In industry when a link, crank, or other mechanical component is to be rotated from one rest position to another, it is necessary to establish appropriate functional relationships for angular displacement, velocity, and acceleration versus time such that the output motion satisfies certain kinematic and dynamic requirements. In the work presented here, a new type of motion is developed which has distinct advantages over constant velocity motion, constant acceleration motion, simple harmonic motion, cycloidal motion, and polynomial motions. The “variable-rate transymmetric” motion allows a designer to assign specific portions of the motion to be described by a linearly varying acceleration and other portions by a constant acceleration. As a result, the designer can decrease the power required, decrease the operating cost, and decrease dynamic responses such as shock, vibration, and shaking force.

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