Screw theory and Chasles' theorem

[Liferider]

I am currently working on my masters and happened to stumble upon screw theory, of which I have no previous experience with. Fundemental to screw theory is Chasles' theorem or Mozzi's theorem that states that any rigid body motion can be produced by a translation along a line and rotation about the same line, and vice versa. However, I find this hard to believe. Consider a body falling towards the ground while also rotating about an axis parallel to the ground and passing through the objects center of mass. How is it possible to represent this motion in screw-terms?

 

[Liferider]

I believe I am thinking of the translational displacement as along, say z-axis towards the ground and then expect the rotation to be around this axis (for Chasles' theorem to be corrrect), and of course that is not always the case... But, is there some other line that can represent the translation, where the rotation axis can also be placed?

 

[Liferider]

Question 1:
Does a line through the object have to lie on the axis of translation and rotation? Or can the trans./rot. axis lie outside the object (relative to an inertial frame)?

Question 2:
Which coordinate systems do I have to consider in order to understand the notions of twists, wrenches and screws?

 

[Philip Wood]

http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/lecture4.pdf

Try this. I found it fascinating.

 

[Liferider]

http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/lecture4.pdf

Try this. I found it fascinating.

Thanks, I think I learned something just there. Still not quite there though, will try to explain when I truly understand and feel confident enough.

 

[dauto]

Your example can be described with just a rotation around an axis parallel to the ground (way out). as the object accelerates (free fall), the location of the rotation axis changes.

 

[Liferider]

Your example can be described with just a rotation around an axis parallel to the ground (way out). as the object accelerates (free fall), the location of the rotation axis changes.

That was my conclusion as well, in the end.. Now that I realize that the theorem actually have two versions, the infintesimal one and the configuration-to-configuration version, the theorem seems pretty obvious to me. Following the different proofs out there comes naturally. I thank you both for explaining this to me.