A new approach to synthesizing free motions of robotic manipulators based on a concept of unit motions

A concept of unit motions and a new scheme based on it for synthesizing free motions of robotic manipulators are proposed. First, unit motions for free motions having some smoothness properties are defined. Various operations on the free motions that can be executed in a dynamical way are also defined. Then, formal representations of motions by means of the so-called control polygons are presented. Formal representations of operations including joining and separating motions are also presented. Such formal representations yield concise descriptions of motions and operations. Finally, using some simulation examples it is shown how to synthesize free motions. Properties of resulting motions by this approach are described. Conditions for control systems to generate unit motions are also described. The concepts of unit motions and control polygons offer a basis to deal with the motions formally