Difference between revisions of "A-matrices"
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So the A-matrix for link <math>n</math> can just be determined by setting in the parameters <math>\theta_n</math>, <math>d_n</math>, <math>l_n</math> and <math>\alpha_n</math>. As shown in the figure on the right, <math>A_n</math> then describes the transformation between the coordinate frames <math>K_{n-1}</math> at the beginning and <math>K_n</math> at the end of link <math>L_n</math>. | So the A-matrix for link <math>n</math> can just be determined by setting in the parameters <math>\theta_n</math>, <math>d_n</math>, <math>l_n</math> and <math>\alpha_n</math>. As shown in the figure on the right, <math>A_n</math> then describes the transformation between the coordinate frames <math>K_{n-1}</math> at the beginning and <math>K_n</math> at the end of link <math>L_n</math>. | ||
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[[Category:Article]] | [[Category:Article]] | ||
[[Category:Denavit-Hartenberg]] | [[Category:Denavit-Hartenberg]] |
Revision as of 12:27, 17 November 2015
← Back: Denavit-Hartenberg parameters | Overview: Denavit-Hartenberg Convention | Next: Typical link examples → |
The A-matrices describe the precise transformation between each two successive manipulator links. In the previous articles, it was described how the transformation can be described using local coordinate frames and the 4 Denavit-Hartenberg parameters. The parameters describe 2 translational and 2 rotational degrees of freedom, which correspond to 4 transformations, that are applied successively to transform coordinate frame with respect to frame like shown below.
The A-matrices now are used to combine the 4 successive transformations of the Denavit-Hartenberg parameters in one matrix. According to the figure above and following the rules for combinations of transformations, the combined A-matrix is determined as follows:
So the A-matrix for link can just be determined by setting in the parameters , , and . As shown in the figure on the right, then describes the transformation between the coordinate frames at the beginning and at the end of link .