Abstract: A method and apparatus are provided for controlling interpolated linear motion of a tool centerpoint associated with a function element carried by a machine. The motion is defined by input signals representing locations relative to an input coordinate system and path velocities therebetween. The machine includes at least one member rotating about an axis which is subject to movement at a velocity greater than the path velocity. Control is effected by producing projected velocity signals for the machine axes for each interpolative iteration and reducing the iterative path velocity in response to detecting a projected axis velocity in excess of an associated axis velocity limit. The control is applicable to machines incorporating a structure in which members must instantaneously change position to maintain the tool centerpoint on the path.