Optimal dynamic trajectory planning for linearly actuated platform type parallel manipulators having task space redundant degree of freedom

Two types of dynamic trajectory planning problems associated with task space redundant degree of freedom of parallel manipulators are investigated. The first problem involves synthesizing the point-to-point trajectory of the moving platform such that the distribution of the cutting force of the tool bit along a specified machining contour is optimized. The second problem is to determine the maximum constant cutting force along the contour while maintaining an optimal distribution of the actuator forces. The numerical algorithms developed for solving these problems are based on the method of approximate programming and take into account all of the dynamic and kinematic constraints imposed on the system.