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I would really appreciate it if somebody could help me calculate the singular configuration of this simple manipulator3 link manipulator

I am confused since J is a 2x3 matrix and I cannot simply calculate the derivative.

Thanks in advance.

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  • $\begingroup$ Are you sure J is 2x3? it seems 3x3 to me $\endgroup$ – 50k4 Jun 2 '17 at 19:50
  • $\begingroup$ The third line refers to the angular velocity. I am looking for the linear velocity singularities (the first two lines, generally 2xn ). I was thinking maybe det (JJ^T)=0. $\endgroup$ – Tasos Kontaxoglou Jun 2 '17 at 22:32
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If $J$ is not square, solve $$|J^TJ| = 0$$ for $\theta_i$.

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Singular configurations are configurations at which the Jacobian is rank-deficient. In this case $J$ is a square matrix, you can find conditions for singularity by solving $\det(J) = 0$.

The last row of $J$ being all ones means that no matter the configuration, you can always generate some angular velocity. This actually implies that the conditions you get from solving $\det(J) = 0$ will be the conditions for linear velocity singularities.

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