The origami waterbomb base (WB) is a single-vertex bistable mechanism that can be generalized to accommodate various geometric, kinematic, and kinetic needs. The traditional WB consists of a square sheet that has four mountain folds alternating with five valley folds (eight folds total) around the vertex in the center of the sheet. This special case mechanism can be generalized to create two classes of waterbomb-base-type mechanisms that allow greater flexibility for potential application. The generalized WB maintains the pattern of alternating mountain and valley folds around a central vertex but it is not restricted to eight total folds. The split-fold waterbomb base (SFWB) is made by splitting each fold of a general WB into two “half folds” of the same variety as the parent fold. This study develops kinematic, potential energy, and force–deflection models for the rigid-foldable, developable, symmetric cases of the generalized WB and the SFWB, and investigates the relative effects of numbers of folds and split-fold panel size, on device behavior. The effect of selected key parameters is evaluated, and equations are provided to enable the exploration of other important parameters that may be of interest in the design and analysis of specific mechanisms. The similarities and differences between the two general forms are discussed, including tunability of the bistable and force–deflection behavior of each.