Balancing dice – Willem Pennings
This dice manages to steadiness itself on a nook, and might concurrently rotate round its axis in a managed method. It does so utilizing intelligent controls and a set of three response wheels.
The unique concept for this gadget comes from researchers at ETH Zürich, who reveal their “Cubli” in this video. Its design has been improved in some methods in later years. Notably, Bobrow et al (College of São Paolo) introduce an improved controls idea, decreasing the variety of required IMUs (inertial measurement items) to only one as a substitute of six.
I made a decision to pursue the problem of constructing one myself. Although the concept isn’t new, earlier works are largely closed-source. I plan to vary that. Which means that I needed to reverse-engineer and draw all the things from scratch. The results of my work, which is totally open supply (GitHub), is proven within the video under.
You may assume: ANOTHER USELESS MACHINE?! Once I printed my M&Ms sorting machine, I acquired a lot of related remarks. Certainly, it has no sensible worth, however related functions akin to sorting of fruits, greens and nuts primarily based on color do. For this dice, the state of affairs is analogous: whereas that is largely an important studying expertise and analysis challenge, response wheels are sometimes utilized in satellites (such because the James Webb telescope) for angle management functions.
Mechanical design
The mechanical design of this dice is generally the identical as that of the unique Cubli, however it has some refined variations. The primary construction consists of eight “cornerstones” and 6 face plates. Three of those face plates have further options to help a motor and response wheel meeting. All components had been drawn in (con)Fusion 360. My scholar days are over, so I needed to say farewell to Siemens NX. The latter isn’t used a lot (if in any respect?) within the DIY group anyway, so I can share my designs with others extra simply now.
Most structural components are fabricated from chrome steel for its glorious power. The faceplates are fabricated from aluminium to save lots of weight. These don’t should be fabricated from metal because the assembled construction shall be greater than stiff sufficient when fabricated from aluminium anyway.
All metallic components on this challenge have been manufactured by PCBWay. I’ve used their PCB prototyping service earlier than and was excited about their CNC capabilities. A part of the price for these components was sponsored by PCBWay. The ordering course of was simple and I like {that a} quote was mechanically calculated straight after importing the half and specifying the fabric sort. I’m glad with the components and their high quality: a small manufacturing situation was shortly resolved and all components match collectively with out situation. Photos under: decide for your self.
I had enjoyable with the design of the motor and flywheel meeting. I used to be on the lookout for a strong design – in spite of everything, the wheels can attain speeds as much as 6000 rounds per minute – whereas additionally conserving it light-weight. Although I’m a mechanical engineer by training, development ideas aren’t my foremost power, however in spite of everything that’s the rationale for tasks like these: to study! I lastly got here up with the next.
The motor is related to a stainless-steel bridge utilizing three countersunk screws. The bridge finally connects to one of many aluminium faceplates.
A small hub is mounted onto the shaft of the motor and secured utilizing three set screws. This hub is crucial: if the middle gap shouldn’t be perpendicular with respect to the flat triangular face, the wheel won’t be aligned with the motor shaft, inflicting vibrations and put on.
A response wheel is mounted onto the hub utilizing three countersunk screws. This step requires a little bit of trial and error to appropriate for imperfections within the hub and wheel, which can trigger the misalignments I discussed earlier. I resolve these by putting tiny items of paper between the horizontal contact floor of the hub and wheel and this supplies passable outcomes. In any case, these components aren’t taken aside fairly often.
A small radial ball bearing is inserted into one of many faceplates and secured utilizing cyanoacrylate (“tremendous”) glue. This ball bearing will help one finish of the motor shaft. The opposite finish of the shaft can be supported by a bearing throughout the motor itself.
Lastly, the motor shaft is inserted into the bearing and the bridge is related to the faceplate utilizing 4 bolts. This course of is repeated two extra instances.
This lead to half a dice. The remaining faceplates don’t require any particular meeting steps and may be straight assembled. Discover how one of many motors is oriented in another way with respect to the bridge to which it attaches? That’s achieved on goal: it simplifies the cabling work afterward.
The result’s a powerful but comparatively light-weight construction. The aluminium faceplates are comparatively weak by themselves, however gained’t budge when assembled collectively.
Electromechanical design
For the motor and motor controllers, different balancing cubes use Maxon motors from the “EC flat” collection. Whereas it’s attainable to seek out cheaper options, the motors and their controllers are crucial components and I don’t need to skimp on them. The dice will steadiness by making use of torques to the motors. Many DC motors don’t even include datasheets that specify the torque fixed (which defines the connection between torque and present), and lots of brushless motor controllers akin to ESCs solely provide velocity management, however not present management. Each are important in making this challenge a actuality, so the selection for parts of top of the range is clear right here.
I chosen a 60 W motor and a appropriate 4-quadrant motor controller which may ship currents as much as 6 A. At 24 V, this corresponds to virtually 150 W. Whereas that is effectively past the nominal energy ranking of the motor, it’s no drawback to briefly overload the motor. Furthermore, the controller has a built-in I2t algorithm which limits present to the motor if the winding temperature is estimated to turn into too excessive. It’s unlikely that the dice hits these limits in regular operation anyway, as a result of currents are typically very low whereas balancing.
The software program that comes with the Escon motor controllers is fairly nice. There are motor commissioning and tuning instruments and a pleasant dashboard exhibiting the standing of the motor and its inputs/outputs throughout operation (proven within the screenshot above).
For the battery, I selected a 6S1P lithium-polymer battery. The motors are rated for twenty-four V so a six-cell LiPo battery (nominal voltage 22.2 V) is an efficient match right here. The battery has a capability of 1300 mAh (29 Wh) which is sufficient to run the dice for at the least an hour, usually.
The motherboard is a customized design and integrates the three motor controllers, IMU (hidden), ESP32-S3 improvement board, and a few supporting parts akin to safety circuits and voltage regulators. The board additionally anticipates including mechanical brakes to the dice, by offering outputs for RC servo motors. Mechanical brakes will allow the dice to leap as much as the balancing place by itself. I haven’t completed the event of the brake design but.
Assembling the circuit board was enjoyable. I began by making use of solder paste and putting the surface-mount components. After reflowing it in a small toaster oven (extra particulars about how this works here), I soldered all of the by way of gap components by hand.
Later, throughout integration and testing of the varied parts, I discovered that I had made a number of small routing errors which I shortly corrected utilizing bodge wires. It seems that just one digital enter on the motor controller helps PWM and I routed the PWM sign to a different (unsupported) enter.
I additionally designed a board to mount the battery onto. It’s a lot less complicated: it has two XT60 connectors and two switches (wired in parallel due to currents as much as 18 A) to show the dice on and off.
Controller design and tuning
I didn’t really design the controller the dice myself, however ported the work by Fabio Bobrow from Arm Mbed to Arduino. I’m additionally utilizing an ESP32 as a substitute of an STM32 Nucleo. However, rewriting the code was chunk of labor. Additionally, since I’m utilizing a special IMU (the ICM20948 by TDK Invensense), I needed to rewrite the corresponding “driver”. I nonetheless spent fairly a while finding out the design of this controller and can spend a number of phrases to spotlight some good issues about it.
The design of the principle angle controller is most fascinating. It’s maybe greatest defined as a negotation between two contradictory goals. The primary goal is to maintain the dice in its desired orientation, that’s, at its unstable equilibrium place. A second purpose, nonetheless, is to maintain the wheel velocities to a minimal. Not contemplating this second goal may result in wheels speeds getting uncontrolled, saturing the motors, and thereby successfully rendering it unable to exert torques on the dice.
The 2 goals are in battle: if the ‘want’ to maintain wheel velocities near zero is simply too nice, the dice merely falls over. Like talked about earlier than, whether it is too weak, the wheels may actually spin uncontrolled. The trick due to this fact is to seek out positive aspects that lead to good balancing efficiency and disturbance rejection whereas conserving wheel velocities considerably low.
There may be one other elegant mechanism within the controller to cope with fixed errors. What are fixed errors? For instance, there could be a small distinction between the configured equilibrium place and the precise equilibrium as a result of imperfections within the weight distributions of the dice. In a PID (proportional-integral-derivative) controller, the integral half offers with these sorts of errors. This controller makes use of the place (in levels) of the wheel because the integral! For my part, that is really a really intuitive means of visualizing an integral controller. Once I modify the burden distribution of the dice (within the video: by putting a tomato on it), you may see the response wheels improve after which lower in velocity: they’re transferring to a brand new place to compensate for the elevated error!
Commissioning and tuning the controller was, by far, the most important piece of code-related work. Like every skilled controls engineer, I spent a number of days flipping the indicators of assorted alerts earlier than I received them proper. Then, I needed to discover the fitting positive aspects for the controller. The tuning methodology as described in Bobrow’s dissertation didn’t work for me, so I resorted to tuning the positive aspects by hand. Observe that my dice makes use of completely different wheels in comparison with Bobrow’s dice, so reusing the positive aspects was not attainable. Utilizing an iterative process, I lastly obtained the positive aspects that consequence within the stabilizing efficiency as proven within the video (which is excellent, in my humble opinion).
That’s it! A balancing dice. It’s the one totally open-source dice on this planet which achieves a balancing efficiency much like that of Cubli, so far as I do know. I hope that others will now even be impressed to construct this cool gadget.
Listed below are some hyperlinks to related cubes that are at the least considerably documented (greater than only a video or photograph):
Subsequent steps: leaping up
I plan so as to add mechanical brakes to the response wheels. These will allow the wheels to be braked quickly, leading to a lot bigger torques than the motors can ship. This allows jump-up manoeuvers which in flip allow the dice to get to its equilibrium place by itself. This function is at present distinctive to the unique Cubli, so far as I do know. I don’t notably just like the braking mechanism that Cubli makes use of for varied causes, so I’m going to make use of a special strategy. I’ll share leads to a future publish!
Thanks for studying.
Supply information and paperwork
You’ll find all design, configuration and code information associated to this challenge on this challenge’s GitHub repository. Be at liberty to reach out you probably have questions concerning the challenge or need to construct your personal. In my case, the BOM was near €2500, so be ready for that.