The output or resisting torque from a constant torque compliant mechanism keeps invariant in a large range of input rotation. Unlike regular constant torque compliant mechanisms that have only one input rotation direction, the input rotation of a bidirectional constant torque compliant mechanism can be either clockwise or counter-clockwise. Its resisting or output torque reverses its direction with the change of the input rotation direction. The unique feature of bidirectional constant torque compliant mechanisms makes their synthesis challenging. In this paper, a synthesis method is introduced to surmount the synthesis challenges. The constant resisting torque is generated through a set of curved beams that are mounted within an annular design domain. Because of the bidirectional requirement, the two ends of each curved beam are aligned along radial direction before deformation to avoid rotational bias. Spline curves are employed to describe curved beams and defined by their control parameters. The synthesis of a bidirectional constant torque compliant mechanism is systematized as optimizing the control parameters of its curved beams. The presented method is demonstrated by the synthesis of bidirectional constant torque compliant mechanisms that have different arrangements of curved beams in the paper.

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