The dual generalized inverses and their applications in kinematic synthesis

Abstract

The left and right dual Moore–Penrose generalized inverses are the subject of this paper. It is shown that, contrary to the real case, these inverses are not unique, those with minimum Frobenius norm being obtained. Their application in kinematic synthesis is discussed. It is shown that, in the case of function-generating RCCC linkages, the left dual generalized inverse leads to a linkage that meets the prescribed input-output relations with both a least-square error and a minimum size. The study concludes with the synthesis of a linkage that approximates a homokinetic transmission between shafts with skew, orthogonal axes.