Trajectory Planning of a Novel 2-DoF High-Speed Planar Parallel Manipulator

An effective method of time optimal trajectory planning is proposed for a high-speed planar parallel manipulator. First, the direct position and inverse position of the manipulator is analyzed according to its vector relation between each chain in order to get set of displacement in working and joint space. Second, cubic spline functions are used for constructing joint trajectories for the manipulator and piecewise cubic polynomials are used to fit the sequence of joint displacements for each joint. On this basis, the method of flexible polyhedron search is employed to plan the time intervals between each pair of adjacent knots so that the total time is minimized subject to the physical constrains on joint velocities, accelerations and jerks. The approach has been applied to the novel parallel manipulators and the desired displacements, velocities and accelerations of each joint have been obtained to meet the need of high-speed operations. The results show the method is feasible and practical.