(Table 1), there was no difference in the path of the COM trajectory under all trunk conditions. Moreover, the whole-body COM trajectory during the squatting motion formed
Figure 3. (a) The mean trunk angle for all subjects under each condition. The error bars represent the standard deviation. **p < 0.001. (b) The shank (black circle) and thigh (white square) angles as a function of the trunk angle. (c) Three- dimensional phase portrait showing the relationships among the shank, thigh, and trunk angles in all subjects under all conditions. Each plot represents the average of five trials under each condition for each subject.
Table 1. Relative anteroposterior displacement (dimensionless) for all subjects under each condition.
an approximate vertical in all subjects (Figure 2). Although whole-body motions were constrained by biomechanical dynamics (i.e., postural stability and maintaining of equilibrium  ), individuals could maintain equilibrium without falling as long as the body COM remains within the subject’s base of support. During the squatting motion in the present study, the base of support was a foot length of approximately 25 cm in the sagittal plane. When this motion was performed within that base of support, there were innumerable COM paths that could be formed. However, in the present study, the COM showed nearly vertical paths, even though the trunk configuration while squatting varied. It was considered that this verticality of the COM trajectory mighty not only be due to the fact that whole-body motions were constrained by dynamical equilibrium, but also due to the fact that the torques of joints forming the COM trajectory were minimized. Using a quiet standing task, and while assuming that the whole body formed an inverted pendulum with a point mass positioned on the COM, Winter et al.  examined the relationship between the pendulum angle and the plantar flexion torque in the ankle joint; they found that the ankle plantar flexion torque increased as the pendulum angle increased. This finding indicated that, for the squatting motion in the present study, as the COM moved outside the vertical path (i.e., AP excursion), it needed excessive torque (muscle work) to control the joint movements required for adjusting the sway. In addition, Yamasaki et al.  compared the verticality of the COM rising path after seat-off during a sit-to-stand motion in experiments with the verticality simulated by two models (minimum jerk model and minimum torque-change model); they found that the verticality computed by the minimum torque-change model was more consistent with that in the experiment than that computed by the minimum jerk model. This finding suggested that the verticality of the COM trajectory was a form that minimized torques caused by muscles. Thus, the findings regarding the formation of the COM trajectory in the present study indicated that the COM path during whole-body motion would assume a shape that depended on the task and that minimized muscle work.
4.2. Mutual Relation between the COM and Joint Movement
The COM showed a roughly vertical trajectory under all trunk conditions, while the joint movements systematically varied among trunk conditions (Figure 3(b), Figure 3(c)). As shown in Figure 3(b), the shank inclination angle decreased as the trunk angle increased, whereas the thigh angle remained constant. The findings that the joints coordinately varied with altering trunk angles and that the COM trajectory formed task-dependent paths suggested that the joint movements were altered in an organized manner to form the COM path while ensuring that the muscle torques were minimal. Thus, these findings might indicate that the CNS controlled the COM position while minimizing muscle torque, and that joint movements were coordinately organized to form the COM position. Bernstein  proposed that since motions could be performed in a hierarchical structure, as individuals perform motions such as squatting or walking in a space, the muscle-joint linkage at the lower level was involved in background adjustments to obtain the goal of motion. In addition, the uncontrolled manifold hypothesis proposed by Scholz and colleagues  -  indicated that the CNS controlled the task-dependent COM position, but did not control joint movements, and that each joint in whole body motion coordinated to form a task-dependent COM position. Thus, the present findings indicated that joint movements were organized to form the COM position, all of which were controlled by the CNS.
As joint movements organize to form a task-dependent COM position, these organized joint movements should in theory have a lawful coordination dependent on the task. However, previous studies have not examined the coordination of these organized joint movements. Herein, the relationship among the segment angles, as observed in the phase portrait in Figure 3(c), indicated a lawful connection of the organized joints―i.e., the shank angle decreased as the trunk angle increased in a plane wherein the angle of the thigh was constant (approximately 40 degrees). This lawful connection suggests that each segment has a different role in squat downward. As the trunk angle is increased with constant angles of the shank and thigh, the COM moves anteriorly; this movement would result in excessive ankle joint torque  . The COM anterior displacement attribute to increase of the trunk angle in theory could be decreased by decrease of the shank inclination angle and increase of the thigh flexion angle. However, in the present study, only the shank angle was altered upon changes of the trunk angle, and not the thigh angle. These findings may indicate that shank movement shows a coordinating relationship with trunk movement in order to adjust AP displacement of the COM. The finding that the thigh angle remained constant as the trunk angles were altered suggests that this angle determines the depth during downward squatting. In the present study, the depth of squatting was set at approximately 15 cm (Figure 2). Therefore, all subjects performed downward squatting of 15 cm under all conditions. We believe that a thigh angle of 40 degrees is essential for squatting downwards by a depth of 15 cm. These findings are novel and suggest that
Figure 4. Schematic of the hypothesis proposed in this study. The central nervous system controls the center of mass (COM). The COM trajectory is constrained by biomechanical dynamics and minimum muscle torques, and the joints (segments) are coordinately organized while being constrained by the COM trajectory.
the joints in the whole body are coordinately organized to adjust the COM position.
The differences in the shank and thigh angles with a change in the trunk angle may be associated with a synergy at the kinematic level. Latash et al.  stated that lawful changes during multi-joint movements can arise only when each element (joint angle) of the system is coordinately organized in synergy, and not when it is independently controlled by the CNS. Furthermore, Rosenbaum  described that multi-joint movements that occur with ease, such as rotation of the elbow and wrist joints in the same direction, are movements occurring with synergy, whereas those that occur without ease, such as rotation of the elbow and wrist joints in opposite directions, are movements occurring without synergy. In the present study, the trunk and shank rotated around the hip and ankle joints, respectively, in a clockwise direction, while the thigh rotated around the knee joint in a counter-clockwise direction. This finding suggests that the coordinative connection between the trunk and shank results from synergy. Moreover, the finding that this coordination arises in a plane with a thigh angle of approximately 40 degrees suggests that the thigh movement compensates for the coordinative connection. Further studies are needed to confirm this hypothesis.
In summary, the present study indicated that the coordination of whole-body segments would be organized in a lawful manner to form the task-dependent COM trajectory. Furthermore, the present study suggested the following: 1) the CNS controls only the COM position and not the joint movement; 2) the COM is constrained not only by biomechanical dynamics (i.e., maintaining equilibrium and postural stability) but also by minimum muscle torques and; 3) the segment movements, which constitute the joint movement, consist of coordination with synergy between the trunk and shank, and of the thigh movement that compensates for the coordination; this has been represented as a schematic in Figure 4.
Cite this paper
YoichiroSato,HiroshiNagasaki,NorimasaYamada, (2016) Joint Coordination Organizes to Form the Task-Dependent Trajectory of the Body Center of Mass. Journal of Behavioral and Brain Science,06,1-8. doi: 10.4236/jbbs.2016.61001