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An ideal constant velocity joint (ball-joint) would be a perfectly symmetric frictionless joint, with no clearance or interference between its perfectly rigid parts. Over the years, many kinematic models of such joints have been developed throughout the automotive industry, and they have supported important insights into the kinematic behavior and performance of ball-joints. Such models are based on an analytic approach, whereby equations prescribing the motion of the parts are first derived and then solved. The realism or accuracy of the simulation produced by such a model depends upon the degree to which important physical effects can be captured by the formulation. The extent to which this can be achieved is ultimately limited by the ability to solve the resulting systems of highly non-linear equations. This paper describes an alternative approach to kinematic ball-joint modelling avoiding this limitation.