Equilibrium and Stability of the Upright Human Body

We propose a new parameterization for describing forward and backward leanings of the straight human body with the feet fixed on the ground. During this motion stability of static equilibrium of the upright human body depends on the basic parameters such as coordinates XCG and YCG of the center of gravity of the body in the upright position and the radius R of the base of support. We introduce two coefficients k1= YCG/R and k2= XCG/R which are enough to calculate critical values of the angle α between the vertical axis OY and the axis of the cylinder the body is fitted into. We have calculated critical values αcr′ and αcr′′ when the body becomes unstable during leanings back and forward correspondingly. It is shown that stability of the upright body may be characterized by the angle αcr= |αcr′ |+|αcr′′| which strongly depends on k1 and weakly depends on k2 and αopt – the value of α for the most stable position when the body’s center of gravity is exactly above the geometrical center of the base of support. Stable equilibrium will be achieved for larger αcr and smaller | αopt|. Introduction Application of principles of balance and stability when performing specified sports skills is necessary to success. Many coaches would be wise to spend more time studying sport mechanics like balance and stability in order to improve the performance of their players [1]. To perform balance skills, athletes must have adequate strength to support the body, and they must be able to shift the weight quickly into the correct position at the right time. They must also know their position in space, called kinesthetic awareness, as well as possess quick reactions, coordination, agility, and flexibility. Within “mechanics” there are two sub-fields of study: statics, which is the study of systems that are in a state of constant motion either at rest (with no motion) or moving with a constant velocity; and dynamics, which is the study of systems in motion in which acceleration is present, which may involve kinematics [2]. In this work we discuss static equilibrium of the upright human body and propose a theoretical biomechanical model how to estimate stability of that equilibrium. General Theory Equilibrium is a state of zero acceleration where there is no change in the speed or direction of the body. Balance is the ability to control equilibrium (either static or dynamic). Stability is the resistance to a change in the body’s acceleration, or the resistance to a disturbance of the body’s equilibrium. Balance within muscle groups and alignment of the skeletal system affect body equilibrium and balance. Small shifts of bones can affect the whole skeletal system. The most important factors for achieving balance are the following [3, 4]: •A person has balance when the COG falls within the base of support (BOS) (the upright body is only stable when the line of gravity lies within the foot base); •A person has balance in direct proportion to the size of the BOS (the larger the base of support, the more balance); •A person has balance depending on mass (the greater the mass, the more balance). A unique point is associated with every body, around which the body’s mass is equally distributed in all directions. This point is known as the center of mass or the mass centroid of the body. In the analysis of bodies subject to gravitational force, the center of mass may also be referred to as the center of gravity (CG), the point about which a body’s weight is equally balanced in all directions or the point about which the sum of the moments produced by the weights of the body segments is equal to zero (Fig. 1). FIGURE 1. Center of gravity and line of gravity of a human body. The CG of a perfectly symmetrical object of homogeneous density, and therefore homogeneous mass and weight distribution, is at the geometric center of the body. However, when mass distribution within an object is not constant, the CG shifts in the direction of greater mass. It is also possible for an object’s CG to be located physically outside of the object (Fig. 1 b.)). Line of gravity is gravity’s action line which is visualized as a vertical line projecting downwards from the center of gravity (Fig. 1). A commonly used procedure for estimating the location of the total body CG from projected film images of the human body is known as the segmented method. This procedure is based on the concept that since the body is composed of individual segments (each with its own CG), the location of the total body CG is a function of the location of the respective segmental CG’s. Some body segments, however, are more massive than others and have a larger influence on the location of the total body CG. When the products of each body segment’s CG location and its mass are summed and then divided by the sum of all the segmental masses (total body mass), the result is the location of the total body CG. The segmental method uses data for average locations of individual body segment CG’s as related to a percentage of segment length. Thus,