# Design optimization method using indices

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???

• 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?
– 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? Jun 15 '20 at 8:18
• 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 Jun 15 '20 at 17:14

## 1 Answer

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.
• 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? Jun 15 '20 at 8:59