# Are Torque-Driven Simulation Models of Human Movement Limited by an Assumption of Monoarticularity?
## 2 Methods
### Model Evaluation  
The kinematics of a squat and countermovement jump with free arm movement were collected for a 28-year-old male volleyball player, height 1.74 m, mass 79.2 kg using a 16 camera (M\({}^{2}\) MCam) Vicon motion analysis system (OMG Plc, Oxford, UK) sampling at 300 Hz [11] along with synchronous measurements of ground-reaction force sampled at 1200 Hz (Kistler instruments Ltd., Hook, UK). Testing procedures were explained to the participant, and written informed consent was obtained in accordance with the guidelines of the [blind for review] ethics committee. The participant undertook four jumps of each, with the maximum height jump of each selected for the evaluation process. In the evaluation process for each jump, the initial conditions were input to the model from the two maximum height jumps recorded performances (Table 1). The two models were customised to the participant using subject-specific torque parameters determined from isometric and isovelocity measurements at each joint with the participant [11; 29; 30] (Table 2) and subject-specific segmental inertia parameters determined from anthropometric measurements on the participant [37] (Table 3). SJ and TJ had the same inertia parameters, and the overall strength at each joint was equivalent. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Squat Jump**} & \multicolumn{3}{c}{**Countermovement Jump**} \\ \cline{3-7}
**Angle and Definition** & **+ve Angular Velocity** & **Angle** & **Angular Velocity** & **Angle** & **Angular Velocity** \\ \cline{3-7}  & & [\({}^{\circ}\)] & [\({}^{\circ}\)\(\cdot\)**s\({}^{-1}\)]** & [\({}^{\circ}\)] & [\({}^{\circ}\)\(\cdot\)**s\({}^{-1}\)]** \\ \hline trunk angle from horizontal & anti-clockwise & 56 & 3 & 88 & \(-\)107 \\ MTP angle from full extension & flexion & 43 & 0 & 43 & \(-\)1 \\ ankle angle from full extension & plantar flexion & \(-\)90 & \(-\)4 & \(-\)75 & \(-\)43 \\ knee angle from full extension & flexion & 96 & \(-\)17 & 20 & 177 \\ hip angle from full extension & extension & \(-\)123 & 5 & \(-\)8 & \(-\)235 \\ shoulder angle from full extension & flexion & \(-\)60 & 97 & 11 & 104 \\ elbow angle from full extension & flexion & 20 & \(-\)13 & 50 & 71 \\ neck angle from full extension & flexion & \(-\)5 & \(-\)65 & 1 & \(-\)65 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The initial kinematics for the simulations of the squat jump and the countermovement jump (where full extension refers to the anatomical position). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**(a) SJ**} & **plantar flexion** & **dorsi flexion** & **knee flexion** & **knee extension** & **hip flexion** & **hip flexion** & **shoulder flexion** & **shoulder extension** \\ \hline T\({}_{\text{max}}\) & 602.69 & 86.65 & 265.55 & 415.95 & 323.9 & 318.53 & 153.34 & 147.31 \\ T\({}_{0}\) & 430.48 & 61.89 & 189.68 & 297.1 & 231.36 & 227.52 & 109.52 & 105.22 \\ \(\omega_{\text{max}}\) & 20.26 & 6.87 & 18.2 & 17.86 & 9.99 & 11.87 & 16.42 & 15.1 \\ \(\omega_{\text{c}}\) & 4.45 & 3.43 & 9.1 & 2.68 & 3.81 & 5.81 & 8.21 & 6.28 \\ k\({}_{2}\) & 0.85 & 1.95 & 0.39 & 1.64 & 0.5 & 0.37 & 0.04 & 0.1 \\ \(\theta_{\text{opt}}\) & 4.89 & 2.38 & 3.12 & 4.22 & 3 & 4.85 & 7.1 & 5.92 \\ a\({}_{\text{min}}\) & 0.7 & 0.73 & 0.99 & 0.95 & 0.93 & 0.94 & 0.8 & 0.76 \\ m & 0.06 & 0.21 & 0.32 & 0.01 & 0.07 & 0.31 & 0.21 & 0.28 \\ \(\omega_{1}\) & \(-\)0.11 & 1.11 & 47.6 & \(-\)1.1 & 1.33 & \(-\)0.61 & \(-\)9.74 & \(-\)5.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Strength parameters for (a) SJ and (b) TJ. Two objective difference functions expressed as an overall percentage difference were defined that incorporated a combination of kinematic and kinetic variables associated with successful vertical jump performance (Equations (3) and (4)) with differences in linear and angular kinematics, rotation potential at take-off and kinetics combined assuming 1\({}^{\circ}\) of rotation was equivalent to 1% for the other variables [38].