dot multiplication of the matrices is not the same when you feed the matrix and concatenate the matrix

I try to constact two matrix from anther matrix by concatnate the matrix in row and clumme as you can see in the code. But the anw is not the same. I do the culcuation by hand the correct anw is the one I feed it by hard code it . What I do wrong?

clc ,clear
syms theta1 theta2 a1 a2 a3 a4
R0_0 = eye(3)
R0_1 = [cos(theta1) -sin(theta1) 0 ; sin(theta1) cos(theta1) 0;0 0 1 ];
R1_2 = [cos(theta2) -sin(theta2) 0 ; sin(theta2) cos(theta2) 0;0 0 1];



d0_1 = [a2*cos(theta1);a2*sin(theta1);a1]
d1_2 = [a4*cos(theta2);a4*sin(theta2);a3]

% constraction the matrix
H0_1 = [[R0_1,d0_1];h] % concatnate the matrix 
H1_2 = [[R1_2,d1_2];h] % concatnate the matrix 

% hard code the matrix
% H0_1h is R0_1 concatnate with d0_1 in colume and concatnate with [0 0 0 1]
% in row 
H0_1h = [cos(theta1) -sin(theta1) 0 a2*cos(theta1) ; sin(theta1) cos(theta1) 0 a2*sin(theta1) ; 0 0 1 a1 ; 0 0 0 1]
% H0_1h is R0_1 concatnate with d0_1 in colume and concatnate with [0 0 0 1]
% in row 
H1_2h =  [cos(theta2) -sin(theta2) 0 a3*cos(theta2) ; sin(theta2) cos(theta2) 0 a3*sin(theta2) ; 0 0 1 a4 ; 0 0 0 1]


% dot product of the matrix

% This is the dot product from the concatnate matrix
% It wrong by my culclation
H0_2 = H0_1 * H1_2
%This is the dot proudct from hard-code the matrxi
H0_2h = H0_1h * H1_2h

[KSSV]

What is h?

[mohammed alshrooqi]

h = [ 0 0 0 1]

Answer 1

[David Goodmanson]

Hi mohammed,

For H1_2 you have switched a3 and a4 between the first calculation and the hand calculation. So you get two different results.