A ball mounting method for mounting a plurality of balls held by a head onto a workpiece. The head is clamped such that a clamping surface mounted to the head is engaged with a rigid lower positioning stop, and then moved above a ball supply section. The balls are held on the head, and the head is moved above the workpiece. The clamping force is then released so that the clamping surface does not engage the lower stop, and the head is counterbalanced between the lower positioning stop and an upper positioning stop. While the head is unclamped and counterbalanced, the balls are mounted on the workpiece. The head is then clamped and moved above the ball supply section again.