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Forces in parallel Joints in series
Statics Kinematics
Can they be reduced to a single force?(Poinsot’s theorem)
Can they be reduced to a single joint?(Chasles’ theorem)
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Recall
An axiom of statics
Two force systems are equivalent if and only if:
They have the same resultant forceThey have the same moment with respect to some point
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Poinsot’s central axis theorem
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Concurrent forces can be addedusing the parallelogram rule
OP
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The shifting operation(in statics)
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The moment of two pure couples(with respect to any point)
is the sum of their moments
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The alignment operation(in statics)
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The alignment operation(in statics)
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The alignment operation(in statics)
Poinsot’s central axis
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Chasles’screw axis theorem
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Concurrent angular velocities can be addedusing the parallelogram rule
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The shifting operation(in kinematics)
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Translational velocities can always be added
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The alignment operation(in kinematics)
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The alignment operation(in kinematics)
Chasles’screw axis
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The helicoidal velocity field
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Can be seen as a rotation about the origin, plus a sliding
Twists reinterpreted
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Table summarizingscrews, twists, and wrenches