Research On Error Analysis Of Planar And Spatial Parallel Mechanisms With Joint Clearance

Due to the friction and wear of the component,the machining precision and the assembly error,the joint clearance is unavoidable in the mechanism,which has a great influence on the motion performance of the mechanism.Based on the analysis method of clearance equivalent link,the uncertainty output error caused by joint clearance can be qualitatively analyzed and calculated quantitatively.Therefore,In view of the phenomenon of joint clearance in the mechanism,the paper point at a typical planar and spatial parallel mechanism,and research on the output error of the parallel mechanism considering the joint clearance.The following work has been done in this paper.1)Combined with the idea of equivalent linkage modeling,the joint clearance is simplified as a virtual link and a kinematic error model of a planar parallel mechanism is established.Based on the N-bar rotatability laws and the joint rotation space(JRS),the output error problem of the planar parallel mechanism is transformed into the problem of the mobility of the linkage mechanism.2)The output error of the planar single-loop parallel mechanism was studied.The 2-dof five-bar mechanism was used as the object.The kinematic error model was used to deeply study the output error under the influence of the joint clearance,and the precise error range was plotted.For the multi-loop parallel mechanism,based on the theory of full differential mechanism error analysis,the characteristics of the secondary rod group are introduced,and a modular method is used to study the output error of the mechanism,and the mathematical calculation is applied to the topology identification of the linkage mechanism.The expressions for solving the end displacement in the positive direction and the angle deviation in the reverse direction are expressed.The example of Planar 2-dof seven-bar parallel mechanism decomposition is applied to verify the effectiveness of the proposed method.3)For the planar 3-dof symmetric parallel mechanism,based on the Invariant link rotatability of the link mechanism,one of the joint clearance is separated from many factors that cause the error,so that all planar 3-RRR mechanisms are in the limit position error configuration.Based on the mobility criteria of single-loop n-bar chains with prismatic joints,two error models of moving pairs and rotating pairs are unified,and the topological configuration of the moving pair is studied.The maximum working space distribution of the mechanism in all directions is drawn by arbitrary actuation of the mechanism.4)Based on the principle of virtual displacement,the error of the spatial parallel mechanism under the influence of the auxiliary clearance is studied,and the output attitude error function is obtained.The kinematic error model is established for the different contact types of the space revolute pair,the spherical surface pair and the cylindrical pair.The maximum error of the output error of the three kinds of motion pairs is solved by the error function.Through the example of three degree of freedom Delta mechanism,the corresponding error area boundary value results are obtained.The paper has certain engineering practical significance for guiding the innovative design of the parallel mechanism and reasonably selecting the clearance value of the motion pair of the mechanism and making the error area within the safe and controllable error range.For the follow-up to reduce the error or compensation method to provide a theoretical basis.