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1. Introduction to Mechanisms & Kinematics

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Adapted From theory of machine and mechanisms
J.E Shigley
1. Introduction to Mechanisms and Kinematics
Qassim University
Unayzah College of Engineering
Mechanical Engineering Dept.
Theory of Machines
 The subject Theory of Machines may be defined
as that branch of Engineering-science, which deals
with the study of relative motion between the
various parts of a machine, and forces which act on
them. The knowledge of this subject is very
essential for an engineer in designing the various
parts of a machine.
A
mechanism is a device which transforms
motion to some desirable pattern and
typically develops very low forces and
transmits little power.
A machine typically contains mechanisms
which are designed to provide significant
forces and transmit significant power.
Front loader
Conceptual design for an
exercise machine
Rear-window
wiper
Lift platform
Device to close the
top flap of boxes
Food Blender
Automatic
Transmission
Spider Robot
Bulldozer
Chapter 1: Stress
Mechanics of Material 7th Edition
© 2008 Pearson Education South Asia Pte Ltd
Amusement
Park Ride
7
2.1 Degrees of Freedom (DOF) or Mobility
 DOF: Number of independent parameters
(measurements) needed to uniquely define position of a
system in space at any instant of time.
Rigid body in a plane has 3
DOF: x, y, θ
Rigid body in space has 6
DOF (3 translations & 3
rotations)
8
2.2 Types of Motion
 Pure rotation: the body possesses one point (center
of rotation) that has no motion with respect to the
“stationary” frame of reference. All other points
move in circular arcs.
 Pure translation: all points on the body describe
parallel (curvilinear or rectilinear) paths.
 Complex motion: a simultaneous combination of
rotation and translation.
9
Backhoe Excavator
Chapter 1: Stress
Mechanics of Material 7th Edition
© 2008 Pearson Education South Asia Pte Ltd
10
Slider-Crank Mechanism
11
2.3 Links, joints, and kinematic chains
 Links: rigid member having nodes
 Node: attachment points
 Binary link: 2 nodes
 Ternary link: 3 nodes
 Quaternary link: 4 nodes
 Joint: connection between two or more links (at their
nodes) which allows motion
 Classified by type of contact, number of degree of freedom
(DOF), type of physical closure, or number of links joined
12
2.3 Links, joints, and kinematic chains
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Joint Classification
14
Joint Classification
15
Joint Classification
16
Joint
Terminology
17
Types of joints
18
Kinematic chains, mechanisms, machines,
link classification
 Kinematic chain: links joined together for motion
 Mechanism: grounded kinematic chain
 Machine: mechanism designed to do work
 Link classification:
 Ground: fixed w.r.t. reference frame
 Crank: pivoted to ground, makes complete revolutions
 Rocker: pivoted to ground, has oscillatory motion
 Coupler: link has complex motion, not attached to ground
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• Ground Link
• Links pivoted to ground:
– Crank
– Rocker
• Coupler
B
Coupler
A
Rocker
Crank
Link 1, length d
Ground Link
Pivot 02
Pivot 04
20
B
Coupler
A
Rocker
Crank
Link 1, length d
Ground Link
Pivot 02
Pivot 04
21
Determining Degrees of Freedom
 For simple mechanisms calculating DOF is simple
Open Mechanism
DOF=3
Closed Mechanism
DOF=1
22
Example
23
2.4 Determining DOF’s
 Gruebler’s equation for planar mechanisms
M=3L-2J-3G
 Where
M = degree of freedom or mobility
L = number of links
J = number of full joints (half joints count as 0.5)
G = number of grounded links =1
M  3  L  1  2 J
24
25
26
Example
27
Example
28
Example
29
Example
30
2.5 Mechanisms and Structures
 Mechanism: DOF>0
 Structure: DOF=0
 Preloaded Structure –
DOF<0, may require force to
assemble
31
2.6 Paradoxes
 Greubler criterion does not include geometry, so it
can give wrong prediction
 We must use inspection
E-quintet
32
2.7 Intermittent Motion
 Series of Motions and Dwells
 Dwell: no output motion with input motion
 Examples: Geneva Mechanism, Linear Geneva Mechanism,
Ratchet and Pawl
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Geneva Mechanism
34
Linear Geneva Mechanism
35
Ratchet and Pawl
36
Four bar Mechanism
Two bar has -1 degrees of freedom
(preloads structure)
Three bar has 0 degrees of freedom
(structure)
Four bar has 1 degree of freedom
The four bar linkage is the simplest
possible pin-jointed mechanism for
single degree of freedom controlled
motion
-1
0
1
37
4-Bar Nomenclature
• Ground Link
• Links pivoted to ground:
– Crank
– Rocker
• Coupler
B
Coupler
A
Rocker
Crank
Link 1, length d
Ground Link
Pivot 02
Pivot 04
38
Where would you see 4-bar mechanisms?
39
Sheet Metal Shear (Mechanical Workshop)
40
Door Mechanism (ACMV Lab)
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Backhoe Excavator
42
Brake of a Wheelchair
Folding sofa
43
Inversions
• Created by attaching different links to ground
• Different behavior for different inversions
44
Inversions of a 4-Bar Mechanism
Crank-rocker
Crank-rocker
Crank-crank
Rocker-rocker
45
2.8 The Grashof Condition
 Grashof condition predicts behavior of linkage based
only on length of links
S=length of shortest link
L=length of longest link
P,Q=length of two remaining links
If S+L ≤ P+Q the linkage is Grashof :at least one link is
capable of making a complete revolution
Otherwise the linkage is non-Grashof : no link is
capable of making a complete revolution
46
For S+L<P+Q
 Crank-rocker if either link adjacent to shortest is grounded
 Double crank if shortest link is grounded
 Double rocker if link opposite to shortest is grounded
47
For S+L>P+Q
 All inversions will be double rockers
 No link can fully rotate
48
For S+L=P+Q (Special case Grashof)
 All inversions will be double cranks or crank rockers
 Linkage can form parallelogram or antiparallelogram
 Often used to keep coupler parallel (drafting
machine)
Parallelogram form
Deltoid form
Anti parallelogram
form
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2.9 Linkages of more than 4 bars
5-bar 2DOF
Geared 5-bar 1DOF
• Provide more complex motion
• See Watt’s sixbar and Stephenson’s sixbar
mechanisms in the textbook
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Linkages of more than 4 bars
Volvo 740 Hood
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Volvo 740 Hood
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Cabinet Hinge
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More Examples: Front End Loader
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Drum Brake
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Kinematics Diagrams
Kinematics Diagrams
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