Kinestatic analysis of serial and parallel robot manipulators using Grassmann-Cayley algebra

In this paper the statics and the instantaneous kinematics of serial and parallel robot manipulators are studied. A projective interpretation of the concepts of twist, wrench, twist space and wrench space - based on the concept of extensor - is presented and a description of the dualistic relation between twist and wrench spaces of serial and parallel robot manipulators is given in terms of the Grassmann-Cayley algebra. The importance of this algebra is that; its join and meet operators are very effective tools for joining and intersecting the linear subspaces involved in the kinestatic analysis of manipulators when they are represented by extensors.