2 is at bottom of cylinder 1 and the

container 5 leans with point M (now M’) on a fixed point of carriage, the open kinematical

chain formed of 3, 4 and 5 element becoming closed (B0 C’ D’ M’).

In lifting phase the mechanism mobility results by using the following formula [1]:

5

1

6

2m r

rm rNmCM (1)

In this phase all six kinematical joints are mono-mobile (m = 1) and there is only one

closed loop of rank 3 (r = 3), so that N3 = 1.

Therefore, by formula (1) results: 31361 M

Fig. 4. Mono-mobile lifting manipulator Fig. 5. Bi-mobile lifting manipulator with

for light bins parallelogram

1

2 3 5

4

6

7


39

Among these three mobilities (DOF) only one is active (controllable) – actuator (1+2).

The others two mobilities are passive – rotation of bar 4 related to joint C and rotation of

container 5 about joint D.

In the second phase there are two closed loops of rank 3, six joints of class 1 and one

joint of class 2, resulting: 2231261 M , but only one is active.

To manipulate light bins of plastic (dashed line – fig. 4) it is used a mono-mobile planar

mechanism with two closed kinematical contours, the first one having the actuator as rotate

cylinder and the second one being a rotate jointed quadrilateral (fig. 4).

The kinematical scheme of manipulator has been represented in two limit positions, the

bottom one displayed with continuous thick line (initial position) and the top one with

continuous thin line (final position). There are three fixed axes on the truck body A0, B0 and

D0. In the initial position (bin grasping) the cylinder 1 and piston 2 are in vertical position

with the minimum length A0B. Bar 4 has two mobile rotate joints C and D, and also the rotate

joint E by which the bin 6 is positioned.

In order to obtain the final position (waste unloading) the piston 2 slides into cylinder 1

to the end of stroke, the length A0B’ being maximum (fig. 4).

It can be observed that in initial position the rotate jointed quadrilateral B0CDD0 is

convex and in the final position it becomes concave (B0C’D’D0), the two rockers 3 and 5

being crossed. As it was mentioned in previous chapter, the bin 6 opens itself by maintaining

the lid 7 in vertical position, this being linked to 6 by a rotate joint F’.

The mobility is checked by formula (1): 12371 M

This type of mechanism (fig. 4) allows 130-145 degrees rotation of the bin, being the

most used lifting manipulator in street salubrity.

Of course, these mono-mobile manipulators (fig. 3 and 4) are achieved as double mobile

structures operating in parallel planes (on both carriage sides). Therefore, the two hydraulic

actuators must be synchronized in order to lift the bin(s) properly. In the case of light bins, the

manipulator lifts two or three plastic bins in the same time by using a horizontal bar (joint E

in fig. 4) which links the two parallel mechanisms. On this connecting bar there are catching

systems mounted, they being equipped with safety devices on manipulated bins.

4. Bi-mobile lifting manipulators

The bi-mobile lifting manipulators operate in the same conditions as mono-mobile ones,

being double systems mounted in parallel planes, between them the waste bins being lifted

and unloaded. The actuation of these mechanisms is provided by four hydraulic cylinders,

each two of them in one working plane.

Let’s now consider a bi-mobile lifting manipulator with rotate jointed parallelogram (fig.

5). The two cylinders work as following: one actuator drives in the first manipulating phase

(bin lifting – bottom and middle positions) and the other actuator drives in the second phase

(bin rotation – top position). This has the advantage of maintaining the bin vertically in the

first phase, the movement being a circular sliding (in the same plane).


40

This bi-mobile mechanism (fig. 5) has the first mobility obtained by actuator (1+2)

(linked to element 6 by rotate joint A and to element 3 by rotate joint C) and the second

mobility obtained by actuator (7+8) (linked to truck body by rotate joint I0 and to element 6

by rotate joint J). The mobility is checked by formula (1): 233111 M

In the first phase, when element 6 is static, the piston 2 slides into cylinder 1 until the

stroke ''21 CCBBs is complete. Therefore, the bar 4 (by which the bin 9 is sustained)

executes a circular sliding reaching the vertical E’F’ position.

In the second phase, with the actuator (1+2) blocked (AB’C’), the actuator (7+8) begins

to drive by sliding the piston 8 into cylinder 7 until the stroke is '' 0087 JIJIIIs . During

this phase the element 6 rotates as a rigid body, together with elements 1, 2, 3, 4 (9) and 5,

around the rotate joint A0 by 130 degrees.

As it was explained in the previous case the bin lid 10 remains in vertical position,

allowing the waste to fall into the receiving bunker of truck.

After the bin is completely unloaded, the actuator (7+8) slides at maximum extended

position I0J and then the actuator (1+2), once it reaches the vertical position, extends to

maximum stroke AC = s21max . Further, we consider a bi-mobile lifting manipulator with rotate

jointed quadrilateral (fig. 6). This may be called as general case comparing with the last one

(fig. 5) because in the first phase the bin is lifted and rotated to about 45 degrees, and in the

second phase it continues to rotate to extra 90 degrees.

The position of fixed rotate joint I0 of the second actuator lies under the fixed rotate joint

A0 on truck body. This is an advantage regarding the length of hydraulic actuator-supplying

pipes: closer actuators–shorter supplying tubes. In initial position of the first phase the

kinematical schema (fig. 6) is drawn by continuous thick line (including the bin).

The actuator (1+2) by cylinder 1 is rotate jointed to the bar 6 (which is rotate jointed to

carriage by fixed point A0) and by piston 2 to the rocker 3 which is also rotate jointed to the

bars 6 and 4. The bars 6, 3, 4 and 5 form a rotate jointed quadrilateral having “the base” 6 and

3 as driving element which is actuated by (1+2).

The kinematical schema (fig. 6) in the final position of the first phase is drawn by

continuous thin line and the bin 9 by dashed thin line.

During this phase from DEFG position the quadrilateral gets to D’E’F’G’ position,

where the bin 9 is rotated to about 45 degrees.

In the second phase the actuator (1+2) is blocked in retreated position (A’B’C’) so that

the quadrilateral becomes as one unitary element, with no movements among its bars, which,

together with bar 6, is rotate jointed in the fixed point A0.


41

Fig. 6. Bi-mobile lifting manipulator with

quadrilateral

Fig. 7. CAD modeling and kinematical simulation

Now, the actuator (7+8) takeovers the command, having the cylinder 7 rotate jointed in

the fixed point I0 on truck body, and the piston 8 linked to element 6 in point J. The mobility

is checked by formula (1): 233111 M . In the final position of second phase the

manipulator is represented by continuous thin line (fig. 6) using the following notations: A”,

C”, D”, E”, F”, G” and K”. In this position the bin 9 is rotated to extra 90 degrees so that the

bin lid 10 takes a vertical position allowing the waste to fall into receiving bunker.

5. Modeling and simulation of the lifting manipulator

Nowadays, by means of advanced CAD software systems, any component or mechanical

assembly having a complex structure can be modeled and simulated. Designing a virtual

entity, with precisely 3D dimensions (using three-dimensional space), requires a spatial vision

and a detail-orientated eye. In order to simulate a process, we need that part to be as much as

7

8


42

possible like the real one. So, a virtual material with real properties can be applied to it. Thus,

we can obtain a component which has its own characteristics that can be updated anytime.

The parametrical design has the advantage that by modifying a geometrical parameter of

the component, all the other dimensions will be automatically changed in correlation with the

given constrains.

Further, certain virtual assemblies, obtained by connecting their mobile mechanical

elements, can be created, accomplishing mechanisms with one or more mobilities that can

be animated and simulated on their operation as if they would have a real behavior.

Let’s consider the mono-mobile lifting manipulator with improved efficiency

depicted in figure 7. The first step is the modeling of the main mechanical components

such as the base 0 (truck body), the hydraulic cylinders 1 (including the pistons 2) as

actuators, the T-rockers 3 linked to cylinder’s pistons, the rods 4 fixed to the transversal

shaft (that connects the two parallel lifting mechanisms and sustains the two waste bins by

special supports), the rockers 5, and the waste bins 6 (including their lids 7).

All these components of the lifting manipulator have been modeled by using a 2D

sketcher. Then, the third dimension for each element, by using the 3D module, was

created. Many other commands were used in order to shape the right configuration of

them. The total number of parts (subcomponents) is 24.

Afterwards, these parts were assembled using a specific virtual workbench by adding

the connection elements (such as shafts, pins and bearings) between them that, in fact,

represent the rotate joints (fig. 7). The only sliding joints are between pistons and

cylinders. It is necessary to be mentioned that before assembling the components, the

accuracy of each part dimension has to be checked, so that the outcome should be a

perfect combined product.

The 3D rendering of the lifting manipulator assembly can be achieved very easy just

by computer mouse. The system can be rotated, moved or zoomed in/out by user in order

to see the final product from any point of view.

For the kinematical joint applying between the mechanism’s components, the

manipulator mobility has to be considered. This lifting mechanism having 1 DOF, the

sliding range of the driving cylinders can be imposed so that the manipulator working

space to be modeled, related to the necessity of a completely waste unloading from the

bins.

The kinematical operating simulation of the lifting manipulator can be achieved by

using the command panel by which the virtual displacement can be controlled.

6. Conclusions

Two simply solutions on lifting manipulators have been proposed. One of them is meant

to reduce the waste truck consumption by implementing a high efficiency mechanism. The

other is to reduce the city pollution by using an electric powered driving transmission. The

first one has been CAD modeled and simulated in order to test its kinematical performances.


43

References

1. Antonescu P., Antonescu O. Mechanism and Machine Dynamics (in Romanian).

Printech Publishing House, Bucharest, 2005.

2. Voicu G., Paunescu I. Processes and Machines for City Cleaning, Matrix Press,

Bucharest, 2002.

3. Coltofeanu R. Structural-Topological Analysis of the Lifting Mechanisms on Urban

Salubrity Equipments. PhD Paperwork, Politehnica Univ. of Bucharest, 2005.

4. Antonescu, O., Coltofeanu, R., Antonescu, P., Geometria manipulatoarelor pentru

descărcarea recipientelor cu reziduuri gunoiere, Rev.Mecanisme și Manipulatoare, Vol. 5,

Nr. 2, 2006, pag. 25-30.

5. Geonea, I.,Coltofeanu, R., Motofeanu, S., Kinematics and dynamic modelling of a plane

manipulator, Journal Mechanisms and Manipulators, Vol. 8, No 2, 2009, p. 41-46.

6. *** www.tigerdude.com/garbage ; www.mechlift.com .


44

THE GEOMETRY OF THE SPATIAL FOUR-BAR MECHANISM

AND OF ITS PARTICULAR FORMS

Păun ANTONESCU, PH.D., Politehnica” University of Bucharest, [email protected]

Ovidiu ANTONESCU, PH. D., Politehnica” University of Bucharest, [email protected]

Constantin BREZEANU, Silcotub S. A. (Tenaris Group) Călărași, [email protected]

ABSTRACT:Starting from the rssr spatial four-bar mechanism, this paper analyses the most

significant particular cases for which the specific transfer functions are written in comparison to

the respective function deduced in the general case. From among the particular cases of the

spatial mechanisms, the authors mention the oscillating washer mechanism and the cardan

mechanism, demonstrating that spherical mechanisms can be obtained as the simplified variants

in which the spherical joints may be replaced by simple rotation joints. For the spherical

mechanism, the respective transfer functions have been determined as the simplest particular

forms of the transfer function achieved by the rssr spatial four-bar mechanism.

KEYWORDS: spatial four-bar mechanism, spherical joint, transfer function, cardan mechanism

1. GENERAL CONSIDERATIONS

The bar spatial mechanisms rssr (fig. 1a) and rsst (fig. 1b) are used in numerous fields of

manufacturing engineering such as: sewing machines in the textile industry, agricultural

equipment, hydraulic pumps and engines, wind screen wiper mechanisms.

These mechanisms consist of a minimum number of kinematic elements, are some of the

simplest spatial mechanisms [1, 2] and have the advantage that they can achieve, for a small

gauge, the transmission and transformation of the rotation motion between the in and out

elements whose axes are displaced randomply in space.

x

1l

ll

A

23

B

0A

1y

y

1x

0

B0

s

s1

3

01

z

l0

l1

A1s

0

0A

B

1 s

0

l0

l2

03

z

B

y1

y

x

s

a. b.

x

y

z

A 1

A 1

A 1

= s

= l sin

= l cos

A

x = s

y =

z = l

B 3

0

cos +

-

l3 sin sin

BB

s3 sin l3 sin cos

B + l3 cos

A

x s= 1A

y A= sinl1

cosz l=A 1

-

+3=x s cos

y B

=z lB 0

sin= sB 3

B

-

sin

cos

s

s

Fig. 1. Kinematic diagrams of the rssr and rsst spatial mechanisms


45

As compared to other types of spatial mechanisms with upper kinematic couplings (with

spatial cams or with conical / auger gears), bar spatial mechanisms are made of lower

kinematic couplings (cylindrical and spherical), which offers simpler technical solutions

(requiring less expensive technologies), and has higher reliability in difficult working

conditions.

Starting from the general case of the rssr spatial quadruple mechanism, the paper deals

with the classical particular cases [2] as well as with the new ones [1, 7]. These mechanisms

have apparently no geometrical or construction characteristics in common.

Thus, the transmission functions for each type of spatial mechanism can be easily

obtained from the transmission function deduced in the general case of the rssr spatial

mechanism [1, 2, 6]. If we take the general case of the rssr spatial mechanism (fig. 1a), as

written out in the diagram, the transmission function can be written as [2, 6]:

0)sinsincoscos(coscossincossin 543210 aaaaaa (1)

The relation (1) is a function of the type 0),( F , where the angles and place

the crank 1 (drive element) and the equalizing bar 3 (driven element) as to the axis oz (fig.

1a). If we use the notations in the kinematic diagram (fig. 1a), the coefficients in the equation

(1) can be expressed as follows:

cos2 31

2

3

2

1

2

3

2

2

2

1

2

00 sssslllla ;

102311 2;sin2 llasla ; (2)

315304313 2;2;sin2 llallalsa .

2. The rssr mechanism with orthogonal axes (090 )

In the particular case of 090 (fig. 2) the o1b0 axis is parallel to the oy axis, so that the

crank 1 and the equalizing bar 3 rotate in perpendicular planes.

x

l1

A 1s

0

0A

B x1

1s

0l0

l20 3

l3

z B

y1

y

= 90o

x

1l

0A

l

l

A

2

3

B

1y

z = z1

y

1x

B0

0

l0

s1

x

A

1l A0

1l

l2

3

B

y

z = z1

y

1x

l0

B0

os = s = 01 3= 0

Fig. 2. Kinematic diagram of the rssr spatial mechanism when 0,0,90 31

00 ss


46

The coefficients 10, aa and 3a which depend on the angle therefore become:

2

3

2

1

2

3

2

2

2

1

2

00 sslllla ;

311 2 sla ; 313 2 lsa . (3)

This mechanism where the in and out axes are perpendicular (fig. 2) is called an

orthogonal spatial quadrangle [1, 5]. For 090 the transmission function (1) is written:

0coscoscossincossin 543210 aaaaaa (4)

3. The rssr mechanism with parallel axes ( 00 )

When 00 the rotation axes of the crank 1 and the equalizing bar 3 become parallel

(fig. 2) when we can consider 03 s , so that the point b0 is on the oz axis and the equalizing

bar 3 rotates in the yoz plane.

For 00 180,0 the 1a and 3a coefficients are null, and the 0a coefficient is

2

31

2

3

2

2

2

1

2

00 )( sslllla (5)

This particular case (fig. 2) corresponds to the plane-parallel of the elements 1 and 3

whose rotation axes are parallel. The transmission function (1) coincides in this case (fig. 2)

to the one of the plane mechanism:

0)cos(coscos 5420 aaaa (6)

4. The rssr mechanism with 031 ss

The two rotation axes of the crank 1 and of the equalizing bar 3 are displaced randomly in

space (fig. 2), but the points a0 and b0 are situated on the oz axis. Since 031 ss , the 1a and

3a coefficients are null ( 01 a , 03 a ), and the 0a coefficient can be inferred from (5)

2

3

2

2

2

1

2

00 lllla (7)

The transmission function (1) becomes in this case

0)sinsincoscos(coscoscos 5420 aaaa (8)

For the orthogonal spatial mechanism ( 090 ), the transmission function (8) becomes

0coscoscoscos 5420 aaaa (9)

The formula (9) can be also inferred from (4) if we introduce the conditions 031 ss .


47

5. The rssr mechanism with 00 l

The condition 00 l imposes the concurrency of the rotation axes of the in and out

elements (fig. 3), which corresponds to the geometrical condition of spherical mechanisms.

From the relations (2) null values for the 2a and 4a coefficients are obtained ( 042 aa ),

and for the coefficient 0a we infer the expression

cos2 3123

21

23

22

210 ssssllla (10)

B

l

A

l

x

y

z

A

B

y

s

l

s

x

0

2

1

3

3

1

0

0

1

1

0

z

B

y

x1

A

x

1l

45o

45o

a. b.

l = 0 ; s =1 ; s = l A0B = 90o

l = 0 0 1 3 3 ;0

Fig. 3. Kinematic diagram of the rssr mechanism with concurrent axes

For the transmission function (1) we obtain the expression

0)sinsincoscos(cossinsin 5310 aaaa (11)

In the particular case when the oa and ob lines are perpendicular (fig. 3b), we have the

following relation between the specific liniar lengths of the mechanism

2

2

2

3

2

1

2

3

2

1 lssll (12)

This condition determines a much simpler expression for the 0a coefficient

cos2 310 ssa (13)

Considering the formulas of the 31, aa and 5a coefficients of (2) versus the formula of the

0a coefficient in (10) or (13), it is inferred that, when 3311 ; lsls , the transmission function

(11) becomes:

0)sinsin1(cos)sin(sinsincoscos (14)


48

Which shows that the function 0),( F no longer depends on the liniar parameters of

the mechanism, this being specific to the spherical mechanism.

Indeed, in this particular case, the s type spherical joints in points a and b (fig. 3a) can be

replaced by r type cylindrical joints (fig. 3b).

For the orthogonal spherical mechanism ( 090 ), the transmission function (14) becomes

0sinsincoscos (15)

6. The rssr mechanism with 0,0 310 ssl

This particular case of the spatial mechanism corresponds to the simple spherical

mechanism of the crank-equalizing bar type (fig. 4).

If we take into account the above mentioned geometrical conditions (fig. 4), the

4321 ,,, aaaa coefficients are null, and the equation of the transmission function is expressed in

a simplified form:

0)sinsincoscos(cos50 aa (16)

l = 0 ; s l= l2

2

2

1

2

3

2

1+ + sl0 3 0 ; =0l0= ; s =03s=1

z

x

y

B0

x1

01

y

2l

1l

l3

B

A0B

1l0

x

2ll

A

3

B

y

1x

z

s

A0

1

Fig. 4. Spherical rssr mechanism Fig. 5. Cardan rssr mechanism

Where the 0a and 5a coefficients are expressed:

2

3

2

2

2

10 llla ; 315 2 lla (17)

When the x and x1 axes (fig. 4) are perpendicular, we can infer the transmission function

from (16) for 0 as below

0coscos50 aa (18)


49

7. The rssr mechanism with 0,0,0 030 asl

For these particular values, between specific geometrical parameters we can infer from (2)

the relation

2

3

2

1

2

1

2

2 lsll (19)

Which corresponds to the kinematic scheme of the rssr mechanism (fig. 5) when the ab0b

triangle is a right triangle, that is 0

0 90)( BAB .

If on the kinematic scheme (fig. 5) we write )( 00 ABA we can write the relation

tgsl 11 , so that the coefficient 1a of (2) becomes

tglla

sin2 311 (20)

The other coefficients of the transmission function (1) are 0432 aaa and 315 2 lla ,

which determines for the implicite function 0),( F the following particular form

0)sinsincoscos(cossinsin tg (21)

In which we have only constant angular parameters ),( together with variable angular

parameters ),( .

The equation (20) shows that the rssr spatial mechanism (fig. 5) can now operate as a

spherical mechanism, where the spherical couplings in a and b are replaced by rotation

couplings (fig. 3b).

If we consider the case of perpendicular axes with this mechanism (fig. 5) )90( 0 , this

corresponds to the spherical mechanism with eqalizing bar of the oscillating washer type [1,

7]. The transmission function is obtained from (21) in its simple form:

cos tgtg (22)

8. The rssr mechanism with 0,0,0 0310 assl

For the new geometrical conditions imposed to the spatial rssr mechanism (fig. 6) the

relation (19) is written 2

3

2

1

2

2 lll .

Which corresponds to the constant 900 angle between segments a0a and a0b (fig. 6).


50

l1

x

l2

A

B

l3

y

x1

y1

A0

1z = z

l0l 0= =3s; ;03

2l=2

2l+1

2s1=

Fig. 6. Kinematic diagram of the cardan rssr mechanism

The spherical mechanism obtained (fig. 6) is of the cardan type, where the transmission

function is inferred from the equation (16) for 00 a as follows:

0sinsincoscoscos (23)

From equation (23) we obtain the expression

cos

1 tgtg (24)

In this case we can replace the spherical couplings in a and b (fig. 6) by rotation cylindrical

couplings, just like with the classical cardan spherical mechanism.

we should mention that formula (23) represents the transmission function of the mechanism

known as simple cardan coupling, its expression being different from the one known and

given in the papers [3, 4, 7].

This is due to the way in which the and angles are measured, so that in this case the two

angles are measured against the same direction parallel to the a0z axis that is common to both

cartesian reference points a0xyz and a0x1y1z1 (fig. 6).

We should also notice that, if the and angles are measured against the a0y axis and the

a0y1 axis (fig. 6), the transmission function is obtained as follows [3, 8]: cos tgtg

If the angle is measured against the a0y axis, and the angle is measured against the a0z1

axis (fig. 6), the transmission function becomes:

l0 =0, s1=s3=0, 23

21

22 lll ,

A

B

A0 A’

B’

x

x1

y

y1

z, z1

l2

l1

l3

l1

l3

.

.

l3

l3

l1

B1

A1

ψ


51

cos

1ctgtg (25)

With cardan transmissions, the angle(between the axes a0x and a0x1 ) is an obtuse

( 090 ), therefore 0cos . If in this case we consider the acute angle 0180 (fig.

6), the transmission function (25) can be written in its well-known explicite form [1, 4, 7, 9]:

cos

tgtg (26)

9. Conclusions

Starting from the representation of the kinematic diagram of the rssr spatial mechanism, in

an axonometric projection (fig. 1a), in the paper we infer the expression of the transmission

function 0),( F in its implicite form (1), of which specific forms are obtained for

different cases.

Of the specific variants of the rssr spatial quadruple mechanism, the authors mention in

particular spherical mechanisms, known as crank – equalizing bar spherical mechanism (fig.

7), called sherical mechanism with oscillating washer and the crank – crank spherical

mechanism (fig. 8) called cardan (coupling) mechanism.

It is proven that these two spherical mechanisms, which have multiple applications in

manufacturing engineering, can be obtained as simplified variants of the rssr quadruple

mechanism (fig. 1a), in which spherical couplings are replaced by rotation cylindrical

couplings. The cardan type spherical rssr quadruple mechanism can be achieved as two

parallel chains (fig. 6), with equal length ab and a’b’ reciprocating rods.

BIBLIOGRAPHY

1. Antonescu, P., Mechanisms - Structural and Kinematic Calculation, Polyt. Inst. Press,

Bucharest, 1979;

2. Luck, K., Modler, K-H., Einfache raumgetribe für getribetechnishe grundaufaben, Wiss.

ZDTU. Dresden, 1978;

3. Manafu, V., Theory of Mechanisms and Machines. Structure and kinematics. The Technical

Publishing House, Bucharest, 1959;

4. Autorenkollektiv, Getriebetechnik Lehrbuch, VEB Verlag Technik, Berlin, 1969;

5. Antonescu, P., Contributions to the Graphic Synthesis of Spatial Mechanisms, Ph.D. Thesis,

The Polytechnics Institute Press, Bucharest, 1969;

6. Alexandru, P. and others., Mechanisms Vol. II, Synthesis, Braşov University Press, 1984;

7. Dudiţă, F., Cardan Transmissions, The Technical Publishing House, Bucharest, 1966;

8. Pelecudi, Chr. and others, Mechanisms, E. D. P. Bucharest, 1985;

9. Antonescu, P., On the Specific Cases of the Spatial Quadruple Mech., SYROM’89, vol. II.1, p.

1-10;

10. Antonescu, P., Mechanisms, Printech Publishing House, Bucharest, 2003.

11. Vişa, I. and others, Functional Design of Mechanisms, Classical and Modern Methods, Braşov,

2004.


52

PLANAR MECHANISMS USED FOR GENERATING

CURVE LINE TRANSLATION MOTION

Dr. Ovidiu ANTONESCU, Politehnica University of Bucharest, [email protected]

Viorica VELISCU, Transport CF High School, Craiova, [email protected]

Daniela ANTONESCU, „Iuliu Maniu” High School, Bucharest,

[email protected]

Abstract: The curve line translation motion can be generated in the particular form of the

circular translation, through mono-mobile mechanisms with articulated links of simple

parallelogram type (with a fixed side) or through transmission with toothed belt with a fixed

wheel. Also, the circular translation can be generated through planar mechanisms with two

cylindrical gears with a fixed central wheel. It is mentioned that the two cylindrical gearings of the

Fergusson mechanisms are both exterior and interior.

Keywords: planar mechanism, circular translation motion, cylindrical gear, kinematic scheme

1. Introduction

Curve line translation motion, in particular circular translation, can be generated by

means of planar mechanisms with articulated links [1, 3, 4] such as the articulated

parallelogram (fig. 1), or by means of planar mechanisms with cylindrical gears [1, 2, 3] such

as the Fergusson mechanism (fig. 2).

With the planar mechanism of the articulated parallelogram type (fig. 1), the

reciprocating rod 2 does a circular translation motion as the velocities of points A and B are

equal, which can be noticed by maintaining the segment AB in a parallel position to itself.

Fig. 1. The parallelogram mechanism Fig. 2. Fergusson planar mechanism

With the multi-level planar mechanism (fig. 2), where the gear wheels 1 and 3 are equal,

if the central gear wheel 1 is fixed ( 01 ), the satellite wheel 3 does a circular translation

motion ( 03 ).

A B

A0 B0

a b

1

2

3

0

A

B

D

C(c)

a

b

d

O

p

3

1(0)

2




53

Indeed, by actuating the planet wheel carrier p ( 0p ), by means of the distribution of

linear velocities (fig. 2), it results that the velocities of points B and D are equal:

;0)( Cc )(2)()( AaDdBb

2. Using the circular translation motion in auxiliary mechanisms of motor vehicles

2.1. Doors closing / opening mechanism without hinges

The doors of some modern buses no longer contain hinges, and they are actuated by

means of the articulated parallelogram mechanism (fig. 3) in which the door side MN is one

with the reciprocating rod AB of this planar mechanism.

Fig. 3. Kinematic scheme of the mechanism Fig. 4. Kinematic scheme of the

used for actuating the bus door screen wiper

The kinematic scheme of the parallelogram mechanism (fig. 3) is presented by

means of a continuous line in an intermediate position (when the door side MN is outside

the bus), and by means of a dotted line in the extreme closing (right) and opening (left)

positions.

The mechanism is pneumatically driven by means of an actuator situated below,

under the bus platform, at the same level with the stairs used by passengers to go on and

off the bus.

2.2. The screen wiper mechanism

The parallelogram mechanism is used as screen wiper (fig. 4) for urban buses, where the

wiping shim is fixed in the MN position perpendicular to the reciprocating rod AB in a point

situated to the right of the AB segment.

The kinematic scheme of the parallelogram mechanism (fig. 4) is shown in three distinct

positions, of which the extreme position to the right is represented by a continuous line, and

the other two positions (middle and left) are represented by means of a dotted line.

This mechanism is usually electrically driven by means of an equalizing rod – crank

mechanism.

This type of parallelogram mechanism with a fixed small edge is used for the doors of

motor vehicles in terms of a crane to lift / lower the glass.

A

A0 B0

B M N

M'

N''

A' B' N'

M''

B A

B0 A0

N

M M'

M''

N' N''

B' A'

A'' B''


54

The reciprocating rod of such a parallelogram does a circular translation motion, and by

means of some rollers, gets into contact with the glass frame, which is vertically guided.

This kind of mechanism is driven manually or electrically by means of a cylindrical

gear having a large multiplication ration, placed inside or outside, which ensures a certain

self-locking degree with regard to the intention of actuating from the led element to the

leading one.

3. Geometry and kinematics of the Fergusson planar mechanism

The Fergusson planar mechanism (fig. 2, 5) consists of three geared wheels to the

outside (1, 2, 3) placed in a series, articulated in points O, A and B on the planet wheel carrier

p, which does a translation motion around the fixed point O.

Providing that the distances between the axes of the wheels 1 and 2, respectively 2 and 3 are

equal (OA = AB), the gear wheels 1 and 3 have equal diameters, and the same number of

teeth (z1 = z3).

If gear wheel 1 is fixed by means of blocking (fig. 2, 5), then point C becomes the

instantaneous rotation centre of gear wheel 2, with a null velocity (Cc=0).

Fig.

5. Kinematic scheme (a) and general kinematic scheme (b)

of Fergusson planar mechanism in a double orthogonal projection

For one rotation of the planet wheel carrier p at an angular velocity , points A and B

have velocities in the ratio OA/OB = 1/ 2. The distribution of velocities (fig. 2) on the gear

wheel 2 is obtained by uniting the point a (the peak of the A point velocity) with point C

whose velocity is null.

Point d, peak of the velocity of point D, is located on the extension of the ac segment,

so that the ratio of the velocities of points A and D is CA/CD = 1/ 2. For the velocities of

points A, B, C and D we can define the ratios (fig. 2, 5):

2

1

OB

OA

Bb

Aa;

2

1

CD

CA

Dd

Aa (3.1,2)


55

Of the ratios (2.1) and (2.2) it results DdBb , that is the velocities of points B and D

on the gear wheel 3 are equal, which determines 03 , so gear wheel 3 does a circular

translation motion.

The same conclusion may be obtained by means of the analytic method, writing the

relative transmittal ratios provided the planet wheel carrier p does not move:

)1( 2

1

2

21

PP

Ppi

;

1

1

2

3

2

3

32

P

P

P

Ppi

(3.3,4)

Multiplying relations (3.3) and (3.4) we obtain

3

1

3221

3 11z

zii pp

p

(3.5)

For 31 zz and 0p it results from (3.5) that 03 , which corresponds to the

circular translation motion.

4. New cylindrical planar mechanisms for generating circular translation motion

A new kinematic scheme (fig. 5b) is obtained starting from the Fergusson planar

mechanism (fig. 5a), where the interim gear wheel 2 has been replaced by two joint and

several gear wheels 2 and 2’ with different radii.

Let us consider the formula (3.5) which is now written as

32

'21

'3221

3 11zz

zzii pp

p

(4.1)

Provided that gear wheel 3 does a circular translation motion, that is 03 , we obtain

from formulae (4.1):

132

'21 zz

zz (4.2)

Thus, if we impose the transmittal ratio 0i of the exterior cylindrical gear (1,2), from

(4.2) we obtain:

10

'2

3

1

2 iz

z

z

z (4.3)

Relation (4.2) can be checked by means of the graphical method of the linear velocities

distribution (fig. 6), where, if the velocities of two points on gear wheel 3 are equal, for

example DB VV , the instantaneous rotation centre is to infinity, that is the angular velocity

3 is null. Considering the distribution of linear velocities (fig. 6) we notice that the

equivalence DdBb implies the relations


56

AB

OA

AD

AC or

3'2

21

'2

2

rr

rr

r

r

(4.4)

Considering the second relation of (4.4), we obtain 32'21 rrrr , equivalent to (4.2), as

the radii of the dividing circles are proportional to the numbers of teeth.

A smaller gauge alternative of the kinematic scheme presented above (fig. 5b) is

obtained if the gear wheel 3 gears with the gear wheel 2’ on the same side of the 2 axis with

the exterior gear mechanism (1,2) (fig. 6).

Fig. 6. Kinematic scheme of the Fergusson mechanism – compact alternative

The position of the 3 axis, correspondingly of point B , is obtained by means of the

distribution of velocities Oa and Ca , depending on the position of point D . Thus, knowing

the vector Dd with Cad , the position of B is given by the peak of its velocity where the

parallel line from d to OA meets Oa .

In this case (fig. 7), following the distribution of linear velocities in the hypothesis

DdBb , that is 03 , the geometrical construction implies

AD

CD

AB

OB or

'2

'22

3'2

3'221

r

rr

rr

rrrr

(4.5)

which leads to the relation 32'21 rrrr , the same as with the previous alternative, namely (4.2),

32'21 zzzz . For the particular case when 0OD it results (fig. 7a) ACOC , and points A

and B are antipodal [1, 3], which allows for better balancing.

O

O

C

A

B

D D

A

C,c

B

a

d

b

2

1

2 2’

3

p

3

1(0)

2

2’

3

p

1(0)


57

Fig. 7a. Kinematic scheme of the planar Fig. 7b. Kinematic scheme of the planar mechanism

mechanism, improved version with interior gears

Fig. 8. Images foto of mechanism model with external cylindrical gearings

Coming back to formula (4.1), for 03 we can write the general expression

1'3221 po ii (4.6)

Analysing the relation (4.6) it results that the transmittal ratios pi21 and pi '32 must have the

same sign, that is the cylindrical gears (1, 2) and (2’, 3) are either both exterior (fig. 7a) or

both interior (fig. 7b).

If both gearings are interior (fig. 7b), we shall start by conveniently choosing the

characteristic points CAO ,, and D , respectively the numbers of teeth of the gear wheels 1,

2 and 2’.

A A

B B

D O,D

C,c

a

d

b

C

1

2

2’

3

p

1(0)

O

d

b

A A

B B

C,c

D D C

O O

a

1

2 2’

3

p

1(0)


58

We build the velocity of point A through the segment Aa oriented to the left (fig.

7b). Knowing that the velocity of point C is zero, the velocity of point D is obtained by

means of the linear distribution of velocities, points ca, and d are collinear.

From point we draw a parallel line to the reference line OA till it crosses the

extension of the Oa segment in point b . Thus we obtain on the drawing (fig. 7b) the

OB segment, positioning the mobile axis of the satellite wheel 3 with interior dents, which

does a circular translation motion.

5. Conclusions

The curve line translation motion can be generated in the particular form of circular

translation, by means of mono-mobile mechanisms with articulated links of the simple

parallelogram type (with a fixed side) or by means of transmissions with a toothed belt

with a fixed wheel.

Also, circular translation can be generated through planar mechanisms with two

cylindrical gears with a fixed central wheel. It is mentioned that the two cylindrical

gearings of the Fergusson mechanisms are both exterior and interior.

The general form of the curve line translation is obtained by means of planar bi-

mobile manipulating mechanisms with articulated links, auxiliary kinematic chains

mounted in parallel with the main kinematic chain.

Bibliography

1. Antonescu, P., Mechanisms –Structural and Kinematic Calculation, U.P.B. Printing

Press, Bucharest, 1979;

2. Maros, D., Theory of Mechanisms and Machines – Gear Kinematics, Tech. Publ.

House, Bucharest, 1958;

3. Antonescu, P., Antonescu, E., Synthesis of Cylindrical Planetary Mechanisms in view

of the Circular Translation, SYROM’81 Bucharest,

Vol. III, pp 9-14, 1981;

4. Antonescu, P., Antonescu, O., Mechanisms and the Dynamics of Machines, Printech

Publishing House, Bucharest, 2005.


59

MAIN TYPES OF MECHANISMS USED AS WINDSHIELD WIPER

Ph.D. Ovidiu ANTONESCU, „Politehnica” University of Bucharest: [email protected]

Viorica VELIȘCU, Railroad Transportation Highschool, Craiova: [email protected]

Constantin BREZEANU, Silcotub S. A. (Tenaris Group) Călărași: [email protected]

Abstract: This paper deals with the main types of windshield wiper mechanisms, consisting of bars

and gear links. These mechanisms are classified into two groups: those with constant length arm and

those with variable length arm. For each type of mechanism used as a windshield wiper, the paper

highlights the main advantages and disadvantages regarding the wiped windshield surface and the

constructive structural complexity.

Keywords: windshield wiper mechanism, bar, gear, degree of mobility, kinematic diagram

1. General considerations

Windshield wipers are plane or spatial mechanisms, having one, two or three driven

elements, in terms of wiping arms, with elastic blades on which the rubber blades that wipe

the windshield glass or the rear window glass are attached [2 - 7].

Electric motors of continuous current are used to drive the windshield wipers, which are

power by the car battery. This electric drive ensures the oscillation of the wiping arm within

certain imposed frequency limits. [2]. With windshield wipers with a single constant length

arm, the wiped surface is smaller than with those provided with two arms that are more often

used [5]. Modern cars have telescopic arm windshield wipers, which ensures maximum

coverage of the windshield surface [4, 8, 9, 10].

Windshield wipers are designed and built as mechanisms with articulated bars, cams and

gears. [7]. The paper analyses the main types of mechanisms used as windshield wipers (ws.

w.) from a structural and topological point of view.

2. Ws. W. Mechanisms with Articulated Bars

a) b) Fig. 1. Kinematic (a) and structural (b) diagrams of the ws. w. mech. provided with two parallel arms

0

B 2 A

4 C

b1 b2

L1 L2

1 5 3

B0 C0

A0

B

0

B

3

2 A A’ C 4

C0

5 A0

1

0


60

This type of ws. w. mechanism with articulated bars (fig. 1) is used for the majority of

road vehicles. It has the advantage of being a simple mechanical structure, which is safe

during operation (at several operating speeds), as well as very reliable.

Each of the two arms b1 and b2 are provided at the upper edge with an elastic blade (L1,

L2). These arms are connected to the equalizing bars 3 and 5, which rotate around the fixed

points B0 and C0.

The two equalizing bars (3, 5) are driven by the same crank 1 (articulated in A0 at the

bottom), by means of the reciprocating rods 2 and 4, articulated in the same point A at the

crank. The degree of mobility of the ws. w. mechanism is determined by formula [11]

6

2

5

1 rr

mm rNmCM (1)

In formula (1) Cm stands for the number of m operational class kinematic couplings, and

Nr stands for the number of r rank independent closed contours. These structural-topological

parameters are highlighted in the matrix

00020

00007

65432

54321

NNNNN

CCCCC (2)

Having these numerical values, formula (1) is written: 12371 M (3)

Which shows that the analysed ws. w. mechanism (fig. 1) has a single degree of mobility; this

consists in the movement of the leading element, that is crank 1.

In fact, the 3 fixed articulations in A0, B0, C0 do not have rigurously parallel axes. That is

the reason why the kinematic couplings in points A, B, C are spherical articulations.

The structural-topological matrix of the actual mechanism is written according to (2) as

20000

00403

65432

54321

NNNNN

CCCCC (4)

And the degree of mobility is inferred from (1): 326)4331( M (5)

The two additional mobilities are represented by the rotations of bars 2 and 4 as to the

axes AB and CD.

If we consider the mechanism in terms of a plane mechanism (fig. 1a), the structural-

topological diagram (fig. 1b) shows that it results from the Watt kinematic chain.

With this plane mechanism we identify two open kinematic chains of the dyad type (2, 3)

and (4, 5), paralleled to the fundamental mechanism MF (0, 1), which corresponds to the

aggregation formula of the motor mechanism (MM):

)5,4(

)3,2()1,0(

LcD

LcDMFMM (6)


61

Even though this kinematic diagram (fig. 1) is simple, the solution has the disadvantage

that the surface wiped on the windshield (by the rotating oscillating arm) is nevertheless

limited. For ws. w. with a single rotating oscillating arm (usually used for the rear window),

longer wiping blades are mounted.

Another kinematic diagram of ws. w. mechanisms [1, 7] uses a complex topological

structure (fig. 2), where the kinematic chains are connected serially.

a) b)

Fig. 2. Kinematic (a) and structural (b) diagrams of ws. s. M. with two serial arms

We can notice a complex topological structure, where 3 and 4 bars (criss-crossing each

other) form together with the kinematic elements 2 and 5, a closed kinematic contour of

the quadrangle type (BCEDB). The wiping arms (connected to bars 5 and 7) are serially

linked by means of bar 6, and the quadrangle F0FGG0F0 is an articulated parallelogram. In

order to determine the degree of mobility of this ws. w. M. (fig. 2a), we write the

structural matrix:

00030

000010

65432

54321

NNNNN

CCCCC (7)

The degree of mobility is obtained from formula (1):

133101 M (8)

The structural-topological diagram of this type of ws. w. m. (fig. 2b) corresponds to a

complex kinematic chain, where we can distinguish two open kinematic chains with zero

mobility, which are identified in the order of a possible disaggregation: LcD(6, 7) and Lc

tetrade type LcTt(2, 3, 4, 5). The structural-topological formula of the complex ws. w. m.

(fig. 4) can be written after stating the driving element, that is crank 1:

)7,6()5,4,3,2()1,0( LcDLcTtMFMM (9)

A0

G0

G

F0

F

E

C

D

B

A 4

3

2

7

6

5 0

1

0 7

6

5 4

3

2 1

G0

G F

F0 D

E C

B

A A0


62

3. Ws. W. Mechanisms with bars and gears with a constant length arm

Ws. w. m. with a constant length arm [3, 10] can be grouped into two variants, different

from the construction point of view: those with a translational gear rack T (fig. 3) and and

with a roto-translational gear rack R+T.

a) b)

Fig. 3. Kinematic diagram of the ws.w.m. with a T gear rack

The Ws.W.M. with translational gear rack (fig. 3) is provided with a single wiping arm,

connected to bar 5; thus it has a plane roto-translational motion.

From crank 1, as driving element, motion is transmitted by means of the reciprocating rod

2 to the B axis of the gear 3 (pinion type).

Pinion 3 engages at the same time to the upper side with the fixed gear rack 0 and to

the lower side with a mobile translational gear rack 4.

To the translational gear rack 4 the kinematic dyadic chain LcD (5, 6) is articulated in

point C, with the fixed articulation D0.

The translational motion of point B along the fixed guide 0 is provided by the double

engagement of pinion 3 with the two gear racks.

Thus, skid 7, ensuring the translational motion of point B (fig. 3b), together with the

two couplings (rotational and translantional) is not represented in the kinematic diagram (fig.

3a).

The structural matrix of the bar and gears plane mechanism (fig. 3a) is completed taking

into account the two kinematic couplings of skid 7:

00040

00029

65432

54321

NNNNN

CCCCC (10)

If these numerical data (10) are replaced in (1), we determine the real mobility degree

1432291 M (11)

0

0

6 5

4

3

2 D

0 D

C B

A 1

A0

3

0

4

0

0 B

7


63

This result (M=1) verifies the existence of a single element 1 with an independent motion.

Ws. W. M. with a roto-translational gear rack (fig. 4) has a single wiping arm connected

to bar 5 with a plane-parallel motion.

a) b) Fig. 4. Kinematic (a) and structural (b) diagrams of the ws.w. M. with a roto-translational gear rack

The rotation motion of crank 1 (fig. 4) is transmitted to the gear sector 4 by means of

the bar – gear rack 2. This is guided in the oscillating box 3, which keeps it in contact with

the gear sector 4:

The oscillating rotation motion of gear sector 4 is sent to an antiparallelogram

mechanism made up of bars 4, 5 and 6, with fixed articulations in B0 and D0. The wiping

blade MN is mounted and fixed on bar 5, perpendicular to CD, whose motion is plane

roto-translation.

The antiparallelogram B0CDD0 mechanism (fig. 4a) is represented by a dotted line in

the extreme left position, in which we notice the position of the wiping blade M’N’

rotated at 1800 as to the initial position MN. The structural matrix of the ws.w.M. includes

the number of the kinematic couplings of functional classes Cm with m =[1,5] and the

number of closed independent contours Nr of rank r =[2,6]:

00030

00018

65432

54321

NNNNN

CCCCC (12)

The mobility of the analysed mechanism is determined by means of the formula (1) in

which we replace the data in (12): 1331281 M

(13)

The structural-topological diagram of this mechanism (fig. 4b) is obtained after

equating the upper coupling (represented by the engagement of gear rack 2 with the gear

sector 4). This engagement equates with a binary element, with two lower kinematic

couplings [3]. The structural-topological formula is: MM = MF(0,1) +LcD(2,3)

+LcD(e24,4)+LcD(5,6) (14)

D

0

D

C

B’0

B’

4

B’

2

B

0

B A

A

0

3 4 5

6

e24

2

1 0

4

6

5

1

D

’ C

’

M

’

M N

N’

D0

C

D

B

0 4

3 A

2

A0


64

4. Ws. W. Mechanism with bars and gears of a variable length arm

With these variable length arm ws.w. M. [4, 7, 10], the wiping blade does a plane roto-

translational motion consisting in a rotation of an oscillating bar and a translational along

this one on a radial direction (fig. 5a).

Fig. 5. Kinematic diagram of the ws. w. M. with a variable length arm

The wiping blade MN is fixed on the rod 5, and the latter does the translational motion

along the oscillating guide 1’ connected to the gear 1, which has inside teeth.

Together with the oscillating rotation of the box-gear 1, motion is sent to crank 3 (by

means of the gears 2 and 3), and from here, by means of bar 4, the rotation motion is changed

into translational motion at rod 5 (fig. 5a).

The surface wiped by the blade MN corresponds to the stroke of rod 5, a relative

translational motion along the oscillating guide 1’ .

The structural matrix of this ws. w. M. (fig. 5a) is

00030

00026

65432

54321

NNNNN

CCCCC (15)

From this numerical data the mobility of the ws. w. M. is inferred with the formula

(1):

1332261 M (16)

The structural-topological diagram (fig. 5b) is done after equating the two upper

kinematic couplings (1, 2) and (2, 3), which are inside and outside engagements. The

structural-topological formula is written (fig. 5b):

MM = MF(0,1) +LcD(2,e12) +LcD(e23,3)+LcD(4,5) (17)

6. Ws. W. M. with the wiping blade in a circular translational motion This kind of ws. w. M. is used for buses where the surface of the windshield screen is flat

and much larger than it is for cars. The wiping blade MN is placed vertically, fixed to the

reciprocating rod 4 of a plane mechanism of an articulated parallelogram type (fig. 6), in

which the sides -bars 3 and 5 are much longer than horizontal sides.


65

In the practical solution, bar 5 is thin as compared to bar 3, which receives the oscillating

rotation motion from crank 1, by means of bar 2 (fig. 6a).

The structural matrix of that mechanism contains:

00020

00007

65432

54321

NNNNN

CCCCC (18)

Thus, the mobility degree of the Ws.W.M. (fig. 6a) is determined with formula (1) in

which we introduce the data in (18): 12371 M (19)

The structural-topological diagram of the Ws.W.M. analysed above corresponds to the

Watt kinematic chain (fig. 6b). The structural-topological formula is (fig. 12):

MM = MF (0, 1) + LcD (2, 3) + LcD (4, 5) (20)

a) b)

Fig. 6. Kinematic (a) and structural diagrams (b) of the Ws. W. M. with the blade doing a R+T motion

7. Conclusions

Ws. W. Mechanisms have a diverse topological structure, being made both as spatial

mechanisms and as plane mechanisms with bars and gears.

The paper aimed at a classification of the Ws.W.M. according to: the kinematic elements

used (bars, gear racks, cylindrical gears with outside and inside teeth), the number of

wiping blades, their motion and their serial or parallel connection. The Ws.W.M. is driven

by means of continuous current electric motors, powered by the car battery.

The wiping arm is moved together with the elastic blade. It is a rotational motion in

the case of bar ws.w.m., or a roto-translational motion for those with bars and gear

elements.

Comparing the 6 kinematic diagrams analysed, we pointed out the complexity of the

variable length arm Ws.W.M. from the structural and the construction point of view.

3

D

’

C

’ C

D

D

0

B

0

4

5

3

2 1

B

’

A

’

N

’

A

M’

N

M

B A

0

D C

A

D0 B0

A0

5

4

2

1

0

3 B


66

From the structural-topological analysis of the main types of Ws.W.M. used for cars,

we find out that most of them consist of dyadic kinematic chains, created either of

articulated bars or of rack and pinion or gear sectors, or outside / inside cylindrical gears.

Bibliography

1. Autorenkolektif – Getriebetechnik Lehrbuch, VEB, Verlag Technik Berlin, 1969.

2. *** - Passengercar windshield wiper systems – SAE 5903 C, 1973.

3. *** - Patent U.S.A. No. 3721878, 1978.

4. Schüche, S. et al., - Windshield wiper arrangement, U.S. Patent No. 4447928, 1984.

5. Antonescu, P., Cocosilă, M., Tempea, I. – A Comparative Study of the Drive

Mechanisms of Windshield Wipers used for Cars, MERO’87, Vol. 4, pp. 11-19,

Bucharest, 1987.

6. Antonescu, P., Mitrache, M., Cocosila, M. – Contributions to the Synthesis of

Mechanisms used as Windshield Wipers, SYROM´89, Vol. IV, pp. 23-32, Bucharest,

1989.

7. Antonescu, P., Tempea, I., Adîr, G. – Windshield Wipers Mechanisms for Passenger

Cars., SYROM’89, Vol. IV, pp. 41-50, Bucharest, 1989.

8. Antonescu, P., Crişan, M., Antonescu, D. – A Synthesis of the Plane Mechanisms

used for Driving Windshield Wipers, ESFA’ 92, Vol. II, pp. 367-374, Bucharest, 1992.

9. Antonescu, P., Cocosila, M., Antonescu, D. – The Geometrical and Building Structure

of Windshield Wipers Mechanisms, ESFA’92, Vol. II, pp. 375-386, Bucharest, 1992.

10. Antonescu, P., Cocosila, M., Antonescu, O. – The Geometrical Structure of

Windshield Wipers Mechanisms, SYROM’93, Vol. IV, pp.125-132, Bucharest, 1993.

11. Antonescu, P., Antonescu, O. – Mecanisme și dinamica mașinilor, Editura Printech,

2005.


67

PROCESSING ELECTRICAL EROSION TO ROTATE

WITEH TEETH TILTED

Dr.Ing. MARIAN G. POP ,

Technical University of Cluj-Napoca

Drd. Ing. IOAN BADIU, Technical University of Cluj-Napoca

Prof.univ.dr.ing. MARCEL S. POPA, Technical University of Cluj-Napoca

ABSTRACT: Static breakage of the teeth is caused by impact or large overload occurring during the

functioning gear due to operating conditions. Toothed wheels right rupture occurs at the base of the tooth and

the toothed wheels inclined falling progressively inclined gear teeth are break portions of the tooth. The

avoidance of static breakage of the teeth can be achieved by Bending gear calculation request to overload by

increasing the precision of execution and shaft stiffness.

KEY WORDS : Still breaking of the teeth, breakage, basic tooth, electrical erosion, materials

1.INTRODUCTION

Damage to teeth pitting active flanks (appearance of nicks on the flanks of the teeth assets) is

due to contact fatigue layer superficial active flanks, is the main form of damage to the gears with

hardness surface <45 HRC. Pinching is a fatigue phenomenon superficial active flanks teeth, the

contact stresses caused by time-varying. The first signs of fatigue occurs usually in the rolling

cylinders in the form of crazing. Initially, micro-cracks appear in the meaning of the forces of friction,

which are the driving wheel from rolling circle to the circle of the foot and the head, and the driven

wheel backwards, because the relative velocity between the two sides change their meaning pole

engagement. and the driven wheel backwards, because the relative velocity between the two sides

change their meaning pole engagement. The oil that adheres to the tooth surface is pressed - conjugate

tooth flank - the existing micro cracks.

In the crack appears hydrostatic pressure that favor the development of micro cracks and

detachment of small pieces of material, resulting in pinching surfaces of the teeth. Nicks develops over

time, leading to a malfunction of the unit. Avoiding decommissioning by pitting is done by: making an

account at the request of contact gear; heat treatment or thermochemical (surface tempering,

carburizing); positive displacement profile; sidewall roughness reduction teeth; the use of lubricants

additives.

2.THE PROCESSING TECHNOLOGY TOOTHED WHEELS

This car is equipped with CNC Fanuc and most powerful generator currently, Clean Cut

(Hence the name suffix CC machine), which can provide a maximum cutting speed of 400 mm²/min.

Cutting is done in immersion. Precision displacement measurement axes 0,5 μm.


68

Fig. 1. Massive electrode electrical discharge machines Charmilles.

Exfoliation of the superficial layer of the tooth flanks is a form of material deterioration and fatigue

that comes from gear teeth were subjected to heat treatment and surface hardening thermochemical

(surface tempering, carburizing). Exfoliation is manifested by detachment portions of the surface layer

of tooth flank, as a result of fatigue cracks occurring at the border of the hardened layer and the core.

Preventing damage by peeling gear is made by adopting Suitable treatment technologies.

Fig. 2. The direction of the friction forces and rolling circles.


69

Fig. 3. Driven-wheel driving wheel assembly.

Fig. 4. Types of fissures.

Fig. 5.Wheel assembly inclined with teeth and inclined pinion.


70

Fig. 6. The 3D graphic of gears.

Fig. 7. Toothed wheels assembly.

Fig. 8. The 3D graphic of gears.


71

Fig. 9. Toothed wheels.

Fig. 10. The 3D graphic of toothed wheels.

Fig. 11. Gear wheels.


72

Fig. 12. Toothed wheel gear-pinion.

Fig. 13. The 3D graphic of toothed wheels.

Fig. 14. Toothed wheel inclined teeth.


73

Fig. 15. Gear toothed wheels

3.EXPERIMENTAL RESULTS FROM THE POCESSING OF ELECTRICAL

EROSION

Fig. 16. Table containing the values parameters of electrical erosion.

Fig .17.The reporting of electric erosion productivity parameters.


74

Fig. 18. The connection between electrical erosion parameters.

Fig. 19. The reporting the electrical erosion productivity parameters.

Fig. 20. The connection between The electrical erosion parameters.


75



Fig. 23. The connection between electrical erosion parameters.


76

Fig. 24.The connection between The electrical erosion parameters.

Fig. 25.The form 3D graphics parameters The electrical erosion.



77



Fig. 29.The 3D graphic of The electrical erosion parameters and their values.


78


Fig. 31. The form 3D graphics parameters The electrical erosion.



79

Fig. 33. The form 2D graphics The electrical erosion parameters.

Fig. 34. The form 2D graphics The electrical erosion parameters and their values.

Fig.35. Table containing the values parameters of electrical erosion.


80

Fig. 36. The form 3D graphics parameters The electrical erosion.

Fig. 37. The 3D graphic of The electrical erosion parameters and their values.



81

Fig. 39. The form 2D graphics roughness values and percentages.




82

Fig. 42. The form 2D graphics roughness and values.

Fig. 43. The connection between The electrical erosion parameters and their values.



83


Fig. 46. The form 2D graphics roughness and values.



84



Fig. 50.The form 2D graphics roughness values and percentages.


85

4.CONCLUSIONS.

Seizure is a form of wear of adhesion to gears and appears strong loaded, working at

peripheral speeds high. Due to large landslides of teeth, large concentrations of tasks, the Large

sidewall roughness oil may be expelled from the surfaces contact. Due to the direct contact of local

tasks large and high temperature in the contact area, micro-welds which occur over time, break and

recover continuously, due to the relative motion of the flanks. Produce welds on conjugated tooth

flank scratches and scuffing strip oriented towards slip. Preventing damage by jamming gear is

through improvement of lubrication and cooling through the use of lubricant additives by increasing

the precision of the execution and assembly by increasing the rigidity of trees by increasing surface

hardness by reduction roughness of tooth flanks.

5.REFERENCES.

[1] Ailincai, G.: Studiul metalelor ,Institutul Politehnic Iasi, 1978.

[2] Balc, N.: Tehnologii neconventionale, Editura Dacia Publishing House, Cluj-Npoca, 2001.

[3] Bolundut, L.I.: Materiale si tehnologii neconventionale, Editura Tehnica-Info, Chisinau,

2012.

[4] Buzdugan, Gh., ş.a. – Vibraţii mecanice, Editura Didactică şi Pedagogică, Bucureşti, 1979.

[5] Constantinescu, V., ş.a. – Lagăre cu alunecare, Editura Tehnică, Bucureşti 1980.

[6] Colan, H.: Studiul metalelor, Editura Didactica si Pedagogica , Bucuresti, 1983.

[7] Domsa, A.: Materiale metalice in constructia de masini si instalatii, Editura Dacia,

1981.

[8] Gafiţanu, M. ş.a. – Organe de maşini, vol. 2. Editura Tehnică, Bucureşti, 2002.

[9] Ghimisi,S. -An elastic-plastic adhesion model for fretting,15th.Symposium “DanubiaAdria”,

Bertinoro, Italia, 181-183.

[10] Nichici, A.: Prelucrarea prin eroziune electrica in constructia de masini, Editura Facla,

Timisoara, 1983.

[11] Olaru, D.N. – Tribologie. Elemente de bază asupra frecării, uzării şi ungerii, Litografia

Institutului Politehnic „Gheorghe Asachi”, Iaşi, 1995.

[12] Popa,M.S.:Masini, tehnologii neconventionale si de mecanica fina-Editie Bilingva, Romana-

Germana, Editura U.T.PRESS, Cluj-Napoca, 2003.

[13] Popa, M.S.: Tehnologii si masini neconventionale, pentru mecanica fina si microtehnica,

Editura U.T.PRESS, Cluj-Napoca, 2005.

[14] Popa, M.S.:Tehnologii inovative si procese de productie, Editura U.T.PRESS, Cluj-

Napoca,2009.

[15] Rădulescu, Gh., Ilea, M. – Fizico-chimia şi tehnologia uleiurilor lubrifiante, Editura Tehnică,

Bucureşti, 1982,

[16] Sofroni, L.: Fonta cu grafit nodular,Editura Tehnica, Bucuresti, 1978.

[17] Trusculescu, M.: Studiul metalelor, Editura Didactica si Pedagogica ,Bucuresti ,,1978.


86

GEAR WHEELS THE PROCESSED BY ELECTRICAL

EROSION

Prof.univ.dr.ing. MARCEL S.POPA, Technical University of Cluj-Napoca

Drd. Ing. IOAN BADIU, Technical University of Cluj-Napoca

ABSTRACT: For low tooth loads and low peripheral speeds between 0.3 and 2 m / s are chosen based alloys

and steels, gray cast iron. In industry are preferable ferrous alloys: bronze, brass and aluminum alloys, and

where speeds and demands are low gears are made of sheet steel or alloys. Wheel group required less include

some hand-operated mechanisms, such as jacks, some trolls. These wheels are larger and they are made of

alloy steel, semi-hard and sometimes gray cast iron FC250, FC300.

KEY WORDS : cogwheels, electrical erosion, materials, processing electrical erosion.

1.INTRODUCTION

For gears subject to high variable operating at low speed and medium (2-8m/s) are recommended

semi-hard steels and low alloy likely to be improved. These wheels are used in various fields. For

example, some large gear drive found in mills and cement kilns, some lifting and transport machinery,

agricultural machinery, combine mining. The blanks are obtained by casting, cast iron or steel, some

elements are obtained from the laminates.For heavy gear required to run high peripheral speeds (12-

16m / s) with high loads and shocks tooth in operation, high toughness steels are used, which applies

superficial hardening by heat treatment and thermochemical. Steels are suitable for manufacturing

these gears are alloy or alloy, and in some cases can be used and tempered steels. In cases where

demand is particularly high, it is advisable to use high alloyed steels, case hardening steels such as Cr

- Ni, Cr - Ni - Mo, Cr - Ni - Ni steels W. use is recommended as we confer high resistance of these

wheels.

2.TECHNOLOGICAL PROCESSING ELECTRICAL EROSION

FIG.1. WIRE ELECTRICAL DISCHARGE (WIRE EDM) MACHINE- 725 × 560 × 215 MM | G22F.


87

Fig.2. The 3D graphic of the toothed wheel.

Fig.3. The values of toothed wheel.

Fig.4.The form 2D gears processed by electrical erosion.


88

Fig.5. The form 2D gears processed by electrical erosion.




89


3.THE EXPERIMENTAL RESULTS PROCESSING ELECTRICAL EROSION

Fig.9. Table containing the values electrical erosion parameters.

Fig.10. Graphic form of electrical erosion parameters.


90

Fig.11. The parameters of electrical erosion.

Fig.12. The connection between electrical erosion parameters.

Fig.13. Surface roughness parameter values.


91

Fig.14. Graphic form of electrical erosion parameters.

Fig.15. The reporting of electrical erosion Surface roughness parameters.

Fig.16. Table containing the values electrical erosion parameters.


92

Fig.17. The connection between electrical erosion parameters.

Fig.18. The reporting of electrical erosion Surface roughness parameters.

Fig.19. 3D The form parameters of electrical erosion.


93



Fig.22. The electrical erosion parameter values in the form of balls.


94

Fig.23. The straight lines and electrical erosion graphical form parameters.

Fig.24. Form 2D electrical erosion parameters and parametric equations.

Fig.25. 2D electrical erosion parameters.


95

Fig.26. 3D the form parameters of electrical erosion.

Fig.27. Points that determine erosion parameters electrical lines.

Fig.28. The straight lines electrical parameters and equations erosion graphs.


96





97


Fig.33. 3D the form parameter intensity.



98


4.CONCLUSIONS

A range of thermal and thermo-chemical treatments are applied in order to increase the workability

(annealing, tempering), increased durability and reliability in operation (carburizing, hardening,

tempering) or for the purpose of hardening surfaces as special treatment (cianizarea, surfizarea,

feroxarea, phosphating, iono-nitrurarea). So to influence and improve the machinability of steels and

cast irons for making gears is necessary to act by heat treatments on materials to improve machining

conditions. If obtained from semi forged gears recommended forging temperature to be 1000-1250oC,

to avoid fissures and cracks-them.If some small gears and pinions are processed cold (cold extrusion

or stamping) have applied annealing. Nitriding steels are used for gears subjected to heavy wear, so

heavily loaded. Alloying elements form nitrides hard and stable. Can be nitrided steels and

39MoCA06 38MoCA09 required to wear wheel (gears, sprockets, chain wheels, snails, racks). These

steels are subjected to heat treatments for improvement: double quenching and tempering. The

hardness of the nitrided layer depth decreases. Nitriding is done at a temperature of about 500-600o C

depending on steel composition, thickness reaching 0,8 mm in a time of about 40-60 hours in two

successive stages

5. REFERENCES [1] Ailincai, G.: Studiul metalelor ,Institutul Politehnic Iasi, 1978.

[2] Balc, N.: Tehnologii neconventionale, Editura Dacia Publishing House, Cluj-Npoca,

2001.

[3] Bolundut, L.I.: Materiale si tehnologii neconventionale, Editura Tehnica-Info, Chisinau,

2012.

[4] Buzdugan, Gh., ş.a. – Vibraţii mecanice, Editura Didactică şi Pedagogică, Bucureşti, 1979.

[5] Constantinescu, V., ş.a. – Lagăre cu alunecare, Editura Tehnică, Bucureşti 1980.

[6] Colan, H.: Studiul metalelor, Editura Didactica si Pedagogica , Bucuresti, 1983.

[7] Domsa, A.: Materiale metalice in constructia de masini si instalatii, Editura Dacia,

1981.

[8] Gafiţanu, M. ş.a. – Organe de maşini, vol. 2. Editura Tehnică, Bucureşti, 2002.

[9] Ghimisi,S. -An elastic-plastic adhesion model for fretting,15th.Symposium “DanubiaAdria”,

Bertinoro, Italia, 181-183.


99

[10] Nichici, A.: Prelucrarea prin eroziune electrica in constructia de masini, Editura Facla,

Timisoara, 1983.

[11] Olaru, D.N. – Tribologie. Elemente de bază asupra frecării, uzării şi ungerii, Litografia

Institutului Politehnic „Gheorghe Asachi”, Iaşi, 1995.

[12] Popa,M.S.:Masini, tehnologii neconventionale si de mecanica fina-Editie Bilingva, Romana-

Germana, Editura U.T.PRESS, Cluj-Napoca, 2003.

[13] Popa, M.S.: Tehnologii si masini neconventionale, pentru mecanica fina si microtehnica,

Editura U.T.PRESS, Cluj-Napoca, 2005.

[14] Popa, M.S.:Tehnologii inovative si procese de productie, Editura U.T.PRESS, Cluj-

Napoca,2009.

[15] Rădulescu, Gh., Ilea, M. – Fizico-chimia şi tehnologia uleiurilor lubrifiante, Editura

Tehnică, Bucureşti, 1982,

[16] Sofroni, L.: Fonta cu grafit nodular,Editura Tehnica, Bucuresti, 1978.

[17] Trusculescu, M.: Studiul metalelor, Editura Didactica si Pedagogica ,Bucuresti ,,1978.


100

INDEX KEYWORDS

B

bio-robot walking bar

breakage basic tooth

C

cardan mechanism circular translation motion

cylindrical gear connecting mechanism

cogwheels

D

durability curves degree of mobility

E

experiment electric grid

electrical erosion

F

fillet welds FEM

fatigue life FEM analysis

fretting

K

kinematic scheme kinematic diagram

L

lifting manipulator

M

mobility materials

P

planar mechanism processing electrical erosion

R

regular microshape roughness

Q

quadruped robot

S

stress concentrators surface plastic deformation process

SolidWorks spatial mechanism

spur gear simulation

spatial four-bar mechanism spherical joint

still breaking of the teeth

T

transfer function topological structure

V

variable stresses

W

wear windshield wiper mechanism

Documents

MEF - PARAMETRII DE DISCRETIZARE A STRUCTURILOR · 2016. 10. 12. · finite element modeling, higher Von Mises stresses can be achieved in the case of convex fillet welding A as compared