Degrees of freedom of "simple bicycle"

[Like Tony Stark]

Homework Statement

Design a very simple model for a bike and state the number of degrees of freedom

Relevant Equations

Generalized coordinates

Hi
I thought that a bike could be simply modeled as two wheels attached by a rigid bar. If the wheels move without sliding, then there is one degree of freedom: one of the wheels moves and so does the other one since they are rigidly attached by the bar. Then, if the wheels can turn to the right or the left, then there are two more degrees: one angle for each wheel.
Is it ok?

 

[wrobel]

in general case the rolling disk (without slipping) has three degrees of freedom
just for information

 

[haruspex]

Homework Statement:: Design a very simple model for a bike and state the number of degrees of freedom
Relevant Equations:: Generalized coordinates

if the wheels can turn to the right or the left

It would be unusual for the rear wheel to be able to turn away from the line of the bicycle.

 

[Like Tony Stark]

It would be unusual for the rear wheel to be able to turn away from the line of the bicycle.

So should I consider just one degree of freedom?

 

[haruspex]

So should I consider just one degree of freedom?

As @wrobel points put, you also need to consider the angle the bicycle makes to the vertical.