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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

Depiction of a robot and mentioned reference frames

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 $\{b\}$?

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