This study proposes a method to calibrate 3D kinematic systems. The authors briefly address typical wand-based calibration, that is, calibration using a rigid bar, both from the computational point of view and the procedural perspective, and then they define their alternative way of calibration. The proposed method takes advantage of a feature of the presently used calibration tools, that is, the orthogonality of calibration wands. The usual two steps in wand calibration are reduced to a single one. In addition, the authors propose an alternative for how to enforce a typically available geometric constraint, that is, the known wand length, during the parameter optimisation procedure (the well-known bundle adjustment). The obtained 3D reconstruction accuracy has proven to be comparable with results of commercial 3D kinematic systems. The relative simplicity of the proposed method offers potential for an implementation by a large number of researchers.