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 the parameters actually describe. <math>\theta</math>, <math>d</math>, <math>l</math> and <math>\alpha</math> define 4 [[Transformations|transformations]] that are applied [[Combinations of transformations|consecutively]] to transform the coordinate frame <math>K_{n-1}</math> to <math>K_n</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 the parameters actually describe. <math>\theta</math>, <math>d</math>, <math>l</math> and <math>\alpha</math> define 4 [[Transformations|transformations]] that are applied [[Combinations of transformations|consecutively]] to transform the coordinate frame <math>K_{n-1}</math> to <math>K_n</math>. First a rotation about the <math>x_{n-1}</math>-axis by <math>\alpha</math> is applied followed by a translation along it by <math>l</math>. Then the coordinate frame is rotated about the <math>z_{n-1}</math>-axis by <math>\theta</math>. Finally a translation along the <math>z_{n-1}</math>-axis leads to the next coordinate frame <math>K_n</math>. Some further aspects about the meaning and the use of the 4 parameters are described in the following article about the [[A-matrices]]. |
[[File:dh-params-steps.png|center|900px]] | [[File:dh-params-steps.png|center|900px]] |
Revision as of 11:18, 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 the parameters actually describe. , , and define 4 transformations that are applied consecutively to transform the coordinate frame to . First a rotation about the -axis by is applied followed by a translation along it by . Then the coordinate frame is rotated about the -axis by . Finally a translation along the -axis leads to the next coordinate frame . Some further aspects about the meaning and the use of the 4 parameters are described in the following article about the A-matrices.