A steering problem

If two circular gear-wheels of different sizes engage, this may be regarded as a mechanism which generates a linear relationship between the angles turned through, the ratio of the angles being constant. In this paper it is shown that, if the circular gear wheels are replaced by suitably shaped oval wheels (or cams) which engage without slipping, it is possible to generate an arbitrary functional relationship between the angles turned through. It is further shown how this mechanism might be used in the steering of a four-wheeled vehicle with theoretically perfect satisfaction of the condition that, at any instant, the vehicle as a whole has a unique centre of rotation, so that no side-slip of the wheels occurs. The angle through which the plane of the inner front wheel is turned might be as great as a right angle, this limit being much greater than that attainable with the usual Ackermann linkage.