Isomorphism In Kinematic Chains

Transcription

1 Intrntonl Journl o Rsr n Ennrn n Sn (IJRES) ISSN (Onln): 0-, ISSN (Prnt): 0- Volum Issu ǁ My. 0 ǁ PP.0- Isomorpsm In Knmt Cns Dr.Al Hsn Asstt.Prossor, Dprtmnt o Mnl Ennrn, F/O- Ennrn & Tnoloy, Jm Mll Islm Unvrsty, Dl-00,In, ABSTRACT :T prsnt work ls wt t prolm o tton o somorpsm w s rquntly nountr n struturl syntss o knmt ns. A nw mto s on tort ppro, sy to omput n rll s sust n ts ppr. It s pl o ttn somorpsm n ll typs o plnr knmt ns. I. INTRODUCTION Ovr t pst svrl yrs mu work s n rport n t ltrtur on t struturl nlyss n syntss o mnsms [-]. Motvs n ts stus rn rom t sr or n orrly lsston systm, to stus o mnsm r o rom to t op o ntyn t mnsms. Mtos or t ronton n ntton o vn mnsm s knmt strutur n v nto two mn tors, rpl mtos s on t vsul nspton o vrous orms o smpl systmt rms n numrl mtos mny o w r s on t tory o rps. Howvr, vn wt t urrnt numrl mtos no nt nrlz mto s known w wll rtrz t vn mnsms y nspton. In ts ppr, nw mto to tt somorpsm n mnsms knmt ns s prsnt y omprn t sum o solut polynoml ont vlus [JJMP ] n mxmum solut polynoml ont [JJMPmx] o Jont-Jont [JJM]mtrx. II. PROPOSED TEST-BASIS T knmt ns r omplx ns o omnton o nry, trnry n otr r orr lnks. Ts lnks r on totr y smpl pn onts. It s t ssmly o lnk/pr omnton to orm on or mor los ruts. Wl onsrn struturl quvln t s ssntl to onsr typ o lnks/onts n lyout o t lnks n t ssmly. An ntton numr s ssn to lnks. Tus nry lnk s vlu o two, trnry tr, qurtr nry our n so on. Lnk vlus r us to ssn vlus to [JJM] mtrx n ts r utlz to nty lyout o t knmt ns. For ttn somorpsm n knmt ns [JJM] mtrx s trmn n rtrst polynomls [JJMP], ompost struturl nvrnts [JJMP ] n [JJMPmx] o [JJM] mtrx r ompr. III. THE JOINT-JOINT [JJM] MATRIX. On possl symolsm or t topoloy or onntvty o knmt n s t lnk-lnk orm o t nn mtrx, mor proprly rrr to s t Jont-Jont [JJM] mtrx. On t onts o t n v n numr rom to n, t [JJM] mtrx s n s squr mtrx o t orr n, row n olumn rprsntn t ont wt t orrsponn numr. T lmnts o t mtrx r tn ntr s tr zro or typ o t lnk, pnn on t sn or prsn o rt knmt onnton twn t onts orrsponn to tt row n olumn. J = = Dr o lnk or typ o lnk, ont s rtly onnt to ont =0, ont s not rtly onnt to ont () IV. STRUCTURAL INVARIANTS [JJMP ] n [JJMPmx] Polynoml ont vlus r t rtrst nvrnts or t ns n mnsms. Mny nvsttors v rport o-sptrl rp (non-somorp rp vn sm n sptrum). But ts n sptr (n vlus or polynoml ont vlus) v n trmn rom (0, ) ny mtrs. T propos [JJM] mtrx provs sm st o polynomls o t o-sptrl knmt rp. To mk ts [JJM] mtrx polynoml sptrum s powrul snl numr rtrst nx, nw ompost P

2 Isomorpsm In Knmt Cns nvrnts r propos. Ts ns r [JJMP ] n [JJMPmx] o [JJM] mtrx. T polynoml vlus o [JJM] mtrx r otn usn MATLAB. It s op tt ts nvrnts r pl o rtrzn ll knmt ns n mnsms unquly. V. ISOMORPHISM Two s knmt ns wll somorp n only, ot t ompost nvrnts [JJMP ] n [JJMPmx] r ntl rsptvly. I ny st o struturl nvrnts o on mtrx o n os not mt t orrsponn st o struturl nvrnt o t otr n, t two ns wll non-somorp. In otr wors, t two s knmt ns wll somorp n only t rtrst polynoml qutons r ntl otr ws non-somorp. Torm: Two knmt ns r somorp to otr, v ntl rtrst polynomls or tr ssot [JJM] mtrs. VI. APPLICATIONS EXAMPLE : T rst xmpl onrns tr knmt ns wt rs, onts, on r o rom s sown n F., n. T tsk s to xmn wtr ts tr ns r somorp. T [JJM] mtrs or ts ns r rprsnt y J, J n J rsptvly. T rtrst polynoml or n = , , , , , , , 0.00, 0.0, -0.00, -0., -0., 0., 0., -0., -.0 T rtrst polynoml or n = , , , , , , , , 0.00, 0.0, -0.00, -0., -0., 0., 0., -0., -.0, T rtrst polynoml or n = , , , , , , , , 0.00, 0.0, -0.00, -0., -0.0, 0.00, 0.0, -0., -. T vlus o ompost nvrnt For n : [JJMP ] =.+0, [JJMPmx] =.0+0 For n : [JJMP ] =.+0, [JJMPmx] =.0+0 For n : [JJMP ] =.0+0, [JJMPmx] =.+0 Our mto rports tt n n r somorp s t st o vlus o [JJMP ] n [JJMPmx] r sm or ot t knmt n n rsptvly. Smlrly, our mto rports tt knm ns n r non-somorp s t vlus o struturl nvrnts [JJMP ] n [JJMPmx] r rnt or knmt n n rsptvly. Not tt y usn notr mto n vtor [] n rtl nurl ntwork [], t sm onluson s otn. EXAMPLE (Multr rom ns): T son xmpl onrns two knmt ns wt rs, onts, tr r o rom s sown n F. n F.. T tsk s to xmn wtr ts two ns r somorp. T [JJM] mtrs or ts ns r rprsnt y J n J rsptvly. T rtrst polynoml or n = , , , , 0.00, 0.0, -0., - 0.0, 0.,., 0.0, -., -. T rtrst polynoml or n = poly(j) = , 0, , , 0.00, 0.0, - 0.0, -0., 0.0,., 0., -., 0.. T vlus o ompost nvrnt For n : [JJMP ] =.+00, [JJMPmx] =.+00 For n : [JJMP ] =.0+00, [JJMPmx] =.+00 Our mto rports tt n n r non-somorp s t st o vlus o [JJMP ] n [JJMPmx] r rnt or ot t knmt ns. Not tt y usn otr mto summton polynomls [], t sm onluson s otn. EXAMPLE : T tr xmpl onrns notr xmpl o two knmt ns wt rs, onts, snl rom s sown n F. n F.. T tsk s to xmn wtr ts two ns r somorp. T [JJM] mtrs or ts ns r rprsnt y J n J rsptvly. T rtrst polynoml or n = , 0, , , 0.00, 0.00, -0.0, - 0.0, 0.,.0, -0., -., -., 0.. T rtrst polynoml or n = , , , , 0.00, 0.00, -0.0, - 0.0, 0.,.0, -0., -., -., 0.. T vlus o ompost nvrnt For n : [JJMP ] =.+00, [JJMPmx] =.+00 For n : [JJMP ] =.+00, [JJMPmx] = P

3 Isomorpsm In Knmt Cns Our mto rports tt n n r somorp s t st o vlus o [JJMP ] n [JJMPmx] r sm or ot t knmt ns. Not tt y usn notr mto rtl nurl ntwork [], t sm onluson s otn. EXAMPLE : T ourt xmpl onrns two knmt ns wt rs, onts, on rom s sown n F. n F.. T tsk s to xmn wtr ts two ns r somorp. T [JJM] mtrs or ts ns r rprsnt y J n J rsptvly. T rtrst polynoml or n = 0.00, , , -0.0, 0.0, 0.0, -.0, T rtrst polynoml or n = 0.00, , -0.00, -0.00,.00,.0, -.0, T vlus o ompost nvrnt For n : [JJMP ] =.00+00, [JJMPmx] =.0+00 For n : [JJMP ] =.0+00, [JJMPmx] = Our mto rports tt n n r non-somorp s t st o vlus o [JJMP ] n [JJMPmx] r rnt or ot t knmt ns. Not tt y usn notr mto s stn mtrx [], n summton polynomls [], t sm onluson s otn. VII. CONCLUSION In ts ppr, smpl, nt n rll mto to nty somorpsm s propos. By ts mto, t somorpsm o mnsms knmt ns n sly nt. It norports ll turs o t n n s su volton o t somorpsm tst s rtr ult. In ts mto, t rtrst polynomls, ompost struturl nvrnts [JJMP ] n [JJMPmx] o [JJM] mtrx o t knmt n. T vnt s tt ty r vry sy to omput usn MATLAB sotwr. It s not ssntl to trmn ot t ompost nvrnts to ompr two ns, only n s t [JJMP ] s sm tn t s n to trmn [JJMPmx]or ot knmt ns. T [JJM] mtrs n wrttn wt vry lttl ort, vn y mr nspton o t n. T propos tst s qut nrl n ntur n n us to tt somorpsm o not only plnr knmt ns o on r o rom, ut lso knmt ns o mult r o rom. T rtrst polynomls n ompost struturl nvrnts r vry normtv n rom tm vlul normton rrn topoloy o knmt ns n prt. Aorn to ts mto, w n n tt t [JJM] mtrx s mp o mnsm knmt ns n rtrst polynomls n otr rtrst nvrnts my rlt som ntur n nnr proprty o t mnsm. T nnr rlton twn rtrst vlu n mnsm knmt n n urtr stuy. P

4 Isomorpsm In Knmt Cns J= J= J= P

5 Isomorpsm In Knmt Cns J= J= J= J= J= J= P

6 Isomorpsm In Knmt Cns L k k L F.: Twlv r n, snl rom F.: Twlv r n, snl rom k l F.: Twlv r n, snl rom P

7 Isomorpsm In Knmt Cns P F.: Tn r n, tr rom F.: Tn r n, tr rom F.: Tn r n, snl rom F.: Tn r n, snl rom F.: Sx r n, snl rom F.: Sx r n, snl rom

8 Isomorpsm In Knmt Cns REFERENCES [] Prn W. Jnsn, Clssl n Morn Mnsm or Ennrs n Invntors, Mrl Dkkr, In. Nw York, (). [] Ur J.J. n Ru A, A mto or ntton n ronton o quvln o knmt ns, M. M. Tory,, - (). [] Ro. A.C., Knmt ns, Isomorpsm, nvrsons n typ o rom, usn t onpt o mmn stn, Inn J. o T., - (). [] Mrutyuny T.S. n Rvn M.R., Computr A Anlyss o t struturl syntss o knmt ns, M. M. Tory,,, - (). [] C.Nswr Ro n A.C. Ro, Slton o st rm, nput n output lnks or unton nrtors mol s prolst systms, M. M. Tory,, - (). [] As Momm n V.P. Arwl, Intton n Isomorpsm o knmt ns n mnsms, prons o t t ISME onrn, IIT Dl, Nw Dl (). [] A.G. Amkr n Arwl V.P., Intton o knmt Gnrtor usn Mn. Cos, M. M. Tory, l,, - (). [] Amkr AG. n Arwl V.P., Intton n lsston o knmt ns usn ntton o, t ourt ntrntonl symposum on lnk n omputr sn mtos, Burst, Romn,, - (). [] V.P. Arwl, J.N. Yv n C.R. Prtp, Mnsm o Knmt n n t r o struturl smlrty s on t onpt o lnk pt o, M. M. Tory,,, - (). [] Do. Nrsn, Grp Tory wt ppltons to Ennrn n Computr Sn, PHI, 00. [] Crossly F.R.E, A ontruton to Grulr s tory n t numr syntss o plnr mnsms, Trns.ASME, J.En.In.B (I), -(). [] Dornsky L. n Frunstn F., Som ppltons o rp tory to t struturl syntss o mnsms, Trns.ASME, J.En.In.B (),-(). [] Busum F. n Frunstn F, Syntss o knmt strutur o r knmt ns n otr mnsms, J.Mnsm (), -(0). [] Mnolsu N.I., A mto s on Brnov trusss n usn rp tory to n t st o plnr ont knmt ns n mnsms, Mnsm n Mn Tory (I), -(). [] Vro A., An xtnson o t onpt o t roup, Mnsm n Mn Tory ()-(). [] Ru A., Mtrs ssot wt knmt ns rom to mmrs, Mnsm n Mn Tory ()-(). [] H.S. Yn, A.S. Hll, Lnk rtrst polynomls: nton, onts y nspton, ASME, Journl o Mnl Dsn, (). [] T.S.Mrutyuny, In qust o rll n nt omputtonl tst or tton o somorpsm n knmt ns, Mnsm n Mn Tory, () ()-. [] Zonyu Cn, C Zn, Yuu Yn n Yuxn Won, Anw mto to mnsm knmt n somorpsm ntton, Mnsm n Mn Tory, (00). [0] T.J. Jonsm t l, An nt lortm or nn optmum o unr unr t onton o nnt r, Prons o Mnl Conrn () -. [] E.R. Tuttl t l., Enumrton o s knmt ns usn t tory o nt roup, ASME Journl o Mnsms, Trnsmssons n Automton n Dsn (). [] E.R. Tuttl t l., Furtr ppltons o roup tory to t numrton n struturl nlyss o s knmt ns, ASME Journl o Mnsms, Trnsmssons n Automton n Dsn (). [] J.K.Cu, W.Q. Co, Intton o somorpsm o knmt ns trou nt-n tl, Prons o ASME Conrn ()0-. [] F.G. Kon, QL,w..Zn, An rtl ntwork ppro to mnsm knmt n somorpsm ntton, Mnsm n Mn Tory,() -. [] Sn S., Ro A.C., Isomorpsm n knmt ns, Mnsm n Mn Tory, () -0 () [] Ro A.C., Prtp B. D., Computr A Struturl Syntss o Plnr Knmt Cns ovton t tst or Isomorpsm, Mnsm n Mn Tory,,-0 (00) [] Ro A.B.S, Srnt A., Ro A.C., Syntss o plnr knmt ns, J. Insttuton o Ennrs (In),, 0 (00). [] Arwl V.P., Ro J.S., T molty proprts o knmt ns, Mnsm Mn Tory, () -0 (). [] Cun S.L., l T., A lsston mto or nput onts o plnr v r mnsms, Mnsm & Mn Tory,, (00). P