Kinematic Design Of 3-PRRU Parallel Manipulator

This paper focuses on the kinematic performances of 3-PRRU parallel mechanism and targets the kinematic optimum design. The main work and research results are as follows:The geometry relationship of each limb is analyzed. The position and orientation of moving platform by can be described byYXZ Euler angles. The relative kinematic frame of reference of one limb is established with D-H method. Based on the above analysis, the forward and inverse kinematic models are formulated.The mapping matrixes of speeds from drive joints to the output of moving platform, namely Jacobian of constraints and actuations are proposed. Then the overall Jacobian is constructed and its determinant is calculated. According to the solution of singular configuration, necessary conditions at the singular configurations of the 3-PRRU parallel manipulator are proposed.The configuration parameters are defined, which makes it possible for kinematic analysis and design. The ranges of configuration parameters are also given. Different configurations can be obtained with changing values of parameters. The mapping models of error, speed, load, stiffness from drive joints to moving platform are formulated and all the indices concerning condition, speed, load and stiffness are defined. Then global performance indexes are proposed. The space model of 3-PRRU parallel manipulator is established according to the size range of the configuration parameters. The relationship between global performances and configuration parameters is studied in this space model, and the figures of global performance are protracted. Optimal design of the manipulator is implemented according to the figures of global performances.According to the design requirements and the size of the prototype are determined. Then the prototype of 3-PRRU parallel manipulator is designed and manufactured.Analyzing the working space of the prototype, the singularities of the prototype can be found and the figures of rotated dexterity, the maximum and minimum speeds, load and stiffness are drawed. Finally, the constraint forces / torques distribution patterns of each limb are given. The achievements stated in this paper lay a solid foundation for the development of the 3-PRRU prototype.