A two-mass-skate bicycle (TMS) is a theoretical model created by a team of researchers at Cornell University, University of Wisconsin-Stout, and Delft University of Technology to show that it is neither sufficient nor necessary for a bike to have gyroscopic effects or positive trail to be self-stable. [1] [2] [3] The two-mass and skates aspects of the model were chosen to eliminate design parameters so that the nine that remain, the locations of the masses and the steering geometry, could be more easily analyzed. [1] Instead of full inertia tensors, the total mass of the bike is reduced to just two point masses, one attached to the rear frame and one attached to the front fork. [1] Instead of rotating wheels, the non-holonomic ground contacts are provided by small-radius skates. [1]
The self-stability of bicycles was reported as early as 1876. [1] Emmanuel Carvallo in 1897 and Francis Whipple in 1899 both developed equations of motion for a bicycle that showed this self-stability. [1]
In 1970, David Jones explained in Physics Today how he experimented with a traditional bicycle to see if cancelling the gyroscopic effect of the front wheel would make it unridable. He added a second, counter-rotating front wheel that did not touch the ground. He reported that his particular bicycle would no longer stay up without a rider, but he could still easily ride it, and he could even just barely ride it no-handed. [4] It was no longer self-stable, it was still controllable, but it was no longer easily controllable. Jones also tried increasing trail, by reversing the front fork, and found that self-stability was dramatically increased, but that this made it more difficult to ride - "it was too stable to be steered." [4] Finally, he made a bike with negative trail, by adding forward extensions to the ends of the fork, and found that it had negligible self-stability and was "indeed very dodgy to ride, though not as impossible as [he] had hoped." [4] By evaluating which modifications made a bicycle easy to ride, with hands on and off, Jones concluded that gyroscopic effects were less important than trail for bicycle stability.
The scientific and popular literature continued to report that positive trail, also called caster trail, [1] was necessary for stability, [5] [6] although not always making a clear distinction between self-stability and controllability. The researchers who developed the two-mass skate bicycle focused solely on self-stability, although they do mention that "rider-controlled stability of bicycles is indeed related to their self-stability." [1]
The existence of the TMS and the self-stability it exhibits suggests that the design envelope of rideable bikes is larger than previously thought. [7] [8] [9] For example, rear-wheel steering may not be as impossible as has been claimed. [1] [10] In the case of the TMS bike, the authors explain that the front assembly center of mass is lower than the rear frame center of mass – so it falls faster in a lean; and it is in front of the steering axis so it tends to steer the front end in the direction of the lean. [1]
They conclude:
As a rule we have found that almost any selfstable bicycle can be made unstable by mis-adjusting only the trail, or only the front-wheel gyro, or only the front-assembly center-of-mass position. Conversely many unstable bicycles can be made stable by appropriately adjusting any one of these three design variables, sometimes in an unusual way.
A physical example has been created that closely approximates the TMS model and exhibits self-stability without gyroscopic effects from the wheels and without positive trail. [1] Since point masses do not exist in nature, the model can only approximate them with pieces of dense material (lead), mounted on a frame of light materials (carbon fiber and aluminum). To prevent the bike with just two masses, as pictured above, from tipping forward, a third mass is located just above the rear wheel contact patch where it does not alter the dynamics. In place of skates, small-radius wheels that drive nearly identical counter-rotating wheels are used to provide the non-holonomic ground contact with minimal gyroscopic effect. This physical example closely mimics the self-stability of the theoretical model. [1]
A tandem bicycle or twin is a form of bicycle designed to be ridden by more than one person. The term tandem refers to the seating arrangement, not the number of riders. Patents related to tandem bicycles date from the mid 1880s. Tandems can reach higher speeds than the same riders on single bicycles, and tandem bicycle racing exists. As with bicycles for single riders, there are many variations that have been developed over the years.
A mountain bike (MTB) or mountain bicycle is a bicycle designed for off-road cycling. Mountain bikes share some similarities with other bicycles, but incorporate features designed to enhance durability and performance in rough terrain, which makes them heavier, more complex and less efficient on smooth surfaces. These typically include a suspension fork, large knobby tires, more durable wheels, more powerful brakes, straight, extra wide handlebars to improve balance and comfort over rough terrain, and wide-ratio gearing optimised for topography and application. Rear suspension is ubiquitous in heavier-duty bikes and now common even in lighter bikes. Dropper posts can be installed to allow the rider to quickly adjust the seat height.
A recumbent bicycle is a bicycle that places the rider in a laid-back reclining position. Most recumbent riders choose this type of design for ergonomic reasons: the rider's weight is distributed comfortably over a larger area, supported by back and buttocks. On a traditional upright bicycle, the body weight rests entirely on a small portion of the sitting bones, the feet, and the hands.
A tricycle, sometimes abbreviated to trike, is a human-powered three-wheeled vehicle.
The penny-farthing, also known as a high wheel, high wheeler or ordinary, is an early type of bicycle. It was popular in the 1870s and 1880s, with its large front wheel providing high speeds, owing to it travelling a large distance for every rotation of the legs, and comfort, because the large wheel provided greater shock absorption.
A cargo bike is a human powered vehicle designed and constructed specifically for transporting loads. Cargo bike designs include a cargo area consisting of an open or enclosed box, a flat platform, or a wire basket, usually mounted over one or both wheels, low behind the front wheel, or between parallel wheels at either the front or rear of the vehicle. The frame, drivetrain and wheels must be constructed to handle loads larger than those on an ordinary bicycle.
A single-track vehicle is a vehicle that leaves a single ground track as it moves forward. Single-track vehicles usually have little or no lateral stability when stationary but develop it when moving forward or controlled. In the case of wheeled vehicles, the front and rear wheel usually follow slightly different paths when turning or when out of alignment.
A bicycle fork is the part of a bicycle that holds the front wheel.
Countersteering is used by single-track vehicle operators, such as cyclists and motorcyclists, to initiate a turn toward a given direction by momentarily steering counter to the desired direction. To negotiate a turn successfully, the combined center of mass of the rider and the single-track vehicle must first be leaned in the direction of the turn, and steering briefly in the opposite direction causes that lean. The rider's action of countersteering is sometimes referred to as "giving a steering command".
Wobble, shimmy, tank-slapper, speed wobble, and even death wobble are all words and phrases used to describe a quick (4–10 Hz) oscillation of primarily just the steerable wheel(s) of a vehicle. Initially, the rest of the vehicle remains mostly unaffected, until translated into a vehicle yaw oscillation of increasing amplitude producing loss of control. Vehicles that can experience this oscillation include motorcycles and bicycles, skateboards, and, in theory, any vehicle with a single steering pivot point and a sufficient amount of freedom of the steered wheel, including that which exists on some light aircraft with tricycle gear where instability can occur at speeds of less than 80 km/h (50 mph); this does not include most automobiles. The initial instability occurs mostly at high speed and is similar to that experienced by shopping cart wheels and aircraft landing gear.
A tilting three-wheeler, tilting trike, leaning trike, or even just tilter, is a three-wheeled vehicle and usually a narrow-track vehicle whose body and or wheels tilt in the direction of a turn. Such vehicles can corner without rolling over despite having a narrow axle track because they can balance some or all of the roll moment caused by centripetal acceleration with an opposite roll moment caused by gravity, as bicycles and motorcycles do. This also reduces the lateral acceleration experienced by the rider, which some find more comfortable than the alternative. The narrow profile can result in reduced aerodynamic drag and increased fuel efficiency. These types of vehicles have also been described as "man-wide vehicles" (MWV).
29ers or two-niners are mountain bikes and hybrid bikes that are built to use 700c or 622 mm ISO wheels, commonly called 29″ wheels. Most mountain bikes once used ISO 559 mm wheels, commonly called 26″ wheels. The ISO 622 mm wheel is typically also used for road-racing, trekking, cyclo-cross, touring and hybrid bicycles. In some countries, mainly in Continental Europe, ISO 622 mm wheels are commonly called 28″ wheels or "28 Incher".
A kick scooter is a human-powered street vehicle with a handlebar, deck, and wheels propelled by a rider pushing off the ground with their leg. Today the most common scooters are made of aluminum, titanium, and steel. Some kick scooters made for younger children have 3 to 4 wheels and are made of plastic and do not fold. High-performance kickbikes are also made.
A bicycle trailer is a motorless wheeled frame with a hitch system for transporting cargo by bicycle. It can greatly increase a bike's cargo capacity, allowing point-to-point haulage of objects up to 3 cubic metres in volume that weigh as much as 500 kg. However, very heavily loaded trailers may pose a danger to the cyclist and others, and the voluntary European standard EN 15918 therefore suggests a maximum load of 60 kg on trailers without brakes.
Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of these motions began in the late 19th century and continues today.
A handcycle is a type of human-powered land vehicle powered by the arms rather than the legs, as on a bicycle. Most handcycles are tricycle in form, with two coasting rear wheels and one steerable powered front wheel. Despite usually having three wheels, they are also known as handbikes.
Bicycle and motorcycle geometry is the collection of key measurements that define a particular bike configuration. Primary among these are wheelbase, steering axis angle, fork offset, and trail. These parameters have a major influence on how a bike handles.
Cross-country (XC) cycling is a discipline of mountain biking. Cross-country cycling became an Olympic sport in 1996 and is the only form of mountain biking practiced at the Olympics.
An ice cycle, ice bike, or icycle is a bicycle adapted for use on ice, usually by replacing the front wheel with an ice skate. Versions exist with and without additional skates to provide lateral stability, that have been based on upright and recumbent bikes, and that have been used for racing. Ice cycles have been in use since at least the 1890s, and theory predicts that a bicycle with a front skate can exhibit riderless self-stability similar to the same bicycle with a front wheel. At least one example has been made with both the front and the rear wheels replaced by skates.
These other three criteria can work in conjunction with fork trail to increase stability, but they are not indispensable like fork trail is.
the most important parameter governing the stability is the castor of the front wheel, as was suggested by Jones