A time-domain 3 Degrees of Freedom model is developed to investigate nonlinear dynamics and impact loads during float-over installations, which generally involve multi-body interactions between wave-induced vessel motions and nonlinear constraint components. By replacing the time-consuming convolution in calculating the retardation function, a more efficient method, i.e. state-space model, is applied to evaluate part of the radiation force. The established model, incorporating the multi-body interactions, is applied to study the nonlinear impact on Leg Mating Unit (LMU) by considering the sway, heave and roll motions of the float-over system. The structural characteristics are considered when modelling the characteristics of LMU. The dynamic behaviors of a given system is investigated in the form of bifurcation diagrams, along with impact map, amplitude spectrum and power spectral density (PSD). It is found that bifurcation phenomena, or a large angle of docking cone could dominate the installation due to the increased impact loads.