Segways and dynamic equilibrium
Segways are electric, two-wheeled personal transportation devices designed to provide an alternative means of mobility in urban environments, addressing issues like congestion and pollution. They operate based on principles of dynamic equilibrium, allowing users to maintain their balance while in motion. The technology behind the Segway relates closely to the inverted pendulum problem, wherein an upright position is unstable unless the base is in motion. When riders lean forward or backward, the Segway responds by adjusting its wheels accordingly, ensuring that the rider remains upright. This dynamic stability mirrors the way humans walk, where shifting weight allows for continued movement without falling. The Segway's operation relies on balance sensors that monitor various factors, including the rider’s pitch angle and wheel speed, which are governed by complex mathematical equations. This integration of physics, engineering, and mathematics highlights the sophisticated design that enables a seamless personal transportation experience. Understanding these principles can provide insight into the mechanisms that support the Segway's functionality and stability.
Segways and dynamic equilibrium
Summary: The Segway is a personal transporter built on the principle of dynamic equilibrium.
The Segway is an electric, two-wheeled personal transportation device that utilizes principles of balance and equilibrium both to create and control its motion. The Segway transporter was developed in part to combat the congestion and pollution caused by automobiles. In many cities, Segway tours are now alternatives to walking or bus tours. The Segway is often cited as an application of a classical dynamical systems problem: the inverted pendulum problem. It can also be referenced in illustrating the phenomenon of dynamic stability that also occurs in human walking.
Inverted Pendulum
In a traditional pendulum problem, the pendulum is composed of a mass attached to a string that is itself attached to a pivot point. In this case, the mass hangs below the pivot point. The position in which the mass hangs below the pivot point is stable—the pendulum eventually returns to that position even if pushed away from that position. In fact, it is relatively easy for the pendulum to rest in this equilibrium position. In an inverted pendulum problem, the situation in which the mass is above the pivot point is considered. Frequently, one can visualize this scenario as a “cart and pole.” With the cart at rest, if the pole is perfectly positioned, it will stand upright on top of the cart. However, this condition is unstable; if the pole is moved away from this resting position, it falls.
An interesting property about the inverted pendulum (or cart-and-pole) problem is that as long as the base, or cart, is resting, the upright position is unstable. However, if the base or cart is in motion, oscillating at the right frequency, the upright position becomes stable. Imagine that the cart is moving forward and backward ever so slightly and very rapidly; in this case, the pole can remain upright. Now, the pole is in a dynamically stable position. This type of motion-induced stability is similar to what happens as humans walk. If an individual leans forward with his or her feet firmly planted on the ground, the individual will fall. However, if the feet are allowed to move, the individual will not fall but instead will move forward (or backward, depending on the direction of the lean). Allowing the feet to move has made the leaning position dynamically stable. With the feet moving, it is much harder for the individual to fall.
Dynamic Equilibrium
The Segway transporter operates on this principle of dynamic equilibrium. Riders lean forward to cause the wheels to move forward and lean back to cause the Segway to stop or reverse. The wheels and base are dynamically moving to keep the rider in an upright position instead of falling to the ground. Balance sensors in the base of the Segway regulate and control the motion by incorporating the pitch angle (or tilt) of the rider, the change in pitch angle, the wheel speed, and the wheel position. Mathematicians, physicists, and engineers relate all these variables through differential equations describing motion; these equations have long been studied in each of these fields. The Segway transporter is one example of a project resulting from the interplay of all three fields.
Bibliography
Kalmus, Henry P. “The Inverted Pendulum.” Journal of Physics 38, no. 7 (1970).
Kemper, Steve. Code Name Ginger: The Story Behind Segway and Dean Kamen’s Quest to Invent a New World. Cambridge, MA: Harvard Business School Publishing, 2003.
Tweney, Dylan. “Dec. 3, 2001: Segway Starts Rolling.” Wired (December 3, 2009). http://www.wired.com/thisdayintech/2009/12/1203segway-unveiled.
Vasilash, Gary S. “Learning From Segway: Innovation in Action.” Automotive Design & Production (January 2006).