Abstract: A multiple step indexing mechanism having a rotary input and a rotary output and intermediate driving members with driving connections to generate a periodic dwell interval of the output member through the kinematic superposition of substantially linear and substantially harmonic motion components including those which include multiple harmonic components together with a dwell extension mechanism which includes timing means driven by the input member, a device for engaging and disengaging one of the driving connections, and a connection between the timing means and engagement device to effect disengagement within one of the periodic dwell intervals and re-engagement within another of the periodic dwell intervals.