Part II: Kinematics, the fundamentals
This section will provide an overview of the fundamental concepts in kinematics. This will
include the following topics:
1. What is Kinematics?
2. Kinematics within mechanics
3. Key definitions
4. Motion and kinematic pairs
5. Transmission of motion
6. Mobility
7. Review of some general classes of Mechanisms
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1: What is Kinematics?
“Kinematics is the study of _________________________________________________
This is kinematics,
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and this is kinematics,
This is NOT kinematics,
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Why Kinematics? Why Machines?
Create / harness energy (non-human energy)
Manufacturing, agriculture
Assistive / serve humans
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What is the future of kinematics and machinery?
Miniature, micro and perhaps even nano-scale machines (motion at a micro or molecular level)
Medical, rehabilitative, prosthetic
Self-replication of machinery, machines design machines
Machines become more biological in nature (compliant, biological muscles, intelligent).
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2. Kinematics within Mechanics
Kinematics and the theory behind machines have a long history. Kinematics has evolved to
become a unique component within Mechanics as demonstrated in this figure
Mechanics
Mechanics of
materials
Dynamics
Statics
Kinematics
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Kinetics
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3. A few key definitions:
Kinematics
Dynamics
Mechanism
Machine
Degrees of freedom
Constraint
Mobility
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4. Motion (of a rigid body): displacement of a rigid body w.r.t. a fixed frame or reference frame
(for dynamics, needs to be an IRF).
Translation:
Rotation:
Planar:
Spatial:
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Kinematic Pairs: Two members (links) are jointed through a connection (joint) that defines the
relative motion b/n the two.
Links
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Joints
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More about joints:
Classically classified into a couple classes: Higher pair (point contact) and Lower pair (line
contact).
Various types of joints:
Revolute:
Prismatic (slider)
Cam or gear
Rolling contact
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Spring
Others?
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5. Transmission of Motion: The motion of a mechanism is defined by its constraints
(kinematic). The following example shows one of the most general cases of motion between two
bodies and demonstrates some key elements in understanding the behavior of motion. Consider
two general kinematic bodies (rigid bodies, known geometric properties) in contact at point P.
Each body rotates about a fixed point, O2 and O3.
N
V2
t
V3
2

O2
O3
K
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Notes:
1)
2)
3)
4)
A common Normal and tangent (N, t) exist and are defined by the 2 surfaces
“Condition of contact”: no relative motion can occur along the common normal
All sliding takes place along the common tangent
The result of these rules (plus some geometric construction):
 2  V2 O P 3  V3 O P
2
3
3 O2 K

 2 O3 K
5) Requirement for constant velocity:
6) Requirement for no sliding:
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A few special cases may be mentioned: (can be treated in the more special case above):
Linkage:
K
O2
O3
Belt and Pulley / Chain drive:
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6. Mobility Analysis:
Mobility is defined as the number of dof. Mobility is calculated as the total number of possible
degrees of freedom, minus the number of constraints. The following diagrams will demonstrate
the process:
Item
One body
Diagram
DOF
Two Bodies
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Two bodies connected
by a revolute
Ground (it is a body)
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Writing these rules as equations yields:
Which is known as Grubler’s or the Kutzbach equation.
Note: when M = 0
M<0
M>0
 Structure, statically determinant
 Indeterminant structure
 Mechanism with M dof
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Mobility Examples (list 4-6 examples for in-class practice 3 line drawings, 3 photos)
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Mobility as a synthesis tool:
Sketch a 1 dof mechanism having exactly 5 links:
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7. Review of some general classes of Mechanisms
(More about each of these general mechanism types to follow later in the course)
1. Linkages:
The most famous types of linkages include the 4-bar, slider crank. Followed by five-bars and six
bars.
The four-bar:
Primary uses: Body Guidance (1dof motion control (can generate 6th order curves)), function
generation (nonlinear transmission), rotary to linear motion.
Number of design variables: 5 (link lengths, input/output offsets)
Advantages: inexpensive to manufacture, strong, durable, easy to design
Slider Crank:
Similar features as the four-bar. Can combine the features of a fourbar and a cam.
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2. Cam mechanisms:
Primary uses: High-fidelity motion control (unlimited control variables).
Number of design variables: infinite (all points defining the cam surface)
Advantages; Can provide any desired type of motion, can take many different forms
Disadvantages: Based on higher-pair contact leads to shorter life, required lubricant, etc. More
expensive to manufacture.
3. Gear Mechanisms
Primary uses: Continuously rotating transmissions, creates constant velocity/ constant torque
transmissions
Number of design variables: 3/4 (pitch, pressure angle, number of teeth) assuming standard gears
Advantages: compact, easy to design, provides timed motion, carries high loads.
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4. Chain and Sprocket / Belt and Pulley
Primary uses: Same as gear mechanisms. Some variations are found, for example extended
distance between input and output, alternate orientation, etc.
Number of design variables: Same as gears
Advantages: light weight, flexible in design. Belts provide quiet, smooth motion, but may suffer
from slippage, require tension. Chains/sprockets carry more load, create vibration (small
variations in velocity transfer), leading to noise, etc.
5. Intermittent motion devices: Geneva Wheel
Primary uses: intermittent motion timed to an input. May be achieved by alternative
mechanisms. The Geneva wheel is simply a type of cam and shares many of the same features.
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