# Moment of Inertia of a planar rotation link with a 6-DOF base

I'm interested in analytic calculation of a moment of inertia of a robot's arm in the following situation.

Let us assume the following:

• Stationary reference frame $$\{b\} = \{X_B, Y_B, Z_B\}$$ and body-attached reference frame $$\{s\} = \{X_1,Y_1,Z_1\}$$
• A robot with four 3-DOF legs consisting of a 3 revolute joints (2 of which have parallel rotation axis)
• Rigid body (with 6-DOF relative to $$\{b\}$$ frame) that connects all legs via a revolute joints
• A leg of interest is constantly bent in a way that $$\alpha = \frac{\pi}{2}$$ and can rotate only along $$Z_1$$ axis about angle $$\theta$$
• Moment of inertia $$I_{1z}$$ of a leg of interest along $$Z_1$$ axis

Given that the leg can only rotate along the $$Z_1$$ axis how does one calculate the matrix of inertia of said leg for reference frame $$\{b\}$$?