A robust classification scheme for spherical 4R linkages

Introduced in this paper is a robust classification scheme for the 4R spherical linkage. The robustness is acquired by means of a systematic and detailed analysis of the relative motions existing between adjacent links. Thus, one can avoid the usual ambiguities encountered in type-identification procedures which have become somewhat standard. Moreover, it is shown that there are only 33 distinct types of 4R spherical linkages instead of 81, as it was reported elsewhere. Finally, an unambiguous terminology is proposed and several examples with numerical values of link lengths for each linkage type are also provided.