tis-but-a-scratch 0.0.1

A physics model for a robot arm to support education of motion control theory.

Tis But a Scratch

Code to support the physical modeling of a robotic arm. The arm is driven by two motors: one at the base and one at tne "elbow." The base experiences the greatest torque and inertia because it must move both the base arm, the fore-arm motor, and the fore-arm with its claw attachment.

Computing the Moment of Inertia

Note that the moment of inertia for an arm with joints is a little tricky to calculate. But there's a theorem that helps. The Parallel Axis Theorem states that if you know the moment of inertia about the centroid of an object, then the moment of inertia about an axis parallel to that centroid can be computed as follows:

Where is the moment about the new axis, is the moment about the centroid, is the centroid, and is the cross-sectional area of the object.

Using this theorem, we can conclude that the contribution of the base arm segment (closest to the robot) remains constant because its centroid is a fixed distance from the axis. Only the forearm's contribution to the total momentum affecting the base drive motor varies. And it does so in an easily predictable way. We just need to know the cross-sectional area of the part and its centroid distance from the elbow to compute the inertia contributed by the fore-arm.