Angle-bound smoothing with applications in kinematics

Distance-bound smoothing is a method to characterize point configurations satisfying a given set of constraints on the pairwise ranges of distances between the points. This technique essentially consists in the iterative application of a set of algebraic conditions to reduce the given initial distance ranges. Although originally developed in a Computational Chemistry context, it has successfully been applied to problems of planar point configurations arising in Robotics, which includes the position analysis of planar robots. In this paper, this technique is generalized to deal with points on a sphere so that the planar case can now be deduced from the one presented here as a limit case. To exemplify the interest of this technique, it is applied to solve the position analysis of multiloop spherical linkages.