Degrees of freedom of "simple bicycle"

AI Thread Summary
A simple bicycle model can be represented as two wheels connected by a rigid bar, which initially suggests one degree of freedom if the wheels move without sliding. However, allowing the wheels to turn left or right adds two more degrees of freedom, one for each wheel's angle. The discussion highlights that in a general case, a rolling disk without slipping has three degrees of freedom. It's noted that the rear wheel typically does not turn independently from the bicycle's line, which raises questions about whether to consider just one degree of freedom. Additionally, the angle the bicycle makes with the vertical is an important factor to consider in the overall model.
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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?
 
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in general case the rolling disk (without slipping) has three degrees of freedom
just for information
Screenshot from 2021-04-17 09-41-32.png
Screenshot from 2021-04-17 09-41-58.png
 
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Like Tony Stark said:
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.
 
haruspex said:
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?
 
Like Tony Stark said:
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.
 
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