Help on trigonometric equation solution. Thanks a lot!
1 Ansicht (letzte 30 Tage)
Ältere Kommentare anzeigen
Jack Dong
am 21 Jul. 2021
Kommentiert: Jack Dong
am 22 Jul. 2021
Hi Matlab Experts,
- I built the "forward script" to calculate R1, R2 from initial inputs: X = 0.9425; Z = sin(X) + 2 = 2.809; beta = 0.531 and results for R1, R2 are showed as below.
ans =
7.7733501156970570278303966915701
ans =
11.261695645672471499665334704332
- Now, I want to use calculated R1, R2 values to input to the "inverse script" for calculating backwards to initial values of X, Z, beta. Expectation is X = 0.9425; Z = sin(X)+2 = 2.809; beta = 0.531 as initial. But the returned beta value is 50.796485621 and even though this is true result in terms of trigonometry but it's not my wanted value (0.531). I think we should assign some conditions for beta, so that it can return the expected value 0.531 but I don't know how, plese help me. Thanks a lot!
ans =
0.94245504646393978078105437144795
ans =
2.8090036222785815735410394206806
ans =
50.796485621630240525665530786852
------------------------------------------------------------------------------------------
FORWARD SCRIPT TO CALCULATE R1, R2:
syms X Y Z alpha beta gama
deg2rad=pi/180;
theta_b=15*deg2rad;
theta_p=15*deg2rad;
R_b=1;
R_p=0.9;
Q0=1; %initial leg length
p=[X;Y;Z];
B1=[R_b*cos(15*deg2rad);R_b*sin(15*deg2rad);0];
B2=[R_b*cos(105*deg2rad);R_b*sin(105*deg2rad);0];
B3=[R_b*cos(135*deg2rad);R_b*sin(135*deg2rad);0];
B4=[R_b*cos(225*deg2rad);R_b*sin(225*deg2rad);0];
B5=[R_b*cos(255*deg2rad);R_b*sin(255*deg2rad);0];
B6=[R_b*cos(345*deg2rad);R_b*sin(345*deg2rad);0];
Bx1=B1(1,:);
Bx2=B2(1,:);
Bx3=B3(1,:);
Bx4=B4(1,:);
Bx5=B5(1,:);
Bx6=B6(1,:);
By1=B1(2,:);
By2=B2(2,:);
By3=B3(2,:);
By4=B4(2,:);
By5=B5(2,:);
By6=B6(2,:);
Bz1=B1(3,:);
Bz2=B2(3,:);
Bz3=B3(3,:);
Bz4=B4(3,:);
Bz5=B5(3,:);
Bz6=B6(3,:);
P1=[R_p*cos(75*deg2rad);R_b*sin(75*deg2rad);0];
P2=[R_p*cos(165*deg2rad);R_b*sin(165*deg2rad);0];
P3=[R_p*cos(195*deg2rad);R_b*sin(195*deg2rad);0];
P4=[R_p*cos(285*deg2rad);R_b*sin(285*deg2rad);0];
P5=[R_p*cos(315*deg2rad);R_b*sin(315*deg2rad);0];
P6=[R_p*cos(405*deg2rad);R_b*sin(405*deg2rad);0];
Px1=P1(1,:);
Px2=P2(1,:);
Px3=P3(1,:);
Px4=P4(1,:);
Px5=P5(1,:);
Px6=P6(1,:);
Py1=P1(2,:);
Py2=P2(2,:);
Py3=P3(2,:);
Py4=P4(2,:);
Py5=P5(2,:);
Py6=P6(2,:);
Pz1=P1(3,:);
Pz2=P2(3,:);
Pz3=P3(3,:);
Pz4=P4(3,:);
Pz5=P5(3,:);
Pz6=P6(3,:);
X=0.9425;
beta=0.531;
Y=0;
gama=0;
alpha=0;
Z=sin(X)+2;
R1=(X+((cos(gama)*cos(beta))*Px1)+(((cos(gama)*sin(beta)*sin(alpha))-(sin(gama)*cos(alpha)))*Py1)+(((cos(gama)*sin(beta)*cos(alpha))+(sin(gama)*sin(alpha)))*Pz1)-Bx1)^2+(Y+((sin(gama)*cos(beta))*Px1)+(((sin(gama)*sin(beta)*sin(alpha))+(cos(gama)*cos(alpha)))*Py1)+(((sin(gama)*sin(beta)*cos(alpha))-(cos(gama)*sin(alpha)))*Pz1)-By1)^2+(Z+((-sin(beta))*Px1)+((cos(beta)*sin(alpha))*Py1)+((cos(beta)*cos(alpha))*Pz1)-Bz1)^2;
L1=R1^0.5-Q0;
R2=(X+((cos(gama)*cos(beta))*Px2)+(((cos(gama)*sin(beta)*sin(alpha))-(sin(gama)*cos(alpha)))*Py2)+(((cos(gama)*sin(beta)*cos(alpha))+(sin(gama)*sin(alpha)))*Pz2)-Bx2)^2+(Y+((sin(gama)*cos(beta))*Px2)+(((sin(gama)*sin(beta)*sin(alpha))+(cos(gama)*cos(alpha)))*Py2)+(((sin(gama)*sin(beta)*cos(alpha))-(cos(gama)*sin(alpha)))*Pz2)-By2)^2+(Z+((-sin(beta))*Px2)+((cos(beta)*sin(alpha))*Py2)+((cos(beta)*cos(alpha))*Pz2)-Bz2)^2;
L2=R2^0.5-Q0;
vpa(R1.')
vpa(R2.')
INVERSE SCRIPT
syms X Y Z alpha beta gama
deg2rad=pi/180;
theta_b=15*deg2rad;
theta_p=15*deg2rad;
R_b=1;
R_p=0.9;
Q0=1; %initial leg length
p=[X;Y;Z];
B1=[R_b*cos(15*deg2rad);R_b*sin(15*deg2rad);0];
B2=[R_b*cos(105*deg2rad);R_b*sin(105*deg2rad);0];
B3=[R_b*cos(135*deg2rad);R_b*sin(135*deg2rad);0];
B4=[R_b*cos(225*deg2rad);R_b*sin(225*deg2rad);0];
B5=[R_b*cos(255*deg2rad);R_b*sin(255*deg2rad);0];
B6=[R_b*cos(345*deg2rad);R_b*sin(345*deg2rad);0];
Bx1=B1(1,:);
Bx2=B2(1,:);
Bx3=B3(1,:);
Bx4=B4(1,:);
Bx5=B5(1,:);
Bx6=B6(1,:);
By1=B1(2,:);
By2=B2(2,:);
By3=B3(2,:);
By4=B4(2,:);
By5=B5(2,:);
By6=B6(2,:);
Bz1=B1(3,:);
Bz2=B2(3,:);
Bz3=B3(3,:);
Bz4=B4(3,:);
Bz5=B5(3,:);
Bz6=B6(3,:);
P1=[R_p*cos(75*deg2rad);R_b*sin(75*deg2rad);0];
P2=[R_p*cos(165*deg2rad);R_b*sin(165*deg2rad);0];
P3=[R_p*cos(195*deg2rad);R_b*sin(195*deg2rad);0];
P4=[R_p*cos(285*deg2rad);R_b*sin(285*deg2rad);0];
P5=[R_p*cos(315*deg2rad);R_b*sin(315*deg2rad);0];
P6=[R_p*cos(405*deg2rad);R_b*sin(405*deg2rad);0];
Px1=P1(1,:);
Px2=P2(1,:);
Px3=P3(1,:);
Px4=P4(1,:);
Px5=P5(1,:);
Px6=P6(1,:);
Py1=P1(2,:);
Py2=P2(2,:);
Py3=P3(2,:);
Py4=P4(2,:);
Py5=P5(2,:);
Py6=P6(2,:);
Pz1=P1(3,:);
Pz2=P2(3,:);
Pz3=P3(3,:);
Pz4=P4(3,:);
Pz5=P5(3,:);
Pz6=P6(3,:);
Y=0;
gama=0;
alpha=0;
R1=(X+((cos(gama)*cos(beta))*Px1)+(((cos(gama)*sin(beta)*sin(alpha))-(sin(gama)*cos(alpha)))*Py1)+(((cos(gama)*sin(beta)*cos(alpha))+(sin(gama)*sin(alpha)))*Pz1)-Bx1)^2+(Y+((sin(gama)*cos(beta))*Px1)+(((sin(gama)*sin(beta)*sin(alpha))+(cos(gama)*cos(alpha)))*Py1)+(((sin(gama)*sin(beta)*cos(alpha))-(cos(gama)*sin(alpha)))*Pz1)-By1)^2+(Z+((-sin(beta))*Px1)+((cos(beta)*sin(alpha))*Py1)+((cos(beta)*cos(alpha))*Pz1)-Bz1)^2;
L1=R1^0.5-Q0;
R2=(X+((cos(gama)*cos(beta))*Px2)+(((cos(gama)*sin(beta)*sin(alpha))-(sin(gama)*cos(alpha)))*Py2)+(((cos(gama)*sin(beta)*cos(alpha))+(sin(gama)*sin(alpha)))*Pz2)-Bx2)^2+(Y+((sin(gama)*cos(beta))*Px2)+(((sin(gama)*sin(beta)*sin(alpha))+(cos(gama)*cos(alpha)))*Py2)+(((sin(gama)*sin(beta)*cos(alpha))-(cos(gama)*sin(alpha)))*Pz2)-By2)^2+(Z+((-sin(beta))*Px2)+((cos(beta)*sin(alpha))*Py2)+((cos(beta)*cos(alpha))*Pz2)-Bz2)^2;
L2=R2^0.5-Q0;
A=vpasolve(R1==7.7731884,R2==11.2615,Z==sin(X)+2);
vpa(A.X')
vpa(A.Z')
vpa(A.beta')
0 Kommentare
Akzeptierte Antwort
David Goodmanson
am 21 Jul. 2021
Bearbeitet: David Goodmanson
am 21 Jul. 2021
Hi Jack,
Fortunately the solver is coming up with the correct angle, except for the 2*pi ambiguity. So, after the solver does its job you can use
mod(50.796485621,2*pi)
ans = 0.5310
1 Kommentar
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Applications finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!