An approach to determine turning points in electromechanical systems is presented and applied to the determination of pull-in parameters. The pull-in phenomenon is an inherent instability in devices using electrostatic actuation where an electrostatic force works against an elastic restoring force. The paper presents a relation between multi-valued characteristics describing MEMS devices and weakly singular tracking problems. The technique of augmented systems that characterize turning points is applied to the analytical and numerical determination of pull-in parameters. The method is discussed using a computer algebra system and a VHDL-AMS simulation engine.