Question 7 of 7: Powered Wheelchair Selection and Design

Question 7: Powered Wheelchair Selection and Design (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(i) Power and torque requirements. The drive motors must overcome rolling resistance (higher on carpet than on hard flooring), climb the steepest ramp/kerb-cut the individual will realistically encounter (commonly designed to at least the ADA/CSA accessible-ramp maximum slope of 1:12), and provide enough reserve torque to accelerate the combined chair-plus-occupant mass promptly from rest, all while carrying the specific combined mass of the chair and its heaviest expected occupant.

Given. Combined chair+occupant mass $m = 150$ kg; ADA/CSA maximum accessible ramp slope 1:12 ($\theta = \arctan(1/12)$); carpet rolling-resistance coefficient $C_{rr} = 0.03$; target cruise speed $v = 1.0$ m/s; target start-up acceleration $a = 0.3$ m/s²; two driven wheels of radius $r = 0.15$ m sharing the tractive load equally. Find. The tractive force and power needed to climb the ramp at speed while accelerating, and the torque required per drive motor.

1. Ramp angle. $$\theta = \arctan(1/12) \approx 4.76^\circ$$
2. Total tractive force (gravity component up the slope, plus rolling resistance, plus the force to accelerate): $$F = mg(\sin\theta + C_{rr}\cos\theta) + ma = (150)(9.81)(\sin 4.76^\circ + 0.03\cos 4.76^\circ) + (150)(0.3)$$ $$F \approx 211\ \text{N}$$
3. Power at cruise speed: $$P = Fv = (211)(1.0) \approx 211\ \text{W}$$, i.e. about 106 W from each of the two drive motors — comfortably inside the continuous rating of a typical powered-wheelchair drive motor, which is usually a few hundred watts.
4. Torque per drive motor (two driven wheels sharing the load equally, wheel radius $r=0.15$ m): $$\boxed{T = \dfrac{F\,r}{2} = \dfrac{(211)(0.15)}{2} \approx 15.8\ \text{N}\!\cdot\!\text{m per motor}}$$

(ii) Stability considerations. A powered wheelchair must resist both forward tipping (heavy braking, descending a ramp) and rearward tipping (climbing a ramp, or a sudden aggressive acceleration), which is governed by the geometry of its centre of gravity relative to its wheelbase: the chair tips about whichever wheel-ground contact line the combined centre-of-gravity vector rotates past. Taking a representative rearward-stability geometry — combined centre of gravity a horizontal distance $x_{cg}=0.25$ m forward of the rear-wheel contact line and a height $h_{cg}=0.5$ m above the floor — the maximum rearward-safe incline is $$\theta_{tip} = \arctan(x_{cg}/h_{cg}) = \arctan(0.25/0.5) \approx 26.6^\circ,$$ which gives a stability safety factor of $26.6^\circ / 4.76^\circ \approx 5.6$ relative to the 1:12 design ramp — well above the safety margin (typically ≥ 2) recommended for powered mobility devices. Anti-tip wheels/casters set slightly clear of the floor at the rear (and, for some designs, the front) arrest any tip that does exceed this angle before the chair actually inverts. A low, centrally-mounted battery pack (the heaviest single component) is the standard practical way of keeping $h_{cg}$ low and hence $\theta_{tip}$ large.

(iii) Electronic motor control, safety and smooth operation. Each drive wheel is driven by an independent motor under closed-loop speed control (tachometer or encoder feedback), with the joystick/input device commanding a differential speed pair for steering (a "skid-steer" scheme, as on a tank). Pulse-width-modulated (PWM) motor drive gives smooth, efficient speed control across the full range without the heat losses of a linear (resistive) speed controller. Acceleration and deceleration are electronically RAMPED (a maximum rate-of-change limit on the commanded speed) rather than applied as a step, both for ride comfort/postural stability of the occupant and so a sudden input spike (spasm, accidental joystick knock) cannot produce a sudden lurch. Safety interlocks include an immediate motor-disable ("dead-man") response if the joystick signal is lost or out of valid range, a mechanical/regenerative brake that engages automatically whenever drive power is removed (so the chair cannot roll away on a slope when switched off), and current limiting so a stalled motor (wheel jammed against an obstacle) cannot overheat or damage the drivetrain.

(iv) Alternative control input for a high quadriplegic with little limb control. Where a standard hand joystick is not usable, the same proportional 2-axis (speed/direction) command can instead be generated by: a chin joystick (a small joystick mounted for chin/jaw operation, giving proportional 2-axis control much like the hand version, for a user with reliable neck/head movement); a sip-and-puff array (four discrete pneumatic states — hard/soft sip, hard/soft puff — mapped to forward/reverse/left/right, usable with no limb or head movement at all, though only in discrete rather than proportional steps unless the pressure magnitude itself is also sensed); or a head array (a set of proximity/pressure switches built into the headrest — forward, left, right, and sometimes a fourth reverse pad — triggered by small head movements against the pads). The choice among these follows directly from whichever muscle group the individual retains the most reliable, fatigue-resistant voluntary control over, since all three can be configured to drive the same underlying PWM motor-control electronics described in (iii).