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Module 6 General Screws (twists and wrenches)

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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  1. Module 6General Screws(twists and wrenches)

  2. 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)

  3. 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

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

  5. Poinsot’s central axis theorem

  6. Concurrent forces can be addedusing the parallelogram rule P O

  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)

  10. The alignment operation(in statics)

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

  12. Chasles’screw axis theorem

  13. Concurrent angular velocities can be addedusing 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 The alignment operation(in kinematics)

  18. The helicoidal velocity field

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

  20. Table summarizing screws, twists, and wrenches

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