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Quarter-car models are popular, simple, unidirectional in kinematics and enable quicker computation than full-car models. However, they do not account for three other wheels and their suspensions, nor for the frame’s flexibility, mass distribution and damping. Here we propose a generalized quarter-car modelling approach, incorporating both the frame as well as other-wheel ground contacts. Our approach is linear, uses Laplace transforms, involves vertical motions of key points of interest and has intermediate complexity with improved realism. Our model uses baseline suspension parameters and responses to step force inputs at suspension attachment locations on the frame. Subsequently, new suspension parameters and unsprung mass compliance parameters can be incorporated, for which relevant formulas are given. The final expression for the transfer function, between ground displacement and …