Modelagem Dinamica Sistemas Multicorpos Rigidos Planares Interconectados - Analise e Equacoes

Ycm1 θ L1m1 C1 b1 p p d p Y1 X X4 X3 k1 L0 A Ycm2 d2 p C2 b2 L2 m2 β B C X2 X4 X3 Ana Gabriela Matthes De Moraes 202020229 Modelagem dinâmica de sistemas multicorpos rígidos planares interconectados b Aceleração linear do CM pela eq de 5 termos B1 u0A a1 d1 0 B3 uAB Lt 0 0 B4 uCB c2 d2 0 τ uOc d 0 0 B1 uOcm 0 Ycm1 0 B2 ucCm 0 Ycm2 0 Matriz transformação Tθ cos θ sin θ cos θ 0 0 0 1 I B1 giro positivo em z Tβ cos β sin β cos β 0 0 0 1 I B2 giro positivo em β Iα cos α sin α 0 sin α cos α 0 0 0 1 I β3 giro negativo em α Velocidade angular ω1 0 0 θ B1 ω2 0 0 β B2 ω3 0 0 α B1 ω1 0 0 θ B2 ω2 0 0 β B3 ω3 0 0 α acm1 a ω1 u0cm ω ω1 u0cm 2 ω Vel cm0 ȧrel cm0 I II B1 I J K 0 0 θ 1 θcm1 0 0 0 0 Ycm1 0 B1 acm1 θ Ycm1 Ycm1 θ2 0 II ω1 u0cm J K 0 0 θ Ycm1 θ Ycm1 θ2 0 acm2 ac ω2 ω2 u0cm2 2 ω Velrel cm0 ȧ rel cm0 I II Ana Gabriela Matthes De Moraes I J K 0 β 0 Ycm2 0 Ycm2 β 0 0 II I J K 0 β 0 Ycm2 0 Ycm2 β ω2 J K 0 0 β 0 0 Ycm2 β2 0 B2 acm2 Ycm2 β Ycm2 β2 0 d Pl ou loop vetorial IuAB Iu0B Iu0A d c2 cos β d2 sen β c1 cos θ d1 sen θ d c2 cos β d2sen β c1 cos θ d1 sen θ C1 sen θ d1 cos θ 0 C1 sen β d2 cos β c1 sen θ d1 cos θ 0 T0AB TB1 L cos α L sin α 0 Lx Ly 0 sen α Ly L cos α Lx L tg α sen α cos α Ly Lx α arctg Ly Lx arctg C1 sen β d cos β c1 sen θ d1 cos θ eq A d c2 cos β d2 sen β c1 cos θ d1 sen θ L Lx2 Ly2 d c2 cos β d2 sen β c1 cos θ d1 sen θ 2 c1 sen β d2 cos β c1 sen θ d1 cos θ 2 eq B c F1y F1z F2y F2x F2x g I F1 F1z F1y 0 F2 F2x F2y 0 B3 Fel K L L0 0 0 I P1 0 m1 g 0 I P2 0 m2 g 0 e 6 equações 6 variáveis Reações dinâmicas F1x F1y F2x F2y EDMs θ β 2ª Lei de Newton Corpo 1 Fel1 F1 P1 m1 a cm 1 F1x 0 KLL0 TθT m1 Ycm1 TθT F1y mg 0 0 0 F1x KLL0 cos α F1y mg KLL0 sen α m Ö Ycm1 cos θ θ2 Ycm1 sen θ Ö Ycm1 sen θ θ2 Ycm1 cos θ 0 I F1x m1 Ö Ycm1 cos θ θ2 Ycm1 sen θ KLL0 cos α eq C e D I F1y m1 Ö Ycm1 sen θ θ2 Ycm1 cos θ g KLL0 sen α Corpo 2 Fel F2 P2 m2 a cm 2 KLL0 Tα F2x 0 m2 Ycm2 TθT F2y mg Ycm2 0 F2x KLL0 cos α F2y mg KLL0 sen α m ß Ycm2 cos β ß2 Ycm2 sen β ß Ycm2 sen β ß2 Ycm2 cos β 0 I F2x m2 ß Ycm2 cos β ß2 Ycm2 sen β KLL0 cos α F2 y m2 g ß Ycm2 sen β ß2 Ycm2 cos β KLL0 sen α eq E e F 9 Equação de Euler Corpo 1 M0 I0 W1 W1 x I0w1 m x0cm1 α eq 1 Lado esquerdo o cm1 x P1 r uon x Fel1 m g sen θ m g cos θ 0 0 Ycm1 0 Ycm1 m g sen θ P1 Tθ m g sen θ m g cos θ 0 P I Fel Tθ KLL0 cos θ KLL0 sen θ 0 Fel M0 0 0 Ycm1 m g sen θ c1 KLL0 sen θ d1 KLL0 cos θ A na Gabriela Mattes de Moraes III I0 w1 G 0 0 IV 0 0 G 0 t rec x Iyy Izz eq 1 M0 0 0 ED M1 Ö Ycm1 m g sen θ KLL0 c1 van α sen θ d1 cos α cos θ Izz Corpo 2 M0 x cm 2 x CB F elba I0 w3 W3 x I2 x w3 m x cm3 a C I II I j k 0 Ycm2 0 0 Y cm2 m g sen β II i j k KLL0 cos d cos β KLL0 sen d Corpos G G M0 0 0 Ycm2 m g sen θ KLL0 c2 sen d sen β d2 cos d cos β III I2 w3 G 0 β Izz M0 G 0 β Izz EDM2 β Ycm2 m g sen θ KLL0 c2 sen d sen β d2 cos d cos β 10 Momento de inercia em relação as articulações O e C O cálculo é feito em relação as articulações devido aos corpos se movimentarem em relação a eles e não ao CM assim o esforço do corpo para voltar em relação as articulações faz mais sentido quando calculado em relação a elas Bi Izz Cmi Izz mi r y cm 2 X cm2 Y cm2 Pl corpo 1 Izz Izz m1 Y cm Pl corpo 2 Izz Izz2 Izz2 m2 Y cm2 i r 0 cm1 Ycm1 sen θ 002579 T Ycm1 cos θ 0146426 m I j uocm3 d Ycm2 sen β 0263 T Ycm2 cos β 0 013737 m Pela eq 1 α 130 rad s Pela eq β L01462 m Pela eq C e D F1 061559 T N 02234 Fazendo a Tp nas eq E e F F2 065146 T 003764 N Pela EDM1 Ö 2802 rads2 Pela EDM2 β 3045 rad s2 4 090223 1805 CUsersanagaOneDricodigo4anam 1 of 4 PROGRAMA MATLAB PARA ANÁLISE CINEMÁTICA Aluno Ana Gabriela Matthes de Moraes clear all close all clc PARTE I CINEMÁTICA syms teta dteta d2teta beta dbeta d2beta alpha dalpha d2alpha F1x F1y F2x F2y L Parâmetros syms g k L0 d L1 ycm1 d1 c1 m1 L2 ycm2 d2 c2 m2 I1xx I1xy I1xz I1yx I1yy I1yz I1zx I1zy I1zz I2xx I2xy I2xz I2yx I2yy I2yz I2zx I2zy I2zz Matrizes de transformação Tteta costeta sinteta 0 sinteta costeta 0 0 0 1 Tbeta cosbeta sinbeta 0 sinbeta cosbeta 0 0 0 1 Talpha cosalpha sinalpha 0 sinalpha cosalpha 0 0 0 1 Vetores posição rb1ocm1 0 ycm1 0 riocm1 Ttetarb1ocm1 rb1oa c1 d1 0 rioa Ttetarb1oa rioc d 0 0 rb3ccm2 0 ycm2 0 riccm2 Tbetarb3ccm2 riocm2 rioc riccm2 rb2ab L 0 0 riab Talpharb2ab rb3cb c2 d2 0 ricb Tbetarb3cb riob rioc ricb Vetores velocidade angular absoluta w1b1 0 0 fulldifftetatetabetaalpha w2b2 0 0 fulldiffalphatetabetaalpha w3b3 0 0 fulldiffbetatetabetaalpha Vetores aceleração angular absoluta dw1b1 fulldiffw1b1tetabetaalpha dw2b2 fulldiffw2b2tetabetaalpha dw3b3 fulldiffw3b3tetabetaalpha Vetores velocidade linear absoluta vb1o 0 0 0 vb1cm1 vb1o crossw1b1rb1ocm1 fulldiffrb1ocm1tetabetaalpha 090223 1805 CUsersanagaOneDricodigo4anam 2 of 4 vicm1 Ttetavb1cm1 vb3c 0 0 0 vb3cm2 vb3c crossw3b3rb3ccm2 fulldiffrb3ccm2tetabetaalpha vicm2 Tbetavb3cm2 Determinação dos vetores aceleração linear absoluta ab1o 0 0 0 ab1cm1 ab1o crossdw1b1rb1ocm1 crossw1b1crossw1b1rb1ocm1 2crossw1b1fulldiffrb1ocm1tetabetaalpha fulldiffrb1ocm1tetabeta alpha2 aicm1 Ttetaab1cm1 ab3c 0 0 0 ab3cm2 ab3c crossdw3b3rb3ccm2 crossw3b3crossw3b3rb3ccm2 2crossw3b3fulldiffrb3ccm2tetabetaalpha fulldiffrb3ccm2tetabeta alpha2 aicm2 Tbetaab3cm2 Loop vetorial riab riob rioa Lx riab1 Ly riab2 alpha atanLxLy L Lx2 Ly212 PARTE II DINÂMICA Vetores de força Fb3M 0 kLL0 0 P1i 0 m1g 0 P1b1 TtetaP1i F1i F1x F1y 0 F1b1 TtetaF1i F1b1M TtetaTalphaFb3M P2i 0 m2g 0 P2b2 TbetaP2i F2i F2x F2y 0 F2b2 TbetaF2i F2b2M TbetaTalphaFb3M Vetores de momentos 090223 1805 CUsersanagaOneDricodigo4anam 3 of 4 Mb1P1 crossrb1ocm1P1b1 M1b1M crossrb1oaF1b1M Mb3P2 crossrb3ccm2P2b2 M2b3M crossrb3cbF2b2M Tensor de inércia I1o I1xx I1xy I1xz I1yx I1yy I1yz I1zx I1zy I1zz I2C I2xx I2xy I2xz I2yx I2yy I2yz I2zx I2zy I2zz 2ª Lei de Newton equa1 P1b1 F1b1 F1b1M m1ab1cm1 equa2 P2b2 F2b2 F2b2M m2ab3cm2 Equação de Euler equa3 Mb1P1 M1b1M I1odw1b1 crossw1b1I1ow1b1 m1crossrb1ocm1 ab1o equa4 Mb3P2 M2b3M I2Cdw3b3 crossw3b3I2Cw3b3 m2crossrb3ccm2 ab3c Resolução do sistema de equações para as variáveis desconhecidas solution solveequa11equa12equa21equa22equa33equa43d2teta d2betaF1xF1yF2xF2y d2teta simplifysolutiond2teta d2beta simplifysolutiond2beta F1x simplifysolutionF1x F1y simplifysolutionF1y F2x simplifysolutionF2x F2y simplifysolutionF2y Dados numéricos L1 0175 L2 0175 c1 0003 c2 0003 d1 0075 d2 0075 d 0113 L0 0115 m1 0026036 m2 0029451 k 23357 I1zz 00021473 I2zz 00021825 g 981 ycm1 014852 ycm2 014619 teta 10pi180 090223 1805 CUsersanagaOneDricodigo4anam 4 of 4 beta 20pi180 dteta 0 dbeta 0 Solução Númerica alpha evalalpha F1x evalF1x F1y evalF1y F2x evalF2x F2y evalF2y riocm1 evalriocm1 riocm2 evalriocm2 d2teta evald2teta d2beta evald2beta L evalL aicm1 evalaicm1 aicm2 evalaicm2 F1i evalF1i F2b2 evalF2b2 FIM DO PROGRAMA MATLAB Command Window Page 1 Tteta costeta sinteta 0 sinteta costeta 0 0 0 1 Tbeta cosbeta sinbeta 0 sinbeta cosbeta 0 0 0 1 Talpha cosalpha sinalpha 0 sinalpha cosalpha 0 0 0 1 rb1ocm1 0 ycm1 0 riocm1 ycm1sinteta ycm1costeta 0 rb1oa c1 d1 0 rioa c1costeta d1sinteta c1sinteta d1costeta 0 rioc d MATLAB Command Window Page 2 0 0 rb3ccm2 0 ycm2 0 riccm2 ycm2sinbeta ycm2cosbeta 0 riocm2 d ycm2sinbeta ycm2cosbeta 0 rb2ab L 0 0 riab Lcosalpha Lsinalpha 0 rb3cb c2 d2 0 ricb d2sinbeta c2cosbeta d2cosbeta c2sinbeta 0 MATLAB Command Window Page 3 riob d c2cosbeta d2sinbeta d2cosbeta c2sinbeta 0 w1b1 0 0 dteta w2b2 0 0 dalpha w3b3 0 0 dbeta dw1b1 0 0 d2teta dw2b2 0 0 d2alpha dw3b3 0 0 d2beta vb1o 0 0 MATLAB Command Window Page 4 0 vb1cm1 dtetaycm1 0 0 vicm1 dtetaycm1costeta dtetaycm1sinteta 0 vb3c 0 0 0 vb3cm2 dbetaycm2 0 0 vicm2 dbetaycm2cosbeta dbetaycm2sinbeta 0 ab1o 0 0 0 ab1cm1 d2tetaycm1 dteta2ycm1 0 aicm1 MATLAB Command Window Page 5 ycm1sintetadteta2 d2tetaycm1costeta ycm1costetadteta2 d2tetaycm1sinteta 0 ab3c 0 0 0 ab3cm2 d2betaycm2 dbeta2ycm2 0 aicm2 ycm2sinbetadbeta2 d2betaycm2cosbeta ycm2cosbetadbeta2 d2betaycm2sinbeta 0 riab d c2cosbeta d2sinbeta c1costeta d1sinteta d1costeta c2sinbeta d2cosbeta c1sinteta 0 Lx d c2cosbeta d2sinbeta c1costeta d1sinteta Ly d1costeta c2sinbeta d2cosbeta c1sinteta alpha atanc2cosbeta d d2sinbeta c1costeta d1sintetad2cosbeta c2sinbeta d1costeta c1sinteta L d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d MATLAB Command Window Page 6 d2sinbeta c1costeta d1sinteta212 Fb3M 0 kL0 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cos beta d d2sinbeta c1costeta d1sinteta212 0 P1i 0 gm1 0 P1b1 gm1sinteta gm1costeta 0 F1i F1x F1y 0 F1b1 F1xcosteta F1ysinteta F1ycosteta F1xsinteta 0 F1b1M kcosalphasinteta sinalphacostetaL0 d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 ksinalphasinteta cosalphacostetaL0 d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 0 MATLAB Command Window Page 7 P2i 0 gm2 0 P2b2 gm2sinbeta gm2cosbeta 0 F2i F2x F2y 0 F2b2 F2xcosbeta F2ysinbeta F2ycosbeta F2xsinbeta 0 F2b2M kcosalphasinbeta cosbetasinalphaL0 d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 ksinalphasinbeta cosalphacosbetaL0 d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 0 Mb1P1 0 0 gm1ycm1sinteta M1b1M 0 0 MATLAB Command Window Page 8 c1ksinalphasinteta cosalphacostetaL0 d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 d1kcosalphasinteta sinalphacos tetaL0 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 Mb3P2 0 0 gm2ycm2sinbeta M2b3M 0 0 d2kcosalphasinbeta cosbetasinalphaL0 d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 c2ksinalphasinbeta cosalphacos betaL0 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 I1o I1xx I1xy I1xz I1yx I1yy I1yz I1zx I1zy I1zz I2C I2xx I2xy I2xz I2yx I2yy I2yz I2zx I2zy I2zz equa1 F1xcosteta F1ysinteta kcosalphasinteta sinalphacos tetaL0 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 gm1sinteta d2tetam1ycm1 m1ycm1dteta2 F1ycosteta F1xsinteta gm1costeta ksin alphasinteta cosalphacostetaL0 d2cosbeta c2sinbeta d1costeta c1sinteta2 d c2cosbeta d2sinbeta c1costeta d1sinteta212 0 MATLAB Command Window Page 9 equa2 F2xcosbeta F2ysinbeta gm2sinbeta d2betam2ycm2 kcos alphasinbeta cosbetasinalphaL0 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 m2ycm2dbeta2 F2ycosbeta F2xsinbeta ksinalphasinbeta cos alphacosbetaL0 d2cosbeta c2sinbeta d1costeta c1sin teta2 d c2cosbeta d2sinbeta c1costeta d1sinteta2 12 gm2cosbeta 0 equa3 I1yzdteta2 I1xzd2teta I1xzdteta2 I1yzd2teta I1zzd2teta c1ksinalphasinteta cosalphacostetaL0 d2cos beta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sin beta c1costeta d1sinteta212 d1kcosalphasinteta sin alphacostetaL0 d2cosbeta c2sinbeta d1costeta c1sin teta2 c2cosbeta d d2sinbeta c1costeta d1sinteta2 12 gm1ycm1sinteta equa4 I2yzdbeta2 I2xzd2beta I2xzdbeta2 I2yzd2beta d2kcosalphasinbeta cosbetasinalphaL0 d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 c2ksinalphasinbeta cosalphacos betaL0 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 I2zzd2beta gm2ycm2sinbeta solution struct with fields d2teta 11 sym d2beta 11 sym F1x 11 sym F1y 11 sym F2x 11 sym MATLAB Command Window Page 10 F2y 11 sym d2teta d1ksinalpha tetad2cosbeta c2sinbeta d1costeta c1sin teta2 c2cosbeta d d2sinbeta c1costeta d1sinteta2 12 L0c1kcosalpha teta L0d1ksinalpha teta gm1ycm1sin teta c1kcosalpha tetad2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta 212I1zz d2beta L0c2kcosalpha beta L0d2ksinalpha beta gm2ycm2sinbeta c2kcosalpha betad2cosbeta c2sinbeta d1costeta c1sinteta 2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 d2ksinalpha betad2cosbeta c2sinbeta d1costeta c1sinteta 2 c2cosbeta d d2sinbeta c1costeta d1sinteta212I2zz F1x gm12ycm12sin2teta2 I1zzdteta2m1ycm1sinteta I1zzL0ksin alphacosteta2 I1zzL0ksinalphasinteta2 I1zzksinalphacos teta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cos beta d d2sinbeta c1costeta d1sinteta212 I1zzksin alphasinteta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 L0c1km1ycm1cosalphacosteta2 L0d1km1ycm1sinalphacosteta2 c1km1ycm1cosalphacosteta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta 212 d1km1ycm1sinalphacosteta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 d1km1ycm1cosalphacostetasintetad2cos beta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sin beta c1costeta d1sinteta212 c1km1ycm1sinalphacosteta sintetad2cosbeta c2sinbeta d1costeta c1sinteta2 c2cos beta d d2sinbeta c1costeta d1sinteta212 L0d1km1ycm1cosalphacostetasinteta L0c1km1ycm1sinalphacos tetasintetaI1zz F1y I1zzgm1costeta2 gm12ycm12sinteta2 I1zzgm1sinteta2 I1zzdteta2m1ycm1costeta I1zzL0kcosalphacosteta2 I1zzL0kcos alphasinteta2 I1zzkcosalphacosteta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 I1zzkcosalphasinteta2d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 L0d1km1ycm1cosalphasinteta2 MATLAB Command Window Page 11 L0c1km1ycm1sinalphasinteta2 d1km1ycm1cosalphasinteta2 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 c1km1ycm1sinalpha sinteta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 c1km1ycm1cosalphacostetasintetad2cosbeta c2sinbeta d1cos teta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sin teta212 d1km1ycm1sinalphacostetasintetad2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 L0c1km1ycm1cosalphacostetasin teta L0d1km1ycm1sinalphacostetasintetaI1zz F2x gm22ycm22sin2beta2 I2zzdbeta2m2ycm2sinbeta I2zzL0kcos beta2sinalpha I2zzL0ksinalphasinbeta2 I2zzkcosbeta2sin alphad2cosbeta c2sinbeta d1costeta c1sinteta2 c2cos beta d d2sinbeta c1costeta d1sinteta212 I2zzksin alphasinbeta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 L0c2km2ycm2cosalphacosbeta2 L0d2km2ycm2cosbeta2sinalpha c2km2ycm2cosalphacosbeta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta 212 d2km2ycm2cosbeta2sinalphad2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 d2km2ycm2cosalphacosbetasinbetad2cos beta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sin beta c1costeta d1sinteta212 c2km2ycm2cosbetasinalpha sinbetad2cosbeta c2sinbeta d1costeta c1sinteta2 c2cos beta d d2sinbeta c1costeta d1sinteta212 L0d2km2ycm2cosalphacosbetasinbeta L0c2km2ycm2cosbetasin alphasinbetaI2zz F2y I2zzgm2cosbeta2 gm22ycm22sinbeta2 I2zzgm2sinbeta2 I2zzdbeta2m2ycm2cosbeta I2zzL0kcosalphacosbeta2 I2zzL0kcos alphasinbeta2 I2zzkcosalphacosbeta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 I2zzkcosalphasinbeta2d2cosbeta c2sin beta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1cos teta d1sinteta212 L0d2km2ycm2cosalphasinbeta2 L0c2km2ycm2sinalphasinbeta2 d2km2ycm2cosalphasinbeta2 d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 c2km2ycm2sinalpha sinbeta2d2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sinteta212 c2km2ycm2cosalphacosbetasinbetad2cosbeta c2sinbeta d1cos teta c1sinteta2 c2cosbeta d d2sinbeta c1costeta d1sin teta212 d2km2ycm2cosbetasinalphasinbetad2cosbeta c2sinbeta d1costeta c1sinteta2 c2cosbeta d d2sinbeta MATLAB Command Window Page 12 c1costeta d1sinteta212 L0c2km2ycm2cosalphacosbetasin beta L0d2km2ycm2cosbetasinalphasinbetaI2zz alpha 15511 F1x 06156 F1y 02223 F2x 05992 F2y 02584 riocm1 00258 01463 0 riocm2 01630 01374 0 d2teta 280207 d2beta 304317 MATLAB Command Window Page 13 L 01459 aicm1 40984 07227 0 aicm2 41805 15216 0 F1i 06156 02223 0 F2b2 06514 00378 0