# Gear testing fixtures

The qdd100 servo uses a planetary geartrain as the transmission reducer. This consists of an outer ring gear, an inner sun gear connected to the rotor as the input, and 3 planets connected to the output. The tolerances of these gears directly impacts the performance of the servo, namely the backlash and noise.

To date, I’ve been hand-binning these and testing each servo for noise at the end of production. To make that process a bit more deterministic, and with less fallout, I’ve built up a series of manual and semi-automated gear metrology fixtures to measure various properties of the gears.

Some of the simple ones are just tools to hold micrometers in convenient locations relative to gears or meshing gears, like this one to measure the OD of the ring gears at various points:

Or this one to measure the meshing of the sun gear with a rack gear:

Or this one to measure the meshing of a ring gear with a reference sun gear:

## Semi-automated tools

As I went to use these techniques for production, manually measuring the gears both was tedious, and still not as useful as it could be. It wasn’t feasible to do more than record a minimum and maximum when measuring a gear by hand, and for some parameters, measuring it at many points around the circumference is helpful. Thus, I’ve started on some automated gear testing fixtures.

The first is one that tests sun gears against a reference planet:

This has a few pieces. The motion platform is a moteus devkit motor with a reference planet gear attached. This spins a “test” sun gear which rests on a linear rail. Then a dial indicator is positioned to record the position of the carriage. An arduino connects to the SPC data port on the dial indicator to programmatically read the position. I used a technique similar to this forum post, except that my iGaging dial indicator runs off about 3V, so I didn’t bother with a separate pull down transistor and just toggled the REQ pin between input and output low to initiate readouts. That meant I could just plug the 4 wires directly into the Arduino.

When this runs, the reference planet is spun through small increments and the micrometer reading is captured at each point. This measures the “double flank” mesh distance of the gear pair. Here, the indicator spring applies a pressure to the test gear, forcing it to mesh with the master gear.

To make this work, I characterized the reference planet gear by running a reference sun gear (which is a 20 tooth M0.5 gear), at all 20 different phases relative to the planet. Then I took the median of the distance across all the runs as the “reference curve” for this planet.

Then test gears are measured relative to that reference curve. That shows the delta between the center distance at each point and the reference distance, so should be relatively well calibrated for the fact that my master gear is not perfect, nor mounted perfectly concentric. Here is a plot from the same gear taken four times at different phases, shifted laterally to compensate for the phase difference and shows that it is relatively consistent and repeatable.

The process is unfortunately slow, primarily because the dial indicator SPC port only emits data at 2Hz, and it takes about 2 readings to settle after each motion. I was using 8 points per planet tooth for the above plot, which works out to 320 total samples per evaluation. At 1.5s per sample, that is around 7 minutes per gear! Fewer points still give reliable results, at a corresponding reduction in fine resolution.

Forgiving the slow speed, this does seem to give profiles that are repeatable to within about 10 microns, which is good enough for the binning I am doing now.

# Improved qdd100 packaging

There are a lot of steps necessary to get a product to market, not just a fancy render. I admit to being far from covering all the bases yet, but we’re getting there. In that spirit, I recently upped the packaging game of the qdd100 with some custom boxes and foam inserts. Pick one up at mjbots.com!

# development kits and fdcanusbs back in stock

mjbots.com had a week long run where we were completely out of fdcanusbs, which meant that we were also out of all development kits too. Well, a production run just came in:

So now we’ve got everything back in stock once again!

# qdd100 beta 2

I’d like to introduce the qdd100 beta 2!

This is the newest version of a quasi-direct-drive servo from mjbots. It has a sleek new look, and improved performance all around:

Additionally, the M3 mounting holes are now 3mm deep instead of the previous 2mm, which gives more flexibility when designing mounts.

It is in stock at mjbots.com now, with more production becoming available in the next weeks and months.

# mjbots November 2020 Update

Here’s the approximately annual giant video update:

If you’re interested in any of the topics in more detail, I’ve collected links to individual posts for each of the referenced items below.

Thanks for all your support in the last year!

## Moteus

Announcement of moteus r4.3: Production moteus controllers are here!

Automated programming and test setup: Programming and testing moteus controllers

Dynamometer: Measuring torque ripple, Initial dynamometer assembly

Continuous rotation: Unlimited rotations for moteus

The virtual wall control mode: New “stay within” control mode for moteus

Handling magnetic saturation: Dealing with stator magnetic saturation

moteus r4.5

## qdd100

Discussion of the overall design, and details on individual sub-components:

And the pre-production mk2 servos: Pre-production mk2 servos

## Accessories

fdcanusb: Introduction and bringing it up

power_dist: The failed r2, the closer to working r3, and the final r3.1

## Demonstrations

Ground truth torque testing: Ground truth torque testing for the qdd100

Skyentific’s telepresence clone: qdd100 telepresence demo

kp and kd tuning: Spring and damping constants

Chassis: The first introduction, and some minor tweaks

Cable conduit changes: New leg cable management

Cartesian coordinate control: Cartesian leg PD controller

Pronking: Successful pronking!

tplot2 and its sub-pieces:

nrf24l01 transceiver and its sub-components

Smooth leg motion: Improved swing trajectory

Balancing

All four feet off the ground: Higher speed gait formulation, and Stable gait sequencing

Improved stand up sequence: quad A1 stand-up sequence part N

Speed records:

# Up-rating the qdd100 beta thermal bounds

When I first posted the qdd100 beta on mjbots.com, I performed a simple “continuous torque” test where I measured the torque that could be applied indefinitely without thermal limiting in a lab environment. It has come to my attention that other servos rate their “continuous torque” for a much lower value of “continuous”, sometimes only 30s. To make the situation clearer, I measured the time to thermal limiting at a range of torques and updated the product page.

For this test, at each torque value I started with the qdd100 in thermal equilibrium with an ambient 20C lab environment, then applied the given torque and waited until thermal throttling set in. No forced airflow was present and no conductive or radiative cooling enhancements were used.

# qdd100 telepresence demo

I saw a recent Skyentific video and decided to have a try at it myself, check out the result:

# quad A1 stand-up sequence part N

I’ve worked through a number of different iterations of the stand-up sequence for the quad A1 (2019-05, 2019-09). The version I’ve been using for the last 6 months or so works pretty well, but because it drags the legs along the ground to get them into position, it can have problems when operating on surfaces with a lot of traction, like EVA foam, besides being uselessly noisy.

To make things just a bit more robust, I’ve now tweaked the startup routine so that the shoulders lift legs clear off the ground before positioning the legs, then lowers them back down into place. This makes the stand up routine much more likely to succeed on just about any surface:

# Dealing with stator magnetic saturation

In my previous experiments demonstrating torque feedback (full rate inverse dynamics, ground truth torque testing), I’ve glossed over the fact that as the stator approaches magnetic saturation, the linear relationship between torque and current breaks down. Now finally I’ll take at least one step towards allowing moteus to accurately work in the torque domain as motors reach saturation.

## Background

The stator in a rotor consists of windings wrapped around usually an iron core. The iron in the core consists of lots of little sub-domains of magnetized material, that normally are randomly oriented resulting in a net zero magnetic field. As current is applied to the windings, those domains line up, greatly magnifying the resulting magnetic field. Eventually most of the sub-domains are aligned, at which point you don’t get any more magnifying effect from the iron core. In this region, the stator is said to be “saturated”. You can read about it in much more depth on wikipedia or with even more detail here. The end result is a curve of magnetic field versus applied current that looks something like this:

To date, moteus assumes that you are operating completely in the “Linear” region, where the torque and current are linearly related.

## Operating in the Rotation Region

To operate in the “rotation” region I ended up using the following formula:

$\tau = K_T * I_c + ts * log2(1 + (I - I_c) * is)$

Where $I$ is the input current, $K_T$ is the motor torque constant, $ts$, $I_c$ and $is$ are three constants that I fit to measured torque data. With some approximations, this can be calculated relatively efficiently on the STM32G4 that drives the moteus controller, adding only a microsecond to the overall loop time to go in both directions.

I then ran a torque sweep with my load-cell fixture from before, and sure enough, the input and output torque match much better now across the entire range of operation, despite the fact that the phase current needs to start growing very rapidly near the top end:

# Testing qdd100 stator windings

My initial design torque for the qdd100 was a little over 17 Nm. However, when I did my first ground truth torque testing, I found that some servos had a lower maximum torque than I had specified. While working to diagnose those, I built a qdd100 that used an alternate stator winding of 105Kv instead of the 135Kv that are in all the beta units. The Kv rating of a stator describes how fast the motor will spin for a given applied voltage. If you assume the same amount of copper mass of wiring, a lower Kv will mean that there are thinner wires that wrap around the stator more turns (or fewer wires in parallel). A higher Kv will have thicker wires with fewer overall turns.

On paper, if you assume a perfect controller, this shouldn’t make much of a difference. The same input power should be required for the same output torque. The only differences should come into play once you have a controller with either a limited maximum voltage or a limited maximum current. The higher Kv motor will be able to go faster given a fixed maximum voltage, and the lower Kv motor will have more torque for a given maximum current.

I wanted to verify that this was true as part of my evaluation to identify the cause of my decreased torque, so I used a slightly upgraded torque testing fixture:

For now, I rigged up the world’s cheapest load cell from amazon to a Nucleo configured to report the load in grams over the serial port. I also wired up my Chroma power supply over USB using the linux USBTMC driver. With those two things hooked up, I was able to run tests that sweeped across torque commands, while recording output torque, phase current, and input power.

At higher torques, the input power was pretty sensitive to the temperature of the windings — hotter windings increased the resistance, which increased the power required to achieve a given phase current, thus my plot isn’t perfect as it was grabbed over several different runs. For the highest power samples I couldn’t use my Chroma, as it is limited to around 600W. Thus those samples don’t record the input power.

Plotting the input power vs output torque on the same chart shows that indeed, modulo some measurement error, they are the same for the two stators:

So, this experiment reaffirmed my understanding of stator magnetics and confirmed that the stator winding was not the cause of my decreased torque.