(C) Definitions
The term "line" refers to a vector quantity according to this measurement
system. This is to avoid conflicts with inaccurate, historical terms for
"lengths", such as step length. So, stepline is the accurate version of
step length.
All lines and angles are purely vertical projections
onto the 2D (step) plane of interest.
All of the terms are derived
using the 4 minimum points of gait and footline.
=
Aberration (A)  Anything that changes the location of
the heelpoint and/or rotates the footline, after initial contact of the
heel and before heelcontact of the other foot's next step. They can be
generally described as movements of the planted foot. This is the 1st
direction change over the step, and it starts at heelcontact of the
previous step.
Aberration = A:10.25(12.3R)23L = 10.25” heelpoint
shift at 12.3 degR to start footline, and 23 degL footline rotation.
The first straight line
over the step, the stepfootline of the previous step, is the start
position for aberrations; and the second straight line over the step, the
startfootline of the current step, is the stop position.
Aberrations do not occur over the entire time the foot is in contact with
the ground, only between sequential heelcontacts. Part of the time, the
second double stance after initial heelcontact, or terminal double stance,
is not included. The heelcontact of the forward foot takes the snapshot of
the rearheelpoint and footline position, the endpoint for aberrations,
and subsequent movements of these are irrelevant, since the reference has
shifted to the front foot, and the next step.
Some rearfoot
movements after front heelcontact may influence the characteristics of an
aberration in the forward foot, but this would require a secondary analysis
to determine. The measurement system would only see the change in footline
and/or heelpoint positions for the front foot, with no reference to cause.
Heelpoint shifts are described by a linear distance from the last
heelpoint and an angle with respect to the first footline; and footline
rotation (foot angle change) is described by an angle wrt the first
footline.
Slides, spins, rotations on the ball of the foot or toe, etc. are
aberrations, as is when the rearheelpoint is raised off the ground when
the stepheel contacts the ground, when pushing off the reartoe. A spin
turn is an aberration, but a step turn isn't. Some aberrations are
controllable, others are not. A spin turn is controlled, a slide may or may
not be.
Also, when the stepheel touches the ground before the
stepheelpoint, this is an aberration, even though it would be a
pathological gait for the heelpoint to contact the ground at the same time.
This is why aberrations may be present in everyone's normal walking pattern.
The time snapshots used to define the parameters is chosen as
heelcontact, rather than heelpoint contact, to separate this very complex
entity from the other, "simpler" parameters.
This is a fundamental
parameter.
Carryline (C) – For the left foot, the line from the
heelpoint of the last left footfall to the referenceheelpoint of the
current step (left foot directly adjacent to the planted right foot, at
straddleline apart, and a line connecting the left and right heel points is
perpendicular to the rearlegline; the left foot is in the air, as for
stepline) after the body has been shifted for aberrations and pushoff
angle. Stride = carry + step (vectors).
Carryline is the part of the
stride that varies when turning, and is dependant on the other foot's last
pelvicstretch, straddle, stepout and rearleglines, foot offset and foot
angle, and the current step’s aberrations and pushoff angle. So, distance
and direction variations in one foot are reflected by changes in the
corresponding carryline for the other foot.
TThis line connects a real point and a theoretical
reference point.
Foot angle (FA) – similar to the foot’s pitch or pitch
angle. The angle the footline makes with the stepoutline. This
measurement must include the designation “left” or “right” ; CCW or CW; or
““ or “+”. The rotation point for foot angle is the heelpoint, and it’s
changed by real or apparent rotation along the 3D axis of the stepoutline,
at the steppelvic, stepknee and/or stepankle joints. With foot offset,
these are the 3rd and 4th direction changes over the step.
NOTE: This
is different from previous definitions of foot angle. Foot angle, in this
method, is measured with the stepoutline as the zero mark, but previous
definitions relied on the line of forward progression (or some other near
equivalent) as the reference line. So, footline rotations from both foot
offset and foot angle would have been seen as all from foot angle.
Foot angle = 10L = 10 deg left
When there's foot offset and foot
angle in the same step, the leg is rotated for the foot offset first and the
footline is held constant wrt the stepoutline, then the foot rotated for
the foot angle.
Reference to foot angle in general discussion is
often a simplified version.
I sometimes refer to foot angle changes
to indicate body DOT changes. Body DOT change is actually defined by the sum
of the foot and pushoff angles. But, since this would needlessly complicate
the discussion, I assume that normal straight foot angle and pushoff angles
are 0 deg, unless otherwise stated. Then, foot angle changes exactly
describe the relevant body DOT changes.
Straight foot angle refers to
the foot angle which equals the pushoff angle in number, but is opposite in
rotation. This results in 0 deg body DOT change (foot offset and aberrations
could still cause a body DOT change in the same step).
So, if a
person steps out with a 6 deg CCW foot angle, and pushes off at an angle of
6 deg CW, body DOT change is 0 deg, and the straight foot angle was 6 deg
CCW. If a person steps out with 2 deg CCW foot angle, and pushes off at an
angle of 6 deg CW, body DOT change is 4 deg CW, and the straight foot angle
was 6 deg CCW for that step.
This is a fundamental parameter.
Footline (FL)  A line connecting the center of the
calcaneus and the second metatarsal head. The line must go through the
heelpoint, so the heelpoint position doesn’t move with foot line
rotations. Since it’s changes that are important, the exact position chosen
isn’t critical, as long as it goes through the heelpoint and is the same
for all measurements.
The stepfootline of the last step is the
first straight line for the current step, and is the start position for
aberration measurement. The footline after aberrations is the second
straight line, the 0 mark for pushoff angle, and the stop position for
aberrations. The stepfootline of the current step is the 5th straight
line, as well as the first for the next step.
The footline is a
vector quantity, showing the length and direction of the foot.
Foot offset (FO) – the distance, measured along the
stepoutarc or as a linear distance (see Fig 3), that the heelpoint is
planted off of the straight line for that foot. This must include the
designation “left” or “right”; “CCW” or “CW”; or ““ or “+”, and is changed
by real or apparent lateral rotations at the step and rearpelvic joints,
with much smaller contributions from the stepknee and/or the stepankle
joint. The rotation point for the measurement of foot offset is the
steppelvic joint. With foot angle, these are the 3rd and 4th direction
changes over the step.
Foot offset = (10)L = 10 deg leg angle left
Foot offset due to pelvic joint rotations may be an important direction
control mechanism.
And, the Step Model implies that foot offset is
due to rotation only at the steppelvic joint. But, foot offset is caused by
rotation at the rearpelvic joint as well (besides the much smaller
contributions from the knee and ankle joints), since the pelvis and stepout
lines maintain a 90 deg relationship during the rotation of the pelvisline.
So, a person could have a large foot offset with no rotation at the
steppelvic joint. Rotation at the rearpelvic joint not only causes a foot
offset, but also changes the straddleline and pelvicstretch.
From
Fig 6, the total contribution to foot offset from step and rearpelvic
joint rotations is defined by:
A  B = foot offset (leg angle) for a
left step and,
B  A = foot offset (leg angle) for a right step.
A is the rearlegline  pelvisline angle, and B is the stepoutline 
pelvisline angle. A negative value is a left (CCW) rotation. So, 0 foot
offset doesn't guarantee there's no rotation at the pelvic joints. When A=B,
pelvic joint rotation does not contribute to direction change via foot
offset. The normal, straight value of A and B is 90 deg.
Foot offset
has a corresponding leg angle, and, during the stepoutline rotation, the
footline remains fixed wrt the stepoutline.
And, there's an extra
angular deviation due to the sidestep nature of the offset. For
L15{0}[15]R15{0}[15]str8:L(10)L:R10R (walking "straight"), the path shows an
extra shift of 2.8 degL because offset was used for direction changes in the
left foot and foot angles in the right.
It's much easier to use foot
offset in terms of degree leg angle. So, with 15" stepoutline, a value of
45 deg leg angle CCW (left) means an offset along the arc of approx. 11.78"
left, or a linear offset of approx. 10.61". So, this is designated as (45)L,
rather than by the linear or arc length values.
This is a fundamental parameter.
Headdot  a dot at the center of the pelvis line. It
doesn't represent the real position of the head at any time, and the actual
location of the head has no effect on the position of the headdot. It's
mainly to help visualize.
Heelpoint (HP) – the
point of contact with the ground if we had peg legs that went to points. The
point that wouldn’t move if you spun around on the heel of one foot. The
foot line must go through the heelpoint. Relevant distance measurements
that do not begin and end at a heelpoint aren't accurate measures of total
distance traveled. The heelpoint pattern exactly defines direction and
total distance traveled for each foot.
Leg angle (LgA)
– when the leg is extended to plant the foot at heelcontact, the angle the
stepoutline makes with an extension of the rearstretchline (actually the
rearlegline, but any line parallel to it can also be used). This must
include the designation “left” or “right” ;CCW or CW; or ““ or “+”, and is
changed by real or apparent lateral rotations at the step and rearpelvic
joints, with much smaller contributions from the stepknee and/or the
stepankle joint. The rotation point for the measurement of leg angle (foot
offset) is the steppelvic joint.
Foot offset is usually expressed as
deg leg angle. Foot offset = (10)L = 10 deg leg angle left
Any foot offset has a corresponding
leg angle, and when the person balances onto that foot to take the next
step, the body DOT is changed by the amount of, and in the direction of, the
leg angle. ie. the new body DOT, before foot angle rotation, is parallel to
the stepoutline.
Leg angle can be calculated from the stepoutline
and foot offset values (see foot offset, above).
L/R (R/L)line (L/R or R/L)  Line from the left (right)
startheelpoint to the next right (left) stepheelpoint. The first letter
designates the rear foot.
A product of 4 distance elements (rearleg,
straddle and stepout lines and pelvicstretch) and one direction element
(foot offset). This is what much current literature calls step length. It's
not an accurate measurement of the distance traveled by the foot over the
step, but is still very useful, since it varies with foot offset, but not
foot angle, pushoff angle or aberrations.
The vector representation
of L/Rline would be equivalent to stepline, except L/Rline also contains
the straddleline (which represents a perpendicular shift of the
stepoutline wrt the rearlegline, see Fig.7).
Pelvicstretch (PS)  Line from the rearpelvic joint to
the point of connection of the straddleline with an extension of the
rearlegline. This is only changed by real or apparent rotations at the
rearpelvic joint.
It can be + or , based on it's affect on
rearstretchline. Rearstretchline = pelvic stretch + rearlegline. For a
step with the left foot, CW rotation at the rearpelvic joint gives "+"
pelvicstretch and increases the rearstretchline, and CCW gives "", which
decreases rearstretchline.
Pelvicstretch and straddleline are the
sides of a right triangle, with the pelvisline as hypotenuse.
This is a fundamental parameter.
Pelvis direction  Arrow starting on the head dot, and
in the center of, and perpendicular to, the pelvisline. This is not a
vector and does not show a DOT, but shows the direction the front of the
pelvis is facing.
Within one step, pelvis direction can be changed by
aberrations, pushoff angle and/or real or apparent rotation at the
rearpelvic joint. Between steps, of course, it's potentially affected by
all 4 of the direction parameters, but none of the linear parameters (ie.
wrt direction, not location).
Pelvisline (PL)  line connecting the centers of
rotation of the pelvic joints. The pelvisline is the maximum value for
straddleline, and is the hypotenuse of a right triangle, with
pelvicstretch and straddleline as the sides.
Pushoff angle (PO) – The angle between the
startfootline and the rearlegline. The startfootline is the zero mark.
This is the 2nd direction change over the step, and is affected by variation
in muscle action in the leg and foot when pushing off the planted foot, as
well as by path specifics (momentum, etc.) prior to the heelcontact.
Pushoff angle = <10>L = 10 deg left
This is a fundamental
parameter.
Rearlegline (RL)  Line from the startheelpoint to
the rearpelvic joint. This is the equivalent of the stepoutline, but for
the rear foot, as far as the 3 vector components: 1) the rearthigh, 2) the
rearshank, 3) a vector connecting the center of the rearankle joint with
the startheelpoint.
An arrow from the startheelpoint to
rearpelvic joint shows the straight line forward at heel contact, and is
the reference line for initial orientation of the Step Model. It's also
related to stepoutline due to the physical connection through the body.
When viewed from the side, a person in double stance forms a
pseudotriangle, through the pelvisline. (see stepoutline, below).
The rearlegline could also be considered the "pushoffline".
This is a fundamental parameter.
Rearstretchline (RSL) – Line from the
referenceheelpoint to the steppelvic joint.
Since
rearstretchline is equivalent to the vector sum of the rearlegline and
pelvicstretch, the rotational relationship between the rearleg components
is relevant. So real or apparent rotations at the rearpelvic joint, the
rearknee joint and/or the rearankle joint change rearstretchline.
Rearstretchline = pelvicstretch + rearlegline (linear and vector)
Rearstretchline + stepoutline = stepline (vectors).
Stepline (S) – For the left foot's step, the line from
the referenceheelpoint of the left foot (when it’s directly adjacent to
the planted right foot, at straddleline apart, and a line connecting the
right and left heelpoints is perpendicular to the rearlegline, left foot
is in the air), to the heelpoint of the next left footfall. It's a product
of 3 distance elements (rearleg and stepout lines and pelvic stretch) and
one direction element (footoffset).
Stepline = stepoutline +
rearstretchline (vectors).
Foot and pushoff angles and aberrations
have no affect on stepline. If there's a foot offset, the stepline will be
less than stepout + rearstretch lengths, because it's a vector, not
linear, sum.
This connects a theoretical reference point and a real
point.
Stepoutline (SO) – Line from the steppelvic joint to
the stepheelpoint. The start of this line, the steppelvic joint, is one
of the rotation points for foot offsets. The stepoutline is the 4th
straight line forward over a step, and is the sum of 3 vector quantities; 1)
stepthigh, 2) stepshank, and 3) a vector connecting the center of the
stepankle joint with the stepheelpoint.
Stepoutline +
rearstretchline = stepline (vectors).
When there is foot offset
(leg angle), the stepoutline shows the new straight line when the person
balances on that foot.
Stepoutline is changed by appropriate
rotation at the steppelvic joint, the stepknee joint, and/or the
stepankle joint.
This is a fundamental parameter.
Stepoutarc  the arc described by the stepheelpoint,
when the leg is extended at the instant of contact, and the stepfoot is
moved left and right. The rotation point for the stepout arc is the
steppelvic joint. The radius of the stepout arc is the stepoutline. (see
also, foot offset).
Stepplane  the 2D plane of the Step Model, which must
include the start and stepheelpoints, but is otherwise arbitrary. All the
lines and points in the Step Model are projections onto the stepplane,
which is usually the flat floor, but can be any 2D plane.
The
orientations of sequential stepplanes show effects of terrain and other
vertical factors.
Adjacent stepplanes are related since the
stepheelpoint from the current plane is the same as the startheelpoint
in the next one.
Straddleline (str) – Line perpendicular to the
rearlegline, connecting the steppelvic joint with an extension of the
rearlegline. This value is constant with angular changes to the body DOT.
Real or apparent rotation at the rearpelvic joint is the only thing that
affects the straddleline, and this rotation also changes the pelvicstretch
and induces a foot offset.
The maximum value for straddleline is the
pelvisline. The straddleline and pelvicstretch are the sides of a right
triangle, with the pelvisline as the hypotenuse.
When the subject is
walking straight with no aberrations, foot or pushoff angles or foot
offsets, straddleline = walkingstraddle, but this is the only condition
where that's true.
This is a fundamental parameter.
Strideline (St) – Line from the heelpoint on one foot
to the heelpoint on the next footfall of the same foot. This connects two
real points.
Strideline between the current and next step is a
product of 9 distance elements (current and next step's: rearleg, straddle
and stepout lines and pelvicstretch; and aberrations from the next step)
and 5 direction elements (current step's foot offset, foot angle; and foot
offset, pushoff angle; and aberrations from the next step).
Strideline = carryline + stepline (vectors).
If there are any body
DOT changes, the strideline will be less than step + carry lines, because
it's a vector, not linear, sum.
Walkingstraddle (Wstr)  The perpendicular distance
between a line joining the two corresponding heelpoints of interest and the
other foot's heelpoint within that stride. Almost the same as walking base,
but the measurement is to the heelpoints, rather than the points of initial
contact of the heels.
Walkingstraddle is a product of the same 14
elements as strideline. Left and right Wstr aren't the same if there are
asymmetric turns or straddleline differences in adjacent steps.
In
order to compare walkingstraddle and walking base, since the distance from
heeledge to heelpoint is about 1.5" for an adult, walkingstraddle should
be about 3" longer than walking base. Literature walking base measurements
suggest an average of 3", so an average walkingstraddle should be about 6".
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