I am working on some manipulator projects and come across a few variants of the homogenous transformation matrix. I've been working on matlab and they give slightly different answers. Assuming both are correct, I would like to ask which one to use and under what circumstances? Are there any conventions that follow along with these trransformation matrices.

variant 1 variant 2


1 Answer 1


On serial manipulator modelling, we commonly use Denavit-Hartenberg system. One important thing you need to know, there are 2 variant of it, that is Denavit-Hartenberg system and Modified Denavit-Hartenberg. The main difference between two is coordinates system attachment to links and order of performed transformation [1].

  • Denavit-Hartenberg System DH System

Fig 1. DH Coordinate System Attachment

Will have HTM


  • Modified Denavit-Hartenberg System MDH System

Fig 2. MDH Coordinate System Attachment

Will have HTM


And both are correct. My professor recommendation was to use MDH because it use less variable to represent manipulator.

Reference :

  1. Denavit Hartenberg Modelling Wikipedia
  • 1
    $\begingroup$ Thanks! @Albert H M, I found a clearer explanation of the exact differences here. researchgate.net/post/…. $\endgroup$
    – trex98
    Commented May 10, 2021 at 14:40

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