01905nas a2200133   4500000000100000008004100001100002600042700002100068700002200089700001800111245013400129856003700263520147100300       2026                            d1 aAgnieszka Anna Tomaka1 aKrzysztof Domino1 aMichał Tarnawski1 aDariusz Pojda00aQuantifying mandibular positioning error and simulated temporomandibular joint-space changes in patient-specific occlusal splints  uhttps://arxiv.org/abs/2604.253223 aPatient-specific occlusal positioning splints can be regarded as physical realisations of planned mandibular transformations. However, the achieved mandibular pose may differ from the planned one because of acquisition, registration, fabrication, and positioning errors. This study presents a transformation-based biomedical engineering framework for quantifying mandibular positioning accuracy and propagating the resulting error to a simulated temporomandibular joint configuration. Multimodal 3D data, including CBCT, facial motion acquisition, and dental scans, were integrated in a common coordinate system. Positioning splints corresponding to selected mandibular poses were designed and fabricated, and their realised positions were evaluated using repeated scans of plaster models. Discrepancies between planned and achieved positions were represented as rigid-body error transformations and analysed in SE(3), together with surface-distance metrics. The estimated transformations were propagated to CBCT-derived TMJ structures to quantify changes in condyle–fossa distance maps. The results demonstrate a systematic translational component and anisotropic variability of mandibular positioning error, with measurable propagation to simulated TMJ-space changes. The proposed framework provides an objective method for documenting planned and achieved mandibular configurations and for analysing positioning uncertainty in patient-specific splint workflows.