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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???

Milan
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hamedmh
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  • The root of this question seems to be a duplicate of https://robotics.stackexchange.com/questions/20779/dexterity-calculation-with-dual-quaternions. Did that post not clear up your question about calculating manipulability with a dual quaternion based Jacobian? – Ben Jun 14 '20 at 18:31
  • @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? – hamedmh Jun 15 '20 at 08:18
  • That sounds like a completely different question. Please start a new question thread for that. – Ben Jun 15 '20 at 16:16
  • link it's what i understand @Ben – hamedmh Jun 15 '20 at 17:14
  • Does it really make sense to optimize kinematics without regard to dynamics? – guero64 Aug 11 '22 at 23:05

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I think it is likely that you are confusing two uses of the word “singular”:

  1. The singular values of a matrix as found via singular value decomposition.
  2. The singular configurations (or singularities) that occur when the Jacobian loses rank.
RLH
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  • I agree that the OP is likely confusing these terms. But can you elaborate on your answer and provide some detail? – Ben Jun 14 '20 at 18:35
  • 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. – RLH Jun 14 '20 at 18:51
  • @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? – hamedmh Jun 15 '20 at 08:59