Enumeration of parallel manipulators

In this paper, we present a new method of enumeration of parallel manipulators with one end-effector. The method consists of enumerating all the manipulators possible with one end-effector that a single kinematic chain can originate. A very useful simplification for kinematic chain, mechanism and manipulator enumeration is their representation through graphs. The method is based on group theory where abstract structures are used to capture the internal symmetry of a structure in the form of automorphisms of a group. The concept used is orbits of the group of automorphisms of a colored vertex graph. The theory and some examples are presented to illustrate the method.