Module 6 general screws twists and wrenches
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Module 6 General Screws (twists and wrenches). Statics. Kinematics. Forces in parallel. Joints in series. Can they be reduced to a single force? ( Poinsot’s theorem ). Can they be reduced to a single joint? ( Chasles’ theorem). Recall An axiom of statics.

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Module 6 General Screws (twists and wrenches)

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Module 6 general screws twists and wrenches

Module 6General Screws(twists and wrenches)


Module 6 general screws twists and wrenches

Statics

Kinematics

Forces in parallel

Joints in series

Can they be reduced to a single force?(Poinsot’s theorem)

Can they be reduced to a single joint?(Chasles’ theorem)


Recall an axiom of statics

RecallAn axiom of statics

  • Two force systems are equivalent if and only if:

  • They have the same resultant force

  • They have the same moment with respect to some point


Moment of a pure couple

M = r x F

Moment of a pure couple

r

F

A

B

-F

O


Module 6 general screws twists and wrenches

Poinsot’s central axis theorem


Module 6 general screws twists and wrenches

Concurrent forces can be addedusing the parallelogram rule

P

O


Module 6 general screws twists and wrenches

The shifting operation(in statics)


Module 6 general screws twists and wrenches

The moment of two pure couples(with respect to any point)is the sum of their moments


Module 6 general screws twists and wrenches

The alignment operation(in statics)


Module 6 general screws twists and wrenches

The alignment operation(in statics)


Module 6 general screws twists and wrenches

Poinsot’s central axis

The alignment operation(in statics)


Module 6 general screws twists and wrenches

Chasles’screw axis theorem


Module 6 general screws twists and wrenches

Concurrent angular velocities can be addedusing the parallelogram rule


Module 6 general screws twists and wrenches

The shifting operation(in kinematics)


Module 6 general screws twists and wrenches

Translational velocities can always be added


Module 6 general screws twists and wrenches

The alignment operation(in kinematics)


Module 6 general screws twists and wrenches

Chasles’ screw axis

The alignment operation(in kinematics)


Module 6 general screws twists and wrenches

The helicoidal velocity field


Module 6 general screws twists and wrenches

Twists reinterpreted

Can be seen as a rotation about the origin, plus a sliding


Module 6 general screws twists and wrenches

Table summarizing screws, twists, and wrenches


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