I ran across some discarded stroller wheels on the way home, which I resisted the temptation to bring home. They had hard rubber around the outer rim (of about 200-mm diameter and 20-mm thickness), and it occurred to me that a motor shaft pressed directly against that outer rim would be an effective way to drive it with a fairly large mechanical advantage for mobile robotics.
Suppose we mount a motor above the wheel with its axis parallel to the wheel and its 10-mm-diameter shaft running across the top, held in one bearing on each side of the wheel, each of which is pressed toward the wheel axis by some kind of mounting preload, thus pressing the shaft into the rubber. Steel on rubber has a frictional coefficient around 1, so the bearing radial load needs to be a bit larger than the maximum drive force we need to be able to apply to the wheel. And we have about a 20:1 mechanical advantage in the torque sense (but 1:1 in the sense of linear motion).
Let’s say the robot weighs 10 kg and thus 98 N, so we want at least 30 N of force to be able to handle reasonable slopes with some reasonable acceleration and deceleration. With the 5-mm radius of the shaft, we need 0.15 N m of torque from the motor, or 0.11 foot-pounds in medieval units. This is a reasonably large amount of torque; many small electric motors cannot provide it. Ten watts at 30 N is 330 mm per second, a very slow walking sort of speed, at which speed the wheel would be turning 1.9 revolutions per second (113 rpm), and our hypothetical 10-mm-diameter shaft 38 revolutions per second (2300 rpm), which is not an outrageously low speed for a modern small motor, but somewhat lower than optimal. Also, the 10-mm shaft is enormously larger than most small motors have.
So it would be nice to be able to use a smaller shaft in this way, thus getting more mechanical advantage and not needing to attach a thicker shaft to the motor. But if we take a shaft that’s much thinner than 10 mm, mount it through bearings on both sides of the wheel 20 mm apart, and press down on the bearings with, say, 50 N or 100 N of force, the shaft will probably bend in the middle, yielding, and be ruined.
I don’t know what a typical motor in this power range is like these days, but on the strength of Digi-Key having 221 of them in stock, I’ll consider the Minebea DIA42B 10W 31A as a representative. Digi-Key charges US$33 for it, which seems high.
The DIA42B 10W is a ten-watt 24-volt BLDC motor optimized for 500-3500 rpm (running up to 4000 rpm with no load at 300 mA), and although it’s only rated for ten watts, it’s also rated for ten amps. It weighs 150 grams and it’s 42×42 mm with a 6-mm-diameter shaft. It has a 100-pulse-per-revolution rotary encoder. The torque curve on p. 13 of the datasheet shows it at almost 6000 rpm at no load, 60 mN m of torque at 3500 rpm, 90 mN m of torque at 2000 rpm, 100 mN m of torque at 1000 rpm, and about 105 mN m at its 500-rpm minimum speed. At these high torques it’s sucking up to 2 amps of current, so if you keep it up it’ll burn up; what I think is its top sustainable current of about 400 mA would give you about 20% to 40% of those torques, about 20 mN m.
At the surface of its 6-mm-diameter shaft, 20 mN m works out to 6.7 N, which is significantly lower than 30 N but would still permit significant robot movement, especially if the robot ends up lighter than suggested above. Clearly gearing it up further by using a thicker shaft would be bad!
So, how could we press this 6-mm shaft against the wheel, other than running it between bearings 20 mm apart on opposite sides of the wheel? We could press it onto the wheel by backing it with two rollers, not themselves in contact, which trap it in a triangle of compression between the wheel and the rollers.
But the rollers can’t be very large. If they’re 6 mm in diameter themselves, then they could be as far as 180° apart viewed from the motor shaft before they hit the wheel, but then we haven’t really solved the problem, just reduced it by a factor of 2 or 3. If we make them larger, we can improve that situation, but soon they hit the wheel.
However, if we make the rollers out of stacks of parallel discs with spacers between them on a shaft, like hard disk platters, we can overlap them, though not arbitrarily far. If the shaft diameter approaches zero, each disc of roller A can extend to the center of roller B, and vice versa; with a physically plausible shaft diameter, they need to be somewhat further out. The discs could be, for example, 1.4 mm in thickness with a 1.6 mm space between them, with somewhat rounded edges, so that the 6-mm shaft only needs to span spans of about 2 mm unsupported from one direction.
For example, you could imagine 16-mm-diameter discs on 9-mm shafts (including the spacers), yielding 11 mm distance from roller center to motor-shaft center and 13 mm distance between roller centers (including ½ mm of clearance). This means that the motor shaft center will be sqrt(11² - 6½²) mm or about 8.87 mm away from the roller-center-to-roller-center axis. This means that the bottom of the motor shaft will be 11.87 mm from the roller-center-to-roller-center axis, while the roller edges are only 8 mm from it, so they won’t touch the wheel. They could even be a little bigger than that.
Bigger rollers would mean not only more stiffness but also improved leverage to overcome the friction in the rollers’ bearings, and thus less friction loss.
Consider a higher-powered modern BLDC motor, the Turnigy BC2836-8 quadcopter motor I used as my example in Drone cutting. It has a 4-millimeter shaft and delivers 336 watts at 15000 rpm on 14 volts; this suggests an output force of almost 100 newtons at the surface of the 4-mm shaft --- ample to drive the wheel in this way, but definitely needing something like this roller system.
If you try using the same two rollers, the motor shaft center will be sqrt(10² - 6½²) mm or about 7.6 mm from the roller-center-to-roller-center axis, and the shaft edge 9.6 mm from it, slightly over the 8 mm of the rollers themselves.
You could reasonably easily connect multiple motors to the same wheel in this fashion, just clamping them on around its upper rim.
The wheel in this system is only being used to transfer linear motion from the surface of some motor shaft to the road or floor, so the calculations here are entirely insensitive to the wheel size --- it would work in precisely the same way with rollerblade-sized wheels as stroller-sized wheels, applying the same amount of force to the road at the same speeds. The only relevant difference would be that, driving a smaller wheel, the rollers would have a bit more clearance to avoid contacting the wheel.