| (A) Introduction A2. Five Central Concepts Five concepts are very important in this measurement system: i) the four 
	minimum points of gait (and foot-line), ii) using the heel-point for 
	measurements, iii) the time point of the snapshot as heel-contact, iv) the 5 
	straight lines over the step, and v) the standard start position.  i) The identification of the 4 minimum points of 
	gait: 1) the step-heel-point, 2) step-pelvic joint, 3) rear-pelvic joint and 
	4) start-heel-point, is the main principle. Foot-line is included, if 
	possible, because it adds a great deal of detail for such a simple factor, 
	but it's not essential. These 4 points (and line) are all that's necessary 
	to describe distance and direction for a person walking, wrt any 2D plane.
 The entire gait measurement system, and all the terms and definitions, 
	are based on the projection of the 4 points (and line) onto a specific 2D 
	plane. Their relative positions are what's represented by the 8 fundamental 
	parameters of gait. But, they don't define how people walk. They describe a 
	series of consistent, relevant measurements, based on body segments, which 
	will be useful to investigate how people walk.
 
 Only the two 
	heel-points are required to take measurements like step, stride and walking 
	base, but adding the pelvic joints allows the identification of 6 of the 8 
	fundamental parameters, with foot and push-off angles being seen as a single 
	direction change. Step, stride and walking base are products of these 
	parameters.
 
 Adding the foot-line allows the separate measurement of 
	foot and push-off angles, as well as the identification of 3 of the 5 
	straight lines over the step.
 
 Fortunately, because the body can also 
	be represented as vectors, analysis is much easier since vector techniques, 
	equations and properties are relevant. This validates the 2D projection, and 
	allows for the definition of the standard start position, among many other 
	things.
 
 Now, direction and distance changes over the step can be 
	separated into contributions from specific joints and body segments, so 
	changes in each parameter can be related to variations in more strictly 
	definable muscle and joint sets.
 
 Other reference points or lines can 
	be tracked by incorporating them into the model, but the projection of the 4 
	points (and line) is the base reference.
 
 
 ii) The heel-point is 
	the point on the bottom of the heel that wouldn't move if you spun around on 
	your heel on one leg, assuming your leg was a stationary vertical axis. When 
	this is used as the point for measurements, distance and direction 
	variations introduced when the edge of the heel is the reference point are 
	removed, and it also eliminates the requirement for contact with the ground.
 
 
 iii) The time point chosen for the snapshots, the instant of 
	heel-contact, allows the isolation of the 8th parameter, aberrations, which 
	is very important. Aberrations are slides, spins, etc, - anything that 
	changes the heel-point and/or foot-line position between sequential 
	heel-contacts of opposing feet. It's a large and complex set of movements 
	and may have controlled and/or non-controlled elements.
 
 But, though 
	the time of the snapshot is heel-contact, the measurements are still to and 
	from heel-points.
 
 That the heel-point is usually off the ground at 
	heel-contact is an annoyance, but a much smaller one than choosing the time 
	as heel-point contact, since that position may include all or part of an 
	aberration. For eg, if there was a slide just at heel-contact, but before 
	heel-point contact, among others.
 
 And, heel-contact is better in that 
	it makes the system universal by removing the requirement of actual contact 
	of the heel-point with the floor. This measurement system could track the 2D 
	path a person would make on the ground if they were pretending to walk while 
	floating in space, with arbitrary designation of the times of heel-contact. 
	The snapshots would define 7 of the 8 parameters, and any shifts and 
	rotations in between would be considered an aberration, and so measured as a 
	separate entity, independent of the other parameters. Variations in the 
	parameters due to the 3rd dimension can be correlated as a separate factor.
 
 It's just a matter of geometry, mathematics and interpretation. But, 
	it's only 2D progression. The 3rd dimension can be integrated, but it should 
	be treated as an extra, like time and many others, by showing variations in 
	the 2D wrt the 3rd.
 
 
 (iv) Body segments define the 5 straight 
	lines over the step, and they are:
 1) step-foot-line 
	of the previous step,
 2) foot-line after aberrations,
 3) rear-leg-line,
 4) step-out-line and,
 5) step-foot-line of the current step.
 These allow the continuous 
	determination of direction changes over the entire step and path. (See Fig. 
	2)
 
 
 v) The standard start position is a purely theoretical, and 
	arbitrary, "body" position which is established at the instant of 
	heel-contact. Only 3 of the minimum points of gait are needed to define it, 
	the step and rear-pelvic joints and the start-heel-point.
 
 To 
	visualize it, imagine yourself frozen at the instant of heel-contact. Now 
	draw yourself back along a straight line, until you're standing straight up 
	at a stop, with the step-foot in the air, and the left and right feet at a 
	distance of straddle-line apart (not pelvis line). In the Step Model, the 
	reference-foot model represents the position of the foot that's in the air 
	(the step-foot), in the standard start position.
 
 Aberrations and 
	push-off angle change the position of the standard start position, but foot 
	offset and foot angle don’t.
 
 This provides a separate, consistent 
	measurement standard, the reference-heel-point, which is still defined by 
	the heel-contact snapshots. It allows the measurement of the step and carry 
	lines by taking advantage of the vector nature of all the measured 
	distances.
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