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The parallel axis theorem gives: $$ I = I_{\textrm{cm}} + md^2 \\ $$ where $I_{\textrm{cm}}$ is the moment of inertia about the object's center of mass, $m$ is the mass of the object, and $d$ is the distance from the center of mass of the object to the axis of rotation. You can also look at load acceleration and torque, where: $$ \tau = I\alpha \\ $$ Or, ...


Using Euler angles and the velocities expressed as a difference between Euler angles over time will work, but it does not give you the minimum distance between the angles. If you calculate the velocity once like this, the end effector will move towards your goal. If you actually want to stop at your goal you will need to periodically recalculate velocities ...


I think it is likely that you are confusing two uses of the word “singular”: The singular values of a matrix as found via singular value decomposition. The singular configurations (or singularities) that occur when the Jacobian loses rank.

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