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If the fixed links are defined．the information ofmechanisms will be established．the number of themechanisms will be certain，and the data of the links andkinematic Pairs will be alSO assigned to the relatedmechanisms．The models of mechanisms should beestablished at this time．In this section．a method of establishing models ofmechanisms automatically is presented． The methodprovides precondition for simulating multi-mechanismsmotion process at the same time in virtual assembly system．Amechanism should be considered to be surrounded bythe fixed links．SO the process of searching mechanisminformation(information of links and kinematic pairs)canstart from one fixed link to the others．shown in Fig．1． Fig．1．Process ofsearching the information ofmechanismThis process iS independent of the type of kinematic pair,and it only relates to whether there is a connection betweentwo components．Since the incidence matrix Can expressthe relations among the components，in this section，theincidence matrix eliminating element method which iS usedto obtain information of mechanisms and to calculate thenumber of mechanisms iS presented to establish the modelsof mechanisms automatically．First of all，the relatedelements and some signs are defined as follows： CHINESE JOURNAL OF MECHANICAL ENGINEERING ·75l·When a／j2 0，there IS not any connection betweencomponent i and componentJ．When a0-=缸component iand componentj are connected by kinematic pair k．If a“≠0，i andj are the related elements．For example，Eq．(6)shows that 2 and 3 are the related elements．Notions of some parameters are defined as follows．彳{}is the assembly which contains all the information oflinks and kinematic pairs，A{}=A{P{}，K{}}．There maybe notonly one mechanism in the assembly．尬{Pf{}，K{}}represents the mechanism i．尸{}=P{nl，n2，…，‰}represents all the numbers of n components．K{}=K{nl，疗2，…，珂Ⅲ}represents all the numbers of m kinematic pairs．只{}=Pi{行1，n2，…，‰}represents the numbers of thecomponents which belong to mechanism i，namely,therelated elements noted in the process of eliminatingelement，and尸《，zf)=nf．Ki{}=Ki{_，z1，n2，…，nf}representsthe numbers of kinematic pairs which belong to mechanismf，namely,the nonzero element in the matrix noted in theprocess ofeliminating element，and g,(ni)=ni．B{}=B{nl，n2，一o 9 nk}represents all the numbers of k fixed links，andB(ni)=ni．a(n)represents no operation of eliminatingelements in row n．火n)represents the operation ofeliminating elements in row n．The detailed roles are showninEq．(7)：f(n1=a巧=0，a和=0，￡{}=e／{…，n，／}，Kf{}=Kf{．一，anj}，anj≠0，矽(no operation)，anj2 0，(7)where anjis the first nonzero element in row n．For example，if the operation of eliminating elements inrow 2 in matrix shown in Fig．2(a)is done，the result willbe shown in Eq．(8)，and the new matrix is shown in Fig．2(b)：f(2)={a23=0，a32=0，a24=0，a42=0，
2，3，4}，K{}=墨{··o 91，2)}． (8)O 0O OO lO 2O O1 2O 33 O(a)Matrix beforeeliminating elements0 0O OO 00 OO 00 O0 33 O(b)Matrix after eliminatingelements irl row 2Fig．2．Process of eliminating elements in row 2The detailed rules of eliminating elements operation areas follows．Rule(1)：只(，z1)∈曰{}． (9)At the beginning of search，the row chosen first shouldcorrespond to one fixed link．Rule(2)：筠郴卜％=0'％=嗍㈨耽n硎=K咐 (10)At the beginning of searching mechanism f and eliminatingelements，the operation of eliminating elements An)is notdone to row n which the first element is in．Here only oneelement is noted in Pf{}；Pi{月l}，and the elementcorresponds to a fixed link according to rule(1)．Only thefirst nonzero element is set 0：the nonzero element is notedin K{}，and the related elements are noted in Pf{}．Rule(3)，The row n which贝以)operates in must correspond to thenon．fixed links．Rule(4)：， 七=1 I i=1 Jaz≠0’o∈曰{}，p仁B{})j黝． (12)If all the elements in the rows corresponding to thenon-fixed links in Pi{}are 0，the operation of searchingmechanism f is over；mechanism i consists of all theelements noted in K{}and the elements noted in Pi{}．Otherwise，An)continues operating in row n whichcorresponds to the non．fixed link and is nonzero elementsyet contained Pi{}．Rule(5)：喜[喜％]：o，cp叫纠删删同”： 肜l U鸩U…U鸭U曰． (13)If a11 the elements in the rows in B{}are 0，search is overand a11 the mechanisms are obtained．The process of search is displayed in Fig．3
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