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???

  • $\begingroup$ 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
    Jun 14, 2020 at 18:31
  • $\begingroup$ @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? $\endgroup$
    – hamedmh
    Jun 15, 2020 at 8:18
  • $\begingroup$ That sounds like a completely different question. Please start a new question thread for that. $\endgroup$
    – Ben
    Jun 15, 2020 at 16:16
  • $\begingroup$ link it's what i understand @Ben $\endgroup$
    – hamedmh
    Jun 15, 2020 at 17:14
  • $\begingroup$ Does it really make sense to optimize kinematics without regard to dynamics? $\endgroup$
    – guero64
    Aug 11, 2022 at 23:05

1 Answer 1


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.
  • $\begingroup$ I agree that the OP is likely confusing these terms. But can you elaborate on your answer and provide some detail? $\endgroup$
    – Ben
    Jun 14, 2020 at 18:35
  • $\begingroup$ 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. $\endgroup$
    – RLH
    Jun 14, 2020 at 18:51
  • $\begingroup$ @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? $\endgroup$
    – hamedmh
    Jun 15, 2020 at 8:59

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