The Differential Drive - A New Breed of Actuator

[Music] i've designed what i believe to be a fairly unique actuator it's something that i have not seen anywhere else before which is not to say it doesn't exist before me it's just something i haven't seen this project started out really as just a thought experiment i was wondering what would happen if you had an actuator in which the output was the sum of two inputs it's not very uncommon to want to couple the outputs of two motors together let's say if i made an electric bike but it's not quite making it up those steep hills i might add another motor and then just directly couple the two output shafts to increase my torque that method of coupling motors when you just directly connect the two outputs via gears or belts or something like that that is the standard method to couple motors you've probably seen this coupling method quite a bit it doesn't take a genius to figure it out when you couple motors in this way the output will have twice the torque of one of the motors because you've got two motors pushing on it but it'll have the same max speed as one motor so the standard coupling mechanism does not result in an output whose rotation speed is the sum of its two inputs so a motor coupling method that would sum the inputs though i can explain it pretty simply and clearly it's a lot less intuitive than it may seem i can't think of any examples in which you have a mechanism whose output is the sum of its two input speeds except for one and that would be a car's rear differential when a car goes around a turn its rear wheels have to be traveling at different speeds this is because the outer one is going to be moving along a longer arc than the inner one the rear differential is a mechanism that allows both wheels to be powered but to rotate at different speeds in fact it does this by having the two speeds of the individual wheels sum to the engine speed a rear differential has one input that is the engine and two outputs that is the individual wheels i want two inputs that would be my two motors and then one output so i need to make a kind of mechanism to emulate a backwards differential the only issue then is that the rear differential of a car is a pretty complicated mechanism and requires some precise machining so is there a way in which this can be simplified actually most gearboxes can be used as a simplified differential mechanism this is a common planetary gear set i'm sure you're familiar generally you have one input that's on the yellow sun gear at the center and you have one output that's on the green carrier but that assumes that the red outer ring is fixed in place what if it wasn't imagine i have one motor driving the sun gear at the center like normal but then i have a second motor that's driving the outer red ring gear if they were driving it in opposite directions you can probably imagine that the net rotation would be zero in this case the output is the sum of two input speeds granted the second motor driving the outer ring would need an initial reduction so that it would match the speed of the other motor but given this you have effectively created a backwards differential you have two inputs and the output speed is the sum of those two inputs once i came to the realization that i could manipulate these common mechanisms to able to create this weird coupling mechanism in which the output is the sum of two inputs i then began to think about what would this actually do what would this look like practically and i generated a handful of hypotheses about what this could do and potential benefits of this mechanism the first and most obvious hypothesis about this mechanism is that the output maximum rotation speed would be twice that of any individual motor after all the entire purpose of this mechanism is to sum two inputs so that's hypothesis one i also realized that this alternative coupling system would have some unique properties since neither motor is directly attached to each other the rotation of one does not affect the other in any way so when the motors are rotating in the same direction they can sum to give you that output but if they're rotating in opposite directions their motions are going to cancel out and your output will be zero so even if my motors are running ten thousand rpms as long as they're running in the opposite direction and at the exact same speed the output won't move at all my second hypothesis was that when the motors are running in opposite directions the same speed that virtual stall torque will have twice the torque of each individual motor my thought process was that since neither motor is biased in this mechanism they're both affected the same way and external torque will be evenly distributed across both so then my maximum torque is going to be the sum of my two input torques and then my third and fourth hypotheses extrapolated more on what would happen if you had the motors running in the opposite direction my third hypothesis was that you would have an additional stall torque increase by around 50 in a normal motor configuration the stall torque is when the motor isn't moving at all it's locked in place what that means is it's not turning so you can only use two-thirds of the coil sets to be able to hold it in place what that then means is that at a stall torque your motor is using only approximately two-thirds of its thermal mass of the stator in this alternative coupling method this summing method the stall torque would be achieved when motors are at speed which means that over time you're using all three of your your electromagnet sets which means you can use the entirety of the thermal mass of your motor stators that one is a little bit difficult to explain but hopefully you get the idea and then finally my fourth hypothesis was that using this mechanism you could achieve arbitrarily precise movements without encoder feedback if a motor has encoder feedback then it becomes a servo motor and all servo motors have arbitrarily precise movements so it might not seem that special but with this mechanism since the output rotation is the sum of two inputs if both motors are moving in opposite directions i could have one motor going say 100 rpms and the other going 99.9 rpms so then the output is 0.1 rpms an extremely slow movement so based off of that logic without any encoder feedback just controlling the speeds of my motors i can achieve arbitrarily slow and thus arbitrarily precise movements on the output and you wouldn't even need all the fancy and expensive foc control so those were my four hypotheses going into this project and i'll just tell you up front two of them are totally wrong and they were naive of me to think from the beginning i suppose i was overly hopeful but we'll talk about those wrong hypotheses in a bit and at this point i was running into the limits of what i could just intuitively understand and visualize after all there's a lot of weird movements and nothing's really directly coupled to each other so it's hard to really understand this intuitively so i just went ahead and i built the mechanism so that i could test these things empirically unfortunately there's no build montage for this one i've actually been working on this project on and off over the past few months so i decided that i didn't want to have to keep track of a bunch of little clips over that long of the time period anyways here's the cat model so here you go this is the completed mechanism and i'm not gonna lie it looks really cool this mechanism is based around two bldc motors which you can't see because they're both inside of these these uh circular casings here but you can see their wires coming out the bottom again this type of motion can be achieved using many different types of mechanisms i chose to use a cycloidal drive it's because it's what i'm most familiar with it's what i've designed most often so the red parts you see in there those are cycloidal disks that's what's doing the primary gear reduction as you can see it is symmetric this side is exactly the same as this side the only difference is the output parts here so what's on top on either side i'm calling this side the primary motor and this side the secondary that's just because the output is more directly coupled to the primary motor than it is the secondary as with any cycle drive the wobble of each of these discs is driven by the motor itself except unlike most cycloidal drives the outside here is also free to rotate and there's a timing belt that goes all the way around here it's tensioned via some bearings in there that couple the outer casings of both of these so that they rotate together so the primary motor is driving the primary cycloidal gear and the secondary motor via an additional reduction here is driving the outside there's an 8-1 reduction on the primary cycloidal gear and then there's an additional 8-1 reduction on driving this outside here so the result of that is if i hold the secondary motor in place just by holding on to this casing and i rotate the output the the motor will rotate at an eight to one reduction then instead if i don't touch the primary but rotate the secondary by the same amount by rotating this outside the output will also rotate by that same reduction so if either motor is held rigidly one rotation on the opposite motor will yield the same result as if the rolls were switched and thus you have a mechanism in which the output speed is the sum of its two inputs except that there is an overall eight to one reduction which is again arbitrary that reduction could be any value it it may be overly complicated and have more parts than necessary but dang it does look good and it is shiny in order to drive this actuator i'm going to be using an o drive for the uninitiated this is a really high quality foc motor controller foc stands for field oriented control what that means is that the o drive takes positional data from an encoder attached to the the motor and then it uses that data to be able to control it in its most efficient way and via really any possible control mode the o-drive is also really great for this actuator because it can control two motors at the same time all on the one board all right now it's time to test here's my setup i've got a 24 volt 20 amp power supply and that's powering my o drive here which is wired up to my actuator which is bolted here horizontally so i can do some torque testing on it and then that's wired up to my laptop which is running the the python code to control the o drive before i start doing the actual testing i need to do some calibration on these motors i remove the output from the actuator so that i can calibrate the motors without any resistance i should be good to go for the calibration right now let's try this out oh it's totally working that's awesome my motors are calibrated now and i have full control over their velocity in both directions i'm going to get them turning here and i can even give them a negative velocity to to switch their directions everything's working out so far so now i can reattach my output and get to doing some some real testing i reattach the output but i left off one of the tensioners this allows me to pin up the belt here which is holding this outer casing rigid this makes it so that the second motor is negligible and the overall mechanism is just an eight to one reduction of the primary motor the first test i'll be running is going to be a control test for the stall torque this slightly modified mechanism is analogous to the other method by which you would use two motors to drive a single output that's where their outputs would be directly coupled i pulled out my variable benchtop power supply and i'm going to use this to run eight amps through my primary motor and i will test the stall torque on that i'm running eight amps because that's the current limit i have set on my o drive for each individual motor that way when i test the full mechanism i can make a fair comparison as you can see i attached this lever arm here this is how i'll be testing the torque and then i've tied the cap of a water bottle to it that's this water bottle so now i can put water in my bottle screw it on here and then test it that way so now i can incrementally add more and more water until the maximum torque is exceeded i'll start by turning on my power supply and the lever arm is holding it can hold that mass so we go up and i have a second water bottle here to supplement that mass [Music] oh there we go so it seems we've reached our limit there i can now weigh this mass and measure the lever arm length to be able to calculate the output torque i've now put the second tensioner back in so it should be operating normally again i'm now ready to spin up the motors and we can test the overall output of the complete mechanism this is not working out great if you can't tell yeah that was um that was less than impressive there was still a result and it was a telling result at that as you saw the testing did not go spectacularly there were multiple times that i thought i broke it but i didn't somehow and because of the rockiness of that testing procedure this isn't ending up being the most scientific of testing i'm not going to be able to to compare quantitative results as i would like to but the qualitative results i think speak for themselves in my control test i was able to hold a pretty considerable torque using just the one motor since i wasn't able to test the stall torque of the alternative method that is the method in which the output is the sum of its two inputs the exact torque of the first test doesn't really matter what matters is that it was able to hold a stall torque now look back to the second test this is me testing the mechanism in full in which the output is the sum of two inputs this alternative coupling method did not go well at all i mean you can see that i was not able to hold any kind of stall torque in fact the stealth torque was so weak that it wasn't even able to hold up that wooden lever arm that i used for torque testing in the first test so the reason i'm not too worried about comparing quantitative results is that in the first test i could see that it did in fact hold assault torque that was the control test and then in the second test which was my new mechanism this alternative coupling mechanism it wasn't really able to hold any stall torque even under a really small load so what does this mean why did this happen well it disproves my second and third hypothesis remember my second hypothesis was that the output torque would be the sum of the two input torques and then my third hypothesis was that this mechanism would have an increased power density under a stubble torque thus increasing the stall torque by a maximum of like 50 percent so then both of these have to be wrong or at least inconsequential because as you can see it could barely hold anything so that's all fine but the bigger question is why why was i so wrong well it's all actually pretty obvious and again i was pretty naive to think otherwise the day before i ran these tests i went through one final thought experiment about this mechanism and that thought experiment was what would happen if one of the motors had infinite torque so that's like if the motor was just locked into place it couldn't move at all well since the two motors are not directly coupled to each other the second one would still be able to rotate and the output would still be able to rotate in the case in which one of the motors is rigidly held in place so effectively infinite torque the output will still be overloaded at the same point that the one other motor is overloaded this is to say that when you're looking at a stall torque it doesn't matter what the interaction of the two motors is what matters is the weakest link even if one is infinite torque if the other is exhibiting less torque then it's going to fail at that point and this is really something that i should have realized months ago when i started to think about this but here we are you live you learn and the other explanation for this super low stall torque when the motors are at speed comes from just a simple power calculation the power of a motor in watts can be calculated by the rotation speed of that motor times its torque so then for a given motor power the torque and the speed are inversely related so when i have those motors they were running in the tests around 600 rpms because they were rotating so fast their maximum torque is really low just because of that simple equation so even if the output was the sum of the two input torques which i don't believe is the case it would still be extremely low because when they're at speed they have low torque so using this mechanism if you are looking for a high stall torque you would not rev them up to full speed or anything you would just lock them in place like any other motor you're trying to stall there is an even more intuitive way to understand the behavior of this mechanism despite it being kind of complex think about the standard method by which to couple the outputs of two motors that is directly attaching their outputs in that mechanism as compared to only using one of its motors the output will have twice the torque but the same speed but in this alternative method again in which the output is the sum of two input speeds it's the opposite compared to one of the motors the torque will be the same but the maximum output speed will be double and that just makes sense you do it one way you get twice the torque the same speed you do it this other way you get twice the speed but the same torque so in conclusion this mechanism did not meet my highest hopes but of course it didn't i was thinking about it all wrong initially but that is certainly not to say that this mechanism this alternative coupling method is useless it's just very different from what people are usually used to i'll remind you there still are two useful benefits of using this coupling method first the output has twice the maximum speed of each input so if you're looking for a higher speed in your system then this could be useful and two you can achieve arbitrarily precise movements without any encoder feedback so speed and precision is where this mechanism can shine as an example i think that something like a 3d printer could be an application for this generally 3d printer motors don't require a lot of torque instead you're more interested in speed so you can get your print done so this actuator could help out there it could also get you again arbitrarily precise movements with stepper motors with this mechanism you wouldn't need an foc servo conversion for every one of your stepper motors which can be somewhat expensive to get that arbitrarily precise movements in your system you instead just use two stepper motors and control their speeds relative to each other to control the output to infinitely exact amounts and my design can absolutely be improved upon again you can use really any kind of mechanism i chose cycloidal drives arbitrarily you very easily could have designed this with planetary gearboxes and my design was overly complex and it could have been simplified significantly i would love to see other people's iterations of this and improvements upon my my theory i guess but if you are interested in the cad files i use for this project or are just wanting to help me out and support future projects you can do so via patreon there will be a link for that in the description i've recently been getting a lot of support on patreon which is helping me get new tools and new camera gear and stuff like that you can also join my discord server and talk to me and other engineering minded people talk about projects get help on projects stuff like that there'll also be a link for that in the description and you can also follow me on instagram i'm gonna try and start posting more uh regular updates on projects and stuff on there i know i've been lacking in the past this project has been months in the making it's been really fun again i'd really love to see everyone else's improvements on this design i appreciate you being here i appreciate your support that's all i have for now so bye you

Channel: Levi Janssen

Views: 488,011

Keywords:

Id: 2SUiwQVWe8w

Length: 19min 42sec (1182 seconds)

Published: Wed Apr 28 2021