This paper gives a fair descrioption of the geometry used in the Craig modified
This paper gives a lot of good information also:
- Alan Kilian <alank(at)timelogic.com>
Director of Bioinformatics, TimeLogic Corporation 763-449-7622
Ignoring indices, Asada-Slotine's (Paul's) Denavit-Hartenberg notation uses
the following rigid-body-transformation sequence for each link:
[z-rotation (by theta), z-translation (by d), x-rotation (by alpha),
x-translation (by a)]
Craig's notation uses the following:
[x-rotation, x-translation, z-rotation, z-translation]
(The order of rotation and translation along the same axis can be exchanged
wherever it appears in both forms.)
So, converting from Craig's notation to Asada-Slotine is doable in most
cases by concatinating the sequences for all the links and regrouping. For
example, assuming a two-link manipulator for brevity,
[z-rotation1, z-translation1, x-rotation2, x-translation2] [z-rotation2,
z-translation2, 0-rotation, 0-translation] (Asada-Slotine)
The indices used here (1 and 2) are just placeholders. It is hopefully easy
to see how this would extend to manipulators with more than two links.
Direct conversion only works when the Craig form has zero x translation and
rotation for the first link. When this is not the case, the manipulator's
reference frame will need to change.
The conversion will always produde an Asada-Slotine form with zero x
rotation and translation for the last link.
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