Dynamic performance comparison and counterweight optimization of two 3-DOF parallel manipulators for a new hybrid machine tool

The dynamic performance of two 3-DOF parallel manipulators, the HALF and the HALF ⋆ , is compared and a new optimization method for the counterweight masses is proposed for the development of a new hybrid machine tool. Since the manipulators have the same mobility of two translational and one rotational DOFs and the machine tool is designed for high-speed machining, it becomes significant to determine which manipulator has better dynamic characteristics. For this purpose, the dynamic models of the manipulators are derived via the Lagrangian formulation and the translational and rotational quantities are separated due to the unit inhomogeneity. Performance indices are proposed to measure the acceleration, velocity, and external loading capabilities, and then are used in counterweight optimization to minimize the actuator forces for the required acceleration and velocity limitations. Simulation results show that the HALF ⋆  provides better linear acceleration and linear velocity performance than the HALF, thus it is chosen for the hybrid machine tool. With the counterweight optimization, the actuator forces for the required maximum accelerations and velocities can be reduced by ten percent