Difference between revisions of "Denavit-Hartenberg parameters"
From Robotics
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[[File:dh-params-general.png|right|250px]] | [[File:dh-params-general.png|right|250px]] | ||
| − | When the [[Assigning coordinate frames|coordinate frames]] are assigned to a manipulator, the transformation between each two consecutive frames <math>K_{n-1}</math> and <math>K_n</math> have to be described. Therefor the 4 Denavit-Hartenberg parameters are used, which are defined as follows: | + | When the [[Assigning coordinate frames|coordinate frames]] are assigned to a manipulator, the transformation between each two consecutive frames <math>K_{n-1}</math> and <math>K_n</math> have to be described. Therefor the 4 Denavit-Hartenberg parameters illustrated in the figure on the right are used, which are defined as follows: |
;<math>\theta</math> | ;<math>\theta</math> | ||
| − | : | + | :The angle <math>\theta</math> is defined as the angle about the <math>z_{n-1}</math>-axis to align <math>x_{n-1}</math> with the new <math>x_{n}</math>-axis. |
;<math>d</math> | ;<math>d</math> | ||
| − | : | + | :<math>d</math> is the offset or translation, respectively, along the <math>z_{n-1}</math>-axis from the origin of <math>K_{n-1}</math> to the intersection with the [[Common normal|common normal]] (shown as a dashed red line in the figure). |
;<math>l</math> | ;<math>l</math> | ||
| − | : | + | :The parameter <math>l</math> corresponds to the length of the [[Common normal|common normal]] which is equivalent to the translation along it. |
| + | :If the related joint <math>J_n</math> is a revolute joint, <math>l</math> can also be regarded as the radius of the rotation about the <math>z_{n-1}</math>-axis | ||
;<math>\alpha</math> | ;<math>\alpha</math> | ||
| − | : | + | :The angle <math>\alpha</math> corresponds to the angle about the [[Common normal|common normal]] to align the <math>z_{n-1}</math>-axis with the new <math>z_{n}</math>-axis |
[[File:dh-params-steps.png|center|850px]] | [[File:dh-params-steps.png|center|850px]] | ||
Revision as of 18:11, 12 November 2015
| ← Back: Assigning coordinate frames | Overview: Denavit-Hartenberg Convention | Next: A-matrices → |
When the coordinate frames are assigned to a manipulator, the transformation between each two consecutive frames 
and 
have to be described. Therefor the 4 Denavit-Hartenberg parameters illustrated in the figure on the right are used, which are defined as follows:
- The angle is defined as the angle about the
-axis to align 
with the new 
-axis.
- is the offset or translation, respectively, along the -axis from the origin of to the intersection with the common normal (shown as a dashed red line in the figure).
- The parameter corresponds to the length of the common normal which is equivalent to the translation along it.
- If the related joint
is a revolute joint, can also be regarded as the radius of the rotation about the -axis
- The angle corresponds to the angle about the common normal to align the -axis with the new
-axis
