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Automotive suspensions invariably exhibit asymmetric damping properties in compression and rebound, which is partly attributed to asymmetric damping and in-part to the suspension linkage kinematics together with tire lateral compliance. Although automotive suspensions have invariably employed asymmetric damping, the design guidelines and particular rationale for such asymmetry has not been explicitly defined. The influences of damper asymmetry together with the suspension kinematics and tire lateral compliance on the dynamic responses of a vehicle are investigated analytically under bump and pothole excitations, and the results are interpreted in view of potential design guidance. A quarter-car kineto-dynamic model of the road vehicle employing a double wishbone type suspension comprising a strut with linear spring and multiphase asymmetric damper is formulated for the analyses.