A novel and improved rotary shaft coupling including a ball-type speed reducer. A driving disc is coupled to a driven disc through a plurality of balls loosely held in a circular array of holes. Each ball registers with opposing faces of elliptic and hypocycloidal grooves of the driven and driving disc, respectively. When the driving disc is rotated, the balls transmit a turning force through the grooves to the driven disc. Speed reduction is determined by the number of waves in the hypocycloidal groove exceeding, by an even number, the number of balls.