Teach-in '98: The Ground Reaction Vector & Centre of Mass

In normal quiet standing, the centre of pressure (CoP) weaves around the center of mass (CoM) to maintain balance. In this experiment, the task is made a little more complicated by asking the subject to balance on one leg. The difference between the CoP (base of the force vector) and CoM (the small cross in the pelvis) is proportional to the linear acceleration of the body, and in this way the CoP can be seen to act as the controller of the CoM (Winter, 1995).

Looking at the upper end of the ground reaction vector (GRV), we can see that it too weaves around the CoM, creating an alternating moment of force about it, which is responsible for an angular acceleration of the body. The discrepancy between the CoM and GRV at the same horizontal level is measured in the animated upper graph (directly below the stick figure). 

The same phenomenon occurs during normal gait:

As the lower graph shows, the CoP leads the CoM at the beginning of stance (causing a braking deceleration of the CoM, i.e. loading response), but trails it towards toe-off (causing a propulsive acceleration, i.e. push-off). Note that at the beginning and end of stance there are some strange effects, because the other foot is in contact with the floor and there are two vectors at these times. Once again, the animated upper graph shows the discrepancy between the CoM and the GRV at the same level.  Clearly, the GRV also leads the CoM at in early stance, and trails it from mid to late stance.


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The animations on this page were made using BodyBuilder software on a Vicon 370 motion analysis system (Oxford Metrics, UK). The model used to calculate body CoM was kindly supplied by Richard Baker & Michael Eames (Musgrave Park Hospital, Belfast, N. Ireland) and was adapted to calculate the discrepancy between GRV & CoM. It can be downloaded here, along with the associated model parameters & marker set files. Please drop them an email if you use their model. The .C3D motion files used were: Oneleg.c3d & Gait.c3d from the Hong Kong Polytechnic Univ.


Winter, DA (1995) A.B.C. (anatomy, biomechanics and control) of balance during standing and walking, Waterloo, Ont..

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