Air-tyre hub motors for the wheels (issue #18, 2026-10-27)

The user: "for the wheels can we do something more like a 10" hub motor with air filled tires? That would give us some suspension, ability to drive through puddles, and a step up I think? ... Maybe 8" or similar? In general I want air tires." and "I don't think we would be able to jump, but we could maybe walk up stairs? Not sure if the hub motor would be able to brake/lock in place?"

Air tyres are decided. This note picks the size and the part, and answers the engineering questions with the leg rig (sim/wheel_study.py, run on a GB10), the full-robot kerb scenario, the leg's clash sweep (cad/wheel_fit.py) and hand calculations. Raw results: exports/wheels/*.json. Nothing in cad/fivebar.py or sim/leg_rig.py was edited.

1. The answer up front

• Primary: a 10 in single-shaft hoverboard-class hub motor with a 10 x 2.125 (or 10 x 2.5) pneumatic tyre, 36 V 350 W, hall sensors, D-shaft Ø16 mm with 13.5 mm flats x 76 mm long, about 3.5 kg. It is the only class of 8-10 in air-tyre hub motor that is single-sided by construction (a hoverboard clamps the axle on one side only), runs at our 36 V bus, and sells at a listed price from several sellers. Sellers in section 2.
• Backup: the same motor in 8.5 in (an 8.5 in hoverboard "off-road" motor, ~3.3 kg): the same shaft and electricals, a 22 mm lower ride height, 15 mm more jump, 16 mm less rolling kerb.
• Alternative with a real brake: a 10 in 36 V 350 W scooter wheel with a drum brake and a two-sided M12 axle (Amazon kits about $225 with a controller we would not use). It needs a fork on the leg (section 2.4): not recommended for v1.
• Does the leg support it? Yes. Every rig scenario at 18.05 kg a leg (16.25 + the heavier wheel) stays under the RS-04's 120 N m (109 N m at the uncapped jump, the same as today); the landing loads on the knees and axle are within the cases the leg's FEA already carries (the 150 mm drop's axle spike falls from 1,727 to 1,470 N); the clash sweep is clean at every stance and stop pose. The jump falls from 206 to 167 mm (the wheel is 1.3-1.8 kg heavier, unsprung, and the leg carries it). Section 4.
• Stairs: no, not for v1 with any wheel. Rolling alone climbs about 25-30 mm (friction-limited at 0.22 r); the full-robot sim passes a 25 mm kerb and falls at 40 mm with every wheel. A jump-climb needs the wheel to clear a 178-197 mm riser plus a 250-280 mm hop: our jump is 167 mm (10 in), 182 mm (8.5 in), 206 mm (BotWheel) at the 60 N m cap and about 7 mm more uncapped. A single 100 mm kerb by jump is marginal even with the BotWheel. Section 5.
• Braking and holding: yes while powered, by the balance controller (3.8 N m a wheel on a 10 deg slope, inside the motor's continuous 5 N m), or by the VESC's handbrake/position hold when sitting; unpowered, the robot sits on its skids (D55's sit-down) and the skids are the parking brake. Phase-short braking is a damper, not a lock (3.5 N m at 0.3 m/s, 11 N m at 1 m/s). No mechanical or electromagnetic brake for v1. Section 6.
• Drivers: keep the Flipsky 75100s (14-84 V, hall + encoder ports). Hall-only FOC is fine for torque control; the risk is the wheel-speed estimate at near-zero speed (90 hall edges a turn). Mitigation in firmware first, a magnetic encoder on the rotor cover as the upgrade. Section 7.
• Puddles: the motors are IPX4-class as sold; sealed as in section 8 they take a 40 mm puddle (the hub's seam sits 45 mm above it on a 10 in wheel). The belly box goes to IP54 with a gasket; the harness gets Deutsch DT/DTP connectors.
• Mass: +2.7 kg (3.53 kg wheels) to +3.6 kg (4.0 kg) on a P3 ledger already at 32.27 kg against the 32.0 kg gate. The gate must move (proposed D69: 35.0 kg) or the 8.5 in backup is taken (+2.2 kg). Section 4.4.

2. Candidates

Prices were checked 2026-10-27. Amazon, eBay, Walmart and AliExpress blocked the fetcher, so their prices come from search snippets and are marked [snippet]; the implementer confirms the live listing before ordering (plan task W1). Everything not read on a page is marked [unverified].

2.1 Hoverboard single-shaft hub motors (group A)

The whole family (6.5, 8, 8.5, 10 in) shares one motor core: an outer-rotor BLDC, 30 magnets / 15 pole pairs, three phase leads plus a 5-wire hall harness through a hollow D-shaft, the shaft clamped on one side in the hoverboard's frame. ODrive's hoverboard guide (docs.odriverobotics.com/v/0.5.5/hoverboard.html) gives the electrical character: "30 permanent magnet poles, and thus 15 pole pairs", Kv "a typical value is 16" rpm/V (so Kt = 8.27 / 16 = 0.52 N m/A), a measured phase resistance of 0.18 ohm and inductance 0.34 mH, "quite high resistance compared to the hobby aircraft motors", and a current range of 25 A. Hoverboard controllers run them at 15 A; a VESC can push 30 A for seconds (15.5 N m, 243 W of copper loss). A 10 A continuous current (5.2 N m, 27 W) is a safe thermal rating until the bench measures the case temperature.

What is still unverified for the primary: the shaft's steel (section 2.4 assumes 45 steel, 355 MPa yield), the tyre's pressure rating (10 x 2.125 tubes are marked 30-50 psi on scooter tyres), the no-load speed, the 8.5 in mass. Task W1 in the plan buys two 10 in motors first and measures mass, shaft, Kv, resistance and the hub's run-out before any CAD is cut.

2.2 Scooter hub motors (group B; two-sided axles)

Every one of these needs a fork: a clevis spanning the wheel, bolted to the wheel link's foot, with the axle's flats in its dropouts. Cost: two SendCutSend 6061 arms (about $25-40 each at an instant price) plus a cross-piece and the wider track (the arm on the outboard side adds 15-20 mm a side). It also puts a part outboard of the wheel for kerbs to hit. The drum-brake kit is the one reason to do it, and section 6 says the brake is not needed.

2.3 Robot hub motors (group C)

Nothing robot-grade exists at 8-10 in with an air tyre at a listed price. The hoverboard motor is the practical part.

2.4 The single-sided shaft: cantilever capacity

The D-shaft (Ø16, 13.5 across the flat): about the flats' axis I = 2,450 mm^4, Z = 363 mm^3 (a full Ø16 circle is 402). With the foot's clamp covering the shaft and the tyre's centre plane 45 mm from the clamp's inner edge (the hub is 65 mm wide, the shaft 76 mm long), the bending moment is F x 45 mm:

The hoverboard carries 590 N static a wheel and survives riders' kerb hits, so the shaft is sized for this class of load; the stress raiser where the flat ends is inside the clamp if the clamp covers the whole flat. The foot must clamp the shaft over 40 mm or more (a split clamp with four M5s, as the hoverboard's bracket does with four M8s) so the lever stays at 45 mm; a short clamp would double it. Plan task W3 adds the shaft to cad/leg_studies.py as a steel beam at the rig's axle spikes, and W1 measures the shaft's hardness (a file test or a Rockwell check) to settle the yield.

3. The tyre model

3.1 Radial stiffness of a 10 x 2.125 pneumatic tyre

Method: the membrane (inflation) model, k = 2 pi p sqrt(R r), with R the wheel radius and r the tyre's section radius; the pressure carries the load and the contact patch grows with deflection. Calibrated against measurements:

• Rothhaemel (KTH, 2023), "Measuring vertical tyre stiffness of bicycle tyres", 20 in tyres: "31 N/mm to 147 N/mm", "tyre inflation pressure is the main factor", "values below 50 N/mm are related to extremely low inflation pressure". The model gives 162 N/mm for a 20 x 1.75 at 50 psi: the measured top is 147, so the model runs about 10 % high at pressure and more at low pressure (the carcass carries less than the model assumes).
• Cano-Moreno et al. (UPM, 2024), "The Vertical Stiffness of E-Scooter Tires", Latin American Applied Research 54(3): compression tests on e-scooter wheels, "from 0.9 E5 N/m to 3.6 E5 N/m" (90-360 N/mm; the range includes solid tyres at the top).

So k = 0.75 x 2 pi p sqrt(R r) is taken, with r = 27 mm for a 2.125 in section (32 mm for 2.5 in):

The rig's solid BotWheel tyre is an estimated 150-250 N/mm (sim/leg_rig.py), so the air tyre at 35 psi is a third of it, which is what research/leg-suspension.md's tyre_pneumatic variant assumed. The bench test "the tyre's stiffness" already in the leg plan (docs/handoff.md, M3) measures it: press the wheel against a scale through 10 mm at three pressures.

3.2 In MuJoCo

The contact is a spring-damper with time constant tau on the mass behind it, so k goes as 1/tau^2: tau_p = 7.7 ms x sqrt(200 / k_p). The study ran 14.1 ms / 0.5 for 60 N/mm (a conservative 35 psi), 18.4 ms / 0.45 for 35 N/mm (20 psi) and 11.5 ms / 0.55 for 90 N/mm (50 psi). Damping ratios are the contact's, not the rubber's; the sensitivity below covers them.

4. Does the leg support it?

4.1 The rig

rig/run.py's scenarios (its controller at 500 Hz, a tick of latency, the FLEXVOLT pair at R_int 0.1 ohm, 38 V static and 40.5 V for the dynamic cases, the bottom bumpers at 140 mm), with the leg carrying 16.25 kg (D65's design mass) plus the wheel's extra mass over the BotWheel. The wheel's mass was taken at 4.0 kg (the listed 3.53 kg plus the tube, a heavier tyre and margin) with 4.5 kg as a sensitivity. The rotor share is 0.6 as for the BotWheel.

Reading it:

• Gearbox: every case stays under the RS-04's 120 N m, with 109 N m at the uncapped jump for every wheel (the push-off sets it, not the wheel) and 68-75 N m at the capped jump's landing. Nothing spends time over the peak.
• Jump: 206 to 167 mm for the 10 in, 182 mm for the 8.5 in. The push is the same; the wheel is unsprung mass the leg has to lift and the carriage is heavier. The uncapped jump adds only 6-10 mm, because the pack's 40.5 V start rule limits the push as much as the torque cap does.
• Landings: the 150 mm drop is 15 % kinder to the axle with the 10 in wheel (1,470 against 1,727 N) and 30 % kinder to the gearbox (50 against 70 N m). The capped jump's landing is about neutral (1,643 against 1,542 N on the axle): the tyre is three times softer but the wheel is 1.8 times heavier, and the spike is mostly the wheel's own mass stopping. At 20 psi the tyre wins (1,314 N); at 50 psi it loses (1,896 N). So run the tyre soft: 30-35 psi.
• Stand torque is unchanged at 15.8 N m: the wheel hangs below the leg; the motors hold up the body, not the wheel. (The issue's first table rose with wheel mass because it added the wheel to the carriage.)
• The power cut is 1,900-1,940 N on the knees for every wheel: that is the 16.25 kg leg (1,713 N at 14.75 kg in exports/leg/rig-results.json), not the wheel. D39's fault case scales with the robot's mass whichever wheel it has.
• The knee-pin loads (1,311 N capped jump, 893 N drop) are inside the leg's FEA cases (R1w carried the 2,065 N drop spike at 14.75 kg; cad/leg_studies.py reads the rig's joint forces). The front link's compression (1,269 N jump) is under its 1,243 N at the uncapped jump today by 2 %: re-run the studies (task W3).

4.2 Fit on the leg

cad/wheel_fit.py: fivebar.clashes() with the candidate's solid (a 254 x 64 tyre ring, a Ø165 x 65 hub, the Ø16 shaft into the foot) in place of the BotWheel, at 130-380 mm with -20/0/+20 deg leans and at the six stop poses, with every bought part: 0 clashes for the BotWheel, the 8.5 in and the 10 in (exports/wheels/fit_clashes.json). The tyre sits in its own y band (82-146 mm from the upper links' face against the links' 0-80 mm and the motors at -56..0), so it can only meet the hip frame or the body, and neither reaches out there. The tyre's top passes 17 mm above the hip axis at the shortest leg (101.5 mm) with the 10 in wheel; nothing is in that plane.

What does change:

The wheel link's foot changes (task W2): the BotWheel's Ø50 boss recess and 4 x M6 on PCD 36 become a Ø16 D-bore clamp, 45 mm long, split on the outer face with four M5 x 30 and heat-set inserts (or a steel clamp block from SendCutSend if the PA6-CF clamp slips in the test), the cable exiting the shaft's hollow end into the link's Ø22 cable hole as now. The foot's outer face moves out by the shaft's stand-off so the hub's inner cover clears the link (the hoverboard's bracket sits 8-10 mm from the cover): about +8 mm, which the track numbers above include.

4.3 Body height and centre of mass

Standing at the same leg length the body rises 41 mm (10 in) or 22 mm (8.5 in); the robot's centre of mass (P3 ledger: 16 mm below the hip axis) rises with it and the balance model's pendulum gets 10 % longer: slower, easier to balance, a touch more wheel torque in a push recovery (the sim's push scenario is in the plan's re-run). Standing at 259 mm instead keeps the hip height and the camera and lidar geometry, and leaves 158 mm of crouch (against 199 mm today) and the same 140 mm of ground clearance. The full-robot sim's H_RANGE (sim/robot_v2.py) and the designer's height slider need the new wheel radius either way (task W4).

4.4 The mass ledger

P3 is 32.27 kg today against the 32.0 kg gate (exports/body/mass.json; docs/body-next-plan.md lists the levers).

The foot's change is about neutral (a smaller recess, a longer clamp). No lever on the body's list is worth 3 kg, so the gate moves: the proposed D69 sets the as-built ceiling at 35.0 kg with the design mass at 35.5 kg (17.75 kg a leg), which the rig results above already bracket (18.05 kg a leg simulated). The 8.5 in backup is the choice if the ledger must stay near 34.5.

5. Steps and stairs

5.1 By wheel torque alone

A wheel pressed against a step of height h with its axle load W, driven only by its own torque T and no push from the body: moments about the step's corner need T >= W d with d = sqrt(2 r h - h^2); and the corner contact slips unless d / (r - h) <= mu, i.e. h <= r (1 - cos(atan mu)). With mu = 0.8 on dry concrete that is h <= 0.22 r:

A two-wheeled balancer meets a kerb with both wheels at once, so there is no body push to lean on; what it has is momentum. The full-robot sim (sim/robot_v2.py's balance controller, driving at 0.6 m/s, the kerb scenario of sim/scenarios.py at 25-100 mm) agrees with the table: the 10 in wheel passes 25, 30 and 35 mm at 0.6 m/s and 40 mm at 1.2 m/s, and fails 50 mm; the BotWheel passes 25 mm and fails 30 mm at either speed, the wheel torque pinned at its peak for 1.3 s before the robot falls forward over the kerb (exports/wheels/curb_*.json, summary_curb.json). The 10 in wheel's radius buys 15 mm of kerb over today's; the rolling step is a 35-40 mm lip (a door sill, a paving edge, a shallow kerb cut). A 100-150 mm US kerb is a jump.

5.2 By jump

The rig's jump height is the carriage's rise: 167 mm (10 in), 182 mm (8.5 in), 206 mm (BotWheel) at the 60 N m cap and the 40.5 V start rule; 7-10 mm more uncapped. To land on a step the wheel's bottom must clear the riser by a margin, and the robot must also travel the tread's 250-280 mm forward in the 0.4 s of flight (0.6-0.7 m/s at take-off, feasible). Ascento does this with a 10 kg robot and a 0.4 m jump; we are 35 kg.

5.3 Stairs for v1

No. The jump does not clear a riser with any wheel at this mass, each step would be a maximal jump with a landing on a 250 mm tread, and a miss is a fall down a flight with a 35 kg robot and a foam-ball turret on top. The honest v1 envelope: 25-30 mm lips by rolling, a 100 mm kerb by jump as a later firmware milestone (the BotWheel would do it today; the 10 in wheel needs the uncapped 120 N m and a fresh pack), and ramps up to the slope scenario's 10 deg. Stairs want a lighter robot or a leg with more jump, which is a different project (a lighter body without the J501, or the knee-to-knee spring of research/leg-suspension.md section 8 for energy return).

6. Braking and holding

While powered and balancing, the wheels are current-controlled and the balance loop holds the robot where it is: on a 10 deg slope that is 3.8 N m a wheel for a 35.5 kg robot (1.9 N m at 5 deg, 5.7 N m at 15 deg), inside the motor's 5.2 N m continuous, 27 W of copper loss a motor. The sim's slope scenario (10 deg ramp, hold) is re-run with the new wheel in task W4. Above about 14 deg the hold exceeds the continuous rating and the motors warm: the firmware sits the robot down after a thermal timer.

While powered and sitting (on the skids, legs folded), the VESC can hold the wheels: handbrake (a DC current through the phases locks the rotor to the stator field, like a stepper's detent: holding torque = Kt x current, 5 N m at 10 A, and it works with halls alone) or its position loop on the hall interpolation. Not needed: with the legs folded the skids carry the robot and the wheels are unloaded (section 4.2).

Unpowered: a short across the phases gives a braking torque proportional to speed, through the phase resistance and inductance (Kt 0.52, R 0.18 ohm, L 0.34 mH, 15 pole pairs): 3.5 N m at 0.3 m/s, 11 N m at 1 m/s, 21 N m at 2 m/s (28 / 90 / 168 N a wheel). It is a damper that stops a roll-away in a metre; it does not lock. The robot's answer to a power loss is the sit-down (D55, D39): the legs fold, the skids (TPU 95A, mu 0.6-0.8 on concrete) take the weight and hold it on any slope the robot can stand on (a 10 deg slope needs mu > 0.18). A passive phase-short on power loss is cheap if P1 shows the robot rolling during the fold: three 40 A SPDT automotive relays with their NC contacts tying the phases to a star, or the turret's brake-FET pattern (D47), about $15 a wheel; the plan leaves it out of v1 and names it as the fix.

A mechanical or electromagnetic brake is not worth it. The hoverboard motor has no brake mount and its outer cover is the rotor, so a disc or drum means the two-sided scooter wheel plus a fork (section 2.2), a cable or hydraulic caliper, and an actuator to pull it: 0.5-0.8 kg and $100-250 a side for a parking function the skids already give. An electromagnetic brake needs a shaft that turns, and a hub motor's shaft is fixed. If a holding brake is ever wanted while powered, the VESC handbrake is free.

7. Drivers

Keep the 75100s. Set-up for the hoverboard motor: FOC, 15 pole pairs, hall sensor detection in VESC Tool, hall interpolation on, motor current max 30 A, absolute max 40 A, battery regen -15 A a wheel (the bus's 60 V fault is far away at 41 V), a temperature cut-off from the motor's own sensor if it has one (most hoverboard motors do not: add a 10 k NTC on the stator under the cover during W1's teardown and use the VESC's motor temperature input).

Low-speed balance quality. Torque control with halls is sound at zero speed: FOC commutates from the hall sector (60 deg electrical) and the VESC interpolates the angle once the wheel moves; the torque ripple from a 30 deg electrical angle error at standstill is 13 % and it averages out across a hall transition. The risk is the wheel-speed estimate: 90 hall edges a turn is 4 deg mechanical, so at a balancing creep of 0.05 m/s on a 10 in wheel (0.4 rad/s) there are 6 edges a second, and the controller's wheel velocity is a staircase. Three fixes, in order:

1. Firmware (v1): the balance loop takes pitch and pitch rate from the VN-100 and uses the wheel speed only in the slow outer loop (position and speed tracking); the wheel-speed estimate blends the hall edges with the commanded torque through a first-order model (the hoverboard FOC firmware and every hoverboard-motor balancing build do this). The simulation's controller (sim/controller_v2.py) is checked with the wheel speed quantised to 4 deg and delayed by the VESC's 500 Hz CAN tick (task W5): if it still passes stand, push and drive, this is enough.
2. An encoder on the rotor cover: a 6 x 2.5 mm diametric magnet glued at the centre of the rotor's outer cover (on a single-shaft hub motor the outer face spins and its centre is free) read by an AS5047P (14-bit, SPI, on the 75100's ENC port) on a printed arm from the foot, in a shroud; or, inboard and protected, a magnetic ring (a 32-pole ring magnet on the inner cover round the shaft) read by an AS5304/AS5311-class off-axis sensor fixed to the foot. About $20 a wheel, a 3D-printed bracket, no change to the motor.
3. ODrive Pro does not help: the problem is the sensor, not the driver.

Speed: Kv 16 at 41 V is 656 rpm, 8.7 m/s on a 10 in wheel. The firmware's speed limit stays at 2.1 m/s (the sim's speed_limit_mps) and the VESC's own max ERPM is set to 15,000 (1,000 rpm) as a hard ceiling.

8. Puddles: ingress protection

Rule for the manual: puddles to 40 mm (the tyre's lower quarter), no fords; dry the robot before charging.

9. What is still unverified, and where it is settled

Sources

• ODrive hoverboard motor guide: https://docs.odriverobotics.com/v/0.5.5/hoverboard.html (15 pole pairs, Kv 16, R 0.18 ohm, L 0.34 mH, 25 A)
• Robokits RKI-9013 10 in 36 V 350 W hub motor: https://robokits.co.in/e-bike/hub-motor/10inch-36v-350w-brushless-bldc-hub-motor-with-tyre-for-e-bike-and-hoverboard (Rs 3,256; shaft Ø16 / 13.5 flat / 76 mm; hub 163 mm; 2.96 kg airless; IP4)
• e-gizmo 10 in 350 W BLDC hub motor, pneumatic: https://www.e-gizmo.net/gizmoshop/index.php?route=product%2Fproduct&product_id=49630 (PHP 999; 10 x 2.125; 3.53 kg; halls)
• Alibaba 10 in hoverboard motor wheel 36 V 350 W: https://www.alibaba.com/product-detail/10-inch-Hoverboard-Motor-Wheel-36V_1600933431463.html [snippet]
• Hover-1 Titan (10 in pneumatic, tubed, 36 V, 265 lb): https://eridehero.com/?p=5576 and https://www.hover-1.com/products/hover-1-titan-hoverboard
• iFixit, Hover-1 Titan wheel and motor replacement: https://www.ifixit.com/Device/Hover-1_Titan
• ATO 10 in hub motor: https://www.ato.com/10-inch-hub-motor ($438.54, 4 kg, IP65, 119 mm dropout, 30 N m)
• Amazon 10 in 36 V 350 W drum-brake wheel kits: https://www.amazon.com/Brushless-Motor-Electric-Scooter-Wheelbarrow/dp/B0GT9RBLTT, https://www.amazon.com/Brushless-Off-Road-Pre-Assembled-Controller-Wheelbarrow/dp/B0GTM5CRMY [snippet]
• esk8.news, 10 in hoverboard hub motors on VESC: https://forum.esk8.news/t/4wd-mountainboard-10-inch-hoverboard-hub-motor-vesc4-trampa-holypro-deck/16307
• DDT M1502D_233: https://www.roboticscenter.ai/store/product/direct-drive-tech-m1502d233-directdrive-motor/ (24 V, Kt 0.88, IP55, 2.3 kg, backorder)
• Unitree Go2-W: https://unitree.com/go2-w (7 in pneumatic)
• Rothhaemel, KTH 2023, bicycle tyre vertical stiffness: https://dapp.orvium.io/deposits/650c004def25b2f0766f520b/view
• Cano-Moreno et al. 2024, e-scooter tyre vertical stiffness, LAAR 54(3): https://www.laar.plapiqui.edu.ar/OJS/index.php/laar/article/view/1069
• VESC handbrake and hall hold threads: https://vesc-project.com/node/180
• The rig and the sweeps: sim/wheel_study.py, cad/wheel_fit.py, exports/wheels/ (this branch)