Research On Positioning Error Of Planar 2R Open-loop And 5R Closed-loop Mechanisms With Joint Clearance

With the rapid development of high-technology,the requirements for mechanisms position precision are becoming higher and higher in the aerospace industry,precision machinery,medical equipment,industrial automation and other industrial fields,especially for high speed,high precision and high reliability occasions,positioning precision is one of the important indicators to measure the performance of mechanisms.The joint clearance is easy to cause the collision,friction and wear between the moving pair elements,reducing the movement precision and the running stability of the mechanism s.Therefore,considering the joint clearance in the mechanical system,in this paper,the planar two degree of freedom 2R open-loop mechanism and 5R closed-loop mechanism are studied,to research the effect of joint clearance on the positioning error and dynamic characteristics of the mechanism from different aspects,and provided a theoretical basis for the reliability analysis and error compensation.This paper mainly includes the following contents:The kinematic error analysis model of planar 2R open-loop and 5R closed-loop mechanism has been established according to the planar mechanism of joint clearance under static action.The rotating joint is considered as a massless link,the end effector positioning error formulas in the two mechanisms have been derived using the geometric method.This paper has proposed error index as the evaluation index of mechanism positioning accuracy and gave the variation of positioning error of the end-effectors in the workspace using Matlab simulation.Considering the planar mechanism with joint clearance under static and inertia action,the dynamic error analysis models of planar 2R open-loop and 5R closed-loop mechanism considering joint clearance are established.The two mechanisms' static analysis has been carried out,then dynamic equations of two mechanisms has been established by the Newton-Euler method,the constraint force of each joint has been solved;establish joint local error model,the mapping relationship has been established between end-effector positioning error and the joint local error using the principle of virtual work.The distribution results of positioning error in the two mechanisms respectively under static and dynamic conditions in the configurational space using Matlab simulation analysis.Considering at the phenomenon of collision and friction between the pair elements caused by joint clearance,the vector model and mathematical model of rotating joint clearance have been established.Then the collision model and friction force model have introduced.The dynamic models of planar 2R open-loop and 5R closed-loop mechanisms with joint clearance have been established using the Lagrange multiplier method.This paper has researched the influence of different sizes of joint clearance and joint rotational speeds on the dynamic characteristics of the two mechanisms by Matlab simulation.The effect of joint clearance and rotational speed on the motion accuracy of the two mechanis ms are analyzed with the position and the velocity error reliability index.