Design and Realization of a Non-Circular Cable Spool to Synthesize a Nonlinear Rotational Spring

In this paper we present a cable mechanism that realizes a nonlinear rotational spring from a linear translational spring. The spring is pulled by a cable wound around a non-circular spool, which is rigidly attached to the joint. The non-circular shape of the spool induces a nonlinear relationship between its angular position and the torque created by the tension of the cable. Depending on the shape of the spool, various torque– angle relationships can be realized. We show that for a given nonlinear torque–angle relationship, there is an explicit expression (closed-form solution) of the shape of the spool that synthesizes this function. First, we present the geometry of the problem. Then, we derive the methodology to calculate the shape of the spool to synthesize a prescribed torque–angle relationship. Finally, we verify the design methodology by experiments with three different spools realizing a constant force spring, an exponential softening spring and a cubic polynomial spring. We discuss the possible sources of errors between the theoretical and experimental results. © Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2012