This paper introduces a novel contactless sensing principle conceived for measuring the rotation angle of a shaft. The sensor is based on a smart combination of low-cost components that can be effectively integrated in a mechanical assembly of a rotary joint. The working principle is based on the relative rotation of a small diametrically magnetized cylindrical or annular magnet and at least one Hall effect sensor. One of the main strengths of the new sensing principle is to be adaptable to any assigned dimensions and encumbrances without typical design limitations given by the use of standard components. A numerical model is developed for predicting the sensor output characteristic on the base of the concept of magnetic charge. Such a model is validated against results from laboratory experiments. The parameters that define the geometry and layout of the sensor are optimized in order to maximize linearity over an assigned angular range of measurement. Two examples of mechatronic systems that employ the new sensing principle are presented in order to show the possibility of obtaining with the new principle a compact/integrated sensor-design.