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This work presents a control-oriented structural design approach for a 2-DOFunderactuated mechanical system, with the purpose of generating an optimaloscillatory behavior of the end-effector. To achieve the desired periodicmotion, we propose to adjust the dynamic response of the mechanism by selectingits mass distribution and the characteristic of a nonlinear spring. Inparticular, we introduce a two-step optimization strategy to shape the system'szero dynamics, obtained via input-output linearization. The first part of theprocedure aims to minimize the root-mean-square value of the input torque byoptimizing the mechanism's mass distribution. In this context, we show that aperfect matching with the desired trajectory can be reached by assuming theability to design an arbitrary shape of the system's elastic properties. Then,in order to favor a simpler physical implementation of the structure, wededicate the second optimization step to the piecewise linear approximation ofthe previously defined stiffness characteristic. The proposed procedure isfinally tested in detailed numerical simulations, confirming its effectivenessin generating a complex and efficient periodic motion.

Low-Input Accurate Periodic Motion of an Underactuated Mechanism: Mass Distribution and Nonlinear Spring Shaping