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Renee' Turner/jennifer Bridges
10-05-1999, 09:10 AM
Thanks to all of the responses to my question.

Most of the responses were very similar so I've included this one as a
representative example:

The center of mass of the bicycle/rider system can be relatively easily
determined using a two step approach. First (the easy part), find the
bicycle
cg using a double suspension experimental method (suspension as in hanging,
not
as in shock absorbers). Hang the bicycle by one wheel from a ceiling hook,
beam
etc. You will probably have to tie the front wheel to the frame to keep it
in
line with the bicycle frame. Hang a plumb bob from the upper wheel
attachment
point so it hangs vertically along side the bicycle frame. The bicycle cg
is
along this line. Mark the intersection of this line on two points of the
frame
(say, the chainstay and the headtube) to establish this line for future use.
Now hang the bicycle again, using another attachment point (not the other
wheel). The seat post might be a good option. Repeat the plumb bob
procedure
with the bike in its new orientation (again, the plumb bob should be a
continuation of the suspension point towards the ground). Again, the bike
cg
lies along the plumb bob line. The intersection of the two lines
established
during the separate suspensions approximates the bicycle cg. The more
perpendicular these lines are to each other, the more accurate your
approximation of the bike cg.

Note that the horizontal cg of the bike can also be determined using a
reaction
board (knowing the bike weight, the bike position on the board, and the load
necessary to support one end of the board. Or the horizontal cg can be
determined by simply finding the point on the bike where a string can be
attached to suspend it in a perfectly level orientation. This approach also
works for the rider plus bike system, in the horizontal direction only of
course. But I find the double suspension system to be quick and easy, and
requires only some string, a small weight (for making a plumb bob), and a
ceiling hook.

Step two (the more complicated) is to find the cg of the rider - in the
riding
position. I refer you to a text by David Winter entitled Biomechanics of
Human
Movement for this procedure. Simply stated, you need to find the joint
locations, in two-dimensions (in the sagittal plane), describing the segment
orientations, locations, and lengths. Then, regression equations can be
used to
identify the center of mass locations for each segment. This can all be
done
manually using a good side view photograph of the rider and some grid
tracing
paper (digitize the joint centers, measure the separation distances defining
segments, determine center of mass locations within segments from regression
equations, and digitize centers of mass onto tracing paper). I assume you
do
not have motion capture and analysis systems which, from digitized video
images,
locate total body center of mass automatically.

The whole body cg (relative to one of the axles - for simplicity) is then
determined using the relation:

Xo = (m1x1 + m2x2 + m3x3 ..... mixi)/Mtotal
Yo = (m1y1 + m2y2 + m3y3 .....miyi)/Mtotal

where
Xo = horizontal location of body cg - relative to axle
Yo = vertical location of body cg - relative to axle
mi, m2, etc = mass of each segment (thigh, shank, arm, trunk, foot, etc.).
Don't forget two legs and arms.
x1, x2, ... xi = horizontal positions of centers of mass, relative to axle,
of
each segment (thigh, shank, foot, etc.)
y1, y2, ... yi = vertical positions of centers of mass, relative to axle, of
each segment
Mt = total mass of rider

Finally, the rider plus bike center of mass is determined from:

Xt = (mbxb + msxs)/Mbs
Yt = (mbyb + msys)/Mbs

where
Xt = horizontal location of rider plus bike cg, relative to axle
Yt = vertical location of rider plus bike cg, relative to axle
mb and ms = mass of bike and subject, respectively
xb, xs = horizontal position of bike cg and subject cg, relative to axle
yb, ys = vertical position of bike cg and subject cg, relative to axle
Mbs = the mass of the bicycle and subject combined

I hope this helps. The equations are easily put into a computer program
form.

In addition, the following discussion list "hardcore-bicycle science" was
also suggested:

http://www.sheldonbrown.com/hbs.html

Thanks again,
Jenni Bridges,
Michigan

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