Bipedal Balance
Methods
The animations shown below were developed using our second-generation biomechanical model, while the motion was generated with the data collected from experimental trials. The experimental trials consisted of a healthy subject walking on and instrumented treadmill (Bertect Corporation) at different speeds and the motion was captured with an optical motion capture system (Visualeyez VZ3000, PTI). Three experimental trials are shown Slow Walking (0.7 m/s), Normal Walking (1.3 m/s), and Fast Walking (2.0 m/s). Each trial consists of ten consecutive gait cycles. Note that since the animations repeat, there is a sudden change from the end of the tenth cycle to the beginning of the first cycle.Theory
The forces acting on the human body while walking are the ground reaction forces (FGR) and the resultant of the inertial and gravitational forces (FF). In order to be in kinetic equilibrium, these forces must have the same but opposite direction, although they can be collinear or separated by a distance, the latter would result in a rotation of the whole body about its Centre of Mass (CM). FGR must act within the boundaries of the support area and passes through the Centre of Pressure (CoP). FF passes through the CM, thus it would have the direction of the red dashed line, shown in the animations, intersecting the ground at the Centroidal Moment Pivot (CMP). In the animations below, FF was translated to eliminate the inertial moment caused by the rotation of the body (change of rate of angular momentum); consequently, FF intersects the ground at another point called the Zero Moment Point (ZMP). Under dynamically balanced conditions, the translated force FF and FGR are collinear, i.e. CoP = ZMP, and thus the body is in equilibrium. Under dynamically unbalanced conditions, while FGR remains under the foot-support area, FF exists the support area, i.e. CoP ≠ ZMP. The distance from the ZMP to the CoP quantifies the imbalance moment.Discussion of Results
The results show that the individual undergoes a completely dynamically balanced gait at slow speed. There is little imbalance at the end of the single stance period during normal speed, which is characterized by the exit of the ZMP from the support area. This imbalance is even more noticeable during fast walking, as the body is significantly ahead of the support area and the ZMP exists earlier the support area. The ZMP exiting the support area implies that the body is experiencing a free but controlled fall, as balance will be recovered when the swinging foot strikes the ground.| Slow Walking | Normal Walking | Fast Walking |
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| Healthy subject walking 10 consecutive gait cycles on an instrumented treadmill at three different speeds (slow, normal and fast). Shaded area represents the foot-support area. FGR is the ground reaction force and FF is the resultant of inertial and gravitational forces. The point around the pelvis is the Centre of Mass (CM) of the whole body. The reference points on the ground are the Centre of Pressure (CoP), the projected Centre of Mass ( pCM), the Zero Moment Point (ZMP) and the Centroidal Moment Pivot (CMP). | ||
F. Firmani and E.J. Park, “Theoretical Analysis of the State of Balance in Bipedal Walking”, ASME Journal of Biomechanical Engineering, 135(4), 041003, 2013.