A solution to the approximate spherical burmester problem

Abstract

The synthesis of spherical linkages is of the utmost importance because (a) it poses challenges to the kinematician that are not present in the planar case and (b) its spatial counterpart depends on the synthesis of a spherical linkage. While the synthesis of spherical linkages for rigid-body guidance is a classic subject, and well documented in the literature, this has been limited to the exact-synthesis case, with four and five prescribed poses. The extension to approximate synthesis, more realistic and more appealing to the mechanism designer, has been reported in the past, but the synthesis method proposed therein is too cumbersome to be readily implementable. The approach proposed here obviates the constraints imposed by the unit vectors determining the center point and the circle point of each of the two dyads making up the four-bar linkage, thereby ending up with an unconstrained nonlinear least-squares problem. An example is included, that illustrates the procedure.