A unibike curve is a nonstraight plane curve that can be followed by both wheels of an ideal bicycle, so that its track can also be
made by a unicycle (Finn 2002, Wagon 2025). For unit wheelbase and a continuously
differentiable parameterization 
with 
, the front track is obtained by adding the unit tangent vector, giving
 |
Writing 
for the trace of 
,
the unibike condition is 
for every 
.
The unibike error measures the distance from the front-wheel point to the rear track,
 |
where 
denotes the l2-norm and 
is the infimum (Wagon 2025,
p. 1).
Finn (2002) constructs a unibike curve from a seed segment 
for 
, where the bump function
is 
for 
and is zero outside that interval.
The height and all its derivatives vanish at both
endpoints. Successive segments are obtained by 
for 
and join to form a smooth
curve extending indefinitely (Wagon 2025, p. 2).
The illustration shows a finite initial segment of this construction. Arrows show unit tangent vectors from blue rear-wheel positions to orange front-wheel positions.
