Optimal passive dynamics for physical interaction: Throwing a mass

The passive dynamics of actuators may impose serious limitations to the performance of a system. Existence of inertia for example makes it impossible for the actuators to react immediately. A throwing mechanism (with electric motors) is composed of two inertias (object and motor) that decreases the performance of the system and can not be overcome with software control. But, we can use other elements (like a spring) to make the motor inertia a benefit to improve the performance of the system. Moreover, when the object is directly connected to the motor, the maximum velocity that the object can achieve is limited to the maximum velocity that can be provided by the motor. Previous research shows that passive dynamics is not always harmful, and can increase the performance of a mechanism. Here, we will extract mathematical formula that gives us the required optimum value for stiffness and/or damping of the system to give us the optimal performance given physical limitations.