7: Robot arm kinematics

Kinematics is the branch of mechanics that studies the motion of a body or a system of bodies without consideration given to its mass or the forces acting on it

A serial-link manipulator comprises a chain of mechanical links and joints. Each joint can move its outward neighbouring link with respect to its inward neighbour. One end of the chain, the base, is generally fixed and the other end is free to move in space and holds the tool or end-effector.  The chain can be branched leading to a robot with multiple hands and/or feet.

This chapter covers:

• describing the link and joint structure of a robot using elementary transformations
• determining the pose of the end effector given joint coordinates — forward kinematics
• determining the joint coordinates given the pose of the end effector — inverse kinematics
• generating smooth paths for the end-effector
• branched robots
• joint angle offsets, base and tool transformations
• other ways to describe kinematic models: URDF, standard and modified Denavit-Hartenberg notation
• Examples
  • drawing on a surface
  • a simple walking robot

The approach differs from many contemporary textbooks by not starting with Denavit-Hartenberg notation.  This notation is challenging to understand, not helped by their being two different forms of the notation (standard and modified).  Instead a more intuitive approach, elementary transform sequences, based on pose graphs is used initially.