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I found this picture on the web and was working through it to make sure I understood the derivation for a PPP arm. I believe for link 2, alpha_2 ought to be -90 and not +90.

Additionally, I don't understand why theta_3 is -90, give that link_3 is only a translation of link_2.

Am I misunderstanding something or are the provided DH parameters incorrect with respect to the provided drawing?

enter image description here

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  • $\begingroup$ where did you get that picture? $\endgroup$
    – jsotola
    Apr 3 '19 at 1:14
  • $\begingroup$ I was googling for 'dh parameters PPP arm' and found it under the image search result. Why do you ask? $\endgroup$
    – blueether
    Apr 3 '19 at 13:15
  • $\begingroup$ i did not ask you how did you find the picture? ...... i guess that i should have said please provide a link to the picture ...... the reason that i ask is that there may have been a link to an explanation regarding the calculation $\endgroup$
    – jsotola
    Apr 3 '19 at 16:00
  • $\begingroup$ ah, apologies for misunderstanding. I found the picture here - reddit.com/r/robotics/comments/5fga3d/dh_parameter_check. The link has some short discussion but doesn't seem to agree on an answer. $\endgroup$
    – blueether
    Apr 3 '19 at 16:59
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The DH parameters comes from the common normal between two consecutive Z axes. Every time you're in doubt about the DH parameters, you can follow common guidelines between two consecutive axes.

In this case, $d_i$ is the distance along previous Z starting from the previous origin O to the intersection of the new X and previous Z axis, which is variable in the case of prismatic joints.

$r_i$ (or $a_i$) is the distance in current X starting from current origin O to the intersection between previous Z and current X.

$\theta_i$ is the angle in previous Z to align the previous X with the new X.

$\alpha_i$ is the angle in current X to align previous Z to current Z.

From the picture, starting with link 1:

  • $d$: The distance from previous O to the intersection of previous Z and current X is variable, so it's d1.

  • $a$: The distance in current X starting from current O to the intersection between previous Z and current X is 0.

  • $\theta$: The angle in previous Z to align previous X with the new X is 0.

  • $\alpha$: The angle in current X to align previous Z to current Z is -90 (right hand rule).

For link 2:

  • $d$: The distance from previous O to the intersection of previous Z and current X is variable, so it's d2.

  • $a$: The distance in current X starting from current O to the intersection between previous Z and current X is 0.

  • $\theta$: The angle in previous Z to align previous X with the new X is 90 (right hand rule).

  • $\alpha$: The angle in current X to align previous Z to current Z is -90 (right hand rule).

For link 3:

  • $d$: The distance from previous O to the intersection of previous Z and current X is variable, so it's d3.

  • $a$: The distance in current X starting from current O to the intersection between previous Z and current X is 0.

  • $\theta$: The angle in previous Z to align previous X with the new X is 0 (right hand rule).

  • $\alpha$: The angle in current X to align previous Z to current Z is 0 (right hand rule).

So the correct DH Table for this robot would be:


Link 1: $a=0$, $\alpha=-90$, $d=d1$, $\theta=0$


Link 2: $a=0$, $\alpha=-90$, $d=d2$, $\theta=90$


Link 3: $a=0$, $\alpha=0$, $d=d3$, $\theta=0$


You can see some guidelines here.

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  • $\begingroup$ I did try to edit, but it was rejected. You have an error in your final table of D-H parameters for link 1. d should be d1, not d2 (as noted earlier in your answer). $\endgroup$ Apr 3 '19 at 23:56
  • $\begingroup$ thank you, this makes sense to me. Also, I believe you meant d1 for link 1 in your table at the bottom? $\endgroup$
    – blueether
    Apr 3 '19 at 23:58
  • $\begingroup$ Yes, it's d1. I edited. Glad to help. $\endgroup$ Apr 3 '19 at 23:59

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