Configuration Design And Workspace Solving Method Of Reconfigurable Spherical Parallel Mechanism

Reconfigurable parallel mechanism has become one of research hotspots in parallel mechanism field because of its characteristics of good adaptability and variability of the structure and the function.Spherical parallel mechanism is a special type of the parallel mechanism.It not only has the characteristics of parallel mechanism such as high bearing capacity,high stiffness,small rotating inertia and symmetry structure,but also its end-effecter is always running on a sphere whose center is located at the intersection point of the axes of all revolute pairs.Its workspace is one of the parts of the spherical surface,and it has the characteristic of spatial three-dimensional rotation.Spherical parallel mechanism can be used as the azimuth tracking system of satellite antenna,and it also can be used as the structure scheme of the wrist joint,the shoulder joint,and the waist joint of bionic robot,and of engraving machine and various types of aircraft ground automatic tracking equipment.In this paper,taking 3-RPR and 3-RRP spherical parallel mechanisms as the original mechanisms,and taking 3-RPRP spherical parallel robot as the research object,the configuration reconfigurable method,kinematics performances and the workspace solving method of reconfigurable spherical parallel mechanism are studied.The main contents of this study are as follows:First of all,two kinds of original mechanisms,i.e.3-RPR and 3-RRP spherical parallel mechanisms,are integrated.Each limb has four kinematic pairs.The conversion among different configurations is realized by the self-locking of the part of kinematic pairs.According to the permutations and combinations of the number and position of the self-locking kinematic pairs,ten different kinds of kinematic limbs with different degrees of freedom and configurations,including two kinds of original limbs,can be reconstructed after integration.The reconstruction of the configurations without disassembly can be realized.The installation positions of drivers are used as the design basis for the reconfigurable 3-RPRP spherical parallel mechanism.Then,the positions of the drive pairs and the self-locking pairs in the RPRP limb are determined.At last,the structure of reconfigurable 3-RPRP spherical parallel mechanism is designed according to the type and sequence of combination of kinematic pairs of limbs.Secondly,the screw system and reciprocal screw system of different configurations of reconfigurable 3-RPRP spherical parallel mechanism are established based on screw theory.Then the common constraints and kinematic characteristics under different configurations of the reconfigurable 3-RPRP spherical parallel mechanism are obtained.The degree of freedom of the mechanism is calculated.Using the geometrical relationship of the mechanism as the constraint conditions,the mathematical model of the closed kinematics of the mechanism is established using rotation matrix.Then,three-dimensional dynamic solving method for solving the reachable workspace of reconfigurable spherical parallel mechanism is presented.Using the solving method,the reachable workspaces of reconfigurable 3-RPRP spherical parallel mechanisms are obtained.Based on the positive solutions of the mechanism and Matlab programming,the reachable workspaces of reconfigurable 3-RPRP spherical parallel mechanisms are also obtained.The results of the two methods are compared.The maximum error rate of their reachable workspace boundaries is 0.09%.The correctness of the proposed three-dimensional dynamic solving method is verified.The scale of the symmetrical 3-RPR spherical parallel mechanism is synthesized.Finally,the virtual prototype of reconfigurable 3-RPRP spherical parallel mechanism is established using SolidWorks software.According to the target trajectory,the kinematics and dynamics are simulated.The coupling relationship between input and output is analyzed.The reconfigurable spherical parallel mechanism designed in this paper realizes the rapid reconstruction of the various configurations,and enlarges the application scope of the mechanism and enhances the adaptability of the mechanism to the environment.The three-dimensional dynamic solving method has not only high accuracy and can be used in various types of parallel mechanisms.