Abstract: We propose a novel generalized method for mass measurements based on the singularity structure of the kinematic phase space that can be applied to any event topology with missing energy. By analyzing the local properties of the observable phase space near a given singularity point, we provide a systematic way to obtain optimized normalized coordinates for the case of interest. Our method subsumes the well-known end-point and transverse mass methods and yields new techniques for studying ``missing particle" events, such as the double chain production of stable neutral particles at the LHC.