Absolute Motion - University of Tennessee

Absolute Motion

Lecture 10

ME 231: Dynamics

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Question of the Day

ME 231: Dynamics

The cable reel rolls without slipping on the horizontal surface. Point A on the cable has a velocity vA = 0.8 m/s to the right.

Compute the velocity of the center O and the angular velocity �� of the reel.

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Outline for Today

� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)� Answer your questions!

ME 231: Dynamics

� Question of the day

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Absolute-Motion Analysis

� The method relates the position of a point, A, on a rigid body to the angular position, ��, of a linecontained in the body

� The velocity and acceleration of point Aare obtained in terms of the angular velocity, �, and angular acceleration, �, of the rigid body

ME 231: Dynamics

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Recall: Constrained Motionof Connected Particles

� Application of absolute-motion analysis

� Successive differentiation of cable length

� Geometric relations are simple (i.e., linear variables only)

ME 231: Dynamics

yx �� 20 ��yx ���� 20 ��

BA vv 20 ��

BA aa 20 ��

bryrxL ����� 12 22

��Constraint Equations

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�

�

Geometric Relations

ME 231: Dynamics

Linear � Position� Velocity� Acceleration

Angular� Position� Velocity� Acceleration

y

xz

Rigid-body motion includes both linearand angular variables

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Maintaining Consistent Sense

ME 231: Dynamics

��

���� ���

dtd

����� ��� ���� 2

2

dtd

dtd

� Angular position of moving line is specified by counter-clockwise angle (�)

� Angular velocity (�) is positive in the same counter-clockwisesense

� Angular acceleration (�) is positive in the same counter-clockwise sense

A key concept in dynamics!

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Outline for Today

� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)� Answer your questions!

ME 231: Dynamics

� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense

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Absolute Motion: Exercise

A wheel of radius rrolls without slipping.

Determine the wheel’s angular motion in terms of the linear motion of its center O.

Also determine the acceleration of point C on the rim of the wheel as it contacts the ground.

ME 231: Dynamics

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Absolute Motion: Another Exercise

Determine the angular velocity of bar AB in terms of the linear position of displacement xA.

ME 231: Dynamics

Slider A moves horizontally with a constant speed v.

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Absolute Motion: Yet Another Exercise

Derive an expression for the upward velocity of the car hoist in terms of ��.

ME 231: Dynamics

The piston rod of the hydraulic cylinder is extending at the rate s.

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Outline for Today

� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)� Answer your questions!

ME 231: Dynamics

� Question of the day� Absolute-motion analysis� Geometric relations� Maintaining consistent sense� Absolute motion: exercise(s)

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Homework Survey

ME 231: Dynamics

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Homework Survey

ME 231: Dynamics

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For Next Time…

� Begin Homework #4 due next Thursday (9/20)

� Read Chapter 6, Section 6.2

ME 231: Dynamics