An improved method for the geometrical calibration of parallelogram-based parallel robots

This paper presents an improved method for the geometrical calibration of parallel robots for which the structure is based upon some parallelogram mechanisms. Its originality is to identify the complete geometry of the mechanism´s parallelograms, and to compensate the positioning error of the TCP (tool centre point), due to the infinitesimal rotation of the traveling plate, induced by the parallelogram geometrical errors. The main difficulties are: (i) to derive the calibration model relative to all geometrical parameters, and (ii) to reuse the identified errors in a control model in order to compensate the positioning errors. In fact, the position relationship taking into account the full geometry of the parallelograms is difficult, not to say impossible, to derive in a close form; therefore a linear approximation of the model is proposed. The formulas necessary to run the method on a Delta robot are given. Then a simple mechanism is used to illustrate the benefits of this method compared to classical ones