Abstract: A method and apparatus are provided for cooperatively controlling motion between a tool centerpoint associated with a function element carried by a manipulator and rotation of a workpiece carried by a positioner. The tool centerpoint follows a linear path interpolated between programmed locations at a velocity resulting in a relative velocity between the tool centerpoint and the workpiece surface equal to a programmed velocity. Differences in radial distance of the tool centerpoint from the axis of rotation of the workpiece at successive programmed locations result in incremental velocity modifications along the path to maintain the relative velocity at the programmed value.

Abstract: An apparatus and method are provided for controlling the motion of a point associated with a function element carried by a machine. The motion describes an oscillatory pattern in a selectable plane through a path between two positions defined by input signals. The oscillatory motion pattern defines cyclic excursions about the path. Motion is effected by iteratively interpolating intermediate positions along the path, computing incremental excursion amplitudes associated with the intermediate position displacements, calculating coordinates of the intermediate position excursions and producing machine actuator control signals to move the machine members to advance the point from its position along the pattern to an intermediate position.