# Module 6 General Screws (twists and wrenches) - PowerPoint PPT Presentation

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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 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)

### 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

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 shifting operation(in statics)

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

The alignment operation(in statics)

The alignment operation(in statics)

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)

Translational velocities can always be added

The alignment operation(in kinematics)

Chasles’ screw axis

The alignment operation(in kinematics)

The helicoidal velocity field

Twists reinterpreted

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

Table summarizing screws, twists, and wrenches