Difference between revisions of "Denavit-Hartenberg parameters"
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: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 | :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 | ||
| − | The 4 parameters can rather be determined by just regarding the two coordinate frames, their axes and the [[Common normal|common normal]] like visualized above. To completely understand the parameters and their meaning, the figure below illustrates what they actually describe. <math>\theta</math>, <math>d</math>, <math>l</math> and <math>\alpha</math> define 4 transformations that are applied consecutively to transform a coordinate frame <math>K_{n-1}</math> | + | The 4 parameters can rather be determined by just regarding the two coordinate frames, their axes and the [[Common normal|common normal]] like visualized above. To completely understand the parameters and their meaning, the figure below illustrates what they actually describe. <math>\theta</math>, <math>d</math>, <math>l</math> and <math>\alpha</math> define 4 transformations that are applied consecutively to transform a coordinate frame <math>K_{n-1}</math> to <math>K_n</math>. Assume there is a coordinate frame <math>K_n^'</math> coincident with <math>K_{n-1}</math>. This coordinate frame is first rotated about the <math>x</math>-axis by <math>\alpha</math> and then translated along it by <math>l</math>. After that, a rotation about the <math>z</math>-axis by <math>\theta</math> is applied. Finally a translation along the <math>z</math> |
[[File:dh-params-steps.png|center|850px]] | [[File:dh-params-steps.png|center|850px]] | ||
Revision as of 11:08, 13 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 has to be described. Therefor the 4 Denavit-Hartenberg parameters 
, 
, 
and 
are used. The figure on the right shows two coordinate frames 
and 
and the corresponding common normal represented by a dashed red line. The figure illustrates the Denavit-Hartenberg parameters, that 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.
- 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
The 4 parameters can rather be determined by just regarding the two coordinate frames, their axes and the common normal like visualized above. To completely understand the parameters and their meaning, the figure below illustrates what they actually describe. , , and define 4 transformations that are applied consecutively to transform a coordinate frame to . Assume there is a coordinate frame 
coincident with . This coordinate frame is first rotated about the 
-axis by and then translated along it by . After that, a rotation about the 
-axis by is applied. Finally a translation along the
