Part IV  The Step Model and Footfall Plots
 Introduction
 The Standard Model
 Test Step Model
 Creating Footfall Plots
 Plotting Results
 Plotting Results Analyses
 Stepline
 Strideline
 R/Lline
 Walkingstraddle
 Etc., etc.
1. Introduction
The Step Model geometrically displays the critical measures and rotation
points needed for the creation of realistic footfall patterns.
It
exactly defines foot placement, not the real movement of any body segment
during a step, and organizes the distance and direction relationships for
the 4 minimum points of gait and footline, at the instant of heelcontact.
Each Step Model defines a 2D stepplane. The orientation of this plane
is arbitrary. Sequential planes are related since the stepheelpoint in the
current plane is the same as the startheelpoint in the next.
Direction changes during a step are described by 4 of the fundamental
parameters: 1) aberrations 2) pushoff angle 3) and 4) foot angle
and foot offset.
They are all accounted for by rotating the whole
model, then aligning the appropriate heelpoint. The sidestep nature of
foot offset is built into the model, and doesn't need extra treatment. If
there's an aberration, the whole model is rotated for the rotation part, and
then the model's start heelpoint aligned with the end heelpoint of the
aberration.
The circle for the head (COM, more or less) doesn't
represent the real position of the head, it's just to help visualize. And,
hip joint architecture may introduce a minor variation in the stepout arc
characteristics, but that's left off for now.
2. The Standard Model
These are the values for
the standard model, and are the minimum number of measurements needed.
Stepoutline = 15” Pelvic stretch = 0" Rearlegline = 15”
Straddleline = 8”
Unfortunately, literature walking base
measurements can't be used to estimate straddleline. Walking base changes
with angular changes in the body DOT (even if walking straight), but
straddleline doesn’t, so the two aren’t comparable, even though they're
related. Walking straddle is walking base, but measured at the heelpoints
instead of the point of contact of the heel. For str8, Wstr varies as shown
below.
Walking Straddle 
L15{0}[15] str8 and
R15{0}[[15] str8 
8.00 
 walking straight, no turns, walking
straddle (Wstr) = straddleline (str) 
L15{0}[15]str8:L10R and
R15{0}[15]str8:R10L 
10.57 
 walking straight, both feet 10 deg
internal turns, Wstr > str 
L15{0}[15] str8:L10L
and R15{0}[15]str8:R10R 
5.35 
 walking straight, both feet 10 deg
external turns, Wstr < str 
For the standard model, I also include the foot models to make analyzing
the plot more intuitive, but it isn’t required. I could just as easily be
using a dot or cross, since the heel point position is the only thing that
matters for distance and direction. But adding the foot model is very easy
to do and gives a much more realistic graphic representation. It also makes
it possible to see body DOT relationships, and much easier to see plotting
errors, distance relationships, and characteristics derived from plot
overlays.
Foot model length = 8”, measured from the heelpoint (which is the
rotation point for foot angle) to the tip of the toe, along the footline.
The horizontal line is 2” and is only to help visualize.
Gray
stepfoot models represent footprints, and black referencefoot models
indicate a foot in the air, or some other standard reference.
When
the straight foot angle is 0 deg, so there's no pushoff angle, as in all
the plots so far, the stepfootline is parallel to the rearlegline of the
other foot's next step.
Group the horizontal line and footline, and
change the rotation point to the heelpoint.
Group the stepoutline and the stepfoot model and change the rotation
point to the bottom of the stepoutline (The rotation point for foot offset
is the steppelvic joint, which is the bottom of the stepoutline.). Then
group this figure with the rearstretchline and referencefoot model.
Complete the figure as shown in Fig.10.
Group the whole thing
after it’s built.
3. Test Step Model
When applied to real data,
each step would have a unique model constructed from the data points.
For standard plots, though, it's easier to have just one. Luckily, the
left and right steps can be put into one, even if each has different
stepout and rearleg lines, as well as independent foot angles and offsets,
pushoff angle and aberrations. As long as the straddlelines are the same,
which means the same pelvicstretch.
If the notation for a Step Model
has no reference to the other foot, it's for only one step. Eg.
L15{0}[15]str8:L(5)R10R shows only the parameters for the left step. In
this model, the right stepline has no foot angle or offset, is dimensioned
the same as the left, and is only to help visualize.
L15{0}[15]R15{0}[15]str8:L10L represents both steps, with only the left
showing a direction change.
So far, I've kept the straddleline
constant in all plots, and include both steps on a single model.
Foot offset / Leg angle Calculations:
The linear
value of foot offset is difficult to use, though it may be easier to
visualize. Luckily, this can be converted to leg angle, if the stepoutline
is known.
At the instant of heelcontact, 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 stepoutline, its path would
describe an arc, the stepoutarc.
Stepoutline = radius of the stepoutarc = r = 15”
If you could spin your leg all the way around, the stepoutline would be
the radius of a circle,. Since r is known, the circumference of the circle
can be calculated.
circumference of stepoutcircle = 2 (pi) r
=2
(3.14)15.0”
=94.2”
and,
360.0 deg leg angle / 94.2"
foot offset
= 3.82 deg leg angle / " foot offset
or,
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" (along the arc) foot offset. It's much
easier to refer to foot offset as deg leg angle, eg. (10)L.
Changes
to the standard model change it's overall dimensions, making it more
difficult to accurately place (if you want to also use a stationary line or
point as a reference), so set up a standard page with the standard step
model already positioned on the start. Somewhere on the page, add a blank
table to record the distance values from the dimension lines, and a box with
the line description of the sample Step Model values.
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(3)L2L:R5R (this person
would have equal left and right stride measurements, but the path would have
an extra shift left at every left step):
 Select the standard Step Model and ungroup.
 Select the left stepoutline/foot model and rotate 3 deg CCW.
 Ungroup the left stepoutline/foot model, then select the left
stepfoot model.
 Rotate 2 deg CCW.
 Select the right stepoutline/foot model and ungroup.
 Select the right stepfoot model and rotate 5 deg CW.
 Select entire figure, then group.
 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.
Foot
offset is built into the model. Foot, pushoff and leg angle rotations are
done when plotting.
4. Creating Footfall Plots
 Start with the standard page and modify the standard Step Model.
 Copy and paste the test Step Model and move the copy off the
original to keep.
 Copy and paste the test model again. This will be for the first left
step.
 Move the copy off the original, and rotate for the left foot offset
and angle and pushoff angle. For L(3)L2L:R5R, rotate 5 deg CCW.
 Align the left startheelpoint on the copy with the left
stepheelpoint of the last model.
 Copy and paste this model, then move the copy off the original.
 Rotate the copy for right foot angles, offsets etc., 5 deg CW, then
align the right startheelpoint with the last model's right
stepheelpoint.
 Copy, paste, and move the copy off the original and rotate, etc.,
for as many steps as you like.
 Copy and paste the entire path figure with models, and move to a
reference page. Make sure to keep its line description with it. Footfall
patterns look alike without the descriptions.
 Go back and select the first model. By ungrouping and deselecting
lines and points, you can drop any reference figures you want. For the
first, I drop the stepfoot model (the left), startfoot model, trunk
direction, pelvisline and head dot. Delete the rest of the figure.
 Select the next model. Ungroup and deselect the referencefoot model
(for right step and carry measures), the stepfoot model, trunk
direction, pelvis line and head dot. Delete the rest of the figure.
 Select the next model. Ungroup and deselect the stepfoot model,
referencefoot model (for left step and carry measures), trunk
direction, pelvisline and head dot. Delete the rest of the figure.
 Select the next model. From here on, drop the trunk direction,
pelvisline and head dot, and the foot model of interest. (The right for
this one, left for the next, etc.) For recreating a real path, the
referencefoot models would be dropped for every step as well, not just
the first two. Also, other reference points and/or lines can be added to
the original model and dropped at each step.
 Continue until you get tired of it.
I use 7 models, including the first one. This is to help recognize
plotting error. For example, if the right strides aren't the same length,
there's been an error. Theoretically, they should be identical.
Throughout the entire sequence, "outside" points or lines can be dropped to
see the variations in these factors.
Plots can be made with any
number of steps to see even broader patterns, if desired, or a different
type of test Step Model for each step. Because the start footfall position
is always known, any type of Step 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.
The black footfalls represent a foot in the air at the reference
position, and are used to define the left and right carry measurements.
Dimensioning yields the distances between relevant heelpoints. A table
such as the one below is the result.
To manipulate the path, select all the footfalls in a plot then group.
Since the start footfall is identical for all the plots, they can be
overlaid to show subtle elements of path deviation impossible to see
otherwise.
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