1. Planar Kinematics of a Rigid Body: Review II
1. Relative motion
2. Strategy for solving kinematics problems
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2. 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.
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3. Relative Motion “Absolute motion” A reference object An object
The earth
An object
A reference object
“Absolute motion”
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4. 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
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5. 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).
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6. Relative Motion
3. Relative
motion
equation
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7. Relative Motion Relative rotation (B: reference body)
Absolute angular velocity of body B
Relative angular velocity
Absolute angular velocity of body A
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8. Relative Motion the angular velocity of the assembly of A and B.
the relative angular velocity of object A with respect to object B
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9. Relative Motion Relative translation (B: reference body)
Relative Translation is measured by two points selected from body A and body B, respectively
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10. Relative Motion PB PA Relative translation (B: reference body)
- Suppose the translating axis is
- Pick up two points PA and PB on body A and body B
- Project the velocities at PA and PB along
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11. Relative Motion
Relative translation between any two points on different bodies (the previous figure on page 9)
Absolute velocity of point PB
Relative velocity
Absolute velocity of point PA
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12. (Total) Relative Motion (Velocity)
Relative Translation
Relative Rotation
(Total) Relative Motion (Velocity)
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13. Relative Motion
When two objects are joined into a relative translation relation and their angular velocity is zero, we have
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14. Relative Motion
When two objects are in contact, at their contact point (PA and PB), the relative translation between these two points are: A B A B PA PB
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15. Relative Motion: Example
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16. 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 rad/sec clockwise?
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17. Relative Motion
Solution (to be filled)
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18. Relative Motion
Solution (to be filled)
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19. Solving Kinematics Problem
Transfer: Known variables -> Unknown variables
Begin with a single body and then a system of bodies
Translation
Rotation at a fixed axis
General plane motion
Motion transfer
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20. Solving Kinematics Problem
Case 1. A B
Rigid body equation P
Case 2.
Share the motion at this point 2 1
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21. Solving Kinematics Problem
Case 3. 1 2 P1 P2
Relative Translation Equation
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22. Example
Given θ, V0. Find: ω(θ) A B V0 θ 1 2 a
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23. Solving Kinematics Problem
Solution (to be filled)
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24. Solving Kinematics Problem
Solution (to be filled)
ME 316 Handout 2

25. Solving Kinematics Problem
Solution (to be filled)
ME 316 Handout 2