Among the challenges currently being faced by the wave energy industry, there are the ones related to the mathematical and numerical modelling of Wave Energy Converters. Because various levels of physical complexity are reflected in the dynamics of wave converters, the mathematical modelling of such systems usually comes up with nonlinear dynamic equations to be solved. The nonlinearities, however, may appear in many ways. In this paper, the nonlinear geometric constraints that arise naturally in hinged structures are investigated for floating multi-body systems including wave point absorbers. To achieve that, a method of constraint linearization is proposed and applied to a realistic case study. The method is based on generalized coordinates and generates a robust first-order dynamic matrix to characterize the multi-degrees of freedom hydrodynamic system. The simulation outputs the motion response for all floating bodies, as well as the constraining forces responses, among other parameters. The method requires knowledge of the geometries of the system but rather few assumptions, namely, to perform the linearization of constraints. The method is illustrated with a case study, where three wave point absorbers are concentrically attached to a Floating Offshore Wind Turbine platform with an onboard hydraulic Power-Take Off system.