Six-degree-of-freedom (6-DOF) platforms are widely employed in aerospace, marine and precision-machinery fields. Conventional Gough-Stewart configurations, however, suffer from joint backlash and friction, and their dynamic performance degrades under high-frequency vibration, ultimately degrading positioning accuracy and stability. Rigid–flexible coupling mechanisms, whose topology is deliberately engineered to circumvent these drawbacks, have recently attracted intensive attention because of their superior vibration-attenuation capacity and favorable transient response. In this paper a 6-DOF rigid–flexible parallel platform that employs V-shaped composite beams as supporting legs is investigated. System dynamic equations are established within the framework of Timoshenko beam theory and the extended Hamilton principle. Geometric and force matching conditions at boundaries and junctions are derived in closed form, coupling the elastodynamics of each leg with the rigid moving platform. Global mode shapes are extracted by Global Mode Method (GMM), yielding analytical expressions for natural frequencies and vibration modes of the rigid–flexible assembly; the predictions are corroborated against finite-element solutions. Modal contribution factors of individual sub-domains are subsequently quantified to clarify how rigid-body dimensions influence the global dynamic characteristics. Results demonstrate that the global modes faithfully capture the elastic vibrations of all constituents, enabling an efficient and accurate prediction of the intrinsic dynamics. Variations in rigid-body dimensions exert negligible influence on the lower-order natural frequencies, implying that the overall modal behavior remains essentially unchanged. The study furnishes a theoretical basis for the design and optimisation of 6-DOF rigid–flexible parallel platforms and offers a rigorous methodology for subsequent dynamic analysis.