MER212: Kinematics of Rigid BodiesCh 16 Pl Ki ti f Ri id B diChap 16: Planar Kinematics of Rigid Bodies

Relative Motion Analysis: Velocity (16.5)

Relative Motion Analysis: Acceleration (16.7)

Relative Motion analysis using Rotating Axes Relative Motion analysis using Rotating Axes (16.8)

Instantaneous Center of Zero Velocity (16.5)

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Example 1Rods “R” and “L” are pinned at “O” and “O’” to a frame. Rod “L” is also pinned to the slotted body “B” at “B”. ?The upper end of “R” is pinned at upper end of R is pinned at P to a roller that moves freely in the slot of “B”. The angular velocities of the rod “R” d li k “L” “R” and link “L” are constants:

ωR=-0.2 rad/s

ωL=-0.4 rad/s

Determine the velocity of “P” and the angular velocity of

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g y“B” at the given instant.

Diagram of Problem

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Problem Geometry

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3D Example Problem

0 / 0 /Let ωz=0.5 rad/s and ωx=0.7 rad/s in the directions indicated. With the dimensions given find the maximum value of ωy for which the acceleration magnitude of the astronaut’s head will not exceed 5g at the given instant. Let ωy = constant.

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at the given instant. Let ωy constant.

Problem Diagram

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Example 3Two men, a tall one and a short one, travel up identical inclines, pulling identical spools by means of ropes wrapped around the hubs. The men travel at the same constant speed vo, and the ropes are wrapped in the opposite directions.

1 If the spools do not slip on the plane one of the men will be run over by 1. If the spools do not slip on the plane, one of the men will be run over by his own spool. Prove which one it is.2. show how long it will take, from the instant depicted, for the spool to roll over him.

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Instantaneous Center of Zero Velocity

General Plane MotionGeneral Plane MotionNo point is fixed at all timeAt any instant a point exists that has zero velocityvelocity

Instantaneous CenterInstant Center does NOT have zero Acceleration

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Instant Centers

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Example

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Example 2At the instant shown slider A is moving to At the instant shown, slider A is moving to the right with a speed of 3m/s. Find the location of the instantaneous center of zero velocity and use it to find the angular velocity and use it to find the angular velocity of the arm ωAB and the velocity of the slider B

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