Singularity analysis of platform-type multi-loop spatial mechanisms

In parallel manipulators and multi-loop mechanisms, singularity is associated with either loss or gain of a degree of freedom. This paper deals with the singularity analysis associated with gain of degree of freedom in a class of spatial mechanisms. We present a geometric condition 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 the concept of a common tangent. We show that this condition also implies that the determinant of certain matrices, formed by the differentiation of the loop-closure equations, are zero. We illustrate our results with the help of several multi-loop mechanisms. In particular, we describe the singularity surface for the three-degree-of- freedom RPSSPR-SPR 'wrist' mechanism. (C) 1997 Elsevier Science Ltd.