Abstract: A linkage mechanism, such as an industrial robot, comprises an electronic motion controller and a set of self-driven joints. A controller receives a series of end effector positions from memory or from a host control system which define a routine for the mechanism to execute in relation to a predetermined reference frame such as cartesian coordinates. Angular values for the joints are computed in real time which follow the predetermined reference frame values in a manner which avoids the problems of singularities and which efficiently accommodates kinematic redundancy. A corresponding drive signal is generated for each joint.