This paper presents some advances in condition monitoring for rotary machines (particularly for a lathe headstock gearbox) running idle with a constant speed, based on the behaviour of a driving three-phase AC asynchronous induction motor used as a sensor of the mechanical power via the absorbed electrical power. The majority of the variable phenomena involved in this condition monitoring are periodical (machines having rotary parts) and should be mechanically supplied through a variable electrical power absorbed by a motor with periodical components (having frequencies equal to the rotational frequency of the machine parts). The paper proposes some signal processing and analysis methods for the variable part of the absorbed electrical power (or its constituents: active and instantaneous power, instantaneous current, power factor, etc.) in order to achieve a description of these periodical constituents, each one often described as a sum of sinusoidal components with a fundamental and some harmonics. In testing these methods, the paper confirms the hypothesis that the evolution of the electrical power (instantaneous and active) has a predominantly deterministic character. Two main signal analysis methods were used, with good, comparable results: the fast Fourier transform of short and long signal sequences (for the frequency domain) and the curve fitting estimation (in the time domain). The determination of the amplitude, frequency and phase at origin of time for each of these components helps to describe the condition (normal or abnormal) of the machine parts. Several achievements confirm the viability of this study: a characterization of a flat driving belt condition and a beating power phenomenon generated by two rotary shafts inside the gearbox. For comparison purposes, the same signal analysis methods were applied to describe the evolution of the vibration signal and the instantaneous angular speed signal at the gearbox output spindle. Many similarities in behaviour among certain mechanical parts (including their electrical power, vibration and instantaneous angular speed) were highlighted.