# Parallel axis theorem to determine the moment of inertia

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:

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

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?

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).