Building a Test Plot Model Foot offset / Leg angle
calculations: The linear value of foot offset is difficult to
use, though it's easier to visualize. Luckily, this can be converted to leg
angle, if the step out length is known or can be estimated. Using leg angle
means step-line and both DOT rotations can just be typed in as rotations,
rather than using dimensioned lines.
At the end of a step, if you could freeze yourself in space,
just before you plant the front foot, you could move the foot from side to
side, and, with constant step out length, its path would describe an arc,
the step out arc. This is the line your heel point would touch if you always
had the same step out length, but changed foot offset (foot angle doesn’t
affect step-out arc). Step out length = radius of the step
out arc = r = 15” (for my model) If you could spin your foot
all the way around, the step out line would be the radius of a circle,.
Since the radius, r, is known, the circumference of the circle can be
calculated. circumference of step out circle = 2 (pi) r
=2 (3.14)15”
=94.2”
and,
360 (deg) leg angle / 94.2” foot offset
= 3.82 deg leg angle / “ foot offset
or, this can be inverted to give,
0.26” foot offset / deg leg angle So, if the foot moves 1”
along the arc, that’s a leg angle of 3.82 deg, and a leg angle of 1 deg is a
0.26" foot offset. Therefore, a foot offset given as (2d) oL
means a 0.52” foot offset left. See Part IIc, Plotting Results for
explanation of the shorthand notation. You will also be able
to produce different plots more quickly if you set up a standard page with
the standard plot model already positioned on the start. Changes to the
standard model change the dimensions, and make it more difficult to
accurately place. Draw a standard vertical line from about 1”
from the bottom of the page to the top, at a place where the final footfalls
will be on the page. Type in the X-Y co-ordinates and make them exact and
convenient numbers. I set the scale at 1:10 and use a page
size of 110” by 280”. My standard vertical line for left turn models is 260”
long and is at X-90.0000” and Y-135.0000”. That means the bottom of the line
is at 5.0000”. Position the model on the start point,
centered on the line and the bottom even with the bottom of the line. My
standard plot model dimensions are 4.0000” wide by 36.0000” high, so the
co-ordinates X-90.0000” and Y-23.0000” will position the model properly.
Then, somewhere on the page, add a blank table to record the distance values
from the dimension lines, and a box with the description of the sample plot
model standard values and deviations. (see Fig. 6) When
changes to the standard model are complete, copy and paste, and leave the
copy on the other side of the page for posterity.
For L(2d)oL-2dL:R4dR (this person would be walking
straight): (Please refer to Part IIc - Plotting Results for
an explanation of the shorthand notation.) Rotations are done by typing in
the exact value.
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Select the standard plot model and ungroup.
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Select the left step-line model and rotate 2 deg CCW.
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Ungroup the left step-line model, then select the left
step foot model.
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Rotate 2 deg CCW.
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Select the right step-line model and ungroup.
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Select the right step foot model and rotate 4 deg CW.
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Select entire figure, then group.
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Copy and paste, then move the copy to the other side of
the page. This one is kept on the page as an example of the sample
model, in case there are errors.
That’s all there is to it, you’re ready to plot. The model
is already positioned correctly at the start if you used the standard page.
The foot offset is built into the model. Both foot and leg angle rotations
are done when plotting. Creating Footfall Plots
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Start with the standard page and modify the standard
model.
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Copy and paste the test model and move the copy off the
original to keep.
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Copy and paste the test model again, and move the copy
off the original. This will be for the next step.
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Select the original and ungroup. While holding the shift
key, deselect the two start foot models (heel points) and the left step
foot model, then press delete. This will delete the rest of the model
except the three foot models. This represents the first step with the
left foot.
Note: If you didn’t have to change the foot angle value in the model,
that step-line model will still be grouped. That just means you have to
ungroup one more time before selecting the step foot model you’re
dropping.
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Rotate the copy the amount of the foot angle plus the
leg angle (from foot offset) for the left foot. So, for a (2d ) foot
offset left with a 2 deg foot angle left, the copy is rotated 4 deg CCW.
This will make the angle of the start foot models on the copy the same
as the left step foot model that was just dropped.
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Align the left start foot model of the copy onto the
left step foot model just dropped from the original.
I make both step foot models gray in my plot model so it’s easier to
align with the next step’s start foot model, which is black. I put the
copy to the back, then position it over the gray footfall. With the
arrow keys and the smallest movements, I move it until there is no black
showing under the gray arrow.
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Copy and paste the model, then move the copy off of the
original. (For the next step.)
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Select the original model, ungroup and deselect the
right step foot model, then press delete. This will leave only the right
step foot model.
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Rotate the copy for the right foots angles and offsets,
and align the copy’s right start foot model with the gray one just
dropped.
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Copy and paste, then move copy off original.
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Select the original, ungroup and deselect the left start
foot model and the left step foot model, then press delete.
For the first right footfall, I also drop the left start foot model to
use for measurement of the left carry. The end R-R is the right carry.
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Rotate the copy for angles and offsets, then position
the left start foot model over the gray step model just dropped.
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Copy and paste, move copy off original.
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Continue for as many steps as you like.
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At the last footfall, the left one for me, I do all the
rotations and placement as if for another normal step, then drop the
right start foot model instead. This gives the measurement for the right
carry.
I make two full strides for each foot, using 6 models. This
is to help recognize plotting error. For example, if the two right strides
are not the same length, there has been an error. Theoretically, they should
be identical. To incorporate a normal straight foot angle of,
for example, 6 deg, select all the footfalls of the new plot, and the
vertical line, and group. Copy and paste, then use the arrow keys to move
the copy to the side so you maintain the original. Select the copy and
ungroup. Select each footfall and rotate the left footfalls by 6 deg CCW,
and the right footfalls by 6 deg CW. If footprints were put over the foot
models, this would look like a normal set of footprints, but not realistic
in that they are perfect except for one or a few constant deviations.
Throughout the entire sequence, things like the DOT line or a COG point can
be dropped at various stages of the step to get an idea of the changes to
these factors. However, since the model doesn’t represent real body
movement, only step line position, care has to be taken that the elements
actually reflect something relevant. Things like this will come out as more
people work with the model. Plots can be made with any number
of steps to see even broader patterns, if desired, or a different type of
test foot model for each step. Because the start footfall position is always
known, any type of plot model could be inserted into the pathway, as long as
it starts at the proper orientation. This is one of the many advantages of
this method and will help in the development of the analytical model.
The gray footfalls represent a foot in the air, and are used
to define the left and right carry measurements (see Fig.7). For my plots,
these are black and regular footfalls are gray. Measuring
Distances After the plot is made, ungroup each footfall
once. Select the hidden line under each and extend the top end to the heel
point of the next footfall of interest. Usually, two lines from each
footfall are needed, so copy and paste the line, the extend the end of the
copy to the next point of interest. I use a 6000%
magnification to help place the end of the line on the heel point When all
the heel points are connected, move each line to the side with only the
arrow keys, and use the dimension tool to determine exact length. Record the
values in a table, and leave it on the page with the copy of the sample
model. If I select all the footfalls in this plot then group
them, I can move or rotate it as a unit in order to overlay onto other plots
(see Fig.8), to see variations in pattern, or take parts of different plots
and put them into one, even for each stride or step.
A lot more could be said regarding this kind of manipulation, but I’ll
let you experiment on your own first, to see what kind of information you
can come up with. All this is new, so you may be the first to see something
important.
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Part I (Page
1, Page 2) Part IIa Part IIb
(Page 1, Page 2)
Part IIc Part III
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