7.1.1 Calculation of the vertical components of the reaction forces at the foot supports

The calculation begins by determining the vertical components of the reaction forces. The sum of these components must equal the total normal reaction required to balance body weight and the vertical components of the external forces. In addition, their combined line of action must pass through the center of pressure so that their resultant moment about this point is zero.

Given these conditions, Ergoniza Intelligent calculates the reactions by distributing them between both feet and among the support points of each foot, based on the position of the ankles relative to the center of pressure (CoP).

The procedure is illustrated in Figure 15, which shows a bipedal stance with the red sphere indicating the position of the CoP on the base of support. Points T_d and P_d represent the heel and metatarsal area of the right foot, respectively; T_i and P_i represent the equivalent points on the left foot. Points X_d and X_i are the projections on the floor of the right and left ankle joint centers, respectively.

Vertical reaction forces act at the four contact areas: T_d at the right heel, P_d at the metatarsal area of the right foot, T_i at the left heel, and P_i at the metatarsal area of the left foot.

The line joining X_d and X_i is translated parallel to itself until it passes through the center of pressure. Its intersections with the lines joining the heel and metatarsal area of each foot determine the zero-moment points O_d and O_i. The vertical reaction is distributed between the heel and front of each foot in inverse proportion to the distance from each support point to its corresponding zero-moment point.

Once O_d and O_i have been obtained, the total reaction is distributed between both feet using the same equilibrium principle: the load supported by each foot is inversely proportional to the distance from the center of pressure to the corresponding zero-moment point. This geometric criterion, together with the equilibrium equations, yields a unique distribution of the vertical components.

Under certain circumstances—for example, when one foot is markedly rotated and the CoP is close to the boundary of the base of support—the zero-moment point may lie outside the segment between the heel and the front of the foot.

This situation is illustrated in Figure 16, where the zero-moment point of the right foot (O_d) lies outside the segment joining the foot contact points (P_d-T_d). The unconstrained solution would then require a negative vertical reaction at one of the points, which is equivalent to assuming that the foot can exert a tensile force on the floor.

Because negative vertical reactions are not admissible, Ergoniza Intelligent places the zero-moment point of the affected foot at the nearest support point. In the example, O_d is moved to P_d, the reaction at T_d becomes zero, and the entire reaction of the right foot is concentrated at P_d. In other words, placing the zero-moment point of the right foot at the front support causes the entire load on that foot to be carried by that support.

The line joining this point to the center of pressure determines a new zero-moment point O_i^’ on the left foot, from which the distribution between the front and rear supports of that foot is recalculated.

Furthermore, changing the distances between the CoP and the new zero-moment points increases the loads on the left foot—which is better positioned to support them—and therefore decreases those supported by the right foot.

A similar procedure is used in bipedal stance when one foot has only one contact area (Figure 17). The reaction of that foot is concentrated at this point. The line joining the contact to the CoP determines the zero-moment point (O_i) on the foot that retains two supports. The vertical reaction components are distributed between the two supports of this foot in inverse proportion to the distance from each support to the zero-moment point.

7.1.1.1 Vertical components of the reaction forces at the foot supports under imbalance

When the center of pressure (CoP) lies outside the base of support (BoS), static equilibrium cannot be achieved using only nonnegative vertical reactions at the available supports. Ergoniza Intelligent then identifies the posture as unstable, but continues to calculate and display a diagnostic distribution of the reactions to indicate the edge or support toward which the load is concentrated and the direction of the tipping tendency.

If the center of pressure lies in front of the base of support, as in Figure 18, the heel reactions are taken as zero and the entire vertical reaction is concentrated at the fronts of the feet. The distribution between the right and left feet is inversely proportional to the distances from each support to point O, defined as the perpendicular projection of the center of pressure onto the line joining both supports. If the center of pressure lies behind the base of support, the procedure is analogous, but the reactions are concentrated at the heels.

If the center of pressure lies to one side of the base of support, the reactions are concentrated on the nearest foot. Figure 19 shows the case in which the center of pressure lies to the left: the reactions of the right foot are zero and the entire load is supported by the left foot. The distribution between the heel and the front of this foot is calculated from the perpendicular projection of the center of pressure onto the line joining the two support points. The procedure is symmetrical when the center of pressure lies to the right.

When the center of pressure lies outside the base of support near a corner, both criteria are combined and the reaction may be concentrated at the nearest support point.