Application of Geometric and Kinematic Chain Equations
Observe the same mechanism with different degrees of freedom
1. The three coordinates with which the mechanism can be delimited are independent, as well as the three generalized velocities (three degrees of freedom).
2. There is a imposition of the contact condition between disk and ground, so no only two of the generalized coordinates will be independent, but the height will be imposed by the contact condition.
Also, two generalized velocities will be independent (two degrees of freedom)
3. Imposing the conditions of contact and rolling now there will be a single generalized speed that will be independent. The mechanism will therefore have an independent generalized velocity (a degree of freedom)