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Summary- COM 'bent cycling

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  • Summary- COM 'bent cycling

    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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