# Order of DH parameters

My textbook uses the following order:

I would really like to know why are the parameters in the D-H table ordered (in columns) the way they are from left to right, can someone please help?

It is important to note that the order of multiplication does not matter. For example, you can multiply $$Rot_{z,\theta}*Trans_{z,\theta}$$ or $$Trans_{z,\theta}*Rot_{z,\theta}$$.

The order in which the columns are arranged do not matter in the D-H table. It's information given by each row taken collectively that matters, i.e. the 4 variables together decide what the transformation from frame $$(i-1)$$ to $$i$$ (Link $$i$$) will be.

From the indices you use, your textbook may be using the modified DH convention that inverts the X and Z transforms.

The order of the columns in the DH table does not matter, but please look at the following transformation built from each row and the transformations order from left to right. This is Equation 3.1 from the book "Robot Modeling and Control" by Mark Spong. Notice that other books may follow other conversions.

We have the four chained transformations from each row in the DH table: (1) Rotation about the Z-axis by an angle theta. (2) Translation along the Z-axis for a distance d. (3) Translation along the X-axis for a distance a. (4) Rotation about the X-axis by angle alpha.

This makes the ordering of columns of the DH table as theta, d, a, and alpha very intuitive because the operations and their related parameters have the same order. This makes each row's transformation calculation more straightforward.

To answer your question, the order is unimportant, but it is recommended to stick to one conversion in which the order to calculate the transformation and the order of finding DH parameters is the same to make things less confusing and easy to remember.

• Thank you for your answer, your columns will align with the formula you have defined for A, in my textbook the same transformation is given but in terms of alpha, a, theta d but then the columns of the matrix are alpha a d theta so I am still a little because of the chosen ordering, but it seems like the order does not matter...
– Tom
Commented Feb 21 at 8:36
• Thanks for your comment. Yes, the order is unimportant, but stick to a convention that is easy to remember and not to be confused when doing the DH parameters calculation. This topic of transformations and their related chaining/multiplication in 3D geometry calculations are very important to master now when you are studying them. I updated my answer accordingly. Happy learning! Commented Feb 21 at 23:26