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A bicycle in zero gravity is unrideable (The bricycle).

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Published on Mar 17, 2014

Owen Dong, Christopher Graham, Anoop Grewal, Caitlin Parrucci and Andy Ruina
Mechanical Engineering Cornell University,
http://ruina.tam.cornell.edu

A bricycle can be adjusted to be a bicycle, a tricycle, or anything in between.

The spring mechanism in the rear provides a restoring force proportional to lean. Using a so called 'zero rest-length spring', the effective spring constant can be adjusted by moving the attachment point of one end of the spring. Clamping the spring, infinite stiffness, makes a tricycle. Detaching the spring, zero stiffnes, makes a bicycle.

A person can balance and steer a normal bicycle, navigating the course and staying upright, counter-steering to start a turn and leaning into turns.

When we detach the spring of the bricycle it is in bike mode and can be balanced and steered like a bicycle, counter-steering, and leaning into turns.

If we clamp the spring, effectively making the bricycle into a tricycle, it is held upright and can also be steered, with the centripetal acceleration balanced by the outer 'training' wheel.

At some intermediate value of stiffness, the spring restoring torque cancels the gravity capsizing torque and the bricycle is, for balance purposes, effectively in zero gravity; when not going forwards it is in neutral equilibrium for leaning.

But this vehicle, a bricycle, a bicycle in zero gravity, cannot be both balanced and steered. Attempts at steering the bicycle, tip it. It can't be righted and also steered in a desired direction. And steady turns are impossible as there is no torque available to balance the centripetal acceleration.

As best we can tell, nobody can steer the bricycle around the simple obstacle course. The first attempt a steering causes a lean which can't be corrected, at least not while trying to steer in a desired direction.

A controlled bicycle is really just an inverted pendulum, it is balanced with sideways accelerations of the support (on a forwards-moving bicycle this happens because of steering) which, if coordinated can also control the position of the base while balance is maintained.

However, if there is no gravity, as for a horizontal pendulum, the sideways displacement and the pendulum angle cannot be controlled independently, they change in proportion to each other. In fact, there is a point on the pendulum stick which can't be moved at all.

The bricycle is really the same as the gravity-free pendulum. Assuming friction and so on are negligible, if we start from an upright position, the lean and the sideways displacement of the ground contact point are always in proportion to each other. So changing direction would cause both an ever-growing distance for the original line of travel, and an ever-growing lean angle. The riders don't tolerate this. Instead, they maintain balance and thus are stuck going about straight.

So gravity, superficially the thing that makes it hard to balance a bicycle, is the thing that allows you to steer it.

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