Math & Kinematics

Kinematic Chain

A kinematic chain is an assembly of rigid links connected by joints, the structural abstraction underlying manipulators and legged robots. Chains may be serial, as in most robot arms, parallel, as in Delta robots and Stewart platforms, or branched, as in humanoids with multiple limbs from a common torso, and robot description formats like URDF encode them as trees of links and joints.

Why it matters for physical AI

The chain abstraction is what makes kinematics, dynamics, and simulation computable for arbitrary morphologies, letting one software stack serve arms, hands, quadrupeds, and humanoids alike.