ADU
Lecture
MEC 411
1
1
Kinematic and Dynamics
of Machinery
MEC 411
MEC 411
2
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Tentative Lectures Schedule
Topic
Reading
Introduction of Mechanism and,
1&2
Kinematics, mobility, applications,
2
Vectors, loop equations, position analysis,
4
Velocity Analysis,
5
Velocity Analysis
5
Acceleration Analysis,
6
Acceleration Analysis,
6
Cam and cam synthesis
7
Cam and cam synthesis
7
Static and dynamic force analysis in planer mechanisms,
8
Static and dynamic force analysis in planer mechanisms
8
Balancing of rotating machinery,
9
Balancing of rotating machinery,
9
Introduction to kinematics of robot manipulators
10
2
Lecture 1
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3
One thing you learn in science is that
there is no perfect answer, no perfect
measure.
A. O. Beckman
Topic 1: Mechanism and
Kinematics
MEC 411
Introduction and Basic Concepts
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Lecture 1
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Chapter Objectives
Up on completion of this chapter, the student
will be able to
 Explain the need for kinematic analysis of
mechanism.
 Define the basic components that comprise
a mechanism.
 Draw the kinematic diagram from a view of
a complex mechanism.
 Compute the number of degrees of
freedom of a mechanism.
 Identify a four bar mechanism and classify
it according to its possible motion.
 Identify a slider crank mechanism.
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1.1 ANALYSIS AND SYSTHESIS
 Analysis: the techniques that allow the
designer to critically examine an already
existing or proposed design in order to
judge its suitability for task.
 Synthesis (or Design): the process of
prescribing the sizes, shapes, material
compositions, and arrangements of parts
so that the resulting machine will perform
the prescribed task.
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Lecture 1
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1.2 DESIGN PROCESS
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Lecture 1
 There are several systems of units used in
engineering. The most common in the
United States are:
◼ The U.S. foot-pound-second (fps) system,
◼ The U.S. inch-pound-second (ips) system,
and
◼ The System International (SI)
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1.4 UNITS
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1.4 UNITS
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1.5 THE SCIENCE OF MECHANICS
 Statics: deals with analysis of stationary
systems, that is, those in which time is
not a factor.
 Dynamics: deals with systems that change
with time.
 Kinematics: the study of motion, quite
apart from the forces which produce that
motion. More particularly kinematics is
the study of position, displacement ,
rotation, speed, velocity, and acceleration.
 Kinetics: the study of force on system in
motion.
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1.5 THE SCIENCE OF MECHANICS
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1.5 THE SCIENCE OF MECHANICS
Definitions:
 Kinematic Link or Element: It is each part of a
machine, which moves relative to some other
part. A link may consist of several parts,
which are rigidly fastened together (resistant
body), so that they do not move relative to
one another. Types of links are: Rigid,
Flexible, and Fluid.
 Kinematic Pair: The two links or elements of a
machine, when in contact with each other, are
said to form a pair. If the relative motion
between them is completely or successfully
constrained (i.e. in a definite direction), the
pair is known as kinematic pair. Types of
Kinematic Pairs are: Sliding, Turning, rolling,
screw, and spherical.
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1.5 THE SCIENCE OF MECHANICS
Definitions (cont.):
 Kinematic Chain: is defined as a combination
of kinematic pairs, joined in such a way that
each link forms a part of two pairs and the
relative motion between the links or elements
is completely or successfully constrained.
 Kinematic Chains should satisfy the following
two conditions:
1. L=2P-4, where L is the number of links, P is
the number of pairs which constitute a
kinematic chain.
2. h/2+J= 3/2 L – 2, where J is the number of
binary joints and h is the number of higher
pairs which constitute a kinematic chain.
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1.5 THE SCIENCE OF MECHANICS
Definitions (Cont.):
 Mechanism: an assemblage of resistant bodies,
connected by movable joints, to form a closed
kinematic chain with one link fixed and having
the purpose of transforming motion with low
forces and little power transmitted.
 Machine: a combination of resistant bodies
connected by joints so arranged (designed) to
transmit significant forces and power (work)
accompanied by certain determinate motion.
 Structure: also a combination of resistant
bodies connected by joints, but its purpose is
not to do work or to transform motion. A
structure is intended to bear load (be rigid).
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1.5 THE SCIENCE OF MECHANICS
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Lecture 1
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One thing you learn in science is that
there is no perfect answer, no perfect
measure.
A. O. Beckman
Topic 2: Mechanism and
Kinematics
MEC 411
Kinematics Fundamentals
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Lecture 1
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2.1 DEGREE OF FREEDOM (DOF) OR MOBILITY
 A mechanical system’s mobility (M) can be
classified according to the number of
degrees of freedom (DOF) that it
possesses.
 The system’s DOF is equal to the number of
independent parameters (measurements)
that are needed uniquely to define its
position in space and at any instant of time.
 The system of the pencil in the plane has
three DOF.
 The pencil in this example represents a
rigid body, or link, which for the purposes
of kinematics analysis we will assume to be
incapable of deformation.
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2.1 DEGREE OF FREEDOM (DOF) OR MOBILITY
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2.1 DEGREE OF FREEDOM (DOF) OR MOBILITY
3 DOF of Rigid body in
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6 DOF of rigid body in Space
Plane
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2.2 TYPES OF MOTION
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 Pure translation
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Rectilinear Motion
Curvilinear Motion
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2.2 TYPES OF MOTION
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 Pure rotation
Reference line
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Reference line
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2.2 TYPES OF MOTION
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 Complex Motion : Rotation + Translation
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q
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2.3 LINKS, JONTS AND KINEMATIC CHAINS
 Linkages are the basic building blocks of all
mechanisms. A linkage consist of links (or
bars), generally considered rigid, which are
connected by joints, such as pins (or
revolute), or prismatic joints to form open or
closed chains (or loops).
 Such kinematic chains, with at least one link
fixed, become:
◼ (1) mechanisms if at least two other links
retain mobility, or
◼ (2) structures if no mobility remains.
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2.3 LINKS, JONTS AND KINEMATIC CHAINS
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Kinematics Mechanisms.avi - YouTube
 Kinematics:
https://www.youtube.com/watch?v=8JtcEja
qc4Y&list=PLB059985630300733
(By Kinematics with MicroStation)
https://www.youtube.com/watch?v=4Y8Pg
UlR0bQ&list=PLpe3qgeJLpB2psRDpvi1dprhT
PW5p0Tt_&index=3 (By Magic Marks)
 Automobile Engineering:
https://www.youtube.com/watch?v=c3Calfd
YZYw&list=PLpe3qgeJLpB2wAoaRSY9_yAeOt
7u0LTNd (By Magic Marks)
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2.3 LINKS, JONTS AND KINEMATIC CHAINS
https://youtu.be/4Y8PgUlR0bQ?list=PLpe3qgeJLpB2psRDpvi1dprhTPW5p0Tt_&t=53
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 A link is a rigid body that possesses at least
two nodes that are points for attachment to
other links.
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2.3 LINKS, JONTS AND KINEMATIC CHAINS
 Link of different order:
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◼ Binary link : has 2 nodes
◼ Ternary link : has 3 nodes
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◼ Quaternary link : has 4 nodes
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2.3 LINKS, JONTS AND KINEMATIC CHAINS
 A joint is a connection between two or
more links (at their nodes), which allows
some motion, or potential motion,
between the connected links.
 Joints (also called kinematic pairs) can be
classified in several ways:
1. By the type of contact between the elements,
line, point or surface.
2. By the number of degrees of freedom allowed
at the joint.
3. By the type of physical closure of the joint:
either force or form closed.
4. By the number of links joined (order of the
joint).
https://www.youtube.com/watch?v=TYq_0v66ucM&index=2&list=PLB059985
630300733
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2.3 LINKS, JONTS AND KINEMATIC CHAINS
The kinematic pairs can be:
 Higher pair (point or line contact): are
the joints with point or line contact
between the pair elements.
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 Lower pair (surface contact): are the
joints with surface contact between
the pair elements.
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2.3 JOINT PAIRS: THE SIX LOWER PAIRS
 Lower Pair:
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Name (symbol)
DOF Contains
Revolute (R)
1
R
Prismatic (P)
1
P
Screw or Helical (H)
1
R+P
Cylindrical (C)
2
R+P
Spherical (S)
3
R+R+R
Planar or Flat (F)
3
R+P+P
Planar Mechanism
3-D Mechanism
DOF: Degree of Freedom
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2.3 JOINT PAIRS: THE SIX LOWER PAIRS
 Revolute (R): Rotating full pin joint
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Dq
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2.3 JOINT PAIRS: THE SIX LOWER PAIRS
 Prismatic (P): Translating full slider joint
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DX
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2.3 JOINT PAIRS: THE SIX LOWER PAIRS
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 Helical (H):
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2.3 JOINT PAIRS: THE SIX LOWER PAIRS
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 Cylindrical (C):
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2.3 JOINT PAIRS: THE SIX LOWER PAIRS
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 Spherical (S):
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2.4 JOINT PAIRS: THE SIX LOWER PAIRS
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 Flat (F) :
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2.3 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT
 Roll-slide (Half or RP) joint
Dq
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DX
Linkage against Plane (Force close)
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2.3 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT
 Higher Pair: 2 DOF
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DX
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Dq
Pin in Slot (Form Close)
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2.3 PLANAR MOTION
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 Lower pair or Full joint : 1 DOF joint
 Higher pair, half joint : > 1 DOF, roll-slider
 Joint order = number of link joined - 1
First
order
pin
joint
First o
rder pin
join
t
S
econd ordorder
er pin jopin
int joint
Second
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2.3 PLANAR MOTION
 KINEMATIC CHAIN: An assemblage of links
and joints, interconnected in a way to
provide a controlled output motion in
response to a supplied input motion.
 CRANK: Link that makes a complete
revolution and is pivoted to ground.
 ROCKER: Link that has oscillatory (back and
forth) rotation and is pivoted to ground.
 COUPLER (or connecting rod): Link that has
complex motion and is not pivoted to
ground.
 GROUND: defined as any link or links that
are fixed (nonmoving) with respect to the
reference frame.
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
 Degree of Freedom (DOF): Number or
inputs that need to be provided in order to
create a predictable output. Also: number
of independent coordinates required to
define its position.
 In Planar Mechanisms:
MEC 411
◼ 1 link in the plane has 3 DOF
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
◼ 2 links in the plane have 6 DOF
Dq1
Dy2
Dx1
Dx2
Dq2
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Dy1
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
◼ 2 links connected by a full joint have 4 DOF
Dx
Dq1
Dq2
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Dy
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
◼ 2 links connected by a roll-slide (half) have
5 DOF
Dq2
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Dx1
Dy
Dq1
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Dx2
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
https://youtu.be/6HPFzqA1p04?list=PLB059985630300733
 Gruebler’s equation
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DOF or M = 3L – 2J – 3G
Where:
M=degree of freedom or mobility
L= number of links
J=number of joints (Count as 1 for full
0.5 for Half joint)
G=number of grounded links (always 1)
M = 3(L - 1) – 2J
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
 Kutzbatch’s modification of Gruebler’s
equation
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M = 3(L – 1)– 2J1 – J2
Where:
M= degree of freedom or mobility
L= number of links
J1= number of DOF (full) joints
J2= number of DOF (half) joints
Note:
J1=Full Joint = 1 & J2=Half Joint = 1
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
MEC 411
M = 3(L - 1) – 2J
=3(8-1)-2x10=1
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Lecture 1
M = 3(L - 1) – 2J
=3(6-1)-2x7.5=0
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2.5 DETERMINING DEGREE OF FREEDOM OR MOBILITY
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 If the DOF is positive, it will be a mechanism, and
the links will have relative motion. If the DOF is
exactly zero, then it will be a structure, and no
motion is possible. If the DOF is negative, then it is
a preloaded structure, which means that no motion
is possible and some stresses may also be present
at the time of assembly.
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2.6 MECHANISMS AND STRUCTURES
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Decoding Earth Moving Machines
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https://youtu.be/b8c_9ZZX5_8?l
ist=PLB059985630300733
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Lecture 1
https://youtu.be/0lui6cdRnCw?list=PLB0599856
30300733
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1.12 EXAMPLES
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1.12 EXAMPLES
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1.12 EXAMPLES
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1.12 EXAMPLES
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1. Number or links L = 4
2. Number of (full joint) 4 joints J=4
3. Number of ground link G=1
M = 3(4 - 1) – 2x4
M= 1
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1.12 EXAMPLES
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1. Number or links L = 9
2. Number of full joints J=12
3. Number of ground link G=1
M = 3(9 - 1) – 2x12
M= 0
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Lecture 1
MEC 411
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