Robot positioning accuracy is a key factory when performing high-precision manufacturing tasks. To effectively improve the accuracy of a manipulator, often up to a value close to its repeatability, calibration plays a crucial role. In the literature, various approaches to robot calibration have been proposed, and they range considerably in the type of measurement system and identification algorithm used. Our aim was to develop a novel step-by-step kinematic calibration procedure - where the parameters are subsequently estimated one at a time - that only uses 1D distance measurement data obtained through a draw-wire encoder. To pursue this objective, we derived an analytical approach to find, for each unknown parameter, a set of calibration points where the discrepancy between the measured and predicted distances only depends on that unknown parameter. This reduces the computational burden of the identification process while potentially improving its accuracy. Simulations and experimental tests were carried out on a 6 degrees-of-freedom robot arm: the results confirmed the validity of the proposed strategy. As a result, the proposed step-by-step calibration approach represents a practical, cost-effective and computationally less demanding alternative to standard calibration approaches, making robot calibration more accessible and easier to perform.