Comprehensive Constraint Error Assessment And Extreme Value Characterization Of Mechanism Synthesis

The purpose of the mechanism motion synthesis is to design the corresponding mechanism according to the given motion requirements,its essence is to find the trajectory on the motion rigid body for the(approximate)normative curve and surface of the point or line,and in essence is the plane(circularity and straightness)and space(sphericity,spherical like circularity and cylindricity)constraint curve and surface error assessment problem.In error assessment,the minimum zone assessment criterion ensures the best uniform approximation,but the current mathematical model based on the minimum zone method and the corresponding solution method have problems such as tortuous solution process and local convergence.In addition,for the plane linkage mechanism,the essence of its motion synthesis is to find the extreme value points on the moving rigid body that satisfy the discrete trajectory as the(approximate)canonical curve.By analyzing the characteristics of the extreme value points on the moving rigid body,the characteristics of the extreme value points in the feasible domain under the constraints of the mechanism motion synthesis need to be studied.To address the above problems,this paper finds the optimal solutions for the approximation errors of trajectory curves and surfaces with canonical curves and surfaces satisfying the minimum zone evaluation criteria based on the idea of saddle point planning,and explores the extreme value characteristics of the points in the feasible domain under the constraints of the mechanism motion synthesis,which is then applied to the motion synthesis of planar and spatial linkage mechanisms.The main contents are as follows:Firstly,based on the extreme value condition of optimization theory,the minimum condition of plane trajectory curve corresponding to saddle circle and saddle line is constructed,which reveals the distribution law of feature points,and the optimal solution of roundness and straightness error can be obtained only by simple geometric analysis and algebraic operation,and it can effectively prevent the problems caused by optimization search.Additionally,according to the minimum conditions of saddle circle and saddle line,the positioning equation and the feasibility condition equation are derived,and thus the unified solution model of saddle circle and saddle line is established,and the minimum zone evaluation of the plane trajectory curve error is realized.Secondly,according to the solution model of saddle circle and saddle line,the characteristic position area corresponding to the trajectory curve saddle circle and saddle line error evaluation characteristic point of the point on the rigid body plane is obtained,and the characteristics of the extreme value point of the error on the rigid body plane are studied according to the characteristic position area.Further,based on this,the characteristics of the error extremum points in the feasible domain under the comprehensive constraints of the mechanism motion are analyzed and verified by the data.Then,the evaluation model for evaluating the error of spatial trajectory curve(saddle sphere)and trajectory surface(saddle spherical like circle and saddle girdle cylindrical surface)is established,and the distribution law of characteristic points is revealed,and the optimal solution of sphericity and spherical like circle error can be obtained by simple geometric analysis and algebraic operation.In addition,based on the distribution law of the characteristic points of the cylindrical surface of the saddle girdle,the geometric evaluation and the area search are combined for the evaluation of the cylindricity error,and the influence of the initial distribution position and the initial value of optimization on the optimization results can be effectively overcome by the coordinate projection transformation,and the minimum area evaluation of the spatial trajectory curve and surface error can be realized by giving multiple sets of examples.Finally,Matlab is used to create the trajectory curve and surface error evaluation system of points or lines on the rigid body in plane and space motion to analyze the telescopic arm mechanism of the trolley machine,and transform the telescopic arm motion synthesis problem into the synthesis of two-parallel rod R-R.Based on the minimum condition of the saddle circle and the characteristics of the extreme value point of the saddle circle error on the rigid body in plane,the error evaluation system is used to obtain the parameters of the telescopic arm mechanism of the trolley machine,and the kinematic simulation and the above optimization synthesis results are compared by Solidworks to prove the accuracy of the optimization results.