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
Module 6General 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


Poinsot’s central axis theorem


Concurrent forces can be addedusing the parallelogram rule

P

O



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




Poinsot’s central axis

The alignment operation(in statics)


Chasles’screw axis theorem


Concurrent angular velocities can be addedusing the parallelogram rule


The shifting operation(in kinematics)



The alignment operation(in kinematics)


Chasles’ screw axis

The alignment operation(in kinematics)



Twists reinterpreted

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


Table summarizing screws, twists, and wrenches


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