Research Of Hybrid-driven Planar3-DOF PRR-PRR Six-bar Mechanism

Hybrid-driven planar3-DOF parallel mechanism is a kind of new mechanisms, whichnot only has the characteristics of hybrid-driven mechanism’s controllable, flexible, highprecision operation, but also has the advantages of parallel mechanism’s high stiffness, strongloading capacity, and fast speed. It could better adapt to the requirements of modernmechanical products to high speed, precise, flexible and diversified development. As a newresearch field, however, the understanding and research on such mechanisms was notthorough. Presently, research on hybrid-driven planar3-DOF mechanism mainly focuses onthe symmetric structure or symmetric driving moving platform, Research on asymmetrichybrid-driven3-DOF mechanism is less. A novel planar3-DOF PRR-RRP parallelmechanism was researched in this paper. Based on configuration analysis of hybrid-drivenplanar3-DOF six-bar mechanism, this paper paid an in-depth study to crank existenceconditions, kinematics, workspace, the structure size optimization, path generation methods,dynamics and dynamic balance of hybrid-driven planar3-DOF PRR-RRP six-bar mechanism.The main work is as follows:Firstly, the configuration analysis of planar3-DOF six-bar mechanism was carried on.The only assembly configuration of planar3-DOF six-bar linkage is obtained based on graphtheory and Assur bar group method. Thirteen kinds of planar3-DOF six-bar mechanismkinematic chain were achieved by kinematic pair substitution, and nine mechanism graphs ofthree kinds of the kinematic chain were given, which was easy to apply. According to thecharacteristics of the hybrid-driven and nine mechanism graphs own characteristic, PRR-RRPsix-bar mechanism became the final research object.Secondly,3-DOF PRR-RRP planar six-bar mechanism is taken as a virtual four-bar chain with variable length links by using virtual link equivalent method. The relationship betweenthe crank existence condition of a four-bar chain and the link lengths of the mechanism wasanalyzed based on the Grashof theorem. According to the law of the mechanism’s assembility,the crank existence conditions are obtained under the different relationship among linklengths. The results are the basis of the design and optimization, the calculation for theworkspace, the analysis of the kinematics dynamics about the planar3-DOF PRR-RRPsix-bar mechanism.Thirdly, the positive and inverse kinematics mathematical model is establishedrespectively by using the method of vector loop method. According to the kinematicsmathematical model and structural constraint characteristics of hybrid-driven PRR-RRPsix-bar mechanism, the size of each link of this mechanism was optimized. Based onPRR-RRP six-bar mechanism kinematic positive solutions and optimization results,workspace equation was obtained. The workspace and dexterous workspace of PRR-RRPsix-bar platform centre could be solved by Matlab software with the definition of theworkspace and limited dexterous workspace. The workspace covered all areas between thetwo guide rails. Limited flexible workspace was in the two guide rail, where the platformcould arrive with a flexible attitude. Then taking “PRR-RRP six-bar work platform centregenerated ellipse curve” as an example, the simulation of six-bar mechanism kinematicscharacteristics was carried on. The change rules of velocity, acceleration, angular velocity andangular velocity were obtained in this simulation. The results showed that the planar six-barwork platform finished the ellipse curve with a smooth velocity, small fluctuation and uniformangular velocity. It possessed good kinematics characteristics. Good kinematic characteristicsof PRR-RRP six-bar mechanism provided reference to practical application.Fourthly, the PRR-RRP six-bar work platform was used to generate cardioids’ path(mathematics) and inspection. At first, through the inverse kinematics model, the regulationsof three drivers were solved by Matlab software，when the cardioids path was achieved. Then,the approximate mathematical functions of drivers were obtained by Matlab curve fitting tothe regulations of three drivers; At last, Substituted the drive regulations into Pro/E software and simulate, the result is reasonable.Finally, dynamics mathematical model of six-bar mechanism was established by themethod of Lagrange, and used the mass balance method to optimize the dynamiccharacteristics of PRR-RRP six-bar linkage. Firstly, the inertial force of links of six-barmechanism was analyzed. Then, the Equivalent moment of inertia of rotating links wouldreduce by balancing the mass of six-bar mechanism to the slide connecting to the guide rail, toimprove the dynamic characteristics of six-bar mechanism. Finally, the simulation ofdynamics characteristics of each joint and drive, before and after the balance, was carried on.Comparison results showed that mass balance made the force and torque of each joint anddrives greatly reduced and smooth. Dynamic characteristics were improved obviously.