PYTHON · NUMPY

The difference between twins

Establish that two motors of the same model differ measurably, and find that number without buying anything.

01Challenge

A stolen robot could be returned with a substituted actuator and nothing in software would know. You want the machine to prove, from physics, that its parts are the parts it left with. First find out whether there is any signal to work with at all.

Predict firstYou want to know how much two identical-model motors differ. What is the cheapest way to find out?

02Model

Silicon has solved this. A physically unclonable function turns the random variation of a chip's own manufacture into an identity that cannot be copied, because copying it would mean reproducing the fabrication accidents. The question is whether a drivetrain has the same property. It should: nobody winds two motors identically. The instinct is that you would need to buy a batch and measure them. You do not. Vendors already publish unit-to-unit tolerance, because design engineers need it to size a system that works with any unit off the line. Torque constant is quoted at plus or minus ten percent, phase resistance at plus or minus eight. That published tolerance is the signal you were going to go and measure.

03Guided practice

Compute the spread in the copper-loss coefficient from the two published tolerances, then compare it to the resolution floor of the power model from Module 1.

04Feedback

PASS WHEN You found the signal in a datasheet instead of a purchase order.

If your run fails, check:

Unit-to-unit spread in the coefficient is about 21.5%, against a 2.94% resolution floor — roughly 7x headroom.
Kt enters squared, so its 10% tolerance contributes 20%. That is why the copper term is the sensitive one.
A tolerance is a manufacturer telling you how much their units differ. That is exactly the quantity an identity would rest on.

05Retrieve & space

Why does the torque constant's tolerance contribute twice as much as resistance's?
What is the headroom between manufacturing spread and the model's resolution floor?
Name a quantity you could look up rather than measure, in your own work.

06Mastery & project

Before designing an experiment, check whether the quantity is already published as a specification.

Pick any component in a system you work on. Find its published tolerance. Decide whether that tolerance is large enough to be useful for anything, or small enough to ignore.

GO FURTHER · THE LIVE PLAYGROUND

Open the instrument ↗ · Set the manufacturing spread and watch what it buys you.

← Who gets to define the method Which number can be a name →

PYTHON · NUMPY

The difference between twins

Published tolerances are given. Propagate them into the model coefficient and compare against the floor.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you