Rubber wheel pinch drive

Kragen Javier Sitaker, 2019-08-16 (7 minutes)

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.

Pressing the motor shaft against the wheel

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.

A 10-watt NMB motor

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!

Rollers

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.

A quadcopter motor

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.

Multiple motors

You could reasonably easily connect multiple motors to the same wheel in this fashion, just clamping them on around its upper rim.

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