I am looking for a curve traced by a moving bicycle when its steering wheel is fully rotated either clockwise or anti-clockwise.
How to model it mathematically?
Is the curve a circle?
My attempt is as follows:
Let $\vec{r}_1(t)$ and $\vec{r}_2(t)$ be the position vectors for the tangent points (between road and tires) on the rear and front tires, respectively. I know that $|\vec{r}_2(t)-\vec{r}_1(t)|$, $|\dot{\vec{r}}_1(t)|=|\dot{\vec{r}}_2(t)|$ and $\dot{\vec{r}}_1(t)\cdot\dot{\vec{r}}_2(t)$ are constants. $\dot{\vec{r}}_1(t)$ is in the direction of $\vec{r}_2(t)-\vec{r}_1(t)$.
Assuming the tires rolls without slipping then their linear velocity is the same.