# Convert Torque to Push

Hey everyone, I was wondering what the relationship between torque and push is. Is there a way to compute the pushing power of a robot given its wheel and motor specs? Say for example, if I had a 490 gram minisumo robot, 4 cm diameter wheels, 60 oz-in motors, and a 30-degree scoop (from the surface), how can I convert this information into the force vector in Newtons?

If take the torque (combined from both motors) and divide by the diameter of the wheels, you get the theoretical pushing power that the robot could have. You then have to subtract the force required to move your own robot, and figure out how well your wheels grip. Unfortunately, these last two items have a tendency to be difficult to measure.

The easy method is to set a scale on it side and simply stall the robot full power into it. Of course, don’t do that for very long. If you don’t have a suitable scale, you could use a large spring. How much force the robot can exert on the spring horizontally will translate into the weight (force) it takes to pull the spring down vertically. This still requires a scale (and a tape measure or ruler), but it doesn’t require one that works on it’s side.

Of course the last suggestion is a fail-safe method and very easy to do, though I haven’t built the robot yet! I’m trying to see which motors to buy based on the needed characteristics. If I can calculate the minimum torque needed to successfully push a 500gram opponent out of a ring, I can know how much torque to safely sacrifice for speed.

Hello, chriswu.

You might find this blog post useful for helping you with your calculations.

- Kevin

Now I have another question.
Say an opponent with a net pushing force of 4 pounds pushed against my scoop (triangle) like so:

How can I calculate, in terms of theta, the x-force being applied to my robot? In other words, given my scoop angle, how much force do I need to apply in order to overpower my opponent?

Since a head on collision with no scoop (90 degrees from surface) would be the total 4 pounds, then is it safe to assume that a 45 degree scoop halves that force?

P.S. And while we’re talking about actuators, would it be safe to put two micro metal HP gearmotors (1600 mA) on one baby orangutan motor channel? The orangutan can support: 1A continuous, and 3A peak per channel. HP gearmotors take 70 mA free run, and 1600 mA stall. If I put two of them per channel…GAH!!
That’s 200 mA over peak output of the orangutan.
Can I still do this? If not, is there a cheap and easy way to simply increase the current capacitance of the orangutan by a simple auxiliary circuit? Or do I have to buy a motor driver, give up I/O’s, and all that business?

4lb on a 45deg angle will not give you 2lb, but ~2.828lb on the x axis and the same on the y axis. You should memorize the side lengths of 30-60-90 and 45-45-90 triangles, as that will automatically give you ratio for those angles. For instance, a 45-45-90 triangles has side lengths of 1, 1 and sqrt(2). So to find the length of the short sides, you can simply divide the hypotenuse by sqrt(2). 4/sqrt(2) == ~2.828. (I use the double equals sign since I’m a C programmer. :D). For other angles, you generally use the trigonometric functions of sin, cosine and tangent.

Also, in your example of 4lb against a 30deg angle, 2*sqrt(3)lb will be exerted down (weight gain for you), and 2lb would be exerted against you. But that would be no slippage numbers, and one of the main features of a wedge is that it the opponent robot slides up it. So if you get the other robot off it pushing wheels, then all you need to push against is the friction of whatever is left touching the ground, and the other robot is only adding weight (more traction for you).
In other words, if you have a fast robot that can get under any other robot and get it off it’s wheels, then you don’t need much pushing power at all. All you do is get under, run to the side, quickly reverse directions and they slide right out of the ring. That’s the theory anyway.

It is not necessary, but might be worthwhile to carry a graphing calculator on you while working on this. Scientific calcs are ok, but graphing calcs scroll to show what you’ve already done. They are expensive though…

For the motor driver problem, I would not suggest going over the current ratings for the driver. If it was just a mobile robot, that might be fine. But this is sumo. Things get fried very quickly, as there is a lot of stalling. I would actually suggest using a driver than can supply the stall current of the motors continuously. Stalling a motor for 15 seconds can possibly fry a motor. Pulling the peak current from a driver for 15 seconds is much more likely to fry the driver. I’ve personally fried a Vex robot motor (very good for the price BTW), and lost because of it (I was very close to winning, and I won the previous year with a similar robot.)

I know the Pololu guys have discouraged running a larger motor driver with the outputs of the on board TB6612FNG, but it is possible. If you are up to some light surface mount soldering (and ok with losing the TB6612), then you could remove the on board driver and run those lines to a larger external driver. Not exactly the easiest solution ever, but far easier than removing a fully soldered in Baby Orang during a competition.

Also, a few suggestions from a former robot sumo competitor and winner; make parts that can break easily replaceable, and have backups on game day. Motors especially. Screw them on if at all possible. Electronics should be accessible, while at the same time well protected. Remember the law: “What can go wrong, will go wrong.” Make sure it can’t go wrong. Having motors that exceed the motor driver max current it something that can very easily go wrong. Wires soldered to pins, headers, etc should be hot glued over. You can remove the hot glue to change/replace something, but it wont shake loose during a competition. Breadboards can’t be trusted to maintain a good connection on a rattling robot, solder stuff in. Have a soldering iron, hot glue gun, and any other tools that you might possibly need with you during the competition.
There are all things which make you think “well Duh!” when you hear them, but if someone doesn’t tell you, you just wont thing of it.

One last thing: >>Charge you batteries, and have a double backup!<<–[very important]

So you’re saying if the robot has a good wedge, it needs minimal torque?

If your robot has a perfect wedge, then you need the least amount of torque. That would be an ideal situation where you could trust that your wedge would always get under the other robot 100% of the time. That does not relate to reality very well. Really what I was going for is that a good design can lower the necessary torque.

For example, lets pretend you are facing a robot which can be pushed back with 4lb of force. If you have a box shaped robot, then you can make able to push 4lb and be set. Or you might have a smarter robot which gets behind the opponent, and since it is pushing the other robot forward (which it probably is already going), you only need to push with 2lb of force. Or you might have a wedge which gets the other robot off it wheels, and again only need 2lb of pushing force.

Take a look at the first three bouts in this video:
The robot on the left is shown to be the stronger pusher in the first bout. But the other robot wins by pushing it from the side (somewhat accidentally in this case – it was a bit of a lucky win.) in the next two bouts. The second robot works better due to it’s speed and apparently better sensors+programming.

So, you can win with a weaker robot. But make sure it doesn’t end up in a head-to-head pushing match.

Thanks, very helpful advice. Based on your mini sumo experience, would you recommend say, 200 rpm 45 oz-in micro motors? Before on my first competition robot I used 60 oz in motors which seemed to die when faced with a head to head pushing match. The robot didn’t have a scoop though. If I added a scoop this time, and programmed algorithms to avoid face offs, do you think 45 oz- in motors will be adequate?

Honestly, I would say use the best you can, or best you can afford. I competed in a non-standard 2lb (~907g) competition with a single pair of Vex servo motors. Most of the competing robots were Lego NXT based, and there were a couple other Vex bots. I didn’t have the best pushing power there. My winning design won with a very low wedge, and tracked onto the other bots very quickly so that it was never being pushed from the side.

The Vex (discontinued 3 wire) motors are 100rpm, 6.5lb-in (104oz-in). Two on each side with 2.5 inch wheels would give 83.2oz of pushing force, if wheel slippage is zero, and a top speed of ~13in/sec. A proportionally equal 500g robot would have 45.9oz of pushing power, and a top speed of 7.2in/sec. I’m going to calculate off of 1.5" wheels. With two 200rpm, 45oz-in motors, you would get 60oz (1700g (force grams, not mass grams)) of pushing force, and a top speed of 15.7in/sec. Assuming good programming and a wedge bot, that should be very competitive. You wont beat the Korean or Japanese bots with it, but it should do well in most other competitions. If you wanted to raise the bar a little, you might want slightly faster motors. ExSpurt, which did very well competitively, has a top speed of 47in/sec, and pushing power of 1080g after wheel slippage

Wheel slippage is a problem. The best wheels only just barely pass the paper stickiness test. Casting your own tires is the best solution, and Brookbots has a guide on how they did it. Not the easiest or cheapest task in the world. Without good tires though, 60oz of spinning wheels doesn’t do very much. You want the weight to be as close to the maximum as possible, as more weight will give you more traction. Make the robot weigh just under 500g, and have some small attachable weight with you in competition day so that you max out on their scale (which might not be exactly the same as yours).

You should try to have at least a couple weeks between finishing the hardware of your robot and the competition day. You want to have plenty of time to make your programming perfect. If your robot fails 1 out of 10 runs, it will fail during a bout. If you can test against other robots, make sure to do so. Even test against larger bot, remote control cars, heavy weights and anything else you can think of. Programming you bot to avoid a head-to-head is a very good strategy, and a wedge or scoop will help a lot.

Just a random fact, this type of sensor does not work well when spinning quickly.

If I’m to boost my speed and use the 320 rpm motors instead, in order to have significant pushing power, I’d need to buy 4 motors and have a 4wd. This would need more space, so the wheel diameters would have to be smaller, assuming I want enough real estate for the wedge. Do you know of any other distributors of good motors besides pololu?

Just a side question: Take a look at the Cobra minisumo chassis from fingertech robotics:

http://www.fingertechrobotics.com/proddetail.php?prod=ft-kit-cobra-4wd-chassis
Its motors have super long axles, yet on the robot they are short. I assume this is because someone had to use a cutoff wheel and shorten the axle?

Hmm, I just realized I made a mistake calculating the pushing force. I used torque divided by diameter instead of radius. I believe if you double all my pushing force numbers, it should come out correct. It also makes a lot more sense compared to some outside resources.

So, my math is this: 2x 320RPM, 25oz-in motors. 1.5" infinite grip wheels. 320rpm/60sec = 5.333rps. 5.333rps1.5inpi = 25.13in/sec. (2*25oz-in)/(1.5in/2) = 66.6667oz.

66.6667oz = 1890.g Plenty of torque, as your wheels probably wont stick that well.
25.13in/sec = 63.8cm/sec Not bad. Still around half the speed of Exspurt and probably most Japaneses and Korean robots.

I’m going to go on a whim and guess that you probably wont be able to make grippier tires than ExSpurt has. If that is the case, then there would be no reason to have more than about 1000g of pushing force. So you could bump up to two 50:1 motors with 625RPM and 15oz-in of torque, which would give you 49in/sec. I would guess that you would have trouble keeping it on the ring by itself at that speed, but you would be able to get around just about anything with good programming. But you would need to spend a lot of time working at it.

All of my calculations have been for 1.5" diameter wheels. Since the motors are the same and only the gearbox changes, the 100:1 motors with 3" wheels should perform nearly identical to 50:1 motors with 1.5" wheels. I would guess that the 50:1 and 1.5" would slightly outperform the other option, since there would be less loss to gear mesh friction. If you plan to use a different size wheel (which is of course very likely), then speed and pushing power numbers will need adjusted. Basically, larger wheels are faster with less power, and smaller wheels are slower with more power.

You should check my math yourself before buying anything. I’m 83.6% percent confident that I got it right this time. Find a high school physics textbook or a similar type reference on the internet.

Actually, I do have quite a bit of experience using polyurethane shore A 20 wheels. I used custom molded ones on my previous mini sumo, Rampant:

If I were to have a 4wd with 625 rpm 20 oz-in motors and 3 cm wheels (1.5 in = approx. 4 cm; too big if I wanted a 4wd), I would move at about 98 cm per second. That’s 38.5 inches; pretty fast for a mini sumo, especially compared to other Atlanta Hobby Robot Rally sumos.

3 cm diameter * pi = approx 9.4. 9.4 * 625 rpm = 5875 cm per minute/60 = 97.9 cm per sec.

Push: 20 oz-in/1.5cm = 13.3 oz per wheel. 13.3 * 4 = 53.3 oz of push. That’s 3.3 pounds of push for the entire robot, without calculating for other factors. That’s pretty competitive, assuming a good wedge and programming? Also, if I were to use rechargeable batteries, which would you recommend for the motors?

Oh and one last and final question: how does speed of the motors affect the push?

I would be willing to compete with those specs. Again, I didn’t compete in 500g sumo, so I’m not entirely certain what the normal pushing power is, but the speed should be great.

You absolutely want to use rechargeable. Rechargeable batteries can supply current much better than Alkalines. You also save money in the end.

I like Lipos for my robots, but they can be a bit pricey to start into. I usually order from HobbyKing as they often have the best prices. Cheap Turnigy “brand” batteries work just fine. I would go with a 2 cell 1300-1600mAh battery, depending on size (and be careful that the battery isn’t too big when you order it. Some 1600mAh Lipos will fit fine, some are too long.) A lower cost 15 or 20C discharge rate is fine, it’s not like you’re flying an airplane. The most current you will pull with four of those motors and some electronics is 8C from a 1300.

No reason you can’t use NiMH batteries though (NiCd is obsolete, I wouldn’t even bother with it.) Use at least a 6V pack, though 7.2V would be better. For capacity, you are limited by size and weight. More capacity is more runs without charging, and less weight you need to add by other means. This option is probably going to be cheaper.

You definitely want at least one backup battery. And you want the battery to be removable. No shame in duct tape or zip ties. Heck, no shame in anything – if it works, it works.

I’m not sure exactly what you mean by whether the motor speed affects the push. If you have a wheel on a motor, then the pushing strength is entirely dependent on torque. If you have a robot making a run from across a ring, then the weight and speed of the robot are what make the hitting force. How speed dynamically affects pushing power in the robot ring is very dependent on strategy and programming. Purely from a motor mechanics standpoint, motors’ speeds and torques can vary quite independently. You could say that the speed has absolutely nothing to do with pushing power. What is more important is the speed-torque ration and curve that is very specific to any motor. That will tell you what speed you can a expect from a motor for a certain torque output. Unfortunately, it doesn’t look like Pololu has the motor datasheet available, which would contain this detail.

Speed can be traded for torque and vice versa, and that is part of the mechanical design. Gear ratios exchange speed and torque, as does wheel size.

Robot design is all about tradeoffs. For example; speed, torque or price. You can have a fast and strong robot, but it will cost much more than a slower stronger bot or a faster weaker bot. You have to decide which way to go. My winning robot was faster and stronger than most of the competitors, but it cost more work to build it, and I spent more experience*time on it (I was a better programmer at the time, so it may not have actually taken longer to do it, but I had spent much more time with previous experience.) Time is another major trade-off. Do you spend time on programming or researching hardware? If you go to either extreme you have nothing (hint, don’t leave too little time to program. It always takes longer than you think.)

What I meant by “speed” is if your robot has little traction, can a fast spin compensate for the weak grip?

Well, my knowledge of physics requires I answer that technically, yes, as long as there is at least some grip. Take a look at a page on static vs kinetic friction. You really don’t want to rely on kinetic friction, which would mean your wheels are spinning on the ground.

Practically, low traction doesn’t get you anywhere. Higher speed will just have you spinning out more. You don’t have to have more traction than the competing robots, but almost no matter what more traction is better. I would place speed and traction as a trade off with cost. Speed could make up for a little traction if you are using hitting force to push the other robot off, but you need a minimum of traction to obtain the necessary momentum anyway, so you might as well have enough to push the other bot effectively.

For me personally, If I found that my robot wouldn’t grip the ground at 38in/sec, then I would either tone the speed down or increase traction.

thanks for all your help Darth Maker!! Maybe in the future I might see you at a contest like CIRC or AHRC!

No problem chriswu. You might see me at the CIRC competition this year or next. I’m in PA though, so AHRC would be quite a trip for me.

I’ll probably be wearing a ThinkGeek tee shirt. Generally it’s “i void warranties” or “I do all my own stunts”. PM on here a couple days before the event.

Heh, I’m a 14 year old chinese kid, so…

Push or the linear force which can be exerted by the robot not only depends on torque, but also on the the weight of the robot and grip offered by the tires. This is ensured to prevent slip and sliding of the robot which will reduce the force applied on the object.