Solving multi-loop linkages by iterating 2D clippings

A multi-loop linkage can be viewed as a graph of kinematic con-strain ts, and its solution entails nding joint congurations satisfying all constraints simultaneously. In this paper, a general algorithm to ob-tain all solution congurations is presented. Each loop provides a matrix equation in homogeneous coordinates, which is handled as a constraint on the involved joint variables. The algorithm uses one constraint at a time to reduce the valid ranges for variables, by iteratively applying tw o simple geometric operations: segment-trapezoid and circle-rectangle clippings. The obtained experimental results qualify this approach as a valuable alternative to other interval-based strategies