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This is a rather simple question, but I'm new to the field so I need some help.

I am trying to compute the forward kinematics using the DH method as shown below:

DH analysis

I extract the rotation and translation matrices. Then I try to check if they are correct. I take the base vector $[1,0,0]^T$ in the $(x_0, y_0, z_0)$ system and using the $A^0_{0'}$ transformation matrix I want to see what vector I get in the $(x_0', y_0', z_0')$ axis.

As you can see, I get the base vector $[0,1,0]^T$ which is the $y_0'$ vector, when I should be getting $[0,0,1]^T$ i.e the $z_0'$ vector.

What am I missing?

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1 Answer 1

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Your transformation matrix should written as $A_{0}^{0'}$. In your case, say we have a vector $q_0$.

And for the formula:

$q_{0} = A_{0}^{0'}q_{0'}$

The vector $q_{0'}$ is originally represented on frame $0'$, and you want to find the value $q_{0}$, which is the value of the vector $q_{0'}$ represented on frame $0$.

From your image, the vector $[1,0,0]$ is already on frame $0$. So the vector $[1,0,0]$ is the result ($q_{0}$), not the transformation matrix multiplier ($q_{0'}$).

$[1,0,0]^T = A_{0}^{0'}q_{0'}$

Where $q_{0'}$ here is $[0,0,1]^T$, the value that you are looking for.

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