A numerical solution of the general kinematic problem

Abstract

The paper proposes a method for the solution of the general kinematic problem, i.e. the transformations between the joint coordinate and the cartesian robot coordinate system. Based on homogeneous transformation matrices the method solves the kinematic problem for a series of n (n >/=/< 6) one-degree-of-freedom joints either revolute or prismatic and with or without branching analytically. The inverse kinematic problem is handled numerically via linearization. The numerical solution is evaluated with respect to some constraints like joint workspace, velocities, energy, e.t.c. The numerical results and the computation time show the applicability of the method for real-time control systems.