Analysis And Kinematic Performance Optimization Of 2R1T Parallel Mechanism Without Parasitic Motion

The 2R1 T parallel mechanism(PM)with two rotations and one translation is a typical low degree of freedom PM.2R1 T PM have become a research hotspot in the field of PM and mechanics due to its advantages of simple structure,strong load-bearing capacity,high precision,and easy control.As the most universal used mechanism of 2R1 T PMs,the 3-PRS PM has been widely used in industries such as automotive,aerospace,high-end equipment manufacturing,and rehabilitation medicine.The parasitic motions commonly presented in general 2R1 T PMs,which has a negative influence on motion accuracy and performances of mechanism.In order to obtain parallel mechanism without parasitic motions,this paper conducts research on key issues such as the judgment criteria for parasitic motions,attitude description methods,screw characterization of rotating axis,motion characteristic analysis,and performance evaluation,which has important academic value and guiding significance for the further application of parallel mechanisms without parasitic motions.The main research contents are as follows:A comparative study was conducted on three Euler angle description methods,Y-X-Z,ZY-Z,and KZ,respectively.Based on the characteristic results of different description methods,and the selection principles of description methods for parallel mechanism were established.Based on the position descriptions of the two rotating axes of the 2R1 T PM,a criterion for determining the existence of parasitic motions was established through the study of influence on the parasitic motions of the relative position relationship between the rotating axis and the moving platform.The conditions for the rotating axis of the 2R1 T PM without parasitic motions were obtained.On this basis,screw analysis was focused on the position of axis of pairs of the PRS branch chain,and the position relationship between the two rotating axes and the moving platform without parasitic motions was obtained,which will lay the foundation for the application and accompanying motion and kinematic analysis of the 3-PRS(P denotes a prismatic pair;R denotes a revolute pair;S denotes a spherical pair)PM without parasitic motions.By selecting the Y-X-Z Euler angle description method,the kinematic models of the 3-PRS PMs with two special branch and general branch arrangements were established.For the two 3-PRS PMs with special branch arrangements,the analytical expressions of parasitic motions under different structural constraints were solved,and the structural and motion parameters that affect the parasitic motions were obtained.Based on the conditions that there is no parasitic motions at the center point of the moving platform and the structural constraint equations,an expression for the 3-PRS PM without parasitic motions under general branch arrangement was established.The positional relationship between the three branch chains of the mechanism was analyzed,and the condition conclusion for the 3-PRS PM without parasitic motions under general branch arrangement was obtained which is the two branch planes are perpendicular to the other branch plane.The position relationship between the rotation axis and the moving platform of the 3-PRS PM without parasitic motions was characterized,and proved that this relationship meets the rotation axis condition of the 2R1 T PM without parasitic motions.Five types of 3-PRS PMs without parasitic motions were obtained through configuration topology.A kinematic model of a 3-PRRU(U denotes a universal joint)PM without parasitic motion was established on account of the Y-X-Z Euler angle description method.The particle swarm optimization algorithm was adopted to verify that the model of the kinematic was correct.The velocity Jacobian matrix of the mechanism was calculated by taking the derivative of the inverse solution,and a dexterity graph represented by local condition number indicators was drawn.In the process of evaluating the local condition number indicators for the dexterity of 3-PRRU mechanisms,the workspace discretization,influencing factors,limitations,and correction analysis were studied.Motion screw,constraint screw,force transfer screw and input/output transfer screw of the mechanism were solved,the local transfer index characterized by input/output transfer screws was defined.A motion/force transfer performance graph characterized by local transfer index was drawn,and the evaluation of the overall motion/force transfer performance of the mechanism was completed.The number of design parameter for the 3-PRRU PM without parasitic motion was optimized,and a parameter design space reflecting performance evaluation index was established.Global transmission index,good transmission index,and good transmission swing index were selected as the evaluation index for the workspace and the performance graphs they representative were drawn.By optimizing the values of design parameter,the optimal workspace was selected from the reachable workspace of the performance graph.A set of design parameters were determined in the optimal workspace,which was regarded as the result of kinematic optimization design.The workspaces of enter point and end effector of the optimized mechanism were solved,and a corresponding testing platform was established.The mechanism could meet the designed degrees of freedom of two rotations and one movement,as well as the range of swing angles.The singularity analysis of the optimized mechanism showed that its motion/force transfer performance had a significant improvement.The minimum value of local transfer index has been increased from 0.1941 to 0.4123,and the range of motion parameter?has been expanded from [-50°,50°] to [-57.3°,57.3°],while ψ has been expanded from [-85°,55°] to [-90°,60°].