# A-matrices

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Overview: Denavit-Hartenberg Convention |
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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 computed by setting in the parameters , , and determined before. 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 including the static transformation as well as the translation or rotation caused by the joint .