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View Full Version : Re: Re Geometric Integration

d3uk61
01-17-2010, 09:03 PM
Thanks for loads of replies They all were pretty much like these ones:

The correct term probably should be "integration over time" or "mathematical integration". Geometric may refer to integrating using trapezoidal integration methods. In fact, to obtain valid displacements of the centre of gravity from force signals is far from easy. First, you must correctly measure the body mass. Second, you need a suitable sampling rate of the force signal (100 Hz should do). Third, you must know the initial velocity and initial position of the body. If the person starts motionlessly, the initial velocity can be assumed to be zero. The initial position can be set to zero so you can monitor the motion from the initial position. There is no way to actually compute the initial position from the force signal. The next steps are the mathematical integrations. You need to create the velocity history by adding accelerations. First, divide the force signals by the person's mass. For the vertical force, you must subtract body weight before dividing by mass. The resulting signals are now accelerations. You now multiply each acceleration by the sampling time (t, e.g., 0.01 seconds if you sampled at 100 Hz) and add them accumulatively. I.e., v(i) = v(i-1) + a(i) * t Note, the first velocity will be zero as mentioned above. Then you do this again to get the displacements (s). In other words, you are doing a double integration over time. I.e., s(i) = s(i-1) + v(i) * t Good luck with making this work. If there is any "drift" in your force platform or an error in the initial velocity or body weight estimate, after a very few seconds the displacements will skyrocket. Try doing this for more than 10 seconds with the person standing motionless. If the displacements stay small, you have probably succeeded. High-pass filters will help if applied after subtracting body weight from the vertical signal (do not do this before the subtraction!). By the way, you will have to do these operations for each axis of the force plate (x, y, z).

Gordon Robertson

It seems that the term "geometric integration" here is a fancy name for "double integration" though I have never come across it. Quickly, if you start with position versus time, taking the first derivative with respect to time gives you velocity versus time. Taking the derivative again (second derivative) gives you acceleration. Differentiating the position twice with respect to time gives acceleration. The opposite of differentiation is integration where integrating takes you from acceleration to velocity and once more gives you position, basically. Double integration (or i guess geometric integration) of acceleration results in displacement/position. That statement left a couple of things out. Forceplates measure what is analogous to the force applied to their surface, not acceleration. We know that the center of mass of the body touching the plate must be accelerating to produce a net force, so what you do to get acceleration is divide by the person's mass: accel = (net force)/mass. From here you can mathematically integrate to find position.

Andrew Kraszewski Hospital for Special Surgery

This was the way I was integrating the Force time curve = a=f/m and v=at and d=vt I'm only considering vertical GRF.

Ted sent some good stuf in his postf and so I used the following in Excell Excel Equation form is trapezoid integral = J7+((A8-A7)/100)*(E8+E9)/2 = previous sum +(change in time(x axis)))/numbered intervals converted to to100hz)*(change in d(y axis))/2 - repeat to next cell from N,o - N,77 (samples total 0.77seconds)

Seems to be the same as Gordon suggeted but what I want is a graph that represents displacement and velocity relative to a ground reference. These integrations give a summation of the total velocity and displacement i.e. always increasing away from zero to the final sum/displacement. How can I achieve the type of graph that is more intuitive I had a mass of 95kg and an estimated initial velocity of 1.2m/s towards the ground.

Help Please

Cheers Dave