A new approach is introduced for the analysis of the vibration signals of turning operations. This technique uses four unified transfer functions to represent the twelve conventional transfer functions of structural and cutting dynamics. To describe the block diagram of three-dimensional cutting, a linear uncut chip area variation model is developed and used with the unified transfer functions. Based on the results of previous studies, the proposed block diagram is simplified for the turning of long slender bars and a new experimental procedure is developed to predict the limit of stability. The new procedure requires excitation of the cutting tool in the feed direction and measurement of two displacement signals. The advantages of the proposed procedure are the use of a dynamic method to identify the machining operation in the cutting environment, and the elimination of any force measurements and inertial force compensations.