We present a resource for designing bistable developable mechanisms (BDMs) that reach their second stable positions while exterior or interior to a cylindrical surface. Analysis of the necessary conditions to create extramobile and intramobile cylindrical BDMs is conducted through a series of three tests. These tests contain elements of both existing and new mechanism design tools, including a novel graphical method for identifying stable positions of linkages using a single dominant torsional spring, called the principle of reflection. These tests are applied to all possible mechanism cases and configurations to identify why certain configurations will always, sometimes, or never be a BDM. Two tables summarize these results as a guide when designing extramobile and intramobile BDMs. The results are compared and demonstrated with a numerical simulation of 30,000+ mechanisms, including several example mechanisms that illustrate the concepts discussed in the work. Discussion is then provided on the implication of these results.