10. Step, Carry and Stride

Stride = carry + step (vectors).

Step-line is a product of step-out and rear-stretch-lines (pelvic stretch plus rear-leg-line), and foot offset, and is the part of the stride that can be controlled.

Aberrations and push-off angle don't affect the step-line.

Carry-line changes as a consequence of the other foot's previous step-line, foot offset and foot angle, as well as the current step’s push-off angle, aberrations, and pelvic stretch (and straddle-line). So, distance and direction variations in one foot are reflected by changes in the corresponding carry-line for the other foot.

For the step and carry lines, it doesn't matter that the foot is in the air at one of the points, it's just assumed the foot is planted at the reference spot, the measurement is taken, and the foot resumes its travel path. Also, it doesn't matter whether the path of the foot in the air ever passes the start/stop position, it's still valid as a standard reference because of the vector nature of the measured distances.

The stride-line is dependent on the step and carry-lines, and, so, varies as they vary.

How each stride-line is changed when turning depends on the foot that's used to make the turn. For a left turn, the right stride must be longer than the left under all conditions.

But, if the right foot makes the left turn (the outside foot, an internal rotation) the left carry is shortened, and so the left stride-line is shortened (the left step-line stays the same) and the total distance traveled for the same number of strides is decreased. (The Wstr is also increased.)

If the left foot makes the left turn (the inside foot, an external rotation), the right carry is lengthened, so the right stride-line is lengthened (the right step-line stays the same) and the total distance traveled for the same number of strides is increased. (The Wstr is also decreased.)

So, if two runners are identical in every way (including cadence) but how they turn, the runner using the inside foot and external rotations should beat the runner using the outside foot and internal rotations.

11. Straddle-line, Straddle, Straddle Width, Stride Width, Step Width, Walking Base and Walking Straddle

The straddle-line is the only measurement independent of DOT changes. It can only be changed by real or apparent rotation at the rear-pelvic joint.

Straddle, straddle width, stride width, step width and walking base are, as far as I can tell, minor variations of two main definitions.

1) The sum of the perpendicular distances between the points of initial contact of each heel to the line of forward progression

or,

2) The perpendicular distance of the point of contact of the heel-edge to a line connecting the appropriate points on the other foot's adjacent two heel-contacts.

For #2, the left stride width, for eg., is the perpendicular distance of the contact point on the right heel-edge, to a line connecting the corresponding points on the heels of the appropriate two adjacent, left footfalls.

Walking straddle (Wstr) is the accurate version of (2), with the measurement taken at the heel-points, not heel-edges. This is an important measurement, since it's also affected by how a person is turning over the stride.

12. Aberrations

Aberrations are everything that introduces foot-line rotations and/or heel-point shifts while vaulting on the planted foot, between the time of heel-contact of the current step and the next heel-contact of the other foot. They represent all relevant movements of the planted foot. However, aberrations do not occur over the entire time the foot is in contact with the ground, only between sequential heel-contacts.

Part of the time that the foot is in contact with the ground, when it's the rear-foot in double stance, is not included. The heel-contact of the forward foot takes the snapshot of the rear-heel-point and foot-line positions, and subsequent movements of these are irrelevant, since the reference has shifted to the front foot. Aberrations are totally isolated from the other parameters by the choice of the time of the snapshot as heel-contact.

This is a fundamental parameter. Aberrations are described by a line description of the foot-line rotation, as well as by the distance from last heel-point and angle from the foot-line for heel-point shift.

Many (most) people routinely balance and rotate on or near the ball or toe of the planted foot when swinging the other foot forward, or the front foot makes contact with the heel-edge before the heel-point. Both of these are aberrations. A spin turn is an aberration, but a step turn isn't.

Aberrations probably occur in virtually every step, such as when the heel-point of the rear-foot is raised off the ground, but the toe is still touching, when the front heel hits the ground. The vertical part doesn't matter, but the path of the heel-point during the rotation up is an arc, not vertical line, so there is also a change in it's 2D position. That matters.

The first straight line over the step, the step-foot-line of the previous step, is the start position for aberrations; and the second straight line over the step, the start-foot-line of the current step, is the stop position.

Unless otherwise stated, in the general discussion it's assumed there are no aberrations.

13. Vectors

A person walking is a vector system. The Step Model is based on this vector character, and all the lines are vectors (unless otherwise noted), which may be projections of other vectors onto the 2D plane of interest. All are derived using the 4 minimum points of gait and foot-line.

14. Accuracy vs Precision

There are many references to the accuracy of measurements.

The term accuracy, however, is often confused with precision. The two are not the same.

All measurements have an accuracy and a precision, and each value is usually described on a general scale from low to high.

Precision can be considered to be conforming exactly to a standard, and higher precision means using smaller and smaller measurement units. So, 3.0000" has a higher precision than 3.0".

Accuracy refers to closeness to the real value. The ability to know or measure an actual real value doesn't negate the fact there's only one real value for any measured distance, with theoretically "infinite" precision.

Higher accuracy means you're getting a number that's closer to the real value, and one way it can be done is using smaller measurement units, that is, with higher precision. So, if the real value is 3.00000...", 3.000" has higher accuracy than 3.0", as well as higher precision.

But, with a real value of 3.00000...", 3.2000" has higher precision, but lower accuracy, than 3.0" A value with higher precision can have lower accuracy, and vice versa.

Accuracy is affected in several other ways, unlike precision.

For eg., the foot (pitch) angle of the planted foot has no effect on the total distance traveled for the foot, so, if changes in the foot angle changes the measured distance for step-line, that method of measurement is not accurate, since it can't be trusted to represent the real measurement for the factor of interest alone, the total distance traveled for the foot. Accurate values, like the total distance traveled for the foot, can't vary with other, independent values, like foot angle or shoe size (eg. when using heel-edges), unless it’s defined as such.

This variation with other, independent variables is a consequence of the point of measurement not being on the actual points of interest, the heel-points, but rather shifted to the side to the heel-edges. Heel-edge measures may be easier, but they're not accurate. They include an extraneous vector component related to the shoe's size, shape, position and the point chosen for measurement. ie. the extra vector is from the heel-point to the point on the heel-edge chosen for measurement. (Note: These measurements could be used if this extra vector was included.)

So, when referring to values or techniques as inaccurate, I mean they can't always be trusted to represent the real value alone. They include one or more undefined, independent elements (like part of the pelvis-line) or vary with other, undefined independent variables (like foot angle or shoe size).

An accurate measurement can contain more than one element, and unknown or "theoretical" elements, as long as it's defined as such.

The L/R line is an accurate measurement of the vector sum of the rear-leg line, pelvic stretch (theoretical), straddle line (theoretical) and step-out line (other vector "sets" also describe L/R). The step-out vector (sum of the thigh and shank vectors, plus a small one from the ankle to the heel-point) could be described as the vector from the step-pelvic joint to the step-heel-point, whether or not it's known exactly what components comprise it.

All types of measurements are important, as long as it's realized exactly what they contain.

For this method, since the required points and line are exactly defined, increasing precision will also increase accuracy. This assumes the 4 points and line can be exactly identified every time. So, the specific experimental methodology used may introduce inaccuracy, even with greater precision.

15. Limb Dominance

Limb dominance was always thought to be the main influence on path deviation, through its effect on step length.

But, although differences in step length for the left and right can't cause direction changes, limb dominance can affect walking pattern by influencing any or all of the 8 fundamental parameters. Each parameter is dependent on a specific physical action, and dominance would show as a standard influence on one or more of these, in the same way as it influences step length (which is a product of the parameters).

For a single person, the exact result of dominance on gait may not be possible to predict every time, but there should be general trends or patterns over a larger group. This has to be discovered.

The study limb dominance and how it affects the parameters, and overall path characteristics, would be a large part of the application to human tracking and SAR.

16. The Rotating Reference Grid

The recognition that the reference grid rotates during walking is one of the most important aspects of this method.

Measurements related to distance and direction while walking have to be based on the orientation of the skeletal frame, not a stationary, or otherwise inappropriate, external reference plane or line. The step-foot-line of the previous step (or rear-leg-line, if there’s no foot-line) provides the required initial angular reference, and the rear-leg-line is used to orient the Step Model.

During a step, aberrations and push-off angle change the orientation of the current Step Model, but foot angle and foot offset do not.

Application of the rotating grid to previous and current gait work may shed light on many apparently anomalous or erratic results.

17. Balance

The fundamental parameters don’t have anything to do with balance directly, but the plane of the floor is used to study both.

Variations in factors affecting balance will likely lead to variations in the parameters. A COM plot wrt each of the parameters will aid in measuring the specific distance and direction changes due to COM shifts.

This provides the opportunity to better understand external factors which affect the COM, and how they alter walking pattern (like a heavy back-pack or other problem changing the control of the body COM). Gait changes due to balance deviations could be important for many areas of gait research, as well as human tracking and SAR.

18. Movements Affecting the 8 Parameters

The 8 parameters are the basic measurements derived from generalizing the human skeleton, wrt walking, into the 4 minimum points of gait and foot-line.

But, changes in these parameters aren’t as simple as the Step Model implies, since lateral joint rotations and segment length changes can come about from factors not associated with those joints or segments.

Though strictly 2D interpretation provides a very great deal of info, the consideration of vertical co-ordinates allows much more specific recognition of the physical processes responsible for anomalies. The 3rd dimension is very useful to highly detailed interpretation of the 2D data.

Apparent rotation at the pelvic joints, for eg., could be the result of several other movements, like lateral ankle or knee rotation, or axial rotation (along the thigh) at the pelvic joints (if the knee is flexed), none of which involve any real lateral rotation at the pelvic joint. Pelvic tilt, for eg., would be measured as a foot offset and foot angle.

Detailed investigation and categorization of the factors affecting each parameter is necessary.

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