A geometrical introduction to screw theory

TL;DR

This paper provides an accessible introduction to screw theory, a mathematical framework that unifies translational and rotational dynamics of rigid bodies, highlighting its analogies and applications in mechanics.

Contribution

It offers a clear, rigorous, and accessible explanation of screw theory, emphasizing its unifying role in rigid body dynamics for undergraduate and general audiences.

Findings

Screw theory unifies translational and rotational degrees of freedom.

Angular velocities are treated as applied vectors, similar to forces.

The theory reveals mathematical analogies between mechanical momenta and velocities.

Abstract

This work introduces screw theory, a venerable but yet little known theory aimed at describing rigid body dynamics. This formulation of mechanics unifies in the concept of screw the translational and rotational degrees of freedom of the body. It captures a remarkable mathematical analogy between mechanical momenta and linear velocities, and between forces and angular velocities. For instance, it clarifies that angular velocities should be treated as applied vectors and that, under the composition of motions, they sum with the same rules of applied forces. This work provides a short and rigorous introduction to screw theory intended to an undergraduate and general readership.