Popular Science Monthly/Volume 6/November 1874/Human Locomotion
THE movements executed by animals in transporting themselves from place to place have long engaged the attention of observers; and, as animals which travel on the land are more easily got at than those which frequent the sea and the air, it is the motions of such that we know most about. Yet much remains to be learned of the modes of progression of even the most familiar of these; and not a little probably will have to be unlearned that recent investigations have shown to be erroneous.
At first sight, the operations of walking and running, as displayed by both two-legged and four-legged creatures, may appear simple enough, but all attempts to analyze and explain them have shown that in reality they are very complex, so that there has arisen a wide diversity of opinion concerning their real nature. These disagreements among the investigators of the subject can only be accounted for on the principle of the insufficiency of the means at their command for complete investigation; and the confusion has been further increased by the difficulty of expressing in words the rhythm, duration, and phases of the rapid and complex movements involved.
Prof. E. J. Marey, of the College of France, a skillful physiologist, and the inventor of the various delicate mechanical appliances for tracing and registering obscure animal motions, has contributed to the "International Scientific Series" a work entitled "Animal Mechanism," in which the subject of terrestrial locomotion, as typified in man and in the horse, is fully treated. Prof. Marey has devised an apparatus which, applied to the extremities of a moving animal, enables each limb to write out a description, or make a picture of its own actions, so that the duration and phases of its movements, its periods of rest, and the relations of these to the corresponding features in the motions of the other limbs, may be seen at a glance. A description of this apparatus, and its mode of operation, with the results that it gives when applied to man, will first engage our attention.
For the sake of clearness, the machine may be described as consisting
Fig. 1.—Experimental Shoe, intended to show the Pressure of the Foot on the Ground, with its Duration and its Phases.
Fig. 2.—Disposition of a Bundle of Muscle between Two Pairs of Myographical Clips. Clip No. 1. holds the electric excitators of the muscle. A wave is represented at the moment when it has just crossed each of the clips.
fixing under the sole of an ordinary shoe, with heated gutta-percha, a strong sole of India-rubber about five-eighths of an inch thick. Within this sole there is an air-chamber, which, in Fig. 1, is represented by dotted lines.
This chamber, having upon it a small piece of projecting wood, is compressed at the moment the foot exerts its pressure on the ground. The air expelled from this cavity escapes by the tube, actuating the recording instrument in the hand of the experimenter, causing it to register the duration and phases of the pressure of the foot.
Fig. 3.—Runner provided with the Apparatus intended to register his Different Paces.
The registering instrument consists of a little drum, with its upper side formed of some elastic membrane. On this membrane rests a lever having the point of its long arm in contact with the surface of a revolving cylinder, which may be made to move at any required rate, and which carries a slip of paper prepared to receive the tracings. Fig. 2 is a representation of this instrument as employed in registering the transverse dilatation of muscular fibre in the process of contraction. If we substitute in this figure an experimental shoe for each of the myographical clips, 1 and 2, we shall have the arrangement of the apparatus necessary for the study of footsteps or impacts of the foot on the ground.
The entire apparatus, as adjusted to the person of the operator, is seen in Fig. 3. The piece of machinery on the head will be described when we come to speak of the movements communicated to the trunk by the actions of the legs.
To understand the indications which the working of the apparatus gives, the reader is referred to Fig. 4, which has been furnished by an experiment in walking. Two tracings are given by the intermittent pressure of the feet on the ground. The full line D corresponds with the right foot; the dotted line G with the left. The lines are read from left to right.
Knowing the arrangement of the apparatus, we can understand that each impact of the foot on the ground will be represented by the elevated part of the corresponding curve. The pressure of the foot on the ground compresses the India-rubber sole and diminishes the capacity of the included air-chamber; a part of the contained air escapes by the connecting tube, and passes into the registering drum. The elastic side of the latter is thus elevated, carrying up the point of the lever, which in turn leaves the mark of its movement on the paper carried by the revolving cylinder. Were the lever to remain undisturbed, it would simply make an horizontal line running round the cylinder; but, with the apparatus in use, each impact of the foot lifts the pen-point of the lever, thus giving the curves traced in the figure. It will be seen that the pressure of the right foot commences at the moment when that of the left begins to decrease; and that in all the
Fig. 4.—Tracings of the Impact and the Rise of the Two Feet in our Ordinary Walk.
tracings there is an alternation between the impacts of the two feet. The period of support of each foot is shown by an horizontal line which joins the minima of two successive curves. The impacts of the right and left feet are seen to have the same duration, showing that the weight of the body passes alternately from one foot to the other. It would not be the same in respect to a lame person; lameness corresponds essentially with the inequality of the impacts of the two feet. The curves traced by walking may also furnish the measure of the effort exerted by the foot upon the ground. The experimental shoes constitute a sort of dynameter of pressure; they compress the drum less or more according to the effort they exert, and consequently transmit to the registering lever more or less extensive movements. In order to estimate, according to the elevation of the curve, the pressure exerted by the foot, we must substitute for the weight of the body a certain number of pounds. We see thus that, if the weight of the body (150 pounds for example) is sufficient to raise the lever to the height it attains at the commencement of each curve, an additional weight will be required to raise it to the maximum elevation which it attains toward the end of its period of pressure. This proves that, in walking, the pressure of the foot on the ground is not only equal to the weight of the body which the foot sustains, but that a greater effort is produced at a given moment in order to elevate and move the body forward. This additional effort, in a man of average weight, is estimated at about forty pounds, and it is much greater in running and leaping.
There are certain oscillations of the body, both vertical and horizontal, produced by the actions of the legs, which M. Marey has carefully traced, but which, owing to their extreme complexity, are difficult to explain. We shall therefore pass them with only a glance, referring the reader to the work itself for details. With each step there is an up-and-down movement of the body, which varies with the length of the step and the rapidity of the pace. In ordinary walking it has an amplitude of from half to three-quarters of an inch. The maximum of these vertical oscillations is constant, and occurs during the pressure of the foot upon the ground, at the moment when the leg is brought into a straight position. The minima, and consequently the extent of the oscillations, will be determined by the length of the step; the longer the step the greater the obliquity of the legs, and, of
Fig. 5.—Instrument to register the Vertical Reactions during the Various Paces.
course, the greater the lowering of the trunk. Put in another form, it amounts to this: in ordinary walking, the body does not rise above the line of its greatest height when standing still, and the distance which it sinks below this line will increase as the length of the step increases.
The instrument by which M. Marey obtains the tracings of these vertical reactions is represented in Fig. 5.
It is an experimental lever-drum, fixed on a piece of wood, which is fastened with moulding-wax on the head of the experimenter, as seen in Fig. 3. The drum is provided with a piece of lead placed at the extremity of its lever; this mass acts by its inertia. While the body oscillates vertically, the mass of lead resists these movements, and causes the membrane of the drum to sink when the body rises, and to rise when the body descends. From these alternate actions a current of air results, which, transmitted by a tube to a registering lever, shows by a curve the oscillatory movements of the body.
A complete horizontal oscillation occupies the time of two steps, and, consequently, of two vertical oscillations. The body is carried toward the right side, at the moment of the maximum of elevation, which corresponds with the middle of the pressure on the right foot, and toward the left at the middle of the pressure on the left foot. This lateral swaying of the trunk is the consequence of the alternate passage of the body into a position sensibly vertical over each foot.
The body is advancing at every moment during the step, but at some parts of it more rapidly than at others. The greatest rapidity of advance is at the end of the pressure of the foot.
With this brief sketch of the movements of the limbs and body in walking, and of the apparatus employed by M. Marey for studying these movements, we are prepared to consider the different paces common to man.
Fig. 6.—Tracing produced by Walking Up-stairs.—D, tracing of the pressure and rise of the right foot (full line); G, tracing of the left foot (dotted line).
In walking, the body does not leave the ground, the footsteps follow each other without any interval, and the weight of the body passes alternately from one foot to the other. The tracings in Fig. 4, obtained by walking on a level surface, illustrate these points. There are exceptions, however, to this definition. For example, in mounting a staircase it will be observed that the step-curves encroach on each other (Fig. 6), showing that each foot is still pressing on its support when the other has already planted itself on the next step. Besides this, it is at the time of this double pressure that the lower foot exerts its maximum force; it is at this moment, in fact, that the work is produced which raises the body to the whole height of a step. Nothing like this is observed in the descent of a staircase; the step-curves cease to encroach on each other, following one another very much as in ordinary walking on level ground.
Running, though more rapid than walking, consists like it in alternate treads of the two feet, whose step-curves follow each other at equal intervals; but it presents this difference, that in running the body leaves the ground for an instant at each step. Fig. 7 shows the principal characters of this mode of progression. The pressures of the feet are more energetic than in walking; in fact, they not only sustain the weight of the body, but impel it with a certain speed both upward and forward. It is clear that, to give a mass a rising motion, a greater effort must be exerted than would be sufficient simply to sustain it. The duration of the pressures on the ground is less than in walking; this brevity is proportional to the energy with which the feet tread on the ground. These two elements—force and brevity of pressure—increase generally with the speed at which a person runs. The essential
Fig. 7.—Tracing produced by Running (in Man).—D (curve formed by a full line), impact and rise of right foot; G (dotted line), action of the left foot; O, oscillations and vertical reactions of the body.
character of running is the time of suspension, during which the body remains in the air between two foot-falls. Fig. 7 clearly shows the suspension by the interval which separates the descent of the curves of the right foot from the ascent of the curves of the left foot, and vice versa. The duration of the time of suspension appears to vary but little in an absolute manner; but, if we compare it with the speed of the runner, we see that the relative time occupied by this suspension increases with the speed of the course, for the duration of each tread diminishes in proportion to this speed. How is this suspension of the body, at each impulse of the foot, produced? We might at first think that it is the effect of a kind of leap in which the body is projected upward in so violent a manner, by the impulse of the feet, that it would describe in the air a curve, in the midst of which it would attain its maximum elevation from the ground. We may convince ourselves that such is not the case by reference to Fig. 7. The upper line (O) is a tracing of the vertical oscillations in running. It shows that the body executes each of its vertical elevations during the downward pressure of the foot, so that it begins to rise the moment the foot touches the ground; it attains its maximum elevation at the middle of the pressure of this foot, and begins to descend again in order to reach its minimum at the moment when one foot has just risen, and before the other has reached the ground. This relation of the vertical oscillations to the pressure of the feet shows plainly that the time of suspension does not depend on the fact that the body projected into the air has left the ground, but that the legs have withdrawn from the ground by the effect of their flexion; and this takes place at the very moment when the body was at its greatest elevation.
Galloping, a gait that children in their amusements sometimes adopt, gives the tracings shown in Fig. 8. The tracings produced by leaping are shown in Fig. 9.
Fig. 8.—Man galloping with the Right Foot first.—Step-curves and reactions. There is an encroachment of one curve over the other, and then a suspension of the body. The curve O, which corresponds with the reactions, shows the effect of the two successive impulses exerted on the body by the feet.
Among the characters belonging to the various modes of progression, the rhythm of the impact of the feet is one of the most striking. The strokes of the feet upon the ground give rise to sounds the order of whose succession is sufficient for a person, with an ear accustomed to them, to recognize the kind of pace which produces them. In order to give the figure of each of these rhythms, Prof. Marey employs the musical notation, modified so as to furnish at the same time the notion of the duration of each pressure, that of the foot to which this pressure
Fig. 9.—Leap on Two Feet at once (D and G).—The line R, the curve of reactions, shows that the maximum of elevations corresponds with the middle of the pressure of the feet.
belongs, and also the length of time during which the body is suspended. This notation of rhythms is constructed in a very simple manner from the tracings furnished by the apparatus. Fig. 10 represents the curve which corresponds with the act of running in man. Below this figure let us draw two horizontal lines, 1 and 2; these will form the staff on which will be written this simple music, consisting only of two notes, which M. Marey calls right-foot and left-foot. From the commencement of the ascending part of one step-curve belonging to the right foot we will let fall upon the staff a perpendicular (a); this line will determine the commencement of the pressure of the right foot. A perpendicular (b) let fall from the end of the curve will determine where the pressure of this foot ends. Between these two points let us trace a broad white line; it will express, by its length, the duration of the pressure of the right foot. A similar construction
made on line 1, from the succeeding step-curve, will give the notation of the pressure of the left foot. The notations of the left foot have been shaded with oblique lines, to avoid confusion.
Between the pressure of the two feet there is found to be silence in the rhythm; that is to say, the expression of that instant of the course when the body is suspended above the ground.
If we note in this manner the rhythms of all the paces used by man, we shall obtain a synoptical table which will much facilitate the comparison of these varied rhythms. Fig. 11 represents the synoptical,
Fig. 11.—Synoptical Notation of the Four Kinds of Progression used by Man.
of the four kinds of progression, or paces, which are regularly rhythmical, and in which the two feet act alternately. Line 1 represents the notation of the rhythm of the walking-pace. The pressure of the right foot upon the ground is represented by a thick white stroke, a sort of rectangle, the length of which corresponds with the duration of the pressure. For the left foot there is a grayish rectangle shaded with oblique lines. These alternations of gray and white express by their succession that in walking the pressure of one foot succeeds the other, without allowing any interval between the two.
Line 2 is the notation which corresponds with the ascent of a stair-case. It is seen that the strokes lap, or encroach on each other, and that, consequently, the body during an instant rests on both feet at once.
Line 3 corresponds with the rhythm of running. After a shorter pressure of the right foot than in the walking-pace, an interval is seen which corresponds with the suspension of the body; then a short pressure of the left foot followed by a fresh suspension, and so on continually.
Line 4 answers to a more rapid rate of running. It shows a shorter duration of the pressures, a longer time of the suspension of the body, and a more rapid succession of the various movements.
This method of representing the different modes of progression by the notation of their rhythms, though hardly necessary to make clear the simple paces of man, will greatly aid us in understanding the more complicated paces of the horse, which will be the subject of another article.