Screw theory

Summary

Screw theory describes the velocities of a rigid body and the forces on it by six-dimensional vectors called screws. Twists describe motions, and wrenches describe forces and moments. Its geometric basis is Chasles' theorem. It says that every orientation-preserving rigid motion of space is a screw motion. That is, it is a rotation about a line combined with a translation along the same line. A screw has an axis, a line in space, and a pitch, the ratio of translation to rotation. It is used in the kinematics and statics of mechanisms and robots. There the power of a wrench on a twist is given by a simple pairing.