# Estimation of Tibiofemoral and Patellofemoral Joint Forces during Squatting and Kneeling
## 3 Results  
The knee bending (\(\alpha_{\mathrm{max}}\approx 80^{\circ}\)) showed a steep increase in musculoskeletal loading as larger flexion angles were produced. The max knee flexion moments achieved were on average 0.79 \(\pm\) 0.07 N\(\cdot\)m/kg (Table 1). The max compressive joint forces were 2.1 \(\pm\) 0.21 BW and 3.3 \(\pm\) 0.7 BW for the tiboifemoral and patellofemoral joints respectively. Figure 5: Comparison of the ratio of \(F_{\mathrm{pl}}/F_{\mathrm{q}}\) between patellar ligament force and quadriceps vs knee flexion angle from the IFA model with data presented by [PERSON] et al. [27]. In squatting and deep kneeling, the load bearing of the thigh-calf contact showed strong reciprocal correspondence to the quadriceps EMG activity. When the thigh-calf contact force increased during lowering, the quadriceps activity was reduced to approximately rest level at full contact (Figure 6). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Knee flexion** & **Ground Reaction** & **Thigh-Calf** & **EMG** & **Knee flexion** & **Quadriceps** & **Tiblefemoral** & **Patello-** \\  & **Angle** & **Force of Right Leg** & **Contact Force** & **Quadriceps** & **Moment** & **Force** & **Joint Force** & **Formal Joint Force** \\  & **(Degrees)** & **(BW \(\gamma\))** & **(BW)** & **(\%MVC \({}^{\ast\ast}\))** & **(N-m/kg)** & **(BW)** & **(BW)** & **Force (BW)** \\ \hline \hline Knee bends & \multirow{2}{*}{\(77\pm 6\)} & \multirow{2}{*}{\(0.52\pm 0.08\)} & \multirow{2}{*}{-****} & \multirow{2}{*}{\(28\pm 9\)} & \multirow{2}{*}{\(0.79\pm 0.07\)} & \multirow{2}{*}{\(3.2\pm 0.62\)} & \multirow{2}{*}{\(2.1\pm 0.21\)} & \multirow{2}{*}{\(3.3\pm 0.77\)} \\  
The three subjects successfully completed the endurance tests of maintaining absolutely static kneeling, squatting, or deep kneeling postures for ten minutes. None complained of any kind of knee strain. During upright kneeling, the average knee-flexion angle of the 13 test subjects was \(111^{\circ}\pm 6^{\circ}\), compared to angles of \(150^{\circ}\pm 6^{\circ}\) to \(156^{\circ}\pm 6^{\circ}\) reached during squatting and deep kneeling. In the static postures, the weight tended to be distributed slightly more onto the right leg, at 0.52 to 0.57 BW. The measured max thigh-calf contact forces during squatting and deep kneeling reached on average a range of 0.47 to 0.49 BW. This indicates that approximately 85% of the relevant ground reaction force was compensated for by the thigh-calf contact. Figure 7 depicts typical examples of force-vector graphics during squatting and deep kneeling. It illustrates the compensational effect of the thigh-calf contact force. In squatting, kneeling, and deep kneeling the knee flexion moment reached on average a range of 0.23 to 0.28 N\(\cdot\)m/kg. Corresponding to this, the max quadriceps muscle activity was on average in a range from 5 to 11% MVC. Quadriceps muscle force calculations yielded on average maxima from 0.9 to 1.0 BW with a tendency for greater variability for kneeling. The max tiboferomal compressive joint force achieved on average a range from 0.5 to 0.7 BW. The max patellofemoral joint forces ranged from 0.8 to 1.1 BW. During lowering to squat or rising from squat and deep kneeling, the knee flexion moment peaked on average at 0.93 \(\pm\) 0.16 N\(\cdot\)m/kg. The max tiboferomal compressive joint force achieved 2.6 \(\pm\) 0.39 BW and the patellofemoral joint force was 3.4 \(\pm\) 0.56 BW. Significant main effects of the factor task were observed for all three parameters (ground reaction force \(p<\) 0.001, tiboferomal \(p<\) 0.001 and patellofemoral joint force \(p<\) 0.001). For the ground reaction force, the pairwise comparisons between lowering/rising and all three postures of kneeling and squatting showed significant differences between 0.002 \(\leq p\leq\) 0.006. However, between the postures of kneeling and squatting, no significant differences were observed with respect to the ground reaction force.