In this paper, an intuitive approach for the mobility analysis of deployable mechanisms involved in a special screw system with two coplanar twist vectors is proposed. First, the coplanar screw system with a pair of parallel/concurrent zero pitch screws is analyzed, and the intuitive allowable mobility set for the screw system is described. Next, kinematic chains containing the coplanar screw system are enumerated. The proposed approach is used to explain the mobility of the deployable Bennett mechanism, Myard mechanism, and Bricard mechanism; some novel deployable mechanisms could be found based on the analysis. Furthermore, it is shown that the proposed approach can be applied to the mobility analysis of multiloop deployable mechanisms and is found to be more intuitive than the traditional approach, which provides a straightforward insight into the mobility of complicated mechanisms.