Kinematic chain

Links and joints form the mechanism#

A link is a modeled rigid body. A joint specifies how one link can move relative to another. An arm with shoulder, elbow, and wrist joints is commonly modeled as a serial chain from a base to an end-effector.

Modern Robotics uses the example of a three-revolute-joint arm to show how an open chain has one path from its base to its endpoint. A branched robot can instead be represented as a tree of links.

Closing a loop adds constraints#

Pinning that arm's endpoint to ground creates a closed chain. The resulting loop means that the joint coordinates cannot all vary independently. Four-bar linkages and parallel platforms are examples.

The closed-chain kinematics lesson explains that loop constraints make both configuration analysis and solution counting more complicated than in a simple serial arm.

A model of geometry and connectivity#

A chain supplies the structure needed for forward kinematics. MIT's manipulation notes describe finding a tool pose by following its parent links and composing their transforms. The chain alone does not specify how the joints are driven or the masses and forces needed for a dynamics calculation.