Their studies have concentrated mostly on the behaviour of mechanisms with a Hooke's joint [11; 12; 13; 14; 15; 16]. However, couplings are key components to ensure the effectiveness of the transfer motion and power in various rotating machines systems, in many industries. It is estimated that misaligned shafts in rotating machines cause more than one-third of all rotor system failures, up to half the cost of downtime and, as a result, misaligned joint and couplings [17]. Such tiny misalignments tend to grow into more significant machine problems as the error often trickles down to affect many other parts of the plant, leading to high vibrations, unbalance and driveshaft crack which is affecting many industries in terms of work stoppages. Thus, the identification of the faults in such rotor systems plays an integral role in the performance of equipment and machinery [18]. Despite the voluminous research works conducted on the propeller shaft, there are only a few well-researched on the torsional vibration of connected shaft systems involving more than one parametric excitation fault. Only a few researchers recently have investigated the dynamic characteristics of the universal joint, misalignment, and crack of the drive or driven shafts in the transmission system using algorithms involving time-frequency representation. Considering the elasticity and energy of the system, [PERSON] [19; 20] proposed a two-axis model for analysing the torsional vibration of a propeller shaft with a crack-induced excitation using wavelet transform techniques. [PERSON] and [PERSON] [21] reconsidered the same problem as [PERSON], developed a six DOF Cardan shaft system based on Lagrangian transformation and carried out a parametric study of the coupled lateral and torsional vibration of an unbalanced Cardan shaft system. Their numerical and experimental investigations included the perturbation parameter characteristic of Hooke's joint distortion and unbalanced parameter in the various speed of rotors. [PERSON] et al., [22] diagnosed numerically and validate experimentally the Cardan shaft unbalance and misalignment using acceleration signal and dual-tree complex wavelet packet transformation method to extract the relevant features for the detection of shaft misalignment. To our best knowledge, the dynamic analysis of a partially cracked Cardan shaft model, which considers the lateral and torsional deflections of both unbalanced drive and the driven shaft, has not been analysed yet. Regarded as a multi-body system consistingof two identical elastic shafts modelled with two discrete rotating discs at its mid-span; the model also has taken into account the local flexibility induced by a breathing crack on the driveshaft and the dynamic excitation of the perturbation function representing the [PERSON]'s joint disturbance. The differential equations of the seven DOF model of a system coupled with a Hooke's joint is constructed from the equations of vehicle dynamics and vibration theory. The impact of a Cardan joint disturbance, shaft-unbalance, and transverse breathing crack fluctuation are the main parameters requiring the time-frequency techniques for effective faults feature extractions. These reliable methods based on the synchrosqueezing wavelet technique (SWT) can extract any instantaneous frequency (IFs) resonance in parameter space and present the results in the form of energy concentration graphs. To provide correlation, the simulation results (parametric resonances) are compared with the experimental results in various scenarios. The remainder of this paper is organised as follows: In Section 2, the modelling of the Cardan shaft with shafts unbalance is established. The derivation of the parametric excitation such as the breathing crack functions is described. Then, the multi-scale signal processing tools for nonlinear crack detection is briefly described in Section 3 as well as the experimental set-up on a rotor test rig to perform real driveshaft crack detection is proposed.