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The concept of dynamic balancing with respect to a given trajectory is proposed in this paper. Trajectory-based dynamic balancing is a technique that brings additional mechanisms to unbalanced mechanisms with the purpose of actuating the original mechanism to move along a predefined trajectory, regardless of the shaking forces and moments. In this work, a planar three degrees of freedom (3-DOF) serial-parallel mechanism is proposed to implement this technique on an unbalanced platform. The overall structure of the system is firstly introduced and the mechanical design and kinematics of the proposed mechanism is then presented. The dynamic model of the mechanism and the platform is derived and analysed. Finally, numerical examples are presented to verify the effectiveness of the active dynamic balancing mechanism and the improved dynamic performance of the system

Dynamics Analysis of a Three-DOF Planar Serial-Parallel Mechanism for Active Dynamic Balancing with Respect to a Given Trajectory