A real-time optimization routine is presented. The routine calculates the “best” coefficients of a fifth-order polynomial trajectory. The trajectory is used to calculate the setpoints given to a servomotor every ten milliseconds to drive a patented hypotrochoidal gear mechanism as part of an industrial food packaging machine (Howard et al, 2000). It is desired to minimize the upward, vertical forces that the gear mechanism exerts on the machine. The optimization routine is shown in simulation to result in a trajectory that can reduce the upward force by 30–40%, without sacrificing the production rate, by explicitly taking into account the hypotrochoidal kinematics of the gear mechanism.

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