## 5 Conclusions  
The present study showed that CAD-CAM-manufactured transpalatal arches (TPA) made of PEEK might be a promising alternative to conventional materials. The FEA was found to be suitable to investigate the mechanical behavior of different CAD/CAM-fabricated TPA geometries. The mechanical in vitro analysis supplemented the FEA by enabling measurement of the forces and moments acting on both molars simultaneously. In combination with the FEA, predictions about the force systems acting on the molars by CAD/CAM-fabricated PEEK TPAs could be obtained in all three dimensions. The TPA geometries presented in this study showed clinically appropriate expansion forces up to 3 N per side. Due to the low load-deflection rate of the flexible PEEK material, the activation ranges are much higher in comparison to conventional TPAs. The four different geometries utilized in the study reflect the wide variability in design options. The _Triple-loop-arch TPA_ with a force system ranging from 2.5 to about 3 N appeared to be most appropriate for the application of moments, whereas the _Double-arch TPA_, which delivered force systems of comparable magnitude, seemed to be most appropriate for the expansion as well as anchorage of the molars. In the future, the development of customized TPAs for specific patients' needs might become possible using CAD. The practical benefits of CAD/CAM-fabricated appliances are currently advancing owing to the development of novel 3D-printable materials and improvements in CAD software. However, their introduction to clinical settings requires validation of their eligibility by means of simulated and biomechanical testing, and analysis of biocompatibility. Whereas PEEK has already demonstrated its suitability for permanent use in the mouth, only a few studies have assessed its applicability as a retention device in orthodontics. This study presented that PEEK may also be effective as a CAD-CAM-fabricated active orthodontic appliance and might offer a metal-free, aesthetic alternative to conventional approaches. As the 5-axis milling out of a PEEK disc is associated with a high material loss, improvements in additive 3D printing technology will most likely reduce costs in the future. The behavior of PEEK under in vivo (intraoral) conditions should be evaluated in future experimental studies. C.M. : Conceptualization, methodology, formal analysis, investigation, writing--original draft preparation. D.D. : Conceptualization, methodology, formal analysis, investigation, writing--review and editing. J.G.S. : methodology, software, visualization, formal analysis. J.H.W. : Conceptualization, methodology, project administration. K.B. : Conceptualization, writing--original draft preparation, writing--review and editing. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The present study was approved by the ethical committee of the University of Dusseldorf (Ref. no. 2019-643, date of approval: 4 September 2019). Not applicable. Data Availability Statement: Data will be provided upon reasonable request. The authors thank the dental laboratory \"Dentes\" (Fraszentrum GmbH, Neuss, Germany) for their kind support in the manufacturing of the different TPAs. The authors declare no conflict of interest. References  
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