Industrial robots need motors with high-precision positioning, large torque output, and small size. However, the conventional motors combined with reducers tend to be large. To solve the problem, we proposed the motor integrated with reducer that could output reduced rotation directly by using the strain wave gearing system. The proposed motor is thought to have advantages not only in downsizing but also in high load-supporting capacity and high stiffness because of the simultaneous engagement of three gear pairs. In this paper, we derive the theoretical input-output relation in the proposed motor with a focus on the deformation of the elastic gear in the motor. The result gives the pushing force of the linear actuators at an arbitrary output rotation angle of the motor. We conduct the experiments to clarify the optimal input pattern for the accurate rotation by using the prototype of the proposed motor. Through the observation and measurement, the optimal input pattern is suggested.

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