Math & Kinematics

Screw Theory

Screw theory is a mathematical framework describing rigid body motion and forces using screws: any spatial displacement can be expressed as a rotation about an axis combined with a translation along it (Chasles' theorem), and any system of forces reduces to a force plus a couple along an axis (Poinsot). Velocities become twists and forces become wrenches, both six-dimensional vectors. It underpins the product-of-exponentials formulation of kinematics popularized by texts like Lynch and Park's Modern Robotics.

Why it matters for physical AI

Twists and wrenches provide the coordinate-free language in which modern manipulator kinematics, dynamics, and contact models are written, and they surface directly in software like screw-based IK solvers.