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I need to use the parallel axis theorem to determine the moment of inertia of each robotic arm link referred to the joints of the 3 DOF manipulator. The moments of each link's centre of mass are:

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The link joints are located according to the following coordinates from each link's centre of mass and the link masses are specified as:

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I know that solve Izz, Iyy and Ixx to use the following equations:

Ixx = Ixx + m(ry^2 + rz^2)

Izz = Izz + m(rx^2 + ry^2)

Iyy = Iyy + m(rx^2 + rz^2)

But I'm not sure how to solve this particular problem, I was thinking since y1 and z1 both equal 0, to solve the question for that link I need to solve I1yy and I1zz is that right?

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If the distance between the axes is zero, then there is no change in the inertia for that specific axis.

You can verify your calculations with a CAD software. Most of them (Solid Works, Inventor, Catia, etc.) can calculate the intertia of solid bodies in any defined reference frame (coordiante system).

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