In this paper, the complete categorization of ail generic 3-revolute jointed (3R) positioning manipulators is established using a homotopy based classification scheme. It is shown that there exists exact/y eight subsets of homotopie generic manipulators which have similar global kinematic properties. The classification of generic manipu-lators serves as an efficient tool for the categorization of cuspidal and non cuspzdal manipulators, i.e., manipulators which can or cannot change posture without meeting a singularity, respective/y. As a result of this classification, it appears that, in contrast with common belief, most 3R manipulators are cuspidal.