Mechanical malfunction is a main failure mode for circuit breakers (CBs). Vibrations generated from CB switching operations contain rich information of its mechanical condition. However, the vibrations are highly time-varying and non-stationary, which makes it very difficult to precisely extract effective features for machinery fault diagnosis. This study presents a methodology to obtain the CB vibration characteristics based on time–frequency and chaotic analysis. A new method, called adaptive chirp mode decomposition (ACMD), is introduced to extract the fast fluctuating instantaneous frequency and catch each signal component individually from the CB's vibration signal. A high resolution adaptive time–frequency spectrum which can clearly represent the mechanical condition alteration in CB is obtained by the ACMD. The component with the most significant time–frequency fluctuation is reconstructed into a high-dimensional phase space to recover and extract the dynamic variation characteristics of the CB. Based on the reconstructed phase space, a new set of features, namely RST (ratio of major–minor axis, shape complexity and trajectory compactness), is proposed for realising the stability and accurate diagnosis of CB faults. Experimental study and practical application cases are presented showing the efficiency of the methodology proposed here.