Connectivity and redundancy in spatial robots

In this paper the concepts of connectivity, degrees of control, and redunda ncy are revisited from a pure topological viewpoint and then applied to rob otics. The redundancy matrix is defined to provide designers with a useful support in the first conceptual phase of the project of a new manipulator A n algorithm for building the connectivity and the redundancy matrices for a large class of manipulators is derived and implemented in an algebraic man ipulation programming language. Based on some results borrowed from graph t heory: the procedure can be used to study open-loop, closed-loop, and hybri d kinematic chains. In particular: it is shown how the biconnected componen ts of the graph corresponding to the manipulator under analysis have to be detected for a correct computation of connectivity and redundancy. Furtherm ore, the study of the connectivity and of the degrees of control led to the development of a full mobility test that automatically detects the type of mobility of any given robot: total, partial, or fractionated. One of the p resented sample cases offers the opportunity to discover some differences b etween the connectivity matrix obtained by means of the new algorithm and t hat presented, on the sa,ne kinematic chain, in a previous one.