<p>Cable-Driven Parallel Robot (CDPR) is widely researched due to its high flexibility, strong load capacity, and large workspace. However, delineating the dynamic behavior of its elastic variable-length cable-pulley coupling characteristics remains a significant challenge. This paper introduces the Dirac function to address the discontinuous stress boundary conditions induced by pulley inertia and friction, which cannot be handled by conventional numerical discretization techniques using continuous functions. This transformation changes the discontinuous stress problem into explicit continuous structure, resulting in a comprehensive dynamic model of the cable-pulley coupling system. Furthermore, the paper incorporates the time-varying terms induced by the variable-length trial function basis, thereby enhancing the existing dynamic analysis method for variable-length cables using Galerkin theory. Numerical simulations reveal that the time-varying term substantially impacts the cable tension, accounting for 81%-92% of the vibration amplitude of cable tension. Finally, a cable-pulley coupling equipment is established to verify the practical feasibility and precision of the proposed method. Experimental results confirm that the method offers advantages in terms of fast computation speed and high accuracy. Compared to the lumped-mass method model, the proposed method is 2-10 times faster. Even with varying numbers of pulleys, the method can still handle the effects of pulley rotational inertia and friction in the time domain and accurately describe the vibration characteristics. In the frequency domain, the method depicts the 2Hz low-frequency vibrations caused by the spring and the 200-300Hz high-frequency vibrations excited by the cable, therefore demonstrating adaptability to low orders of cable discretization.</p>