Inverse Kinematics and Rigid-Body Dynamics for a Three Rotational Degrees of Freedom Parallel Manipulator

Modeling and analysis of inverse kinematics and rigid-body dynamics for a three rotational degrees of freedom (DOF) parallel manipulator are conducted in this research. In the inverse kinematics model, the position, velocity, acceleration, jerk and singularity are considered. The rigid-body dynamic model is developed based on the principle of virtual work and the concept of link Jacobian matrices. In this research, the inverse dynamic analysis of the parallel manipulator is carried out in an exhaustive decoupled way. The total actuating torques, the torques related to the acceleration, velocity, and gravity, the torques related to the moving platform, strut, slider, lead screw, and motor rotor-coupler, and the torques related to external forces are calculated. The total actuating powers, the powers related to the acceleration component of torque, velocity component of torque, gravity component of torque, and the powers related to the moving platform, strut, slider, lead screw, and motor rotor-coupler are also achieved. For the pre-defined trajectory, the required output work for the i-th driving motor is obtained through numerical integration technique. Simulation is conducted to obtain the positions, velocities, accelerations, jerks, torques, powers, and energy consumptions.