Module 6 General Screws (twists and wrenches) - iri.upc.edu · Poinsot’s central axis theorem....
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Module 6 General Screws (twists and wrenches)
Transcript of Module 6 General Screws (twists and wrenches) - iri.upc.edu · Poinsot’s central axis theorem....
Module 6General Screws
(twists and wrenches)
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)
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
Moment of a pure couple
O
r
-F→
F→→
A
B
M = r x F→ → →
Poinsot’s central axis theorem
Concurrent forces can be addedusing the parallelogram rule
OP
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 addedusing 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
Can be seen as a rotation about the origin, plus a sliding
Twists reinterpreted
Table summarizingscrews, twists, and wrenches
