Mechanical tracking systems offer potential advantages over optical and electromagnetic alternatives for surgical navigation, including freedom from line-of-sight constraints, immunity to metallic interference, and high-frequency position feedback. However, passive mechanical tracker arms lack the joint locking capability required for traditional laser tracker calibration, and existing artefact-based methods fail to provide the complete six-degree-of-freedom constraints necessary for accurate kinematic parameter identification. This thesis presents a novel artefact-based calibration methodology specifically designed for passive mechanical tracking arms used in surgical navigation applications. The methodology employs a laser-certified steel calibration artefact featuring 15 asymmetric pillars that provide complete 6-DoF constraint through single contact points. Unlike traditional sphere-based methods that only constrain position, the asymmetric plug design mechanically prevents rotation, enabling simultaneous identification of all kinematic parameters without sequential joint locking. The artefact was precision-machined and certified using a Leica AT960 laser tracker to ±0.001 mm uncertainty, providing metrological traceability one order of magnitude better than the target accuracy. Applied to a custombuilt six-degree-of-freedom Surgical Tracker Arm (SUTA), the calibration methodology achieved 1.01 mm RMS accuracy across 525 independent validation measurements, representing an 81.5% improvement from the 5.45 mm RMS baseline configuration. Dataset optimization analysis revealed that six measurement positions achieve near-optimal accuracy (1.09 mm RMS) while maintaining calibration efficiency, with marginal improvements beyond this point. The research identified mechanical interface compliance as the dominant error source, with clearance in the end-effector-pillar interface contributing approximately 0.5 mm to the total error. While the achieved accuracy does not yet match the 0.3-0.5 mm performance of state-of-the-art optical systems, the methodology successfully demonstrates that passive mechanical trackers can be calibrated to millimeter-level precision with a calibration artefact. The approach establishes a practical framework for calibrating passive tracking systems and identifies clear paths toward sub-millimeter accuracy through targeted hardware improvements, particularly in interface design and consistent seating mechanisms.