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The Method For Automatically Establishing And Solving Mathematical Model Of Kinematic Analysis To Planar Mechanisms With Multiple Joints And Prismatic Pairs

Posted on:2013-02-06Degree:MasterType:Thesis
Country:ChinaCandidate:A H LiaoFull Text:PDF
GTID:2252330401950711Subject:Mechanical engineering
Abstract/Summary:PDF Full Text Request
The purpose of structural type optimize of kinematic synthesis of mechanism is to selectthe mechanism which can realize the objective movement best from many mechanisms ofdifferent structure types. The kinematic analysis is a necessary step in kinematic synthesis ofmechanism. So the kinematic analysis must be carried out for mechanisms before thekinematic synthesis. On the basis of former researches, planar kinematic chains with multiplejoints and prismatic pairs are taken as the research object in this paper. And the method forautomatically establishing and solving the mathematical model of kinematic analysis to thosekinematic chains is discussed. The main works are as follows:Based on connective relations between each links in the component adjacency matrix,the breadth first spanning tree can be got easy and basic loops are obtained from it. Then themathematical model-loop equation for kinematic analysis is generated. This method issystematic. In the sense of mechanism, this method makes the topological structure ofkinematic chains get in touch with the kinematic analysis. Then, according to thecharacteristics of prismatic pairs’ movement, sections with prismatic pairs in the basic loopsare assorted. And a method is put forward to treat those sections. At the same time thecorresponding changing formulas are listed to ensure that the method can eventually unify thekinematic characteristics of prismatic pairs and joints. It is beneficial to automaticallygenerate the mathematical model of kinematic analysis in computer.Taking the C++language and the Matlab software as a development tool, it is discussedthat how to carry out the method which is for automatically establishing the mathematicmodel of the kinematic analysis to planar kinematic chains with prismatic pairs and multiplejoints in the computer. On the basis of the adjacency table, the storage structure of breadthfirst spanning trees is improved and the storage structure of loop elements is defined. They arethe basis of spanning loops. And aimed at the characteristics of prismatic pairs and multiplejoints, the method of judging and gaining offset steering angles and structural angles isinvestigated to combine the elements of loop equations in the M file of loops. Then it isdiscussed that how to generate the M file of the main program and the logical relationship ofthe various modules in kinematic analyzing program is explored. Last, a researcher is workout on how to each other between the C++language and the Matlab software.Because the initial value is difficult to choose for nonlinear equations-position equations,a method of selecting initial values based on concepts of group and fitness is put forward.Founded on the random test method of the interval searching method for initial points and combining the characteristics of intervals, this method use the computer to automaticallygenerate pseudo random numbers according to the uniform distribution. Then the initialgroups are got and they are filtered through the fitness function to gain the most appropriateinitial value. Considering the advantages of the Matlab software, the Fsolve function ischosen as the solving tool for the position equation so as to avoid the phenomenon of noresult or inaccuracy result because of local convergence when the position equation is beingsolving.
Keywords/Search Tags:Multiple joint, Prismatic pair, Planar kinematic chain, Kinematic analysis, Automatic modeling
PDF Full Text Request
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