  In this work, we present the integrated structure-control design of a 2-DOF
underactuated mechanical system, aiming to achieve a periodic motion of the
end-effector. The desired behavior is generated via input-output linearization,
followed by structural optimization of the zero dynamics. Inspired by recent
works on the control-oriented design of multibody systems, we define an
optimization problem based on the simulation of the system's response. In
particular, relevant model parameters are used to match the reference with a
specific orbit of the zero dynamics, while also penalizing the input energy.
For the considered application, the selected parameters are related to the
mechanism's elasticities and mass distribution. Notably, we show that it is
possible to reach a desirable trade-off between mass reduction and periodic
motion accuracy. With an optimal zero dynamics response available, the control
scheme can be completed with established orbital stabilization techniques,
ensuring a robust oscillating behavior.
