SINGULARITY ANALYSIS OF PLATFORM-TYPE MULTILOOP SPATIAL MECHANISMS

In parallel manipulators and multi-loop mechanisms, singularity is ass ociated with either loss or gain of a degree of freedom. This paper de als with the singularity analysis associated with gain of degree of fr eedom in a class of spatial mechanisms. We present a geometric conditi on for platform-type, multi-loop, mechanisms and parallel manipulators , containing spherical joints on the platform, whose existence ensures singularity in such mechanisms. The geometric condition is based on t he concept of a common tangent. We show that this condition also impli es that the determinant of certain matrices, formed by the differentia tion of the loop-closure equations, are zero. We illustrate our result s with the help of several multi-loop mechanisms. In particular, we de scribe the singularity surface for the three-degree-of- freedom RPSSPR -SPR 'wrist' mechanism. (C) 1997 Elsevier Science Ltd.