# Calculating the singular configuration of a 3 revolute joint manipulator

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

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

Thanks in advance.

• Are you sure J is 2x3? it seems 3x3 to me
– 50k4
Jun 2, 2017 at 19:50
• 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. Jun 2, 2017 at 22:32

## 2 Answers

If $J$ is not square, solve $$|J^TJ| = 0$$ for $\theta_i$.

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.