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clear all; clc; close all; digits(25);
%-------------------------------%
% Initialisation des parametres
%-------------------------------%
% Force de contact au pattes
syms NAvGx NAvGy NAvGz real d;
NAvG = [NAvGx; NAvGy; NAvGz];
syms NCeDx NCeDy NCeDz real d;
NCeD = [NCeDx; NCeDy; NCeDz];
syms NArGx NArGy NArGz real d;
NArG = [NArGx; NArGy; NArGz];
%-------------------------------%
%-------------------------------%
% Reaction corps-coxa
syms RBCAvGx RBCAvGy RBCAvGz real;
RBCAvG = [RBCAvGx; RBCAvGy; RBCAvGz];
syms RBCCeDx RBCCeDy RBCCeDz real;
RBCCeD = [RBCCeDx; RBCCeDy; RBCCeDz];
syms RBCArGx RBCArGy RBCArGz real;
RBCArG = [RBCArGx; RBCArGy; RBCArGz];
syms MBCAvGx MBCAvGy MBCAvGz real;
MBCAvG = [MBCAvGx; MBCAvGy; MBCAvGz];
syms MBCCeDx MBCCeDy MBCCeDz real;
MBCCeD = [MBCCeDx; MBCCeDy; MBCCeDz];
syms MBCArGx MBCArGy MBCArGz real;
MBCArG = [MBCArGx; MBCArGy; MBCArGz];
%-------------------------------%
% Reaction femur-tibia
syms RFTAvGx RFTAvGy RFTAvGz real;
RFTAvG = [RFTAvGx; RFTAvGy; RFTAvGz];
syms RFTCeDx RFTCeDy RFTCeDz real;
RFTCeD = [RFTCeDx; RFTCeDy; RFTCeDz];
syms RFTArGx RFTArGy RFTArGz real;
RFTArG = [RFTArGx; RFTArGy; RFTArGz];
syms MFTAvGx MFTAvGy MFTAvGz real;
MFTAvG = [MFTAvGx; MFTAvGy; MFTAvGz];
syms MFTCeDx MFTCeDy MFTCeDz real;
MFTCeD = [MFTCeDx; MFTCeDy; MFTCeDz];
syms MFTArGx MFTArGy MFTArGz real;
MFTArG = [MFTArGx; MFTArGy; MFTArGz];
%-------------------------------%
% Reaction coxa-femur
syms RCFAvGx RCFAvGy RCFAvGz real d;
RCFAvG = [RCFAvGx; RCFAvGy; RCFAvGz];
syms RCFCeDx RCFCeDy RCFCeDz real;
RCFCeD = [RCFCeDx; RCFCeDy; RCFCeDz];
syms RCFArGx RCFArGy RCFArGz real;
RCFArG = [RCFArGx; RCFArGy; RCFArGz];
syms MCFAvGx MCFAvGy MCFAvGz real;
MCFAvG = [MCFAvGx; MCFAvGy; MCFAvGz];
syms MCFCeDx MCFCeDy MCFCeDz real;
MCFCeD = [MCFCeDx; MCFCeDy; MCFCeDz];
syms MCFArGx MCFArGy MCFArGz real;
MCFArG = [MCFArGx; MCFArGy; MCFArGz];
%-------------------------------%
% PGI
%-------------------------------%
g = 9.806E-3;
prec = [eps;eps;eps].*rand(3,1);
% Bras de levier en module des longueurs
a = [0,80,100];
b = [0,0,0];
alpha = [pi/2,0,0];
for o = 1:3
HD(:,:,o) = [a;b;alpha];
end
% Position des centre de masse dans les repere des membrures
oCDMcorps = [0;0;0];
%oCDMtibia = [23;0;0];
oCDMtibia = [50;0;0];
oCDMfemur = [40;0;0];
oCDMcoxa = [0;0;0];
dRtibia(:,:) = [a(3);b(3);0];
dRfemur = [a(2);b(2);0];
dRcoxa = [a(1);b(1);0];
dRcorps = [106,0,-106;45,-118,45;0,0,0];
%-------------------------------%
% PGI_hexapode
%-------------------------------%
% Position des extremite des pattes
cas =1;
if cas == 1 % Orthogonal
pos = [106,0,-106;125,-198,125;-100,-100,-100];
elseif cas == 2 % extreme ortho
pos = dRcorps + [0,0,0;150.71,-150.71,150.71;-70.711,-70.711,-70.711];
elseif cas == 3 % extreme total
pos = dRcorps + [106,0,-106;106.57,-150.71,106.57;-70.711,-70.711,-70.711];
end
%-------------------------------%
Qcorps = eye(3); % Orientation du corps
[art,Qhex,Phex] = PGI_hexapode(pos,HD,dRcorps,Qcorps);
mTibia = 47;
mFemur = 62;
mCoxa = 75;
mCorps = 580 + 413;
mtot = 6*(mTibia+mFemur+mCoxa)+mCorps
Wcoxa = Qcorps*[0;0;-mCoxa*g];
Wfemur = Qcorps*[0;0;-mFemur*g];
Wtibia = Qcorps*[0;0;-mTibia*g];
Wcorps = Qcorps*[0;0;-mCorps*g];
Wtot = Wcorps + 6*(Wcoxa+Wfemur+Wtibia);
%-------------------------------%
% Position des centre de masse dans le repere global
LBcdmCAvG = Qcorps*dRcorps(:,1);
LBcdmCCeD = Qcorps*dRcorps(:,2);
LBcdmCArG = Qcorps*dRcorps(:,3);
% Femur
LCFcdmAvG = Phex(:,:,2,1)*oCDMfemur;
LCFcdmCeD = Phex(:,:,2,2)*oCDMfemur;
LCFcdmArG = Phex(:,:,2,3)*oCDMfemur;
LFcdmTAvG = Phex(:,:,2,1)*(dRfemur-oCDMfemur);
LFcdmTCeD = Phex(:,:,2,2)*(dRfemur-oCDMfemur);
LFcdmTArG = Phex(:,:,2,3)*(dRfemur-oCDMfemur);
LFAvG = Phex(:,:,2,1)*dRfemur;
LFCeD = Phex(:,:,2,2)*dRfemur;
LFArG = Phex(:,:,2,3)*dRfemur;
% Tibia
LFTcdmAvG = Phex(:,:,3,1)*oCDMtibia;
LFTcdmCeD = Phex(:,:,3,2)*oCDMtibia;
LFTcdmArG = Phex(:,:,3,3)*oCDMtibia;
LTcdmNAvG = Phex(:,:,3,1)*(dRtibia-oCDMtibia);
LTcdmNCeD = Phex(:,:,3,2)*(dRtibia-oCDMtibia);
LTcdmNArG = Phex(:,:,3,3)*(dRtibia-oCDMtibia);
LTAvG = Phex(:,:,3,1)*(dRtibia);
LTCeD = Phex(:,:,3,2)*(dRtibia);
LTArG = Phex(:,:,3,3)*(dRtibia);
%-------------------------------%
% Systeme dequation
%-------------------------------%
% Globale
%-------------------------------%
% Force sur dirrection Z seulement
NAvG(1:2) = [0;0];
NCeD(1:2) = [0;0];
NArG(1:2) = [0;0];
RBCAvG(1:2) = [0;0];
RBCCeD(1:2) = [0;0];
RBCArG(1:2) = [0;0];
RCFAvG(1:2) = [0;0];
RCFCeD(1:2) = [0;0];
RCFArG(1:2) = [0;0];
RFTAvG(1:2) = [0;0];
RFTCeD(1:2) = [0;0];
RFTArG(1:2) = [0;0];
% Moment en X et Y seulement
MBCAvG(3) = 0;
MBCCeD(3) = 0;
MBCArG(3) = 0;
MCFAvG(3) = 0;
MCFCeD(3) = 0;
MCFArG(3) = 0;
MFTAvG(3) = 0;
MFTCeD(3) = 0;
MFTArG(3) = 0;
% Contraintes globales
SFGLOB = (Wcorps + 6*(Wcoxa + Wfemur + Wtibia) + NAvG + NCeD + NArG);
SMGLOB = (cross(LBcdmCAvG+LFAvG+LTAvG,NAvG) + cross(LBcdmCCeD+LFCeD+LTCeD,NCeD) + cross(LBcdmCArG+LFArG+LTArG,NArG) + cross(LBcdmCAvG,Wcoxa) + cross(LBcdmCCeD,Wcoxa) + cross(LBcdmCArG,Wcoxa) + cross(LBcdmCAvG+LCFcdmAvG,Wfemur) + cross(LBcdmCCeD+LCFcdmCeD,Wfemur) + cross(LBcdmCArG+LCFcdmArG,Wfemur) + cross(LBcdmCAvG+LFAvG+LFTcdmAvG,Wtibia) + cross(LBcdmCCeD+LFCeD+LFTcdmCeD,Wtibia) + cross(LBcdmCArG+LFArG+LFTcdmArG,Wtibia));
% Resolution pour force de contact en Z
n = solve(SFGLOB(3),SMGLOB(1),SMGLOB(2));
NAvGz = eval(n.NAvGz);
NCeDz = eval(n.NCeDz);
NArGz = eval(n.NArGz);
check = NAvGz+NCeDz+NArGz;
%-------------------------------------------------------------------%
% Autres equations de contrainte interne
% Corps B
%-------------------------------%
% Somme force
SFB = RBCAvG + RBCCeD + RBCArG + Wcorps + 3*(Wcoxa + Wfemur + Wtibia) + prec;
% Somme moment (bras de levier au cdm)
SMB = (cross(LBcdmCAvG,RBCAvG) + cross(LBcdmCCeD,RBCCeD) + cross(LBcdmCArG,RBCArG) + MBCAvG + MBCCeD + MBCArG) + prec;
%-------------------------------%
% Patte
%-------------------------------%
% Coxa C
% Somme force
SFCAvG = (-RBCAvG + RCFAvG + Wcoxa) + prec;
SFCCeD = (-RBCCeD + RCFCeD + Wcoxa) + prec;
SFCArG = (-RBCArG + RCFArG + Wcoxa) + prec;
% Somme moment (bras de levier au cdm)
SMCAvG = (-MBCAvG + MCFAvG) + prec;
SMCCeD = (-MBCCeD + MCFCeD) + prec;
SMCArG = (-MBCArG + MCFArG) + prec;
%-------------------------------%
% Femur F
% Somme force
SFFAvG = (-RCFAvG + RFTAvG + Wfemur) + prec;
SFFCeD = (-RCFCeD + RFTCeD + Wfemur) + prec;
SFFArG = (-RCFArG + RFTArG + Wfemur) + prec;
% Somme moment (bras de levier au cdm)
SMFAvG = (cross(-LCFcdmAvG,-RCFAvG) + cross(LFcdmTAvG,RFTAvG) - MCFAvG + MFTAvG) + prec;
SMFCeD = (cross(-LCFcdmCeD,-RCFCeD) + cross(LFcdmTCeD,RFTCeD) - MCFCeD + MFTCeD) + prec;
SMFArG = (cross(-LCFcdmArG,-RCFArG) + cross(LFcdmTArG,RFTArG) - MCFArG + MFTArG) + prec;
%-------------------------------%
% Tibia T
% Somme force
SFTAvG = (-RFTAvG + NAvG + Wtibia) + prec;
SFTCeD = (-RFTCeD + NCeD + Wtibia) + prec;
SFTArG = (-RFTArG + NArG + Wtibia) + prec;
% Somme moments (bras de levier au cdm)
SMTAvG = (cross(-LFTcdmAvG,-RFTAvG) - MFTAvG + cross(LTcdmNAvG,NAvG))+ prec;
SMTCeD = (cross(-LFTcdmCeD,-RFTCeD) - MFTCeD + cross(LTcdmNCeD,NCeD))+ prec;
SMTArG = (cross(-LFTcdmArG,-RFTArG) - MFTArG + cross(LTcdmNArG,NArG))+ prec;
%-------------------------------%
% Resolution
%-------------------------------%
sol = solve(SFB(3),SMB(1),SMB(2),SFCAvG(3),SMCAvG(1),SMCAvG(2),SFFAvG(3),SMFAvG(1),SMFAvG(2),SFTAvG(3),SMTAvG(1),SMTAvG(2),SFCCeD(3),SMCCeD(1),SMCCeD(2),SFFCeD(3),SMFCeD(1),SMFCeD(2),SFTCeD(3),SMTCeD(1),SMTCeD(2),SFCArG(3),SMCArG(1),SMCArG(2),SFFArG(3),SMFArG(1),SMFArG(2),SFTArG(3),SMTArG(1),SMTArG(2));
NAvGz = eval(sol.NAvGz);
NCeDz = eval(sol.NCeDz);
NArGz = eval(sol.NArGz);
check = NAvGz+NCeDz+NArGz;
MBCAvGx = eval(sol.MBCArGx);
MBCCeDx = eval(sol.MBCCeDx);
MBCArGx = eval(sol.MBCAvGx);
MBCArGy = eval(sol.MBCArGy);
MBCCeDy = eval(sol.MBCCeDy);
MBCArGy = eval(sol.MBCAvGy);
MCFAvGx = eval(sol.MCFArGx);
MCFCeDx = eval(sol.MCFCeDx);
MCFArGx = eval(sol.MCFAvGx);
MCFAvGy = eval(sol.MCFArGy);
MCFCeDy = eval(sol.MCFCeDy);
MCFArGy = eval(sol.MCFAvGy);
MFTAvGx = eval(sol.MFTArGx);
MFTCeDx = eval(sol.MFTCeDx);
MFTArGx = eval(sol.MFTAvGx);
MFTAvGy = eval(sol.MFTAvGy);
MFTCeDy = eval(sol.MFTCeDy);
MFTArGy = eval(sol.MFTArGy);
RBCArGz = eval(sol.RBCArGz);
RBCCeDz = eval(sol.RBCCeDz);
RBCAvGz = eval(sol.RBCAvGz);
RCFAvGz = eval(sol.RCFAvGz);
RCFCeDz = eval(sol.RCFCeDz);
RCFArGz = eval(sol.RCFArGz);
RFTAvGz = eval(sol.RFTAvGz);
RFTCeDz = eval(sol.RFTCeDz);
RFTArGz = eval(sol.RFTArGz);
MCFAvG_patte = Phex(:,:,2,1)*MCFAvG;
subs(MCFAvG_patte)
MCFCeD_patte = Phex(:,:,2,2)*MCFCeD;
subs(MCFCeD_patte)
MCFArG_patte = Phex(:,:,2,3)*MCFArG;
subs(MCFArG_patte)
%-------------------------------%
affichage = 1;
if affichage == 1
figure;
hold on;
plot3([LBcdmCAvG(1),LBcdmCCeD(1),LBcdmCArG(1),LBcdmCAvG(1)],[LBcdmCAvG(2),LBcdmCCeD(2),LBcdmCArG(2),LBcdmCAvG(2)],[LBcdmCAvG(3),LBcdmCCeD(3),LBcdmCArG(3),LBcdmCAvG(3)],k-);
plot3([0, LBcdmCAvG(1), LBcdmCAvG(1)+LFAvG(1), LBcdmCAvG(1)+LFAvG(1)+LTAvG(1)],[0, LBcdmCAvG(2), LBcdmCAvG(2)+LFAvG(2), LBcdmCAvG(2)+LFAvG(2)+LTAvG(2)],[0, LBcdmCAvG(3), LBcdmCAvG(3)+LFAvG(3), LBcdmCAvG(3)+LFAvG(3)+LTAvG(3)],o-b);
plot3([0, LBcdmCCeD(1), LBcdmCCeD(1)+LFCeD(1), LBcdmCCeD(1)+LFCeD(1)+LTCeD(1)],[0, LBcdmCCeD(2), LBcdmCCeD(2)+LFCeD(2), LBcdmCCeD(2)+LFCeD(2)+LTCeD(2)],[0, LBcdmCCeD(3), LBcdmCCeD(3)+LFCeD(3), LBcdmCCeD(3)+LFCeD(3)+LTCeD(3)],o-r);
plot3([0, LBcdmCArG(1), LBcdmCArG(1)+LFArG(1), LBcdmCArG(1)+LFArG(1)+LTArG(1)],[0, LBcdmCArG(2), LBcdmCArG(2)+LFArG(2), LBcdmCArG(2)+LFArG(2)+LTArG(2)],[0, LBcdmCArG(3), LBcdmCArG(3)+LFArG(3), LBcdmCArG(3)+LFArG(3)+LTArG(3)],o-g);
% Femur
plot3(LBcdmCAvG(1)+LCFcdmAvG(1), LBcdmCAvG(2)+LCFcdmAvG(2),LBcdmCAvG(3)+LCFcdmAvG(3),xk);
plot3(LBcdmCCeD(1)+LCFcdmCeD(1), LBcdmCCeD(2)+LCFcdmCeD(2),LBcdmCCeD(3)+LCFcdmCeD(3),xk);
plot3(LBcdmCArG(1)+LCFcdmArG(1), LBcdmCArG(2)+LCFcdmArG(2),LBcdmCArG(3)+LCFcdmArG(3),xk);
% Tibia
plot3(LBcdmCAvG(1)+LFAvG(1)+LFTcdmAvG(1),LBcdmCAvG(2)+LFAvG(2)+LFTcdmAvG(2), LBcdmCAvG(3)+LFAvG(3)+LFTcdmAvG(3),xk);
plot3(LBcdmCCeD(1)+LFCeD(1)+LFTcdmCeD(1),LBcdmCCeD(2)+LFCeD(2)+LFTcdmCeD(2),LBcdmCCeD(3)+LFCeD(3)+LFTcdmCeD(3),xk);
plot3(LBcdmCArG(1)+LFArG(1)+LFTcdmArG(1),LBcdmCArG(2)+LFArG(2)+LFTcdmArG(2),LBcdmCArG(3)+LFArG(3)+LFTcdmArG(3),xk);
xlabel(X); ylabel(Y); zlabel(Z);
axis equal;
% view(3)
view([0,0,180]);
% Affichage du cercle de contact
[cC,r] = cercle3pts(pos(1:2,:));
t = 0:0.01:2*pi+0.01;
for o = 1:size(t,2)
x(o) = cC(1) + r*cos(t(o));
y(o) = cC(2) + r*sin(t(o));
end
plot3(x,y,ones(1,size(x,2))*pos(3,1),c-);
plot3(cC(1),cC(2),pos(3,1),c+);
% Affichage du cercle dancrage
[cA,r] = cercle3pts(dRcorps(1:2,:));
t = 0:0.01:2*pi+0.01;
for o = 1:size(t,2)
x(o) = cA(1) + r*cos(t(o));
y(o) = cA(2) + r*sin(t(o));
end
plot3(x,y,ones(1,size(x,2))*pos(3,1),m-);
plot3(cA(1),cA(2),pos(3,1),m+);
distCentre = norm(cA-cC)
end |
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