Research On Synthesis Theory And Method Of Spatial Linkages Based On Solution Region

This research mainly studies on the synthesis of spatial 4C,RCCC,HCCC linkages with four given poses and discussed the synthesis theory and mehod of the spatial linkages.C stands cylindrical joint;R stands revolute joint;H stands Helical joint.These spatial four-bar linkages mentioned above are the foundation of spatial linkages,therefore,the methods,results and conclusion in this research can be expand to other spatial linkages.Spatial linkages have many advantages,such as easy to control,low cost,and they can achieve complicated spatial motions.Therefore,research on spatial linkages have theoretical and practical significances.This research studies on the synthesis of the spatial four-bar linkages mentioned above based on the solution region methodology.The main contents are outlined below:(1)Synthesis of spatial 4C linkageThis part of work synthesizes 4C linkages based on the solution region methodology that is an extension of the synthesis of spherical 4R linkages.Firstly,a spherical 4R linkage solution region is built based on the spherical Burmester theory,some properties of linkages can be displayed on the solution region,such as mechanism type,circuit defect,and branch defect.Then,a solution line formulation is proposed for set up a spatial 4C linkage solution region,the motion type of the cylindrical joint on 4C linkages’ driving link can be displayed on the solution region.The example in this thesis verifies the correction and effective of the method.(2)Synthesis of spatial RCCC linkageThree methods are proposed for the synthesis of spatial RCCC linkages with four given poses.For these three methods,the way of building solution region are same.The first method is to synthesize RCCC linkage through a spatial 4C linkage solution region,the process of the synthesis is similar to the synthesis of spatial 4C linkage.Firstly,a spherical 4R linkage solution region is built.Then,a spatial 4C linkage solution region is built.A linkage solution can be found on the solution region which driving link’s C joint has no sliding displacement through the four poses.All RCCC linkages obtained are put into the designate plane to establish an RCCC linkage solution region.The example in this thesis verifies the correction of the method.The second method synthesizes RCCC linkages based on the constraints of RCCC linkages.The problem is converted to a problem of solving high-degree equations.The RCCC linkage is usually synthesized via its two defining dyads,RC and CC.For the four poses problem,there are double infinite solutions of the CC dyad,but there is no solution for the RC dyad.This work combines the constrain equation of RC dyad and CC dyad,then solving the constrain equations of RCCC linkages directly.The high-degree equations are solved by the homotopy method.Finally,an RCCC linkage solution region is built.The example illustrates the method is also effective.Finally,the third method is proposed for synthesizing RCCC linkages with four given poses based on a discriminant.The first step is to set up a spherical 4R linkage solution region and all potential solutions that meet the four given orientations can be obtained.The second step is to solve remaining equations to obtain a discriminant.Finally,all potential solutions are substituted into the discriminant to determine if the solution is a RCCC linkage solution.The solutions of RCCC linkage are displayed on a map.The example indicates that the method is effective with short calculation time,has theoretical significance and has important academic value.(3)Synthesis of spatial HCCC linkageThis work proposes a HCCC linkage synthesis theory and methodology for four specified poses.The synthesis process is divided into two parts.The first part determines the direction vectors of the linkages,the second part determines the position vectors of the linkages.In the second part,the synthesis equations are deduced.Finally,a 7th degree equation is obtained.Using this equation,all the HCCC linkage solutions can be obtained.These solutions can be displayed in a designated plane area.The plane area is called solution region.The example indicates that the method is effective,has theoretical significance.Therefore,the method has important academic value and practical value.(4)Software development for mechanism synthesisThe software systems of spatial linkages synthesis are designed and developed by employing a mixed programming method of Visual C++,Matlab and OpenGL,based on the proposed synthesis theory and method.Software systems of linkages synthesis can be used to complete the illustrations,which show the validity and feasibility of the proposed linkages synthesis theory and method of this paper.