Tri-Star Stair-Climbing Wheelchair

Staircase Geometry

Step height 16 cm

Step depth 28 cm

Cluster Drive

Climb speed 45°/s

Live Readout

Steps climbed

0 / 6

Cluster spin Φ

0.0°

Seat tilt

0.0°

Required leg L

0.00 m

How it works

A tri-star (planetary) wheel cluster carries three equal wheels bolted 120° apart around a rotating hub. To climb a stair whose rise h and run d are known, the hub-to-wheel leg length is engineered so the chord between successive step-edge contacts equals the side of the equilateral triangle traced by the wheels:

chord = √(d² + h²)
L = chord / √3          (chord = L·√3 for a 120° arc)

With L set this way, the whole rigid assembly can spin about a fixed contact point on the current step's leading edge P_k = (k·d, k·h). While spoke j is the pivot (down against the stair), its world angle is φ_j(Φ) = Φ − j·120° − 90°, and every wheel position follows the same rigid rotation:

hub  = P_k + L·(cos φ_pivot, sin φ_pivot)
wheel_j = hub − L·(cos φ_j, sin φ_j)

Because the geometry is matched exactly (L = chord/√3), each 120° of spin Φ lands the next spoke precisely on the next step edge P_k+1, with no slipping or re-planning needed — the whole climb is one continuous rigid-body rotation.

Step height / depth — sets the stair rise and run; the required leg length L updates live.
Climb speed — angular rate of the tri-star spin, Φ̇.
Self-Leveling Seat — real assistive wheelchairs (e.g. the iBOT) add a parallelogram linkage that counter-rotates the seat frame so it stays level while the wheel cluster spins underneath. Turn it off to see why that linkage is essential: without it, the seat is bolted rigidly to the hub and tumbles through the same Φ as the wheels.

This is the real mechanism behind stair-climbing power wheelchairs and some rescue/inspection robots — a purely mechanical solution to a terrain problem, with no path planning or sensors required once the geometry is matched to the stairs.

Tri-star wheel cluster Seat frame Staircase

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