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=rxF 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