Research On The Performance Of Planar 3DOF Parallel Mechanisms With Joint Clearances

With the development of modern manufacturing technology,mechanical system requires higher efficiency, higher precision and longer service life. Among the numerous factors that influencing the performance of the mechanical system, joint clearance has become one of the key issues to be solved, both at home and abroad in the field of mechanical engineering. Joint clearance is unavoidable in real mechanisms, and its size will be larger with long time running of the mechanism. The moving accuracy, dynamics performance and the stability of the system will be highly influenced by the joint clearance. Parallel mechanism has the advantages of high stiffness, high positioning accuracy and good dynamical performance, but these advantages failed to fully exhibit because of the existence of joint clearance. Therefore, it has important theoretical value and practical guiding significance to study the performance of the parallel mechanism with joint clearance. In this paper, A planar 3-RRR parallel mechanism with joint clearances is studied, its kinematical and dynamical characteristics are systematically analyzed. Based on these analysis, the joint clearance is restrained by using the redundantly actuated mechanism, experiments are also carried out. This paper mainly concludes the following aspects:The positioning errors of the mechanism caused by joint clearance are studied. six joint clearances of the planar 3-RRR parallel mechanism are taken into consideration, and they are simplified as virtual links. Based on the kinematic constraint equations of the system, the transmission equation of the joint and positioning error is derived, which is a linear relationship. The distribution of the maximum error in the working space is then drawn out, which reveals the relationship between the error distribution and the condition number of Jacobin matrix.Dynamics of the rigid 3-RRRmechanism with joint clearances is then studied. The reference point coordinates are used to establish the dynamics equations of the system, which is expandable and easy to take the contact forces of joint clearances into consideration. Full geometric description of the joint clearance are given, contact force, friction force and lubricate force are considered. The two-step Bathe integration strategy is applied to solve the equations. Results show that the dynamics of the mechanism are greatly influenced by the joint clearances, the contact force is enlarged and the stability of the system isreduced.In order to better understand the performance of the 3-RRR mechanism, the influences of ten different factors on the dynamic performances of the 3-RRR mechanism with joint clearances are analyzed. That is, the joint clearance size, the joint clearance distribution, the joint clearance number, the Young’s module, the restitution coefficient, the friction coefficient, the lubrication, the moving trajectory, the moving velocity and the external load. the acceleration of the moving platform is used as the evaluation index to quantitative analysis the influence of different parameters, which shows that the joint clearance size, the friction and the velocity have the biggest influence on the dynamics of the system.Elastodynamics of the 3-RRRmechanism with joint clearances is studied, in which the driving link is treated as rigid while the positive link is treated as flexible. In order to reduce the system coordinates, the rigid link is described by Nature Coordinates while the flexible link is described by the Absolute Nodal Coordinate Formulation, thus they can share the same coordinates. Moreover, the deep groove ball bearing is considered with clearance, its full geometry descriptions and contact force models are given. Comparisons are made between the dynamics of the systems with rigid links and with flexible links.Based on the analysis of the 3-RRR mechanism with joint clearances, a strategy is proposed to restrain the joint clearances, that is, using the redundantly actuated 4-RRR mechanism instead of the fully actuated one. The mechanism can be statically balanced by preload, the joint clearance is equivalent to the passive link. Moreover, the driving forces of the redundant 4-RRR mechanism is optimized in order to ensure the driving force directions remain unchanged. Results show that the kinematics and dynamics of the system are improved by the restrain the clearance by preload.Finally, experiments are carried out on a 4-RRR mechanism. Positioning errors of the mechanisms with and without clearance restraints are measured and compared,which show that the errors are greatly reduced by preload. After that, the positioning accuracy of the mechanism are improved by error compensation.The experimental results verified the effectiveness of the clearance restraints strategy.