Module 6General Screws

(twists and wrenches)

Forces in parallel Joints in series

Statics Kinematics

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

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

O

r

-F

F

→

→ →

A

B

M = r x F→ → →

Poinsot’s central axis theorem

Concurrent forces can be addedusing the parallelogram rule

O

P

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)

The alignment operation(in statics)

Poinsot’s central axis

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)

The alignment operation(in kinematics)

Chasles’ screw axis

The helicoidal velocity field

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

Twists reinterpreted

Table summarizing screws, twists, and wrenches