In this paper, the mobility analysis of various planar mobile robots are performed. Two different approaches are employed for that purpose. In the first approach, joint screws are used to find the size of a feasible joint motion space for each of independent loops of mobile mechanisms. Particularly, the concept of "representative screws" is introduced to represent the feasible motion spaces for subsets of joints belonging to either a loop or a sub-system consisting of several closed loops. In the second approach, imaginary joints are employed to compensate for the lack of geometric generality of mobile robots. It is confirmed that both approaches are useful in the mobility analysis for various type of planar mobile robots even in the case of lacking geometric generality.