i am tring to use matrices to solve for the linear equation. But the q in the matrices is itself a vector. The answer i need to get is a vector too.

% prerequizte
A_E = 16;
E_C = 13;
F_E = 3;
O_F = 13;
D_F = 13;
B_C = 32;
O_E = 16;
A_E1 = 16;
A_C1 = 29;
D_C1 = 3;
O_F1 = 13;
D_F1 = 13;
D_B1 = 35
O_E1 = 16;
%A_0 = sqrt((x_a-x_0)^2-(y_a-y_0)^2);
r = 2;  % opening time
t = [0:0.2:2]; 
%theta_b = 
%q = acos(0.5)
% for 0
x_0 = 0;
y_0 = 0;
% for A
x_a = 0
y_a = -17.5-12.5*cos(pi*t/r);
y_aa = diff(y_a)
y_aaa = diff(y_aa)
A_0 = sqrt((y_a-y_0).^2);
% find angle
theta_a3 = acosd((O_E^2-A_E^2-A_0.^2)./(-2*A_0.*A_E)); %theta 3
theta_o0 = acosd((A_E^2-A_0.^2-O_E^2)./(-2*O_E*A_0)); %theta 
theta_a33 = diff(theta_a3);
theta_a333 = diff(theta_a33);
theta_o00 = diff(theta_o0);
theta_o000 = diff(theta_o00);
theta_a = 90-acosd((O_E^2-A_E^2-A_0.^2)./(-2*A_0.*A_E)); %theta 3
theta_o = 90-acosd((A_E^2-A_0.^2-O_E^2)./(-2*O_E*A_0));
theta_f = acosd((A_0.^2-O_E^2-A_E^2)./(-2*O_E*A_E))-theta_o;
theta_e = theta_f;
theta_b = 180-(acosd((O_E^2-A_E^2-A_0.^2)./(-2*A_0.*A_E))+acosd((A_E^2-A_0.^2-O_E^2)./(-2*O_E*A_0)))-theta_e;
%define the position of each joint
% for E
x_e = x_0+cosd(theta_a)*A_E
y_e = y_a+sind(theta_a)*A_E;
% for F
x_f = x_0+cosd(theta_o)*O_F
y_f = y_e+sind(theta_o)*F_E
% for D
x_d = x_f+cosd(theta_f)*D_F
y_d = y_f+sind(theta_f)*D_F;
% for c
x_c = x_e+cosd(theta_e)*E_C;
y_c = y_e+sind(theta_e)*E_C;
% for B
x_b = x_c+cosd(theta_b)*B_C;
y_b = y_c-sind(theta_b)*B_C;
% find the velocity and the velocity plot
k = [0:0.105:2]
y_ee = diff(y_e)
y_fe = diff(y_f)
y_de = diff(y_d)
y_ce = diff(y_c)
y_be = diff(y_b)
x_ee = diff(x_e)
x_fe = diff(x_f)
x_de = diff(x_d)
x_ce = diff(x_c)
x_be = diff(x_b)
v_e = sqrt(y_ee.^2+x_ee.^2);
v_f = sqrt(y_fe.^2+x_fe.^2);
v_d = sqrt(y_de.^2+x_de.^2);
v_c = sqrt(y_ce.^2+x_ce.^2);
v_b = sqrt(y_be.^2+x_be.^2);
% find the acceleration and the acceleration plot
p = [0:0.25:2]
y_eee = diff(y_e,2)
y_fee = diff(y_f,2)
y_dee = diff(y_d,2)
y_cee = diff(y_c,2)
y_bee = diff(y_b,2)
x_eee = diff(x_e,2)
x_fee = diff(x_f,2)
x_dee = diff(x_d,2)
x_cee = diff(x_c,2)
x_bee = diff(x_b,2)
mAE = 1.6 %kg
mAC = 2.9 %kg 
mOF = 1.3 %kg
mOE = 1.6 %kg 
mDC = 0.3 %kg 
mDB = 3.5 %kg 
mDF = 1.3 %kg
mB = 2.0 %kg
% find the left hand side equation 
q_1 = -A_E1*sin(theta_a3)
q_2 = A_E1*cos(theta_a3)
q_3 = -A_C1*sin(theta_a3)
q_4 = A_C1*cos(theta_a3)
q_5 = -O_F1*sin(theta_o0)
q_6 = O_F1*cos(theta_o0)
q_7 = -O_E1*sin(theta_o0)
q_8 = O_E1*cos(theta_o0)
q_9 = D_F1*sin(theta_a3)
q_10 = -D_F1*cos(theta_a3)
q_11 = D_C1*sin(theta_a3)
q_12 = D_C1*cos(theta_a3)
q_13 = D_B1*sin(theta_a3)
% find the right hand side equation
F2y = mAC*(y_aaa+ y_cee + y_eee)
F2x = mAC*(0+ x_cee+x_eee)
F3y = mOE*(0+y_fee+y_eee)
F3x = mOE*(0+x_fee+x_eee)
F4x = 0
F4y = 0
F5x = mDF*(x_dee+x_fee);
F5y = mDF*(y_dee+y_fee);
F6x = mDB*(x_dee+x_cee);
F6y = mDB*(y_dee+ y_cee)+mB*9.81;
M_1 = 1/12*mAC*(A_C1)^2*theta_a333;
M_2 = 1/12*mOE*(O_E1)^2*theta_o000;
M_3 = 1/12*mDF*(D_F1)^2*theta_a333;
M_4 = 1/12*mDB*(D_B1)^2*theta_a333%+D_B1.*theta_a3;
equ = [0 1 0 -1 0 0 0 0 0 0 0 -1;1 0 -1 0 0 0 0 0 0 0 -1 0;0 0 0 0 0 0 0 1 0 -1 0 1;0 0 0 0 0 0 1 0 -1 0 1 0;0 0 0 0 1 0 -1 0 0 0 0 0;0 0 0 0 0 1 0 -1 0 0 0 0;0 0 1 0 -1 0 0 0 0 0 0 0;0 0 0 1 0 -1 0 0 0 0 0 0;0 0 q_4 q_3 0 0 0 0 0 0 q_2 q_1;0 0 0 0 0 0 q_6 q_5 0 0 q_8 q_7;0 0 0 0 q_10 q_9 0 0 0 0 0 0;0 0 q_12 q_11 0 0 0 0 0 0 0 0]
equ_2 = [F2y;F2x;F3y;F3x;F4x;F4y;F5x;F5y;F6x;F6y;M_1;M_2:M_3;M_4];
Sol = inv(equ)*equ_2;

[Walter Roberson]

Are you sure that you want to be taking numeric differences all over the place?

That code looks to me as if you would be more interested in the derivatives -- but taking derivatives would require using the Symbolic Toolbox diff() to process symbolic expressions.

Or perhaps you want gradient

[Star Strider]

The ‘equ’ matrix is at least part of the problem.

Consider:

sequ = '[0 1 0 -1 0 0 0 0 0 0 0 -1;1 0 -1 0 0 0 0 0 0 0 -1 0;0 0 0 0 0 0 0 1 0 -1 0 1;0 0 0 0 0 0 1 0 -1 0 1 0;0 0 0 0 1 0 -1 0 0 0 0 0;0 0 0 0 0 1 0 -1 0 0 0 0;0 0 1 0 -1 0 0 0 0 0 0 0;0 0 0 1 0 -1 0 0 0 0 0 0;0 0 q_4 q_3 0 0 0 0 0 0 q_2 q_1;0 0 0 0 0 0 q_6 q_5 0 0 q_8 q_7;0 0 0 0 q_10 q_9 0 0 0 0 0 0;0 0 q_12 q_11 0 0 0 0 0 0 0 0]';
idx = strfind(sequ,';');
didx = diff([0 idx])

didx = 1×11

27 26 25 25 25 25 25 25 32 32 29

All those intervals must be equal, although I do not know what value they should be equal to.

And the diff function does not take the derivative of a vector, it takes the element-wise differences. To calculate the numerical derivative, use the gradient function. To take the second derivative, use it on the gradient of the original vector.

.

[kaixi gu]

Thank you for correcting my mistakes. yes that make sense. i corrected with the gradient. now i just can't figure out how to plug in those 1*11 value into the matrixes. Because i do want to get the Sol with respect to those 1*11 q value.

[Star Strider]

All the columns in ‘equ’ must be equal lengths ‘N’ to create the 11xN matrix. You need to decide what ‘N’ should be, and then create the matrix.

Answer 1

[Arka]

Hi,

The code and the error generated from the code are given below:

% prerequizte
A_E = 16;
E_C = 13;
F_E = 3;
O_F = 13;
D_F = 13;
B_C = 32;
O_E = 16;
A_E1 = 16;
A_C1 = 29;
D_C1 = 3;
O_F1 = 13;
D_F1 = 13;
D_B1 = 35;
O_E1 = 16;
%A_0 = sqrt((x_a-x_0)^2-(y_a-y_0)^2);
r = 2;  % opening time
t = [0:0.2:2]; 
%theta_b = 
%q = acos(0.5)
% for 0
x_0 = 0;
y_0 = 0;
% for A
x_a = 0;
y_a = -17.5-12.5*cos(pi*t/r);
y_aa = diff(y_a);
y_aaa = diff(y_aa);
A_0 = sqrt((y_a-y_0).^2);
% find angle
theta_a3 = acosd((O_E^2-A_E^2-A_0.^2)./(-2*A_0.*A_E)); %theta 3
theta_o0 = acosd((A_E^2-A_0.^2-O_E^2)./(-2*O_E*A_0)); %theta 
theta_a33 = diff(theta_a3);
theta_a333 = diff(theta_a33);
theta_o00 = diff(theta_o0);
theta_o000 = diff(theta_o00);
theta_a = 90-acosd((O_E^2-A_E^2-A_0.^2)./(-2*A_0.*A_E)); %theta 3
theta_o = 90-acosd((A_E^2-A_0.^2-O_E^2)./(-2*O_E*A_0));
theta_f = acosd((A_0.^2-O_E^2-A_E^2)./(-2*O_E*A_E))-theta_o;
theta_e = theta_f;
theta_b = 180-(acosd((O_E^2-A_E^2-A_0.^2)./(-2*A_0.*A_E))+acosd((A_E^2-A_0.^2-O_E^2)./(-2*O_E*A_0)))-theta_e;
%define the position of each joint
% for E
x_e = x_0+cosd(theta_a)*A_E;
y_e = y_a+sind(theta_a)*A_E;
% for F
x_f = x_0+cosd(theta_o)*O_F;
y_f = y_e+sind(theta_o)*F_E;
% for D
x_d = x_f+cosd(theta_f)*D_F;
y_d = y_f+sind(theta_f)*D_F;
% for c
x_c = x_e+cosd(theta_e)*E_C;
y_c = y_e+sind(theta_e)*E_C;
% for B
x_b = x_c+cosd(theta_b)*B_C;
y_b = y_c-sind(theta_b)*B_C;
% find the velocity and the velocity plot
k = [0:0.105:2];
y_ee = diff(y_e);
y_fe = diff(y_f);
y_de = diff(y_d);
y_ce = diff(y_c);
y_be = diff(y_b);
x_ee = diff(x_e);
x_fe = diff(x_f);
x_de = diff(x_d);
x_ce = diff(x_c);
x_be = diff(x_b);
v_e = sqrt(y_ee.^2+x_ee.^2);
v_f = sqrt(y_fe.^2+x_fe.^2);
v_d = sqrt(y_de.^2+x_de.^2);
v_c = sqrt(y_ce.^2+x_ce.^2);
v_b = sqrt(y_be.^2+x_be.^2);
% find the acceleration and the acceleration plot
p = [0:0.25:2];
y_eee = diff(y_e,2);
y_fee = diff(y_f,2);
y_dee = diff(y_d,2);
y_cee = diff(y_c,2);
y_bee = diff(y_b,2);
x_eee = diff(x_e,2);
x_fee = diff(x_f,2);
x_dee = diff(x_d,2);
x_cee = diff(x_c,2);
x_bee = diff(x_b,2);
mAE = 1.6; %kg
mAC = 2.9; %kg 
mOF = 1.3; %kg
mOE = 1.6; %kg 
mDC = 0.3; %kg 
mDB = 3.5; %kg 
mDF = 1.3; %kg
mB = 2.0; %kg
% find the left hand side equation 
q_1 = -A_E1*sin(theta_a3);
q_2 = A_E1*cos(theta_a3);
q_3 = -A_C1*sin(theta_a3);
q_4 = A_C1*cos(theta_a3);
q_5 = -O_F1*sin(theta_o0);
q_6 = O_F1*cos(theta_o0);
q_7 = -O_E1*sin(theta_o0);
q_8 = O_E1*cos(theta_o0);
q_9 = D_F1*sin(theta_a3);
q_10 = -D_F1*cos(theta_a3);
q_11 = D_C1*sin(theta_a3);
q_12 = D_C1*cos(theta_a3);
q_13 = D_B1*sin(theta_a3);
% find the right hand side equation
F2y = mAC*(y_aaa+ y_cee + y_eee);
F2x = mAC*(0+ x_cee+x_eee);
F3y = mOE*(0+y_fee+y_eee);
F3x = mOE*(0+x_fee+x_eee);
F4x = 0;
F4y = 0;
F5x = mDF*(x_dee+x_fee);
F5y = mDF*(y_dee+y_fee);
F6x = mDB*(x_dee+x_cee);
F6y = mDB*(y_dee+ y_cee)+mB*9.81;
M_1 = 1/12*mAC*(A_C1)^2*theta_a333;
M_2 = 1/12*mOE*(O_E1)^2*theta_o000;
M_3 = 1/12*mDF*(D_F1)^2*theta_a333;
M_4 = 1/12*mDB*(D_B1)^2*theta_a333;%+D_B1.*theta_a3;
equ = [0 1 0 -1 0 0 0 0 0 0 0 -1;1 0 -1 0 0 0 0 0 0 0 -1 0;0 0 0 0 0 0 0 1 0 -1 0 1;0 0 0 0 0 0 1 0 -1 0 1 0;0 0 0 0 1 0 -1 0 0 0 0 0;0 0 0 0 0 1 0 -1 0 0 0 0;0 0 1 0 -1 0 0 0 0 0 0 0;0 0 0 1 0 -1 0 0 0 0 0 0;0 0 q_4 q_3 0 0 0 0 0 0 q_2 q_1;0 0 0 0 0 0 q_6 q_5 0 0 q_8 q_7;0 0 0 0 q_10 q_9 0 0 0 0 0 0;0 0 q_12 q_11 0 0 0 0 0 0 0 0]

Error using vertcat
Dimensions of arrays being concatenated are not consistent.

equ_2 = [F2y;F2x;F3y;F3x;F4x;F4y;F5x;F5y;F6x;F6y;M_1;M_2:M_3;M_4];
Sol = inv(equ)*equ_2;

From the error, it seems that the equ matrix cannot be created, because there is a mismatch in the dimensions of the arrays that you are trying to concatenate.

If you check, the q_x (where x = 1:13) variables have a dimension of 1x11, but the other values (0, 1, and -1) are scalars, i.e. they have a dimension of 1x1.

In rows such as [0 1 0 -1 0 0 0 0 0 0 0 -1], the dimension is 1x12, but in rows such as [0 0 q_12 q_11 0 0 0 0 0 0 0 0], the dimension is 1x32.

This is causing the error.

You need to modify the code so that the vector values are consistent. Then, the concatenation will be successful.