Analytic Formulation of the Kinestatics of Robot Manipulators with Arbitrary Topology

In this paper an analytic formulation of the statics and the instantaneous kinematics of robot manipulators based on the Grassmann-Cayley algebra is presented. The notions of twist, wrench, twist space and wrench space are mathematically represented by the concept of extensors of this algebra and the reciprocity relation between twist and wrench spaces of partially constrained rigid bodies is reflected by its inherent duality. Kinestatic analysis of manipulators implies the computation of sums and intersections of the twist and wrench spaces of the composing chains which are carried out by means of the join and meet operators of this algebra when the linear subspaces involved in the kinestatic analysis of manipulators are represented by extensors. The importance of the Grassmann-Cayley algebra in kinestatics is that it has an explicit formula for the meet operator that gives analytical expressions of the twist and wrench space of robot manipulators with arbitrary topology.