There are several methods like manipulability and conditioning index for design optimization kinematics performance, but these methods rely on the singular values of the jacobian matrix. I described kinematics by screw theory using dual quaternion that is singularity-free. I need an index to optimize links length and think, I shouldn't use manipulability and conditioning index for my purpose. What do you think???
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$\begingroup$ The root of this question seems to be a duplicate of robotics.stackexchange.com/questions/20779/…. Did that post not clear up your question about calculating manipulability with a dual quaternion based Jacobian? $\endgroup$– Ben ♦Commented Jun 14, 2020 at 18:31
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$\begingroup$ @Ben i think when we used singularity-free methods , we have infinite solutions at robot's singularity configuration and algorithm will give one solution. it's referred to property of quaternion, now what i dont understand it's end-effector motion. do end-effector becomes blocked in certain directions at singularity configuration? $\endgroup$– hamedmhCommented Jun 15, 2020 at 8:18
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$\begingroup$ That sounds like a completely different question. Please start a new question thread for that. $\endgroup$– Ben ♦Commented Jun 15, 2020 at 16:16
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$\begingroup$ link it's what i understand @Ben $\endgroup$– hamedmhCommented Jun 15, 2020 at 17:14
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$\begingroup$ Does it really make sense to optimize kinematics without regard to dynamics? $\endgroup$– guero64Commented Aug 11, 2022 at 23:05
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1 Answer
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I think it is likely that you are confusing two uses of the word “singular”:
- The singular values of a matrix as found via singular value decomposition.
- The singular configurations (or singularities) that occur when the Jacobian loses rank.
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$\begingroup$ I agree that the OP is likely confusing these terms. But can you elaborate on your answer and provide some detail? $\endgroup$– Ben ♦Commented Jun 14, 2020 at 18:35
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$\begingroup$ I don't think there's really much to add. The question is "how do I analyze something's singular values if it doesn't have a singularity? And the answer is "you're confusing two different meanings of the word singular." Your comment handles the answer to what would be a followup question; feel free to add it here or make a second answer. $\endgroup$– RLHCommented Jun 14, 2020 at 18:51
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$\begingroup$ @RLH you know SVD and singularity are considered together. i used screw theory using dual quaternion so i think it's not necessary using SVD to investigate singularity. but can i apply SVD in order to optimize links length?is it right? $\endgroup$– hamedmhCommented Jun 15, 2020 at 8:59