Kinematic and Dynamic Analysis of Tripteron, an Over-constrained 3-DOF Translational Parallel Manipulator, Through Newton-Euler Approach

Abstract

In this research, as the main contribution, a comprehensive study is carried out on the mathematical modeling and analysis of the inverse kinematics and dynamics of an over-constrained three translational degree-of-freedom parallel manipulator. Due to inconsistency between the number of equations and the unknowns, the problem of obtaining the constraint forces and torques of over-constraint manipulators does not admit solution, which can be regarded as one of the drawbacks of such mechanisms. In this paper, in order to overcome this problem and circumvent inconsistency between the number of equations and the unknowns, two of the revolute joints attached to the end-effector are changed into a universal and a spherical joint without changing the motion pattern of the manipulator under study. Then, the dynamical equations of the manipulator are obtained based on the Newton–Euler approach, and a simple and a compact formulations are provided. Then, all the joint forces and torques are presented. In order to evaluate accuracy of the obtained formulated model, a motion for the end-effector as a case study is performed, and it has been shown that the results of the analytical model are in a good agreement with those obtained from SimMechanics model. Finally, the Root Mean Square error is calculated between the analytical model and the results obtained from the simulation and experimental study.