Difference between revisions of "A-matrices"
From Robotics
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0 & 0 & 0 & 1 | 0 & 0 & 0 & 1 | ||
\end{array}\right] \\ | \end{array}\right] \\ | ||
+ | &= | ||
\left[\begin{array}{cccc} | \left[\begin{array}{cccc} | ||
\cos{\theta_n} & -\sin{\theta_n}\cos{\alpha_n} & \sin{\theta_n}\sin{\alpha_n} & l\cos{\theta_n} \\ | \cos{\theta_n} & -\sin{\theta_n}\cos{\alpha_n} & \sin{\theta_n}\sin{\alpha_n} & l\cos{\theta_n} \\ |
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: