This patent application describes the design of a novel wheel with an epicyclic gearbox that, when fitted to the frame of a manual wheelchair, allows the user to propel the wheelchair in two different modes called ‘Run’ mode and ‘Standard’ mode. In Run mode, the wheelchair is propelled with a continuous push-pull stroke. The user’s hands stay on the pushrim, alternately pushing and pulling the pushrim and advancing the wheelchair with both the pull and push portions of the stroke. Since all of the arm movement is propulsive the average force on the arm is much lower than for standard pushrim propulsion and the harsh stresses on the hand and wrist from grasping and releasing are avoided. The novel wheel offers three gear ratios between the pushrim and the road wheel. It has a no-rollback feature so that if the user releases the pushrim while travelling up a ramp, the wheelchair will not roll back down the slope. When the user changes the wheels from Run mode to Standard mode the wheelchair functions like a normal manual wheelchair (albeit one with gearing) when the user pushes the pushrim the wheelchair goes forward and when the user pulls the pushrim the wheelchair goes backwards.