A bicycle in zero gravity can be balanced or steered but not both
Balancing a bicycle and steering it around are usually considered
separate challenges to overcome by a learning rider. Balance problem
can be removed using springy training wheels that counter the toppling
torque by gravity. But then one can't simultaneously maintain balance
and control the position of the wheels by steering.
A ‘bricycle’:
is a bicycle with springy ‘training’ wheels desgined to resist leaning.
Spring stiffness is adjustable. Zero stiffness (free leaning)
effectively reduces the bricycle to a bicycle. At high stiffness
(locked spring, no leaning) the bricycle is effectively a tricycle.
Bricycle was intended to provide a smooth transition from
tricycle to bicycle, say for learning how to ride.
Springy-training wheel suspension. All
the rear wheels are connected to each other via a parallelogram
mechanism. The connection between points P and Q is effectively a zero
rest-length spring. The restoring torque generated by the spring force
about point O is kabsin φ, it opposes the destabilizing gravitational
torque mghsin φ. Thus the spring mechanism effectively reduces the
gravity for leaning/balance.
Spring stiffness can be adjusted by changing the lengths a and b. At
some intermediate stiffness leaning torque due to gravity is countered
and bricycle is in zero gravity for balance purposes. In zero gravity,
the bricycle becomes uncontrollable, it is hard to steer while
remaining upright. This breaks the smooth transition from tricycle
to bicycle.
Lean angles vs. gravity for various speeds: In
a steady turn a bike leans into the turn so that the gravity torque
balances the centrifugal torque . For zero gravity the steady state
turning angle is 90 degrees, i.e. the bike is ям‚at on the ground. For
negative gravity (e.g. tricycle like situations) the lean angle is
negative (i.e. away from the turn).
The classical cart and inverted pendulum is a bicycle analogue.
The acceleration of the cart is varied in time (say by action of a
horizontal force) so as to control both the angle φ of the pendulum
(mass m) and the position y of the cart. Cart pendulum problem is same
as balancing of a stick on a hand.
The tendency of the pendulum to fall is equivalent to the lean (tilt or
roll) instability of the bicycle. Steering a bicycle causes lateral
acceleration of the base, analogous to accelerating the cart at the
base of the pendulum. Like bicycle, the cart-pendulum looses
controllability in zero gravity. The balance problem is gone, and so is
the ability to change the position of pendulum's bob.
