In some regions in Asia or Arab, there are lifestyles without chair or bed and sitting down on a floor directly, by flexing their knee deeply. However, there are little data about the joint angles, muscle forces or joint loads at such sitting postures or descending to and rising from the posture. In this study, we report the knee joint force and the muscle forces of lower limb at deep squatting and kneeling postures.

The model to estimate the forces were constructed as 2D on sagittal plane. Floor reacting force, gravity forces and thigh-calf contact force were considered as external forces. And as the muscle, rectus and vastus femoris, hamstrings, gluteus maximus, gastrocnemius and soleus were taken into the model. The rectus and vastus were connected to the tibia with patella and patella tendon. First the muscle forces were calculated by the moment equilibrium conditions around hip, knee and ankle joint, and then the knee joint force was calculated by the force equilibrium conditions at tibia and patella.

For measuring the acting point of the floor reacting force, thigh-calf contact force and joint angles during the objective posture, we performed the experiments. The postures to be subjected were heel-contact squatting (HCS), heel-rise squatting (HRS), kneeling and seiza (Japanese sedentary kneeling), as shown in the Fig.1. The test subjects were ten healthy male, and the average height was 1.71[m], weight was 66.1[kgf] and age was 21.5[years]. The thigh-calf contact force and its acting point were measured by settling the pressure distribution sensor sheet between thigh and calf.

Results were normalized by body weight, and shown in Fig.1. The thigh-calf contact force was the largest at the heel-rise squatting posture (1.16BW), and the smallest at heel-contact squatting (0.60BW). The patellofemoral and the tibiofemoral joint forces were shown in the figure. Both forces were the largest at the heel-contact squatting, and were the smallest at the seiza posture. And it might be estimated that the thigh-calf contact force acted anterior when the ankle joint dorsiflexed, and the force was larger when the hip joint extended. The thigh-calf contact force might be decided by not only the knee joint angle but also the hip and ankle joints.

As a limitation of this study, we should mention about the effect of the neglected soft tissues. It could be considerable that the compressive internal force of the soft tissues behind a knee joint substance the tibiofemoral force, and then the real tibiofemoral force might be smaller than the calculated values in this study. Then, the tensile force of quadriceps also might be smaller, and then the patellofemoral joint force is also small.

Thigh-calf contact force is the force acting on posterior side of the thigh and calf during deep knee flexion. It has been reported the force is important to analyze the kinetics of a lower limb and a knee joint. Some previous researches reported the measured thigh-calf contact force, however, the values varied among the reports. Furthermore, the reports indicated that there were large variations even in a single report. One of the reports tried to find the relationship between the magnitude of thigh-calf contact force and anthropometric measurement as height, weight or perimeter of the lower limb, however, there could not found clear correlations. We considered that the cause of the variations might be the difference of the posture. At heel-rise squatting posture, we can bend or stand upright the upper body. Therefore we tried to create the equation to estimate the thigh-calf contact force by multiple regression analysis, using the anthropometric and posture parameters as explanatory variables.

We performed the experiment to measure thigh-calf contact force, joint angles and anthropometric information. Test subjects were 10 healthy male. First we measured their height, weight, perimeter of the thigh and muscle mass of the legs and whole body. Muscle mass was measured by body composition meter (BC-118E, Tanita Co., Japan). Then, test subjects were asked to squat with their heels lifted and with putting the pressure distribution sensor between thigh and calf. And they bent their upper body forward and backward. The pressure sensor to be used was ConfroMat System (Nitta Co., Japan). After that, we measured the joint angles of the hip, knee and ankle, and the angle between the floor and upper body using the videos taken during the experiment. Then, we created the equation to estimate the thigh-calf contact force by linear combination of the anthropometric values and joint angles. The coefficients were settled as to minimize the average error between measured and estimated values.

Results are shown in Fig.1. Forces were normalized by the body weight of the test subjects. Because the horizontal axes show the measured and vertical axis show the estimated values, the estimation is accurate when the plots are near the 45-degree line. Average error was 0.11BW by using only physical values, 0.15BW by angles and 0.06BW using both values. And the maximum error was 0.69BW, 0.43BW and 0.32BW respectively. Thus we could estimate the thigh-calf contact force by multiple regressions, using both physical parameters and angles to indicate the posture. Using the equation, we would be able to analyze the kinetics of a lower limb by physical and motion measurement. Our future work might be increasing the number of subjects to consider the appropriateness, because the test subjects of this study were very limited.