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I'm getting stuck on multiplying matrices together and cannot figure out for the life of me where I'm going wrong.

I'm working on some robotics and reading through a textbook which gives the following example of matrices:

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This gives me a transformation matrix for each joint in a robot, which then gets multiplied together to give a rotational matrix for all 3 joints together.

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When actually doing this multiplication myself, I always come up with the same incorrect matrix.

I start by multiplying A4 * A5 which I get matrix A45 as:

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I then multiply A45 x A6 and get this:

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R12, R21 and R22 have signs that do not match the example.

To multiply, I'm summing the product of each element in a row for the first matrix by each element in a column for the second matrix:

enter image description here

I feel like I'm doing it right and it just doesn't make sense to me how I'm getting different sign values. Can anyone spot where I'm going wrong?

Joe Jankowiak
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  • I think you're right and the textbook contains an error. One way to double check would be to choose random values for the various constants and multiply the matrices in Python. – littleO Oct 16 '21 at 00:40
  • Its weird because I have another example from another paper that I also get a different answer on so I figured I was doing something wrong. Do you happen to know what the little dot next to the A6 and T36 matrices mean? They use that notation throughout the textbook and I can't find anything on it. I will verify with a matrix library that my results are correct. – Joe Jankowiak Oct 16 '21 at 00:51
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    That little dot is just a period marking the end of a sentence. – littleO Oct 16 '21 at 00:59
  • Figured it was some weird math symbol lol, that makes more sense. Thanks – Joe Jankowiak Oct 16 '21 at 01:01
  • Your computed value for the 2nd entry in the top row is correct; the " supposed" value is wrong. Somehow a plus sign became a minus. – DanielWainfleet Oct 16 '21 at 05:48

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