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This robot has 2 revolute joints in advance then one cylindrical joint, then one revolute joint, then another cylindrical joint, then three revolute joints at the end.

There is no D-H table for that and I modeled it in Simulink with the help of Simscape. Now I need the D-H table for the controller part in the Matlab function.

I know that If the rotation of z-axis happens about its X-axis like joint number 2, I can show this change as an Alpha in my D-H table. As it illustrates, rotation of z-axis of revolute joint number 4 happened about the y-axis of TJ2. How can I show this kind of rotation of z-axis in my D-H table?

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Here is a video on what the DH parameters are that I highly recommend to everyone that wants to learn about them.

I think I understand your question, and the trouble you're having is coming from the fact that your frames are not aligned correctly per the DH standard. Since they're not aligned correctly, your terms are not working out right.

The important thing is that, as mentioned around 0:42 in the video, "The DH parameters are derived from the common normal between the z axes. The common normal is orthogonal to both vectors and is also the shortest line between them."

So the problem when you ask,

As it illustrates, rotation of z-axis of revolute joint number 4 happened about the y-axis of TJ2. How can I show this kind of rotation of z-axis in my D-H table?

is that you can't. Your frames are drawn incorrectly; the x-axis should be orthogonal to both axes. Instead, in the case of TJ2, $x_{TJ2}$ is parallel to $z_3$.

In fact, in looking over your diagram again, this looks like a common problem for all of your joints - each of your x axes is parallel to the z-axis of the previous joint. You need to redraw your frames and then you can work out the DH parameters.

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  • $\begingroup$ I see. So the Z-axis are correct I just have to remodel my X-axis in way of making them orthogonal to both Z-axises. I will try it to see if I can make it right. Thank you so much Chuck. $\endgroup$
    – Mana Mirmirani
    Aug 17, 2018 at 15:11
  • $\begingroup$ @ManaMirmirani - Yes, the Z-axis is always the axis about which there is rotation, or along which there is translation. The x-axis is defined by the common normal between the two. Right-handed convention then dictates where the y-axis will be. $\endgroup$
    – Chuck ♦
    Aug 17, 2018 at 15:43
  • $\begingroup$ I remodel my robot axis. First, I modelled the robot arm with Simscape version 1. Now I'm trying to get D-H parameters based on my Simscape model. In fact, first I got the D-H parameters based on the Denavite-Hartunberg parameters law. I got the matrices of rotation from base to each joint. The matrices of rotation from the kinematic model in code and from the Simscape model with respect to the base for each joint should be the same. I remodelled a lot the D-H parameters and also my Simscape model, but I have not got the same matrices transfer. I couldn't realize what the problem is. $\endgroup$
    – Mana Mirmirani
    Aug 20, 2018 at 23:28

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