| In this paper,the hot issues in the field of the complex linkage analysis,such as the position analysis,the determination of singular configuration points,the determination of circuits and branches and the existence condition of crank,are studied deeply and systematically,and a systematic,normative and universal methodology is presented for these problems.Based on the proposed methodology,the visualization software for complex linkage analysis is developed.After the full study of complex linkages analysis,the solution region methodology for path synthesis of four-bar linkages and five-position synthesis of Stephenson Ⅱ six-bar linkages are proposed.The main research contents of the dissertation are as follows:(1)Giving two methods for the position analysis of complex Assur Groups.Method 1:The hybrid method for complex Assur GroupsThe hybrid method refers to using the position analysis polynomial of complex Assur Groups to determine all the position solutions of an external link,and then decomposing the remaining part of the complex Assur Groups into simple two-bar groups whose positions can be determined directly.After the positions of two-bar groups are determined,the positions of the complex Assur Groups are determined.In this paper,the position analysis loop equations of all two four-bar Assur Groups and ten six-bar Assur Groups are built,and the equations are simplified into a highorder polynomial respect to the position angle of an external link.After the position angles of an external link are obtained,four-bar Assur Groups can be split into a two-bar group and a single link,and six-bar Assur Groups(except the six-bar group X)can be split into two two-bar groups and a single link.Then positions of the complex Assur Groups can be determined by solving the positions of the two-bar groups.After the position angles of two external link are determined,the six-bar group X can be split into a two-bar group and a link.This article presents the method of splitting all the two four-bar Assur Groups,ten six-bar Assur Groups and one eight-bar Assur Group into two-bar groups in the form of examples and diagrams.Method 2:Solving the equations of position analysis using BertiniIn chapter 3,the positions of complex Assur groups are determined through solving the position analysis equations directly using the open source numerical solution software Bertini developed based on the numerical continuous method.This paper introduces the instruction manual of Bertini in detail and the problems encountered when using Bertini to solving the position analysis equations.The method using Bertini and the hybrid method for position analysis are compared in detail,and the applicable objects of the two methods are given respectively.(2)Determination of singular configuration points of complex Assur GroupsIn chapter 4,the collinearity of the three instantaneous center points constituting the virtual two-bar group when the complex Assur group is at the singular configuration points is transformed into that the three lines that determine the three instantaneous center points intersect at one point,thus a new discriminant with compact structure and uniform form is deduced for the determination of singular configuration points for complex Assur Groups.The expressions of each element in the discriminants of all two four-bar groups,ten six-bar groups and one eight-bar group are given in the form of examples and diagrams.The expressions of the elements in discriminants are only related to the coordinates of the joints in the Asuur groups,and these coordinates can be obtained directly in the process of position analysis.(3)Determination of circuits and branches of complex linkages composed of complex Assur GroupsIn chapter 5,different angles of the driving link of the linkage are continuously given from 0° to 360°,then the range of the driving link can be determined using the position analysis method proposed,and the locations and number of all singular configuration points of the linkage can be obtained using the determination method of singular configurations proposed in this paper.Then singular configuration points are taken as the starting points to launch the continuity analysis of all the discrete position solutions obtained in the position analysis process to obtain the angular displacement curves of the linkage.After the continuity analysis is completed,the circuit and branch of all discrete position solutions are determined.Numerical examples are presented to demonstrate the correctness,feasibility and universality of the method.(4)Existence conditions of the crank for complex linkagesA method for judging whether complex linkages have cranks through the comparative study of the number of singular configuration points and the total number of branches and circuits of the linkage is presented in chapter 5.That is,when the number of singular configuration points of the linkage is equal to the total number of branches,the linkage has no crank.When the number of singular configuration points of the linkage is less than the total number of branches,it means that at least one circuit of the linkage has a crank.(5)Study on solution region method for multi-point path synthesis of four-bar linakgesIn chapter 6,the exact point path synthesis of four-bar linkeges is studied based on the solution region synthesis method.Firstly,the mathematical model of path synthesis for four-bar linkages is established,and the nonlinear equations of path synthesis are solved by the software Bertini.Taking the nine-,eight-and sevenpoints path synthesis of four-bar linkages as examples,the method and process of building the solution region are introduced in detail,and a detection method for four-bar linkages with circuit defects and branch defects is given.The correctness and effectiveness of the method and the feasibility of the solution region synthesis method in path synthesis are demonstrated by the numerical examples.(6)Study on solution region method for five-position synthesis of six-bar linakgesIn chapter 7,we study the five-position synthesis of six-bar linkages composed of the four-bar group Ⅱ based on the solution region synthesis method,and give a universal and effective method to detect the defective linkages for complex linkages.Firstly,five-position synthesis equations of the Stephenson Ⅱ six-bar linkage are established,then the equations are solved using the software Bertini.Through a numerical example,the establishment process of the solution region and the determination method of defective linkages for complex six-bar linkages are elaborated,and the correctness and effectiveness of the determination method of defective linkages are proved.Finally,the feasible solution region of the fiveposition synthesis for six-bar linkages is obtained.(7)Development of the visualization software for planar linkage analysis and synthesisAccording to the achievements of the planar linkage analysis and synthesis theory in the paper,based on MFC visual program framework and OpenGL,an easy-to-use software for planar linkage analysis and synthesis is developed,which integrates visualization,parameterization and motion simulation functions.The software provides effective methods and tools for the analysis and synthesis of planar linkages. |
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