error in the process of symbol operation of the matrix

Question

Asymptote001 2023-5-29

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编辑： John D'Errico 2023-5-29

It is convenient to use symbol operation to explore the relationship during the multiplication of matrices. And here is my code.

clc;clear;
theta = sym('theta',[1,4])
d = sym('d',[1,4])
a = sym('a',[1,4])
alpha = sym('alpha',[1,4])
T = ones(4,4)
for i = 2:1:4
    T = T*[cos(theta(i)) -sin(theta(i)) 0 a(i-1);
        sin(theta(i))*cos(alpha(i-1)) cos(theta(i))*cos(alpha(i-1)) -sin(alpha(i-1)) -d(i)*sin(alpha(i-1));
        sin(theta(i))*sin(alpha(i-1)) cos(theta(i))*sin(alpha(i-1)) cos(alpha(i-1)) d(i)*cos(alpha(i-1));
        0 0 0 1];
end
T

the answer is :

What is wrong with T?

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Answer 1

Matt J 2023-5-29

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编辑：Matt J 2023-5-29

在 MATLAB Online 中打开

Nothing is wrong with T, though possibly you didn't scroll down far enough to see the definitions of all the sigmas.

T =

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John D'Errico 2023-5-29

编辑：John D'Errico 2023-5-29

I would specuulate the issue is that T ends up as a rank 1 matrix, which it MUST, since T starts out as a rank 1 matrix, as ones(4).

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Answer 2

John D'Errico 2023-5-29

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编辑：John D'Errico 2023-5-29

在 MATLAB Online 中打开

Why do you think there is something wrong with T? We don't know why you wrote this code. It computes what you told MATLAB to compute.

T is displayed there TWICE. The first time it is an array of all ones. A BAD IDEA. I think you wanted T to start as an IDENTITY matrix, not a matrix of all ones.

help eye
 EYE Identity matrix.
    EYE(N) is the N-by-N identity matrix.
 
    EYE(M,N) or EYE([M,N]) is an M-by-N matrix with 1's on
    the diagonal and zeros elsewhere.
 
    EYE(SIZE(A)) is the same size as A.
 
    EYE with no arguments is the scalar 1.
 
    EYE(..., CLASSNAME) is a matrix with ones of class specified by
    CLASSNAME on the diagonal and zeros elsewhere.
 
    EYE(..., 'like', Y) is an identity matrix with the same data type, sparsity,
    and complexity (real or complex) as the numeric variable Y.
 
    Note: The size inputs M and N should be nonnegative integers. 
    Negative integers are treated as 0.
 
    Example:
       x = eye(2,3,'int8');
 
    See also SPEYE, ONES, ZEROS, RAND, RANDN.

    Documentation for eye
       doc eye

    Other uses of eye

       codistributed/eye      codistributor2dbc/eye    fixedpoint/eye
       codistributor1d/eye    distributed/eye          gpuArray/eye

The point is, if you are looking at this as a sequence of rotations, then you need to start with an identity matrix.