A mechanism is disclosed for transforming reciprocating/rotating motion in which the reciprocating member is continuously rotated unidirectionally so as to perform 360 degrees of rotation over the course of each cycle of reciprocity, into any number of simultaneous arcuate motions intersecting at predetermined angles. This mechanism comprises a ball rotatably mounted by a supporting element and centered on a line which is perpendicular to the path of excursion of the reciprocating member at the midpoint of the excursion, which line coincides with the axis of rotation of the reciprocating member at the midpoint position, and a linkage(s) provided to transfer the motions of the reciprocating/rotating member(s) to the ball. Points on the surface of the ball are thereby made to exhibit an infinite number of arcs which intersect a common point at an infinite number of angles. Any number of arcs intersecting at any angle can be obtained by selecting points on the surface of the ball exhibiting those desired vectors. This motion conversion apparatus is the basis for improvements in a variety of existing devices including but not limited to grinders, mixers, pendulum devices, signal lights, scanning devices such as ultrasonic and radar scanners, and dispersing devices such as ordnance dispersing.