# Are Torque-Driven Simulation Models of Human Movement Limited by an Assumption of Monoarticularity?
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Countermovement (Ascent)**} & \multicolumn{3}{c}{**Squat**} \\ \cline{2-7}  & **SJ** & **TJ** & **SJ** & **TJ** & \\ \cline{2-7}  & & **mono.** & **biart.** & **mono.** & **biart.** \\ \hline plantar flexors & 90.4 & 101.2 & 65.5 & 112.2 & 92.7 & 102.4 \\ hip extensors & 92.8 & 92.4 & 58.1 & 87.3 & 85.9 & 24.6 \\ \hline \hline \end{tabular} Note: The torque contribution from hip flexors by either an SJ or TJ model was relatively small, thus not included.  
\end{table} 
Table 10: Mean contractile component shortening velocity as a percentage of the joint velocity. by examining the work generated at each joint (Tables 8 and 9). For both the squat and countermovement jump, the TJ models performed more net plantar flexor work at both joints than the SJ model, which largely explains the closer matching of joint kinematics, and especially those approaching take-off. The direction and magnitude of work performed at the knee joint differed between SJ and TJ models. Net joint moments at the knee for the countermovement jump, differed between models by approximately 20 J. The SJ model performed a small net negative work (knee flexion), whilst the TJ performed a small net positive work (knee extension). This relationship was reversed for the squat jump. In the case of the squat jump, the constituents towards the net joint work warrant some mention. The magnitude of work done by the TJ model for knee flexion and knee extension was approximately 2.53 J\(\cdot\)kg\({}^{-1}\) larger than for the SJ model. The activation profiles of the SJ knee extensors and flexors had small activations of approximately 20%, whereas, for the TJ model, there were small activations of monoarticular knee flexors and near-maximal activation of the biparticular knee flexors (hip extensors), monoarticular and biparticular knee extensors. In this case, the large positive work of the knee extensors acted as a solution to overcoming the negative work of the knee flexors, thus allowing work from the biparticular knee flexors to generate extensor work at the hip. The mechanisms, which enabled the TJ simulation to better match performance, appear to relate to both torque generation and motor control. Firstly, examining the shortening velocities of the biparticular torque generators alongside their monoarticular equivalents, it is evident that biparticular components are shortening at relatively slower velocities than their monoarticular equivalents because of concurrent TJ kinematics. Muscle force-velocity properties [19; 40] predispose that for slower velocities of shortening, the contractile component can exert much larger forces. In the case of the TJ models in this study, by virtue of having favourable moment arms at two joints, the actions of concurrent ankle plantar flexion, knee-extension and hip extension enable the biparticular plantar flexors and biparticular knee flexors to have smaller shortening velocities than the monoarticular components, as such shortening slower whilst exerting favourable torques at proximal joints. The SJ model relative to the TJ model was much less effective at matching the countermovement jump performance than the squat jump (Table 7). The joint velocities of the countermovement ascent phase were much larger than for the squat jump, and this is likely to be a factor differentiating the results of the countermovement jump from the squat jump (Table 7). The concurrent extension of two joints about which biparticular muscles act allows the biparticular shortening velocity to be smaller than for a comparable joint where the torque generator velocity is governed only by one joint's kinematics, as is the case for a monoarticular component or for a similar SJ torque representation. The force-velocity characteristics of muscle mean that for an equivalent length, but a slower shortening velocity, a muscle can exert greater force.