E1 Mechanics of the Center of Mass and Balance

Topic

The center of mass is the point that encapsulates the translational behavior of the entire mammalian body; tracking this single point is largely equivalent to tracking the movement of the whole body. Its trajectory, velocity, and acceleration are determined exclusively by the external forces acting on the body: ground reaction force, gravity, and the aerodynamic or hydrodynamic resistance of the medium in which the animal moves. For terrestrial mammals, locomotion can be described, as a first approximation, as the movement of this center of mass subject only to gravity and ground reaction force.

Depending on the gait, this movement of the center of mass—subject to gravity and ground reaction force—is approximated by two fundamental models. During walking, the center of mass behaves like the mass of an inverted pendulum oscillating over the point of contact with the ground. During running, by contrast, the center of mass behaves like a mass supported by a spring that compresses upon contact and extends at liftoff, storing and returning energy with each stride.

The mechanical energy of the center of mass—the sum of its kinetic and potential energy at any given moment—fluctuates throughout the locomotor cycle, following the exchange patterns described by these two models: in walking, the center of mass's kinetic and potential energies are exchanged, much like in a pendulum, whereas in running, both rise and fall in unison, with the muscular spring absorbing and returning energy between successive contacts with the ground. The efficiency of locomotion is determined by how well the body recovers, from one step to the next, the mechanical energy that the center of mass loses and gains during each cycle.

In addition to determining energy efficiency, the position of the center of mass plays another distinct role: relative to the base of support—the area defined by the points where the body contacts the ground—this position serves as the criterion for defining the animal's static stability at any given moment. During running and jumping, there is an aerial phase in which no part of the body touches the ground; during this phase of free flight, the center of mass is no longer subject to the ground reaction force and—influenced only by gravity—follows a parabolic trajectory until the next contact with the ground.

Experimentally determining this trajectory and the mechanical energy of the center of mass throughout the entire locomotor cycle—in mammals of any size—is achieved by twice integrating the ground reaction force (measured directly during the contact phase) over time: the first integration yields the velocity of the center of mass at any given instant, and the second integration, based on that velocity, yields its position. This procedure is the standard experimental method for reconstructing the complete behavior of the center of mass—as introduced at the beginning of this description—from a single force measurement.

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