Throwing is a complex and highly dynamic task. Humans usually exploit passive dynamics of their limbs to optimize their movement and muscle activation. In order to approach human throwing, we developed a double pendulum robotic platform. To introduce passivity into the actuated joints, clutches were included in the drive train. In this paper, we demonstrate the advantage of exploiting passive dynamics in reducing the mechanical work. However, engaging and disengaging the clutches are done in discrete fashions. Therefore, we propose an optimization approach which can deal with such discontinuities. It is shown that properly engaging/disengaging the clutches can reduce the mechanical work of a throwing task. The result is compared to the solution of fully actuated double pendulum, both in simulation and experiment.