1. Module 6 General Screws (twists and wrenches)

2. Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s theorem) Can they be reduced to a single joint? (Chasles’ theorem)

3. 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

4. Moment of a pure couple O r -F F → → → A B M = r x F → → →

5. Poinsot’s central axis theorem

6. Concurrent forces can be added using the parallelogram rule O P

7. The shifting operation (in statics)

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

9. The alignment operation (in statics)

11. Poinsot’s central axis

12. Chasles’ screw axis theorem

13. Concurrent angular velocities can be added using the parallelogram rule

14. The shifting operation (in kinematics)

15. Translational velocities can always be added

16. The alignment operation (in kinematics)

17. Chasles’ screw axis

18. The helicoidal velocity field

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

20. Table summarizing screws, twists, and wrenches