Design and modeling of a compact rotational nonlinear spring

In this paper, we propose a new method for implementing a rotational nonlinear spring with user defined profile, based on the combination of a linear spring with a nonlinear transmission mechanism. The proposed structure consists of a non-circular cam, a roller which moves along outer circumference of the cam, and a stretched translational linear spring which is connected between center of the cam and center of the roller. We obtain a set of differential equations to design shape of the cam for any given torque-angle profile. Also, it will be shown that profiles with both positive and negative values can be implemented by the proposed method. At last, the cam of some popular nonlinear springs are designed, including constant, cubic, hyperbolic tangent and sinusoidal springs.

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