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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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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)
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
→ → → M = r x F Moment of a pure couple → → r F A → B -F O
Concurrent forces can be addedusing the parallelogram rule P O
The moment of two pure couples(with respect to any point)is the sum of their moments
Poinsot’s central axis The alignment operation(in statics)
Concurrent angular velocities can be addedusing the parallelogram rule
Chasles’ screw axis The alignment operation(in kinematics)
Twists reinterpreted Can be seen as a rotation about the origin, plus a sliding