module 6 general screws (twists and wrenches). forces in paralleljoints in series staticskinematics...
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![Page 1: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/1.jpg)
Module 6General Screws
(twists and wrenches)
![Page 2: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/2.jpg)
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)
![Page 3: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/3.jpg)
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
![Page 4: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/4.jpg)
Moment of a pure couple
O
r
-F
F
→
→ →
A
B
M = r x F→ → →
![Page 5: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/5.jpg)
Poinsot’s central axis theorem
![Page 6: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/6.jpg)
Concurrent forces can be addedusing the parallelogram rule
O
P
![Page 7: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/7.jpg)
The shifting operation(in statics)
![Page 8: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/8.jpg)
The moment of two pure couples(with respect to any point)
is the sum of their moments
![Page 9: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/9.jpg)
The alignment operation(in statics)
![Page 10: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/10.jpg)
The alignment operation(in statics)
![Page 11: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/11.jpg)
The alignment operation(in statics)
Poinsot’s central axis
![Page 12: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/12.jpg)
Chasles’screw axis theorem
![Page 13: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/13.jpg)
Concurrent angular velocities can be addedusing the parallelogram rule
![Page 14: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/14.jpg)
The shifting operation(in kinematics)
![Page 15: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/15.jpg)
Translational velocities can always be added
![Page 16: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/16.jpg)
The alignment operation(in kinematics)
![Page 17: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/17.jpg)
The alignment operation(in kinematics)
Chasles’ screw axis
![Page 18: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/18.jpg)
The helicoidal velocity field
![Page 19: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/19.jpg)
Can be seen as a rotation about the origin, plus a sliding
Twists reinterpreted
![Page 20: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/20.jpg)
Table summarizing screws, twists, and wrenches
![Page 21: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/21.jpg)
![Page 22: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/22.jpg)
![Page 23: Module 6 General Screws (twists and wrenches). Forces in parallelJoints in series StaticsKinematics Can they be reduced to a single force? (Poinsot’s](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d4c5503460f94a2a6ec/html5/thumbnails/23.jpg)