Difference between revisions of "A-matrices"
From Robotics
Line 5: | Line 5: | ||
[[File:dh-params-steps.png|center|950px]] | [[File:dh-params-steps.png|center|950px]] | ||
− | |||
− | |||
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|combinations of transformations]], the combined A-matrix is determined as follows: | 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|combinations of transformations]], the combined A-matrix is determined as follows: | ||
:<math> | :<math> | ||
Line 36: | Line 34: | ||
0 & \cos{\alpha_n} & -\sin{\alpha_n} & 0 \\ | 0 & \cos{\alpha_n} & -\sin{\alpha_n} & 0 \\ | ||
0 & \sin{\alpha_n} & \cos{\alpha_n} & 0 \\ | 0 & \sin{\alpha_n} & \cos{\alpha_n} & 0 \\ | ||
− | 0 & 0 & 1 & d \\ | + | 0 & 0 & 0 & 1 |
+ | \end{array}\right] \\ | ||
+ | \left[\begin{array}{cccc} | ||
+ | \cos{\theta_n} & -\sin{\theta_n}\cos{\alpha_n} & \sin{\theta_n}\sin{\alpha_n} & l\cos{\theta_n} \\ | ||
+ | \sin{\theta_n} & \cos{\theta_n}\cos{\alpha_n} & -\cos{\theta_n}\sin{\alpha_n} & l\sin{\theta_n} \\ | ||
+ | 0 & \sin{\alpha_n} & \cos{\alpha_n} & d \\ | ||
0 & 0 & 0 & 1 | 0 & 0 & 0 & 1 | ||
\end{array}\right] | \end{array}\right] | ||
− | \end{align} | + | \end{align} |
</math> | </math> | ||
+ | |||
+ | |||
+ | [[File:amatrices.png|right|450px]] | ||
[[Category:Article]] | [[Category:Article]] | ||
[[Category:Denavit-Hartenberg]] | [[Category:Denavit-Hartenberg]] |
Revision as of 12:21, 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: