8/22/2019 Structural Issues in Linkages
1/22
6/14/2013Me 3230Page 1
Structural Issues in Linkages
R. Lindeke, Ph. D.
ME 3230 Kinematic &Mechatronics
8/22/2019 Structural Issues in Linkages
2/22
6/14/2013Me 3230Page 2
Topics Of Interest
Grashofs Law
Motion Limits for Slider Cranks
Interference in Linkages
Mechanical Advantage
Practical Considerations
Revolute Joints
Prismatic Joints
8/22/2019 Structural Issues in Linkages
3/22
6/14/2013Me 3230Page 3
Grashof Law
The fundamental 4-bar linkage design law:s + l < p + q
Here, s is the shortest link l is the longest link
p and q are the other two links
This law states that for there to be
continuous relative motion between any 2links, this inequality must be true (GrashofType 1 linkages)
8/22/2019 Structural Issues in Linkages
4/22
6/14/2013Me 3230Page 4
Consequences of Failure ofGrashofs inequality:
Links cant connect!s+l+pq
Links cant connect!s+q+p
8/22/2019 Structural Issues in Linkages
5/22
6/14/2013Me 3230Page 5
Type 1 or 2 Grashof Linkages
Type 1: the inequality holds
We state that these linkages (type 1) have
two joints that perform complete (360)rotation and they are located at eitherend of the shortest link
Type 2: the inequality is not held
They have no fully rotating joints
All 4 joints oscillate between limits
8/22/2019 Structural Issues in Linkages
6/22
6/14/2013Me 3230Page 6
Addition Type 1 Nomenclature
Base frame is the fixed link
Two members connected to base by
revolute joints are Turning Links Member jointed to both turning links is
the Coupler
8/22/2019 Structural Issues in Linkages
7/22
6/14/2013Me 3230Page 7
Type 1 Mechanisms:
s is connected to thebase (a, b) this is acrank rocker
s is the base link (c)this is double crank ordrag-line mechanism
s is the coupler linkthis is a double rockerwhere the coupler can
perform a completerotation relative to thebase
8/22/2019 Structural Issues in Linkages
8/22
6/14/2013Me 3230Page 8
Topological Interference So itshould rotate shouldnt it?
This point is really one of construction making surethat the design will actually operate
Topological interference is a fundamental property of
the structureit cant be eliminated by reshapinglinks
When we are assembling a Linkagethere is a rightway to assure that the various links will not runthrough each other
Motion will be transferred to rotating link usingshafts (perhaps) so this issue also addresses how theshafts are connected to the linkage too
8/22/2019 Structural Issues in Linkages
9/22
6/14/2013Me 3230Page 9
A Simple Crank rocker as astructure
Notice the Positioning of Coupler vs. the turninglinks (a). In this arrangement we can bringin/take out torques with shafts thru the base link(b). And the crank can completely rotate withoutstriking the shaft or coupler!
8/22/2019 Structural Issues in Linkages
10/22
6/14/2013Me 3230Page 10
Setup for Drag Link Mechanisms
Here the drive Shaftsmust be connected directlyto the turning links
In the drag line, the baselink has become a pair offixed bearings and the linkis essentially turned insideout
This is a must otherwisethe coupler must pass thruthe base or shafts thusbecoming locked up
8/22/2019 Structural Issues in Linkages
11/22
6/14/2013Me 3230Page 11
Lets try one:
Problem 1.35 where you are to selectfrom a set of 8 links (2; 3; 4; 7;
9.5; 13 and 9) From this set choose4 links to build a mechanism that canbe driven by a continuous rotational
motor? Identify each link byappropriate name.
What type of mechanism results?
8/22/2019 Structural Issues in Linkages
12/22
6/14/2013Me 3230Page 12
Motion Limits for a Slider Crank
There are 2 rules thatmust be held forfreedom of motion fullrotation
b>a in mechanism b - a > c
Where a is length ofcrank
Where b is length of
coupler Where c is the distance
from ground pivot toslider pin
8/22/2019 Structural Issues in Linkages
13/22
6/14/2013Me 3230Page 13
Design Considerations
Consider Slider Crank Half first A-B-C: does it meet motion criteria? BC>AB (yes) BC-AB>c (yes)
Consider C-BD-EF-AF as a crank
rocker EF must be the crank we will let
upper link (A-B-D) rock to movethe Slider at C
Positioning of E is along the locusof E (from DE length) -- upper
sketch Use Grashof calculation for the
shortest link of Crank-rocker toestablish true limits for E (lowersketch)
8/22/2019 Structural Issues in Linkages
14/22
6/14/2013Me 3230Page 14
Mechanical Advantage in a Mechanism
MA is the ration of the outputtorque to the input torque of amechanism
This ration is directly proportionalto Sin() (coupler to driven turner)and inversely proportional to Sin()
(coupler to driver turner) When is 0 or 180 (position A-B1
and A-B2 in the figure) a smallinput torque delivers a large(infinite) output torque the rockeris said to be in Toggle
When is small MA is very lowthis transmission angle shouldnever be designed to work atangles of less than about 45 . IfMA is too small, only a smallamount of friction can lock up themechanism
8/22/2019 Structural Issues in Linkages
15/22
6/14/2013Me 3230Page 15
Mechanical Advantage in a Mechanism
Considering rin & rout as level arms of theinput and output shafts (and loads), then:
4
2
. .( )
is angle from driven link (4) to Coupleris (smallest) angle from driver link (2)
to Coupler
in
out
Link SinrM A
r Link Sin
8/22/2019 Structural Issues in Linkages
16/22
6/14/2013Me 3230Page 16
Try One?
A crank-rocker linkage has a 100-mmframe, a 25-mm crank, a 90-mm
coupler, and a 75-mm rocker. Draw thelinkage and find the maximum andminimum values of the transmission
angle. Locate both toggle positions andrecord the corresponding crank anglesand transmission angles.
8/22/2019 Structural Issues in Linkages
17/22
6/14/2013Me 3230Page 17
Green Lines AtGamma limits Crank at 0 or 180
is about 53.1 and98.1 respectively
Purple Lines at Toggle
Crank at about 226 and40 (rocker back andforward respectively)
is about 90.9 and59.1 respectively
8/22/2019 Structural Issues in Linkages
18/22
6/14/2013Me 3230Page 18
Practical Design Issues: RevoluteJoints
Lubrication of the Bearing Surfaces in rotation Hydrodynamic lubrication occurs under conditions
of unidirectional rotation under speed
A lubricating film, carrying the bearing load, isestablished between the bearing surfaces and onlylubricant viscous friction (low friction) results
additionally no metal to metal contact is present and norunning wear is observed (only startup and stoppingwear)
Lubricant can by pumped in to assist in establishing HDlubrication
HD lubrication is seen in internal combustion engines forcrankshaft support bearings and connectingrod/crankshaft bearings
8/22/2019 Structural Issues in Linkages
19/22
6/14/2013Me 3230Page 19
Practical Design Issues: RevoluteJoints
Lubrication of the Bearing Surfaces in rotation
Hydrostatic lubrication is a system where lubricantis pumped in to the bearing gap under elevatedpressure to carry the bearing loads
It can be used even if rotational speed is low or evenreverses
Used in main bearings in large turbo-generator sets
Fits need to be made to tight tolerances so oil will notleak out in operation or idle activities
8/22/2019 Structural Issues in Linkages
20/22
6/14/2013Me 3230Page 20
Practical Design Issues: RevoluteJoints
Can use Grease Bearings in slow orreversing motion
Solid Contact bearing (teflon bearings) and
dissimilar metal bearing can be used likebabbitts metal 90% tin 10% copper 89% tin 7% antimony 4% copper 80% lead 15% antimony 5% tin
Also can use roller, ball or pin bearings ascontactor for revolute joint systems
8/22/2019 Structural Issues in Linkages
21/22
6/14/2013Me 3230Page 21
Practical Design Issues: PrismaticJoints
Jamming of the slider is purely a design issue!
This problem is a function of the friction of the slider, theapplied force and its direction If the angle of the coupler to slider is less than the Friction angle:
f = tan-1m (mis coefficient of friction) the slider will jam Sliders loaded by offset forcing loads will also Jam if the width
of the slider b < 2 mawhere a is the offset between the sliderand the forcing load
8/22/2019 Structural Issues in Linkages
22/22
6/14/2013Me 3230Page 22
Practical Design Issues: PrismaticJoints
Since Jamming is a function of slider friction, usingmeans to reduce friction is the most effective way toreduce problems
The use of rolling contact joints is an effect means toreduce the friction