## 1 Introduction  
The transpalatal arch (TPA) is used in orthodontics for three-dimensional adjustment of the molars. The TPA is often used as a passive device to stabilize the molars. However, it can also be employed as an active appliance to expand or compress the dental arch, or to derotate the molars, or to apply differential torque. Usually, the traditional transpalatal arch, according to Goshgarian, is made of 0.9 mm stainless steel wire, which provides a high load-deflection rate [1]. The Goshgarian arch has been modified several times with regard to its material properties and shape. In 1980, [PERSON] et al. introduced the so-called precision transpalatal arch made of titanium-molybdenum alloy (TMA) [2; 3; 4]. The 50% lower Young's modulus of the TMA wire lead to significantly lower force and moments acting on the molars [5] and allowed a wider range of activation [6]. The compound palatal arch developed by [PERSON] et al. in 2004 was composed of a combination of stainless steel and nickel-titanium elements. The incorporation of the more elastic nickel-titanium elements also reduced the expansion forces and torques [7]. By including superelastic nickel-titanium elements, an expansion up to 4 mm and a derotation of the molars up to 10\({}^{\circ}\) could be achieved. Further variants of the classic Goshgarian, as described in the literature [8; 9; 10], were designed to create more precise tooth movements and a reduction in the force and moment magnitudes.  
Computer Aided Design/ Computer Aided Manufacturing (CAD/CAM) technologies have gained an increasing importance in orthodontics and offer new design and manufacturing possibilities. Whereas metal printing is already established [11; 12; 13], only a few studies have investigated the applicability of polyether ether ketone (PEEK) in digital workflows. PEEK is a high-performance polymer with dimensional stability, temperature resistance and excellent biocompatibility [14; 15]. The material can be milled and is--with some limitations--also 3D printable [16; 17]. Due to its excellent biocompatibility, PEEK was also chosen for dental implants as well as for removable and fixed dentures [18; 19; 20]. With its small Young's modulus of 3-5 GPa, PEEK may also be a good candidate for metal-free, aesthetic orthodontic appliances.  
Several applications of PEEK in orthodontics have already been reported in the literature. These are mainly passive appliances, such as space maintainers [21] and removable orthodontic retainers [22]. In addition, applications for fixed appliances were proposed [23; 24; 25; 26]. However, there is very scarce information as to what extent PEEK is eligible to deliver constant forces and may be used as a replacement for conventional wires or transpalatal arches (TPA) in orthodontics.  
Biomechanical properties can be assessed using mechanical testing of 3D-printed specimen, or mathematically by means of finite element analysis (FEA). FEA offers the possibility to simulate and visualize the behavior of complex shapes under mechanical loading. Since FEA can be conducted much faster than mechanical tests, it allows for the assessment of a high number of samples with different shapes. However, since FEA is a numerical approach, it highly depends on material parameters, boundary conditions and the way of modelling. To adjust the underlying parameters and the numerical model, mechanical testing of real samples appears to be mandatory.  
The aim of the present study was to investigate whether PEEK is suitable for orthodontic active appliances by assessing the biomechanical properties of a TPA made from PEEK by means of FEA and mechanical testing.