Evaluation And Analysis Of Constraint Error Of Kinematic Synthesis Of Linkages

The subject of this dissertation comes from the National Natural Science Foundation NO.51705224.The purpose of kinematic synthesis is to design the corresponding mechanism,which complete given kinematic requirements.In essence,its purpose is to find the characteristic points in the moving rigid body whose trajectory is(approximate)standard constraint curve.For the accurate description of the deviation between the actual trajectory curve of the point and the constraint curve,the essence is the shape error evaluation of planar straightness and roundness,and spatial sphericity and cylindricity.On the other hand,it is necessary to analyze the evaluation error of each point in the moving rigid body,and then locate the characteristic points with the minimum evaluation error.The deviation between the point-trajectory and the constraint curve is evaluated by the saddle point programming,and the properties of the evaluation error are analyzed based on the saddle point theory.The dissertation is structured as follows:1.Firstly,the principle of least square method is introduced which is used to evaluate the shape error of plane and space curve.Taking roundness error as an example,there are problems such as the selection of appropriate solution method for the least square evaluation model.Different methods are adopted and the obtained results are analyzed under the conditions of different numbers and distributions of sampling points.The fitting effect and application range are determined for the three least squares methods.2.According to the theory of saddle point programming,the mathematical model is built to evaluate the shape error under the principle of the minimax metric.At the same time,the number and distribution of the feature points are studied when the minimum condition is satisfied.Based on the minimum condition,the evaluation errors of the discretized pointtrajectory and the standard curves based on the minimum area method are described.3.Based on the method of minimum area evaluation,the properties of the evaluation errors of all points in the rigid body are studied.Especially,the evolution of the error surface is revealed when the given positions of the rigid body are increased.The error distribution is demonstrated by the error contour map in the moving body.Based on the characteristic region of the contour map of the saddle line and saddle circle error,the distribution law and extremum characteristic of the evaluation error are studied.The related solving algorithm is introduced,and the numerical example is given to verify the algorithm.4.The software system for evaluating and analyzing the errors between discretized point-trajectories and standard constraint curves is established.The design idea and function modules of the system are described in detail.The GUI tool in MATLAB is used to complete the interactive interface design of the system.Finally,the system is tested through numerical examples,and the results verify the efficiency and accuracy of the system.