Singularity Analysis And Investigation On Avoiding Singularity Method For Parallel Mechanisms

Parallel mechanism has the advantages of high structrual stiffness, highload-bearing capacity, and higher control precision, which meets the needs ofindustrial automatization.Now it has been widely used in the area of aeronautics,mechanical manufacturing, industrial robot and etc.The kinematic singularity, namely,the output movement of the mechanism is uncertain due to kenematic bifurcation atthe singular position, is the intrinsic characteristic of parallel mechanism, and this hasattracted the attention of the robotics researchers in the world.How to control themechanism to pass through the singular position with its given configuration is thekey problem for parallem mechanism.In this paper, using singularity theory, theauthor has investigated the approach of avoiding singularity at the singular positionfor parallem mechanisms, and solved the key problem that parallel mechanisms couldpass through the boundary singular position with its given configuration.The authoralso studied the relationship between the singularity and the parameters of parallelmechanisms and presented a method of improving the singularity.The mainachievements are as follows:Singularity has been studied in complex number field for the first time.Takingthe Watt linkage as an example, the singularity for multi-loop mechanism isresearched.The bifurcation equation in complex number field has visual property, andcan be easily transformed into germ field.On the basis of the multi-solution of thebifurcation equation, the singularity theory is applied to analyze the singularconfigurations and bifurcation characteristic connecting with the structural parametersof mechanisms.The bifurcation equation of Stewart parallel mechanism is established foranalyzing its bifurcation characteristic based on the singularity theory.The Jacobinmatrix is used to identify the singular points, and the static bifurcation condition isused to identify the bifurcation points.The partial differential of the bifurcationequation is applied to analyze its bifurcation characteristic at a bifurcation point.The conception of configuration transforming coefficient is presented in order to revealthe principle of the configuration transforming in the neighborhood of a singularposition.Therefore, it establishes theoretical basis for controlling the movement ofparallel mechanism and for avoiding the turning bifurcation point on the base of theunfolding theory.Numerical method is applied to study the complex singularity for symmetrical6-Dof Stewart parallel mechanisms with multi-parameters bifurcation.Six inputparameters can be selected as the bifurcation parameters.Different composition of thebifurcation parameters would lead to different bifurcation phenomena.Eight cases areobtained for symmetrical Stewart parallel mechanisms with multi-parametersbifurcation.The corresponding singularity and bifurcation characteristics of theparallel mechanisms are investigated, respectively.The results verify the singularconfigurations presented in other literature and also give some new singularconfigurations for Stewart parallel mechanisms.The relationship between the composition of parallel mechanisms and itssingularity is studied for the first time.The key parameters of Stewart parallelmechanisms include: the radiuses R~1 and R~2 for the fixed base frame and themovable platform respectively, the actuators length l~i, and the anglesα~1andα~2these parameters' influence on bifurcation behavior has been disscussed, and themethod of selecting appropriate parameters is presented according to the workspaceand the singularity-free workspace, which can improve singularity of the movement.The method of avoiding the boundary singularity is investigated for the parallelmechanisms based on the singularity theory.The configuration bifurcationcharacteristic is analyzed at the bifurcation point.The problem of'avoiding boundarysingularity is divided into three instances to be researched based on the configurationafter passing through boundary singular position.Then three types of perturbationfunctions are constructed for these three instances.Therefore, the problem that theparallel mechanisms can pass through the boundary singular position with its givenconfiguration has been solved.Finally, the main creative achievements are presented and some of the openproblems in the field of Stewart mechanisms, which are likely to be research interest in the future, are recommended.