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

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