A unified notation for serial, parallel, and hybrid kinematic structures

This paper proposes a new notation for kinematic structures which allows a unified description of serial, parallel, and hybrid robots or articulated machine tools. During the past decades, the Denavit-Hartenberg (DH) parameters have been used widely to describe serial kinematics of robots in science and industry. Till now, such a common notation for parallel manipulators has not yet been accepted. This paper tries to fill this gap by presenting a new notation, which is based on the graph representation known from gear trains. In parallel manipulators, spherical and cardan joints are widely used. In order to describe these kinds of joints, the DH-parameter notation has been extended, so that, to each joint as many joint variables can be assigned as degrees of freedom exist. The notation is not only very useful for design, programming, and simulation of parallel robots; it also can be applied as a convention to refer to parallel or hybrid kinematic structures elsewhere.