## 2 Materials and Methods
### 3D Modeling of Rowing Forces
#### 2.3.8 Configurable Parameters of LIAC for an Individualized Rowing Experience on the Simulator  
A pilot study with three expert rowers, who were not included in main study, was conducted to assess and calibrate the newly developed LIAC model. The goal was to adjust the LIAC parameters, which would yield realistic forces for all sub-phases of the cycle and a corresponding boat velocity. Thus, we chose four parameters as follows that modulated the calculation of the forces: drag and lift adjustment coefficient (\(G_{dl}\)) for drive, curvature of the rowing blade (\(q_{bias}\)) for catch and release, minimum rope tension force (\(\tau_{rec}^{min}\)) for recovery, and boat drag coefficient (\(C_{Bdrug}\)) for the boat velocity. Figure 4: Illustration of the vertical oar rotation-dependent rope tension adjustment for the tendon based parallel robot. A typical rowing cycle is illustrated with the thick elliptic line. Four arrows show the direction of the oar blade within the cycle. For drive, three expert rowers reported that the resulting 3D model forces were greater than the forces felt during actual rowing. Thus, to calibrate the forces in the horizontal and vertical plane, we employed an additional gain, i.e., \(G_{dl}\), for the adjustment of drag and lift coefficients:  
\[C_{D^{\prime}}^{xy} =G_{dl}f_{D}\Big{(}\alpha_{xy}\Big{)} \tag{29}\] \[C_{L^{\prime}}^{xy} =G_{dl}f_{L}\Big{(}\alpha_{xy}\Big{)}\] (30) \[C_{D^{\prime}}^{yz} =G_{dl}f_{D}\Big{(}\alpha_{yz}\Big{)}\] (31) \[C_{L^{\prime}}^{yz} =G_{dl}f_{L}\Big{(}\alpha_{yz}\Big{)} \tag{32}\]  
where \(D^{\prime}\) and \(L^{\prime}\) subscripts define the adjusted drag and lift coefficients, which were replaced in Equations (17)-(20). In the end of the pilot test, \(G_{dl}\) was set to 0.35 by taking the average of the preferred gains reported by three expert rowers. Another critique of the pilot test rowers was that the vertical forces during the air-water transition were low. Thus, we increased the vertical forces in the catch and release by introducing a bias angle, i.e., \(\varphi_{bias}\), which was assumed to account for the lateral curvature of the rowing blade. Originally, the oar blade presented in the LIAC model was designed as a flat plate. Thus, introducing \(\varphi_{bias}\) yielded:  
\[\varphi^{\prime}=\ \varphi_{bias}+\varphi_{act} \tag{33}\]  
where \(\varphi_{act}=\varphi\) is the actual longitudinal rotation of the oar blade and \(\varphi^{\prime}\) is the adjusted oar blade rotation used in the Matlab/Simulink(r) implementation. The initial value of \(\varphi_{bias}\) was set to \(2^{\circ}\). The minimum rope tension force in the tendon based parallel robot was adjusted for the rowing forces during recovery (\(\tau_{rec}^{min}\)). Since \(\tau_{rope}^{min}\) was set to a fixed value of 50 N for the overall cycle in the BIFC model, the initial value of \(\tau_{rec}^{min}\) in the LIAC model was also set to 50 N for the recovery (\(p_{imm}=0\)). All three rowers judged that the recovery force rendered by LIAC was unrealistically resistive; thus, an average value of 35 N was set for a smooth manipulation of the oar in the recovery. Finally, pilot study rowers were asked to assess how well the perceived boat velocity matched the applied forces on the simulator. Based on the implementation of the rowing model, the boat velocity \(\dot{y}_{baut}\), was dependent on the driving forces applied by the rowers on the oar blades (\(F_{propulsion}\)), inertia forces resulting from the movement of the rowers and the oar blades (\(F_{inertia}\)), and drag forces acting on the boat (\(F_{BautDrag}\)). \[m_{baut}\ddot{y}_{baut}=F_{Net}=F_{propulsion}-F_{inertia}-F_{BautDrag} \tag{34}\]  
where \(m_{baut}\) is the combined mass of rowers and the boat, and \(\ddot{y}_{baut}\) is the acceleration of the boat in \(B_{y}\)-axis [28].