Solving the 6r Inverse Position Problem Using a Generic-case Solution Methodology

AlmU'net--This paper considers the computation of all solutions to the inverse position problem for general six-revolute-joint manipulators. Instead of reducing the problem to one highly complicated input-output equation, we work with a system of I I very simple polynomial equations. Although the total degree of the system is large (1024), using the "method of the generic case" we show numerically that the generic number of solutions is 16, in agreement with previous works. Moreover. we present an elEcient nun~rical method for finding all 16 solutions, based on coe~icient-parameter polynomial continuation. We present a set of 41 test problems, on which the algorithm used an average of le-~ than l0 s of CPU time on an IBM 370-3090 in double precision FORTRAN. The methodology applies equally well to other problems in kinematics that can be formulated as polynomial systems.