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Dear Robotics Stack Exchange,

I am trying to calculate the torques and forces for a 2DOF robot.

I’m used the partial differentiation method to find the Jacobian matrix. I managed to find the Transformation martix to find the Jacobian matrix in as shown in the figure but, I have hit a stopping block when I’ve been calculating the torques and forces. I’ve shown my working out below just as a reference.

I was wondering if anyone can shed light into finding the torques as im very close into gathering the equations.

Jacobian Matrix

TorqueCalculation

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Your computations of the transformation matrices are incorrect. DH transformation matrices are computed as a multiplication of four matrices: rotate about z by $\theta$, translate along z by $d$, translate along x by $a$, and rotate about x by $\alpha$. More simply: you are missing the $\theta$ terms in the rightmost columns of your transformation matrices.

The result will be that your Jacobian becomes a 2x2 matrix when differentiated.

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