Planar Kinematics of a Rigid Body20104511514

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```					Kinematics of a Rigid Body: Basic Concept

1. Relative motion
2. Classification of problems
3. GE226 General Equation

ME 316 Handout 2           1
Relative Motion

1. Absolute Motion
When the motion of an object is viewed by
taking the earth as the reference body, the
motion of the object is called the absolute
motion.

ME 316 Handout 2            2
Relative Motion

A reference object

An object
The earth

“Absolute motion”
ME 316 Handout 2               3
Relative Motion
2. Relative Motion

The reference object is another object, say
B. The motion of A is viewed with
reference to B.

B: reference body                   A/B

ME 316 Handout 2            4
Relative Motion

The relative motion of objects A and B can
also be a general planar motion (i.e., the
translation plus a rotation around a point on
the object).

ME 316 Handout 2               5
Relative
Motion

3. Relative

motion

equation

ME 316 Handout 2   6
Relative Motion
Relative rotation (B: reference body)

 A / B   A  B
Absolute angular
Relative angular                        velocity of body B
velocity         Absolute angular
velocity of body A
ME 316 Handout 2                  7
Relative Motion

 AB      the angular velocity of the
assembly of A and B.

A/ B     the relative angular velocity
of object A with respect to
object B

ME 316 Handout 2             8
Relative Motion
Relative translation (B: reference body)

Relative
Translation is
measured by two
points selected
from body A and
body B,
respectively, PA
and PB in the left
figure
ME 316 Handout 2                    9
Relative Motion

Relative translation (B: reference body)

VA / B (T )  VPA/ PB(T )  VPA  VPB

ME 316 Handout 2         10
Relative Motion
When two objects are in
contact, at their contact point
(PA and PB), the relative                  A
B
translation between these two
points are given:

        
VPA / PB(T )  VPA  VPB                    PA
PB
A
The direction of this relative                      B
translation is along the rod.
ME 316 Handout 2                11
Relative Motion: Example
Example
 AB  2

B  0

ME 316 Handout 2              12
Relative Motion
• Question (a). What is the relative angular velocity
between gear B and arm AB, in particular taking
arm AB as a reference object?

• Question (b). What is the angular velocity of gear
A if we have found that the relative angular
velocity of gear A with respect to gear B is 0.5

ME 316 Handout 2                 13
Relative Motion
Solution (to be filled)

ME 316 Handout 2   14
Relative Motion
Solution (to be filled)

ME 316 Handout 2   15
Classification of Problems

B                                  B

A                                      A

ME 316 Handout 2                  16
Classification of Problems
Kinematic pair – Joint
Types of joints               Graphical Representation        Relative motion

Revolute joint (or pair)                                         Relative rotation

Sliding joint (or pair)                                         Relative translation

Fixed (no relative motion)
Fixed joint (or pair)

Both relative rotation
Point contact joint (or pair)                              and translation

ME 316 Handout 2                                    17
Classification of Problems
All joints are a revolute joint

ME 316 Handout 2   18
Classification of Problems
Sliding pair but its axis is fixed

ME 316 Handout 2   19
Classification of Problems
Point contact joint – the bar is fixed

ME 316 Handout 2   20
Classification of Problems
Point contact – both are moving

ME 316 Handout 2   21
Classification of Problems
Sliding pair – the sliding axis rotates

ME 316 Handout 2   22
GE 226 General Equation

VB  VA   AB  r B / A

B
A
The distance between A
and B will not change with
respect to time.

GE226 Equation can only solve problems with Types 1-3

ME 316 Handout 2                        23

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