A New Distance Algorithm and Its Application to General Force-Closure Test

This paper presents an algorithm for computing the distance between a point and a convex cone in n-dimensional space. The convex cone is specified by the set of all nonnegative combinations of points of a given set. If the given set is finite, the algorithm converges in a finite number of iterations. The iterative computation speeds up with the help of the derived recursive formulas and effective choice of initial and stopping conditions. The function of this algorithm is demonstrated by its application to force-closure test, which is a fundamental problem arising in research of several mechanisms. Numerical examples show that force-closure can be verified very quickly by this means.