Transcript Poinsot`s theorem

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
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
Moment of a pure couple
→
→
A
→
-F
O
F
r
B
→
→
→
M=rxF
Poinsot’s
central axis theorem
Concurrent forces can be added
using the parallelogram rule
P
O
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 added
using 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
Twists reinterpreted
Can be seen as a rotation about the origin, plus a sliding
Table summarizing
screws, twists, and wrenches