Kinematic and Dynamic Analysis of 3-DOF Delta Parallel Robot Based on the Screw Theory and Principle of Virtual Work

The linear form of dynamic equation of parallel robots can be used to implement a wide variety of nonlinear adaptive control schemes in real time. Also, in parallel manipulators, linearizing the complex dynamic equation of motion is time consuming as well as complicated, but it is highly rewarding, since it can contribute to the achievement of fast and precise dynamic performance capabilities of the foregoing manipulators. Therefore, in this paper, instead of finding the nonlinear form of the dynamic equation of delta parallel robot by means of virtual work method, a linear form of the dynamic equation is calculated. To this end, kinematic analysis has been performed by resorting to the screw theory, as it provides more compact formulation of Jacobian matrices and facilitates the employment of virtual work principle. After finding the Jacobian matrices of input-output, and the Jacobian matrices between each link and end-effector’s kinematics parameters, the full dynamic equation of motion of robot has been written. The twists comprising the equation has been determined separately and linear form of dynamic equation of robot has been computed. Afterwards, the SimMechanics model of 3-DOF. Delta parallel robot has been constructed and a simulation is performed in order to verify the validity of proposed equations of motion, and the corresponding error of computed torques of actuators comparing with Simscape’s direct results is given.