Why can the unicycle, with its center of gravity high up, stand upright without falling over?

This article focuses on the issue of why a unicycle with a high center of gravity can stand upright without falling over. It explains the principle that relies on the driver controlling the pedals to generate ground friction torque to balance the overturning torque, and introduces the structure and application of the Segway (a powered scooter) based on the same balancing principle and using an automatic control system.

Why can the unicycle, with its center of gravity high up, stand upright without falling over?

The unicycle is a common prop in acrobatic performances. It has only one wheel, with its center of gravity high above, making it seem like an unstable teeter-totter. However, under the control of a skilled rider pedaling the pedals, it can maintain a stable upright position, either standing still or moving forward or backward with flexibility. Why can the unicycle with a high center of gravity stand upright without falling over? It turns out that the secret to the unicycle's upright stability lies entirely in the rider's driving skills. When the rider leans forward with the vehicle, the ground's support force on the wheel no longer passes through the center of gravity, creating a torque on the center of gravity. Torque is an external force that causes an object to rotate, and its magnitude is equal to the support force multiplied by the distance between the force and the center of gravity. If left uncontrolled, the unicycle would fall over in the direction of the torque. At this point, the rider applies force to the wheel through the pedals and sprockets, causing the wheel to roll forward. The friction between the wheel and the ground generates a forward friction force, which counteracts the overturning torque of the support force and helps the vehicle regain its upright stability. By appropriately controlling the pedal force, the unicycle can be made to stand still. If the pedal force is increased further, the wheel will roll forward. To make the unicycle move backward, the rider simply leans back slightly and pedals in the opposite direction, allowing the rearward friction force to balance the overturning torque.

If an automatic control system replaces the rider's control of the unicycle, a new type of self-balancing vehicle can be designed. This is the "Segway", or "powered skateboard", which has appeared in recent years. It consists of a horizontal chassis and two wheels arranged side by side. The wheels are powered by batteries, and a vertical handlebar is used to steer. The rider stands on the chassis, with a high center of gravity similar to that of the unicycle. The vehicle's control system ensures that the rider maintains an upright position and does not fall forward or backward. This unique vehicle once appeared at the 2008 Beijing Olympic Games and has now become a practical means of transportation in sports venues, airports, and train stations.