Ground Reaction Force
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For every action, according to Newton's 3rd Law of Motion (Law of Reaction), there is an equal and opposite reaction. Due to the gravity, we constantly maintain contact with the ground, and in this process, there occur interactions between the body and the ground. The reaction force supplied by the ground is specifically called the ground reaction force (GRF), which is basically the reaction to the force the body exerts on the ground. The GRF, along with the weight, is an important external force. The GRF is normally measured by a force-plate.

Figure 1a shows the reference frame of the force-plate, with the Z- axis being the vertical. The interaction between the body and the ground occurs through the foot as shown in Figures 1b, which shows the reaction force vectors acting on small areas. A force-plate normally has four tri-axial force sensors embedded that measure the force acting between the foot and the ground in 3 axes: transverse (X), anteroposterior (Y), and vertical (Z). Figure 1c show the 4 reaction force vectors measured by the sensors. The sum of all the reactions from the ground shown in Figure 1b is equivalent to the sum of the four forces measured by the sensors (F1, F2, F3, & F4) shown in Figure 1c. Thus, system (b) is equivalent to system (c).

Figure 1

Figure 1d shows a single force, F (F1 + F2 + F3 + F4), and a torque, Tz. F here is the ground reaction force. Tz shown in the figure is the so-called free torque and has the vertical (Z) component only. The free torque is caused by the coupling effects of the forces about the vertical axis. System (d), F + Tz, is again equivalent to system (c). The ground reaction force has three components: Fx, Fy & Fz. Among these, Fy is along the direction of the motion which reflects the propulsive or braking force. Fz always thrusts the body upward.


Young-Hoo Kwon, 1998-