Help on trigonometric equation solution. Thanks a lot!

조회 수: 1 (최근 30일)
Jack Dong
Jack Dong 2021년 7월 21일
댓글: Jack Dong 2021년 7월 22일
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')

이 질문에 답변하려면 로그인하십시오.

채택된 답변

David Goodmanson
David Goodmanson 2021년 7월 21일
편집: David Goodmanson 2021년 7월 21일
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
  댓글 수: 1
Jack Dong
Jack Dong 2021년 7월 22일
Thanks David for your great answer but can we embed it into my script so that after running, I get the correct beta immediately. Thanks!
I tried this but failed!
vpa(A.X')
vpa(A.Z')
vpa(A.beta')
beta1=mod(A.beta,2*pi)
-----> Result is
ans =
0.94245504646393978078105437144795
ans =
2.8090036222785815735410394206806
ans =
50.796485621630240525665530786852
beta1 =
mod(50.796485621630240525665530786852, 2*pi)
------------------------------------------------------
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')
beta1=mod(A.beta,2*pi)

댓글을 달려면 로그인하십시오.

추가 답변 (0개)

카테고리

Help Center 및 File Exchange에서 Applications에 대해 자세히 알아보기

태그

제품


릴리스

R2019b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by