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In this paper by J. W. Burdick, the main result basically says that

for a redundant manipulator, infinity solutions corresponding to one end-effector pose can be grouped into a finite set of smooth manifolds.

But later in the paper, the author said only revolute jointed manipulators would be considered in the paper.

Does this result (grouping of solutions into a finite set of manifolds) hold for redundant robots with prismatic joint(s) as well? Is there any significant difference in analysis and result when prismatic joints are included? So far I couldn't find anyone explicitly address the case of robots with prismatic joints yet.

(I am not sure if this site or math.stackexchange.com would be the more appropriate place to post this question, though.)

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I am not sure if it applies here, but it is usual way in mathematic to prove something simple and then say, that other cases can be transformed to the simple case, so it is proven for them too (usually in some ineffective long way, but it does not matter, if you want to prove existence of solution).

Prismatic joint can be replaced with three revolute joints connected with long enough rodes, working in cooperative way, maybe it is enought to do substitution for the case in the papers?

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  • $\begingroup$ Hm, that's interesting. I never realize before that a prismatic joint can be replaced by three revolute joints with some constraints. That might be a way to go. $\endgroup$ – Petch Puttichai Mar 29 '17 at 12:30

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