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WEEKS 1-2 MECHANISMS
• References • (METU, Department of Mechanical Engineering)
Text Book: “Mechanisms” Web Page: http://www.me.metu.edu.tr/people/eres/ME301/Index.ht
• Analitik Çözümlü Örneklerle Mekanizma Tekniği, Prof. Dr. Mustafa SABUNCU, 2004
• Mekanizma Tekniği, Prof. Dr. Eres SÖYLEMEZ, 2007
• Theory of Machines and Mechanisms, J.J. Uicker, G.R.Pennock ve J.E. Shigley, 2003
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Course Policy
Two Midterms (20%) +Homework (10%) + 1 Final (50%)
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What is a mechanism?
A windshield wiper mechanism
The motion is transferred from the crank driven by a motor through the coupler to the left rocker.
The rotary motion is converted into rocking motion (desired motion)
A mechanism is a device which transforms motion to some desirable pattern and typically develops very low forces and transmits little power. Mechanisms are assemblages of rigid members connected together by joints. A machine typically contains mechanisms which are designed to provide significant forces and transmit significant power
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Crank mechanism: It is mainly used to convert rotary motion to a reciprocating motion
An engine, or motor
Crank mechanism
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suspension system
The vehicle suspension system is responsible for driving comfort and safety as the suspension caries the vehicle body and transmits all forces between the body and the road.
Airplane nose wheel mechanism
These systems damp the vibration.
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Mechanisms are assemblages of rigid members (links) connected together by joints. Rigid link: A rigid link is one which does not undergo any deformation while transmitting motion. Actually, rigid links do not exist. However, as the deformation of a connecting rod, crank etc. of a reciprocating steam engine is not appreciable, they can be considered as rigid links. Flexible link: A flexible link is one which is partly deformed in a manner not to affect the transmission of motion. Example: belts, ropes (halat), chains and wires are flexible links and transmit tensile forces only. Why do we assume that all links are rigid? If the link 2 is assumed that is flexible,
it can be difficult to obtain the kinematic equation between A and B points. Therefore, all links are designed as to be rigid
Mechanical press for Example
A
B
2
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Kinematics: Kinematic analysis involves determination of position, displacement, rotation, speed, velocity, and acceleration of a mechanism.
Theory of machines is separated into two section
Dynamics is also separated into two section
Kinetics: It is that branch of theory of machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts.
Kinematic Synthesis: It is the determination of the mechanism parameters (dimensions of the link lengths, number of tooth on gears, etc) to realize a given motion (including velocity and acceleration)
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TYPES OF MOTION
TRANSLATION. All points on the body describe parallel paths. A reference line drawn on the body changes its linear position but does not change its angular orientation. All the particles forming the body move along parallel paths. If these paths are straight lines, the motion is said a rectilinear translation; if the paths are curved lines, the motion is a curvilinear motion
rectilinear translation curvilinear motion
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GENERAL PLANE MOTION (Complex motion): Any plane motion which is neither a translation or a rotation is referred as a general plane motion. Plan motion is that in which all the particles of the body move in parallel planes. Translation and rotation are plane motions.
ROTATION about a fixed axis. The particles forming the rigid body move in parallel planes along circles centered on the same fixed axis. If this axis, called the axis of rotation intersects the rigid body, the particles located on the axis have zero velocity and zero acceleration
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Kinematic element, is that part of a rigid body which is used to connect it to another rigid body such that the relative motion between the two rigid bodies can occur
Kinematic element
Kinematic element
Kinematic pair (joint) is a connection between two or more kinematic elements. The types of kinematic pairs and their distribution within the mechanism determine the main characteristics of a mechanism.
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Note: DOF is Degree of Freedom
Kinematic pair (joint)
13 Planar pure-roll (R), pure-slide (P), or roll-slide (RP) joint - 1 or 2 DOF (higher pair)
Wheel
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Type of contact
Classification Mechanisms of Kinematic Pairs
Closed kinematic form
Force closed Form closed
Lower kinematic pairs Higher kinematic pairs
Kinematic pairs (joints) may be classified in several diffrent forms.
Open kinematic form
Contact along a surface
Contact at a point or on a line
Closed kinematic pairs are those in which the contact between the kinematic elements is maintained within all possible positions of a mechanism. In force closed kinematic pairs, there exist an external force ( spring force etc.) which keeps the two kinematic elements in contact. In form closed kinematic pairs, one of the kinematic elements envelopes the other. An open kinematic pair is one whose pairing and unpairing of its kinematic elements that form the joint are controlled.
A nut and a bolt have been assembled to each other by its geometry
The spring provides contact between the follower and cam.
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Degree of freedom a kinematic pair:
The degree of freedom (DOF) of a rigid body is the number of independent parameters that define its configuration
Degree of freedom of a rigid body:
Six independent parameters are required to define the motion of the ship.
An unrestrained rigid body in space has six degrees of freedom: three translating motions along the x, y and z axes and three rotary motions around the x, y and z axes respectively.
The degrees of freedom (DOF) of a kinemtaic pairs defined as the number of independent movements it has.
DOF=6, λ=6 (spatial space)
DOF=3, λ=3 (planar space)
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Degree of freedom a kinematic pair:
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Degree of freedom a kinematic pair:
Joint with Highest freedom. Translation perpendicular to the plane is restricted. Translations within the plane and rotation in all three axes are possible
When a Cylinder is confined between two parallel planes, there is no translation perpendicular to the planes and no rotation about an axis within the plane perpendicular to the cylinder axis. Translation about two perpendicular axes within the plane and rotation about the cylinder axis and about an axes perpendicular to the plane are possible
**In force closed kinematic pairs, there exist an external force ( spring force etc.) which keeps the two kinematic elements in contact. **In form closed kinematic pairs, one of the kinematic elements envelopes the other.
the ball can rotate around the x,y and z-axes
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Degree of freedom a kinematic pair:
Joint with Highest freedom. Translation perpendicular to the plane is restricted. Translations within the plane and rotation in all three axes are possible
When a Cylinder is confined between two parallel planes, there is no translation perpendicular to the planes and no rotation about an axis within the plane perpendicular to the cylinder axis. Translation about two perpendicular axes within the plane and rotation about the cylinder axis and about an axes perpendicular to the plane are possible
Three axes of rotation intersect at the center of the sphere
If a pin perpendicular to the axes of translation is inserted into a slot, then rotation about the translation axis is constrained. If the slot is cut in a different direction, rotation about one axis will be constrained.
Translation in two axes (in plane) and rotation (perpendicular to the plane) are possible.
Rotation axes are skew (they do not intersect).
The rotation and translation axes are coincident
Axes of translation and rotation are perpendicular to each other.
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If a rigid body contains at least two kinematic elements we shall call it a link. A link may have more than two kinematic elements (but not less than two). One can classify links according to the number of kinematic elements it contains. These are binary, ternary or quarternary, etc.
The kinematic dimensions of a link in a mechanism are those dimensions which define the relative positions of the kinematic elements on that link and when these dimensions are specified, the link dimensions are known for motion analysis. These dimensions can be distances or angles. For the manufacture of the link or for the dynamics, etc other physical dimensions such as the width, height, thickness, etc. may be important. For the kinematic analysis we shall be interested only with the kinematic dimensions. As seen with the above figure, on the link at points A and B kinematic elements form revolute joins, whereas at D there is a cylinder in slot joint. For manufacture besides the thickness, one must specify the radii ( R1, R2, R3), the slot length and width (L1, L2), the length of the piece (L3) etc. These have no importance for kinematics. Whereas the distance between revolute joints A and B (a), the angle slot makes with respect to the line AB (α) and perpendicular distance from point A to the slot axis (b)are the kinematic dimensions of this link. Once these four parameters are known, the link is kinematically defined.
For the kinematic analysis we shall be interested only with the kinematic dimensions
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Kinematic diagram: A kinematic diagram or kinematic scheme illustrates the connectivity of links and joints of a mechanism or machine rather than the dimensions or shape of the parts. Often links are presented as geometric objects, such as lines, triangles or squares, that support schematic versions of the joints of the mechanism or machine . Connecting rod
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Kinematic diagram
Crank mechanism
Shaping Machine (Quick Return Mechanism)
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There are certain joints where more than two links are connected. For such cases we define the degree-of a joint as the number of links connected at the joint minus one. One must assume that there joints at this point equal to the degree of the joint, ( please do not confuse the degree of the joint with the degree-of-freedom of a joint)
Degree of a joint is equal to the number of joints at that connection. Degree of freedom of a joint is the number of independent parameters required to define the position of one link relative to the other connected by that joint.
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Kinematic chain: The links connected to each other by kinematic pairs will form a kinematic chain. If all the kinematic pairs are closed, than we have a closed kinematic chain. If one of the kinematic pair is of open type, the kinematic chain is an open kinematic chain. Kinematic chain is an idealised representation of the mechanism structure. We are not concerned with the dimensions of the links. Each link is represented as a line or as a polygon and at each vertex we have a kinematic element which joins with another element on another link. The dimensions of the edges are not important.
Shaping Machine (Quick Return Mechanism)
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5
4
3
2
1
6
5
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2
1
Slider element
Sled element 1- The kinematic diagram of all links is drawn 2- All links are connected according to their kinematic pairs
closed kinematic chain.
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43
21 432
1
3
21 32
1
open kinematic chain
For higher kinematic pair
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Degree of freedom of a mechanism depends on: • The degree of freedom of space • The degree of freedom of the joints • The number of links and joints • The distribution of links and joints • Does not depend on the shape of the links.
The degree of freedom of a mechanism (mobility) is the number of independent parameters required to define the position of every link in that mechanism
Determination of the Degree-of- Freedom of a Mechanism
( )1
1=
= − − +∑
j
ii
F j fλ
*** If F=0 or F<0, the mechnisms can be called static or hiperstatic respectively.
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To increase the load carrying capacity there can be several contact points between the two links. Each contact point cannot be treated as a different kinematic pair. There can be only one kinematic element between two links.
There is one kinematic element (lower kinematic pair) between two links.
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Slider crank mechanism
Four-bar linkage
Shaping Machine (Quick Return Mechanism)
( )4
13( 1)4 4 1 1 1 1 1
=
+= − − + + + =∑i
F
( )1
1=
= − − +∑
j
ii
F j fλ
( )7
16 7 1 1 1 1 11 13( ) 1 1
=
+ + + + += − + =+− ∑i
F
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Adjustable Drive Grabber
Second order pin joints
( )8
1
3( 17 8
1 1 1 1 1 1 1 2
)
1=
+ + +
= − − +
=+ + + +∑i
F
13
1
3( 1)
1
1
3
0 13
1=
= − − +
=∑i
F
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( )10
13( 18 10 10 1)
=
= − − + =∑i
F
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A simplified engineering drawing of the front loader assembly is as shown. Note that a lot of details are neglected.
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The Schematic kinematic diagram of the mechanism involved for the front loader is as shown. Note that each link in practice may be composed of several different rigid bodies that are rigidly connected to each other.
The two degrees of freedom refer to the displacement parameters between the piston and cylinders. It can be said that two actuators need for the front loader motion
( )12
1
3( 19 11
11 2
)
=
= − − +
=∑i
F
