Module 6 General Screws twists and wrenches Statics

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 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 → → A → -F O F r B → → → M=rx. F

Poinsot’s central axis theorem

Concurrent forces can be added using 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)

The alignment operation (in statics) Poinsot’s central axis

Chasles’ screw axis theorem

Concurrent angular velocities can be added using 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

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

Table summarizing screws, twists, and wrenches