Force Balance Conditions of Complex Parallel Mechanisms with Mass Equivalent Modeling

A shaking force balanced mechanism is a mechanism that does not exert dynamic reaction forces to its base and to its surrounding for any motion. For mobile mechanisms such as exoskeletons, humanoid robots, drones, and anthropomorphic hands force balance is an important property for, among others, their dynamic behavior, stability, safety, control, and low energy consumption. For the design of force balanced mechanisms with multiple closed loops it can be a significant challenge to obtain the balance conditions, especially when the mechanism consists of closed loops that depend on other closed loops. In this paper it is shown how with mass equivalent modeling the force balance conditions can be derived of a complex multi-degree-of-freedom parallel mechanism with multiple closed loops of which one or more depend on other closed loops. It is shown how such a mechanism can be divided in mass equivalent linkages such as mass equivalent dyads and mass equivalent triads for which each can be analyzed individually with principal vectors and linear momentum equations.