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Focus on the realization of two kinds of function of stabilization and tracking of lowDOF parallel mechanism,by using the screw theory,a 2-SUP（U）parallel mechanism is designed,and the DOF of this mechanism is analyzed.According to the motion characteristic of this parallel mechanism,using vector algorithms with Rodrigues parameters,the kinematics analysis is carried out,and the calculation method of position inverse and velocity inverse is deduced respectively.Moreover,the simulation is carried out with the Matlab,the position,velocity and other characteristics curve are obtained.The theory foundation for the control of position and velocity of this mechanism is provided.