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This paper presents the design of a 6-DOF parallel robot used in the artificial cervical disc replacement surgery, which is used to complete positioning and grinding between prosthesis and bone mating surfaces and whose moving platform is connected to the fixed platform by six UPS (Universal-Prismatic-Spherical) serial chains. In the paper, inverse position, a first-order static influence coefficient matrix, Jacobian matrix, and workspace factors are analyzed for the 6-UPS parallel mechanism and the analysis results of statics, singularity and workspace are given, which is used to guide the robot structure design. What's more, the CAD model of the robot is analyzed by finite element methods, which shows that the robot has adequate stiffness. Finally, a comprehensive analysis shows that the 6-UPS parallel robot is suitable for bone mating surfaces grinding in the artificial cervical disc replacement surgery.