| With a large payload,high stiffness,compact structure,and a high degree of modularity,lower-mobility parallel mechanisms are widely used in hybrid machine tools and robots.In the 2UPR-RPU over-constrained parallel mechanism,some geometric error sources cause non-compensable pose errors of the end moving platform and deformations of the limbs.Deformations will cause the mechanism to be blocked or even stuck and unable to move.To restrict the range of the corresponding geometric error sources,this thesis research the accuracy design of this mechanism.The research results are of great significance for improving the pose accuracy of the end moving platform and motion of the 2UPR-RPU and 2UPR-RPU like lower-mobility over-constrained parallel mechanisms and promoting the application of these parallel mechanisms in the field of machining.Firstly,the constraint forces and couples that the 3 limbs exert on the moving platform are analyzed according to the screw theory.Then,the limbs’ nominal inverse kinematics formula and actual forward kinematics formula including 71 geometric error sources are derived.On this basis,an iterative model is established to evaluate the limbs’ average comprehensive deformations.Based on the iterative model,41 geometric error sources causing deformations are identified and a sensitivity analysis is conducted on them using the Monte Carlo method.The result of the sensitivity analysis indicates that the identified geometric error sources of the two UPR limbs are the same;The identified geometric error sources have greater effects on the average linear comprehensive deformation,which means that the distribution of the global sensitivity index of the average linear comprehensive deformation is more meaningful for restricting the geometric error sources causing deformations.Based on the above work,an accuracy design approach considering limb deformation is proposed and is applied to the 2UPR-RPU over-constrained parallel mechanism.Firstly,by using the approach based on the screw theory,the limbs’ geometric error models are established.Projecting the geometric error models towards the constraint force and couple directions,47 non-compensable geometric error sources affecting the limbs’ noncompensable end pose errors are distinguished.It indicates that the non-compensable geometric error sources of the two UPR limbs are the same;The geometric error sources causing deformations belong to the non-compensable ones.Next,based on the geometric error models and the 3σ principle,the models between the upper limits of the limbs’ noncompensable end pose errors and the non-compensable geometric error sources are established.On this basis,the accuracy prediction is conducted on the first UPR limb and the RPU limb.According to the prediction result,several target poses are selected from the 2UPR-RPU parallel mechanism’s reachable workspace.Taking the upper limits of the non-compensable geometric error sources as the design variables,the minimum manufacturing cost as the target,the non-compensable end pose errors at the selected target poses meeting the accuracy requirement as the constraint condition,the optimization models for accuracy synthesis of the first UPR limb and the RPU limb are established.With the aid of the genetic algorithm,the upper limits of the noncompensable geometric error sources of the first UPR limb and the RPU limb are determined.Then,the upper limits of the non-compensable geometric error sources of the second UPR limb are determined according to that of the first UPR limb.On this basis,the allowable range of geometric errors causing deformations is adjusted according to the limbs’ comprehensive deformations and the global sensitivity index of the average linear comprehensive deformation.Simulations based on Monte Carlo are conducted to validate the effectiveness of the accuracy design approach.The results of the simulations indicate that the probability is99.77% where the moving platform’s non-compensable orientation errors are in [-0.1 °,0.1 °];The probabilities are 99.37% and 99.83% where the moving platform’s noncompensable position errors that along constraint force directions of the UPR limb and the RPU limb are in [-0.1 mm,0.1 mm];The probability is 99.83% where the limbs’ average angular comprehensive deformations are in [0 °,0.06 °];The probability is 99.94%where the limbs’ average linear comprehensive deformations are in [0 mm,0.23 mm].Finally,by the method of SDT(small displacement torsor),the upper limits of the noncompensable geometric error sources are converted to the tolerances of fabrication and assembly of components. |
