The accurate prediction of the transverse vibration in lightweight manipulators, is the motivation towards a model which couples hub rotation, elastic deformation, and payload inertia in single framework. This study presents a dynamical model for the flexible link, which is dealt with as an Euler–Bernoulli beam, where it is clamped to a rigid hub, and has a concentrated tip mass at the free end. The five-mode Assumed Modes expansion, with Lagrange equation, lead to a compact finite dimensional system, which hold the rigid–elastic inertial coupling. The confidence in this model gained from four independent check routes, which all show the same result. First: the closed form analysis where fixed hub fundamental frequency is obtained analytically as (8.179 Hz). Second: the independent built Finite Element discrete model with frequency (8.177 Hz). Third: the obtained spectral identification from the simulated time-domain response with frequency (9 Hz). And, fourth: the closely comparable results from a previously published study which reached to the frequency (8.3 Hz). This agreement across these methodological routes presents a cross validation for this reduced order flexible link manipulator system model, and reflects its applied accuracy. Thus, this model establishes the physical conditions that governs the response, representing by the amplitude growth towards the link tip, and a harmonious damped decay envelope, which is noticed across the observation points. This study provides a dependable analytical, computational basis for work on vibration prediction, and for designing an active vibration’s suppression controller for this system’s applications.