# Differential transmission - power takeoff from the drivetrain motors

In mechanical engineering Differential is primarily associated with a specific drivetrain component connecting axles of the powered left and right side wheels. But formally it is defined as:

A differential is a gear train with three shafts that has the property that the rotational speed of one shaft is the average of the speeds of the others, or a fixed multiple of that average.

For whatever reason, in vex context, any power sharing scheme between multiple motors is called differential as long as inputs and outputs obey the basic formula `a=x+y` and `b=x-y` where (x,y) are inputs and (a,b) are outputs. For example: Differential transmission - Mobile Goal to Drivetrain (DMD)

Video linked above shows two common types of the differentials used by a number of teams over the last few seasons.

The trick is to build it without prohibitively high friction losses. Few of them are described here: Special partially threaded screw joints and HS gear bearings using modified 393 output gears

Below are the pictures of the differential prototype that uses drilled out 393 output motor gears as the coaxial bearings:

This allows the main axles going out from the motors to avoid the load of supporting the 60T gears to which the motors are attached themselves. Also, for stability you need to connect those gears on the left and right drivetrain sides:

Another important thing to consider when building differential is if you need to power both outputs at the same time. They can run independently and simultaneously but only at the reduced power. You get the best efficiency only if power is going to one output at a time.

(short demo illustrating the above design: VEX ITZ MoGo lift & drivetrain motor sharing - YouTube)

Let say you have 4 motors in differential setup (2 per drive side). When you run only one function then you get full power of those 4 motors for each function independently (100%) efficiency.

If you try to run both functions at the same time, then the sum of velocities is capped at 100% and the sum of forces is capped at 100% too. In the worst case (when half of the motors hold 0 rpm) each function gets only 50% of max force (torque) at 50% of max speed, thus resulting in 25% of max power for each of the functions or 50% overall efficiency.

If your game strategy calls for both functions to be used simultaneously most of the time, then differential is a bad option, but if those functions are mostly exclusive, then differential makes a lot of sense.

Peak power is another consideration. It may be ok to sacrifice overall efficiency of the system, to get peak pushing power of the chassis when the lift is not active. For example, if you have 6 motor drivetrain with 4 motors shared with the lift, then you get effective power of 1 motor lift and 1+2=3 motor drivetrain if you use them simultaneously. But if you use them only one at a time, then you get either 4 motor lifting power or 6 motor drivetrain.

This all assumes that you donāt lose too much to friction in the more complex geartrain.

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This is good stuff. Fantastic! Iām going to try and get all my kids to review this and hope that they try it.

Do you have the CAD models that the video is based off of, or should I check with 81K? What I would like to be able to do is have the kids try turning the motors in different directions from within the CAD software. That should help them get a better feel for and understanding of how it works. In the past Iāve used VEX IQ parts to build physical models, and they work great, for a short time. But it seems like whenever I want to use my old models again they are either broken, lost, or taken apart.

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Unfortunately, I donāt have CAD models and, I believe, the video linked in the OP was done in Blender, but Iāve seen other teams posting CAD renders of various differential designs in the past. (@ranOOm do you have any Differential CADs?)

The concept behind differentials is rather simple. If you have two motors and two output linked via formula `a=x+y` and `b=x-y` respectively, then when motors run in the same direction (x=y) you get power on output (a) and, when motors run in opposite directions (x=-y), then output (b) gets power.

There are plenty of FRC Differential Swerve Drives utilizing this principle:

I hope these videos will be helpful to visualize how differentials work:

Differential turret by @tabor473

The trick is to build the geartrain from the limited set of VRC legal parts such that it is strong enough and any friction losses donāt negate any potential advantages of the increased peak power. It is very easy to overdesign such things.

One of the features of the prototype pictured in the OP is that when everything is properly aligned and motorā axles donāt touch 393 gears, then configuration ādefaultsā to an ordinary tank drivetrain. The power from the motors to the wheels doesnāt need to go through the extra geartrain, other than the three 60T gears that it would be going through in any non-differential design that combines power of the two motors into one driving wheel.

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@jrp62 I do my CAD work in inventor, and you can constrain the edges // circumference of the gears together so that theyāll āmeshā virtually - you just have to teach them about gear ratios before you do that and it should be ok. I have a few CAD models, some of them are incomplete, most of them were for prototyping, but Iāll attach them to this message should you wish to review them. (thank you @technik3k for the mention).

This is one robot, I use a vertical channel on the end of the robot to gauge height (so I donāt go over 18") as well as a few c-channels/bars elsewhere to help give me a sense of how ābigā everything is.

What youāre seeing here is now a second version of that same robot, thereās a few differences but generally the concept stays the same (I never finished this, so youāll see a few random gearboxes for the flywheel lying around still).

And of course, thereās the first robot that I cadād this season (first robot I ever did in CAD) which is on my youtube - you can see me build it. Hereās the link to the first video if you wanted to take a look, and if you want the CAD files just shoot me a message and Iāll figure out a way to upload the entire project in a way where it wonāt self-destruct.

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Thank you @ranOOm and @technik3k! Yes please send me the CAD files. Let me explain why I want themā¦

Below are some pictures of sample lifts that we keep around the lab. Made from Vex IQ parts, we have about ten different types of lift models. You can physically move the lifts up and down to see how they work. We have similar models for gear ratios. These are effective, the kids like looking at them and get kind of hypnotized watching them move. But they take up space, break easily, and are not always handy when you want them.

For differentials, what I would like to try instead is having CAD models that would allow someone to control the movement of the model. As with the lifts, you can try and explain how these things work, but letting kids watch the movement while controlling it is what really makes the concepts sink in.

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Hereās a model drivetrain that my older son made that uses differentials for a CVT. The kids loved driving it and watching the gears move, but Iām not sure how many of the IQ kids understood it. They might be ready for it now. Apalrd's CVT/EVT

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@jrp62, I really like your Vex IQ lift models. They look great and literally scream āTake me and learn how it works!ā

Do you have a demo videos of them in action by any chance?

I am not sure if CAD models would work better, because you need a computer with CAD software to play with them. But you can touch the models or watch a video on almost any device and let your imagination fill the gaps.

Also, it is very easy to understand velocities through the animation, like in this example:

(another video here: Misc - jpearman)

But students keep missing that this planetary transmission design lacks torque balance, which is not obvious even from the best of animations. The output will always be weaker than if you had just connected both motors directly to the wheels, because of the backdriving issue with non-locking planetary transmissions.

Yes, Iāve seen that thread and read it a number of times before! Please, tell your son that it is very well written and was very useful when I was working on the Automatic Transmission topic.

There is a way to solve the motor under-utilization in EVT and get close to 100% efficiency in the high torque mode:

One of our teams tried to build an automatic transmission with the worm gear based (non-backdriveable) differential for ITZ Worlds, but run out of time. It would have been great to have all that extra torque. This is the final and the most compact version weāve got:

In high torque mode, you could get 9 motors worth of pushing power from just 3 actual motors at 1/3 of the max speed. But it isnāt an easy build and takes a lot of time to tune it.

So, for the Turning Point season our goal was to build a transmission with the minimal friction losses and lesser complexity, which is shown in OP.

Right now most of our students are busy preparing for tests, but I will definitely talk to them later to make a good CAD. The best I could do now is to link a few more videos.

The first variant is what was frequently called MoGo differential transmission (DMD) or āanti transmissionā (v4 video by @antichamber: Passive mogo transmission v4! - YouTube). Additional explanations:

The second variant of differential transmission uses coaxial motor mounting (in respect to both of its functional outputs) and, in this example, secondary function is used to transform the chassis between the high torque and the high speed modes:

Another video with few more explanations (at 7:40) is here: 2019 US Open Video Submission - YouTube

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Good stuff.

I donāt know anything about CAD, other than what itās supposed to be capable of in a CAD utopia. So it sounds like using a full blown CAD app would have too many obstacles just for demonstrating simple models. RobotMesh has this minimal CAD app integrated into their development studio, that they call āmimicsā. I tried it, it was easy to learn, even for an old dog. Iām going to try to create a differential mimic like the antichamber drivetrain, weāll see how it goes. Part of the motivation to do this in CAD is to get the kids familiar with it earlier. In VEX you donāt really need to use CAD to have a good robot. However, our FIRST team is heavy on CAD, and the kids that join have a steep learning curve, making them less engaged during the design phase.

You are correct, the main issue with that CVT drivetrain my son built was that it was inefficient, especially under the load of a big robot. Some of our teams built it, but no one ever stayed with it for a competition robot. Experimenting with those other drivetrains you posted will be a good summer project

Where do you get this cool stuff?

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Mostly from the āDiscordsāā¦

A lot of teams are building really cool stuff but no longer share it on the forums where it is easily discoverable by a wider audience.

Unfortunately, the virtual vex meeting spaces got very fragmented and, while some alliances believe that keeping everything secret gives them short term competitive advantage, I think, knowledge base fragmentation hurts everybody in the long runā¦

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@jrp62 I spent about an hour today just getting started on a CAD (gift to self for finishing my physics exams?), anyways Iāve uploaded the first bit. Thereās a bunch of issues with the design if you were to use it in matches, thereās a lot of things that still need to be āconsideredā and āfixedā, but the basic idea of how the DMD style transmission is there, and I just spend a bunch of time building it. I took a few screenshots and Iāll attach those as well. Iāll keep uploading the build progress for this robot if I end up finishing it at all.

And no, Iām not competing with this. Iām graduated (sad). Iāll do VexU maybe.

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Thank you @ranOOm for all your work on this. I actually tried to build the same thing in a RobotMesh mimic, and quickly discovered that the build is more complicated than it looks. It takes so much space too. Reducing the size by using the drilled out gears as @technik3k suggested seems essential for a competition bot. Iād like to get some of my students interested in this, but they are focused on their finals right now. Keeping your video book marked. Thanks again.

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Just to add to this discussion, our original TP bot used a standard 4-bar differential between the chassis and lift. It allowed us to have a 6 motor drive, 4 motor lift, 2 motor catapult, and 1 motor intake, while only using 9 motors total.

The original design had an active flipper and a pneumatic claw, but we ultimately scrapped those because we literally never used it. Instead we rebuilt our lift into a descorer, which is what you see in the video.

It worked extremely well once we fine tuned it a bit- this was our first ever test, so donāt be too hard on it lol.

You can see the lift sag a bit when the chassis is moving. This is because I used a fairly weak PID on the lift controller. It was much stiffer when I tightened the controller up. Additional bracing helped as well, since we had more or less none in the video.

The big thing to remember is that both speed and torque are severely reduced when you run both subsystems at once. Not only is the torque being distributed among two systems rather than one, but half of the motors are actually off as well. Less intensive actions such as holding a lift while moving the chassis is probably going to be fine (depending on the load of course), but I would highly recommend not linking any subsystems which will frequently run simultaneously. For instance, a lift for ITZ would have been a bad idea to tie to a chassis. A mogo lift, however, would have been very useful since it was used so rarely and generally could be used while the robot was stationary without losing too much drive efficiency.

Hereās a few photos of our implementation, at different stages in the building process:

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@ranOOm and @ZachDaChampion, thank you for sharing your designs and insights about the implementing working differentials. Build quality and strategy of not using both functions simultaneously matters a lot.

I still need to search through the old posts on some Discord channels for more pictures and videos of ITZ season robotsā¦

For now here is one of a first public sightings of the lift to MoGo differential.

It is 9605A robot at North Andover HS at 8h34m57s:

And also at SNEC:

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This is not much related to this seasonās game, but here is a couple of interesting examples of using kinematically redundant linkages to perform secondary functions (also known here as differentials):

Notice the 4 degrees of freedom (DOF): horizontal, vertical, rotation, and claw that share 4 motors that are powering the belts.

The similarity between them and VRC is that, instead of using separate and potentially differently sized motors for each function, you use an array of identical motors where they power the major speed and torque demanding function together, and then the secondary functions are actuated by differential control of those motors.

This is also related to the design of Delta 3D printers and pick and place robots:

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