## 2 Materials and Methods
### Analysis of Range of Motion  
The ROM analysis was conducted with Creo Parametric (v.2.0, Parametric Technology Corporation, Boston, MA, USA) by deploying a kinematic motion analysis, using a kinematic chain. In this manner, a predefined motion until impingement was applied to the hip joint. The coordinate systems of the femur and acetabulum, respectively, were translated to the center of rotation of the virtually implanted acetabular cup and into the center of rotation of the virtually implanted femoral head. Subsequently, the initial positioning of the pelvic bone and the femur to each other was performed according to the anatomical positional relationships. The collision detection routine of Creo Parametric was considered to detect the occurrence of impingement situations [18]. For this, the contact was defined between the external surfaces of the femur and the pelvis, between the femoral hip stem and the acetabular cup, and between the femoral hip stem and the liner. The motion was stopped when a collision between bone and bone, implant and bone, or implant and implant was detected.  
The rigid bodies of bones and implant components were connected by ideal joints to set up a kinematic chain. The acetabulum was assumed to be ground fixed, followed by the acetabular cup and liner, which were also fixed to the pelvic bone. The prosthetic head, together with the hip stem, was fixed to the femoral bone and these were connected to the acetabular cup and liner fixed to the pelvic bone by a spherical joint, with a fixed center of rotation. The kinematic chain represents an open-loop mechanism. A virtual servomotor with a constant angular velocity was used to impose a specific motion in one degree of freedom between the two bodies along a predefined fixed rotational axis of the joint.  
Generally, the motion was started at the initial configuration for each load case and continued until impingement [23; 63] was detected. In our approach, impingement between femoral configuration--consisting of the femoral bone, stem, and prosthetic head--and pelvic configuration--consisting of the pelvic bone, acetabular cup, and liner--was recognized. The definition of contact in this algorithm is the occurrence of the intersection between pelvic and femoral configuration. The hip joint angle at this specific position was then recorded as the functional ROM of the THR. Within the ROM analysis, three different movements similar to ISO-21535 and typical clinical joint movements [54; 55; 56; 57] were considered (Figure 3): maximum flexion from neutral (maxFlex), combined internal rotation at 90\({}^{\circ}\) flexion (IR@90 Flex), and combined external rotation at 90\({}^{\circ}\) flexion (ER@90 Flex).  
The neutral position of the hip joint for the maxFlex movement is defined by bringing the sagittal plane and transversal plane of the pelvis into coincidence with the sagittal plane and transversal plane of the femur. The flexion axis is defined by the intersection of the transversal and frontal plane. A flexion rotation was applied until impingement was detected.  
For IR@90 Flex and ER@90 Flex, the mechanical axis of the femur, which is defined by the condylar notch and the center of rotation of the femoral head, was used as a femoral rotational axis. The initial configurations of these motions were generated by applying 90\({}^{\circ}\) of flexion, using the neutral position of the maxFlex motion. Subsequently, internal rotation or external rotation started and was performed until impingement was detected.  
Finally, the resulting ROM and type of impingement (bone-to-bone, implant-to-implant, and implant-to-bone) were analyzed during the three movements.