A CAD variation geometry approach is proposed for accurately solving the position-orientation, linear velocity/acceleration, and Euler angular velocity/angular acceleration of a symmetrical 3-dof 3-UPU parallel robot. Based on the finite-difference method as the foundations, using the computer aided geometry constraints and dimension driving technique, the simulation mechanism of the 3-UPU parallel robot with Euler angles is created, and the position-orientation can be got. Then the linear velocity/acceleration simulation mechanisms and Euler angular velocity/angular acceleration simulation mechanisms are created. When modifying the driving dimension of three driving limbs, the configurations of the simulation mechanisms are varied correspondingly, and all of the kinematical parameters are solved automatically. The simulation solutions are verified by an analytic approach. The results show that the CAD variation geometry is not only fairly quick and straightforward, but is also advantageous from viewpoint of accuracy and repeatability.

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