Basics of Biomechanics Ajay Bahl, Sharad Ranga, Rajnish Sharma
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Motion1

Motion is the most common natural phenomenon. Movement of vehicles, flowing of river, rumbling of leaves, flying of birds, movement of normal individuals, and diseased states like hemiplegics, paraplegics, etc. are the common examples of motion in nature.
Some objects like electric motors, fans, machines in factories stay at their own places but their parts like blade, etc. are seen rotating. In some machines different parts are moving differently. For example, when a sewing machine is paddled, the wheel moves round, the needle moves up and down and the cloth keeps moving forward.
As we observe everyday the sun rises in the east in the morning, gradually moves across the sky during the day and sets in the West in evening. At night the moon is seen moving across the sky. Motion of certain objects is not visible but can be inferred indirectly. For example, we never see air moving but we detect its motion when it moves the leaves of tree, small bit of paper or the curtains of our house.
In fact everything in the universe, right from the electron inside the atom to the largest galaxy in the universe is in motion.
All motions are relative and there is nothing like absolute motion. Hence, the motion may be defined as change in position of a body with respect to the positions of other objects with the passage of time. The motion is the continuous change in the position of an object with the passage of time, so in order to study the motion of a body, the position of a moving body at various instants of time should be observed. The simplest type of motion which needs to be explained initially is “motion in a straight line”. The motion by being relative in nature is explained with reference to a fixed point called origin. Like in our body the term proximal and distal are explained in terms of a fixed body part, i.e. head of the body.
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In order to locate the exact position of a body, we should know its direction and distance from origin. As the body moves its position changes with the passage of time.
To locate the position of an object, we first choose the origin. ‘O’ and next a reference line ‘OY’ called reference axis. The position of a moving object at any instant of time can be located by knowing:
  1. The distance of the object from origin say OA as r1, and
  2. θ1 is the angle which the line joining the origin ‘O’ and point A (i.e. the line OA) makes with the reference axis OY.
The two positions A and B of the moving object at two different instants of time are shown in Figure 1.1. The quantities (r1 θ1) and (r2 θ2) locate respectively the position A and B of the moving point object at two different times.
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Fig. 1.1: Locating the position of a moving object
 
UNIFORM MOTION
If a body covers equal distances in equal intervals of time, in the same direction then its motion is called uniform motion or in other words, whenever a body is in uniform motion neither its speed nor its direction of motion changes with the passage of time.
 
NON UNIFORM MOTION
It is observed that a car starting from the rest, gradually gains its speed, it moves faster and faster. It covers large distances in each successive seconds of its motion. If a body covers unequal distances in equal intervals of time its motion is called non uniform motion. Falling of an apple from a tree, a cyclist moving on a rough road, an athlete running on race, people moving through a crowd and a vehicle starting from the rest are the good examples of non uniform motion.
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GRAPHICAL REPRESENTATIONS OF UNIFORM AND NON UNIFORM MOTION
The distance time graph of two men ‘X’ and ‘Y’ when ‘X’ is walking and ‘Y’ is running. They are moving in the same direction as shown in Figures 1.2 and 1.3. The man ‘X’ covers 10 meters in one second, another 10 meters in next seconds and so on. Whereas the man ‘Y’, an athlete runs gradually faster and faster (as shown in Figure 1.3). Therefore, we can see from the Figures 1.2 and 1.3. That the graph of the Uniform motion is a straight line, whereas the graph of the non uniform motion is a curved line.
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Fig. 1.2: Uniform motion
The distance—Time graph is a straight line
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Fig. 1.3: Non Uniform motion
The distance—Time graph is a curved line
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Equation of Motion
First Equation of motion (V = U + at)
Let us consider velocity of a body under uniform acceleration ‘a’ changes from U to V in interval of time ‘t’.
On a velocity—Time graph, the initial velocity U is represented by time ‘t’ = O by a point P on the Y—axis and the line QR is drawn parallel to Y—axis and line PR is drawn parallel to X—axis.
Hence acceleration ‘a’ represented by slope of the line PQ given by
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Second Equation of Motion
(S = ut + ½at2)
In the Figure 1.4, we may see that area enclosed under the curve of the velocity—Time graph, gives the distance covered by a moving body. In Figure 1.4, the total distance ‘s’ covered by a uniformly accelerated body is given by the area of trapezium OS Q P shown shaded.
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Fig. 1.4: Graphical representation of equation of motion
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Third Equation of Motion
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In the velocity —Time graph distance covered
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We get
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Uniform Circular Motion as Accelerated Motion
The motion of a body along a circular path at a constant speed is called uniform circular motion. The direction of the motion of the body undergoing such a motion changes from point-to-point even though it covers equal distances in equal intervals of time. Therefore, the velocity is not uniform as the direction of motion changes at every instant of motion. Since the acceleration is the change in velocity per unit time, a body in uniform circular motion is having an 6accelerated motion. Following illustration will make the above facts clear.
A boy running on a regular hexagonal track is shown in Figure 1.5. Let us suppose that a boy runs at uniform speed along the straight portion, AB, BC, CD, DE, EF and FA of the track. At the corners he quickly turns and changes his direction of motion to keep himself on the track. He however maintains the same speed.
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Fig. 1.5: Boy running on a regular hexagonal track
In completing a full round, he changes his direction of motion five times. Suppose the track is a 8 sided closed Figure 1.6, i.e. regular octagon in place of hexagon. In order to keep on the track, he must change his direction of motion eight times.
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Fig. 1.6: Eight changes in the direction of motion
If we keep on increasing the number of sides of the closed track, then the boy has to change his direction of motion more frequently. The track shown in Figure 1.7 is 15 sides closed figure.
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Fig. 1.7: More frequent changes in the direction of motion
Running along with this path the boy has to turn 15 times in one complete round. If the number of sides of the track is increased to an extremely large number then the shape of the track would almost become a circle. To run on such circular track, the boy will change his direction of motion at every instant of time though he maintains the same speed.
Thus, the motion in a circular path at a uniform speed is an example of accelerated motion in which the velocity changes continuously only due to change in the direction of motion.
 
GALILEO'S STUDY ON THE MOTION OF OBJECTS
Galileo of Italy after making a careful study of motion of objects, came to the conclusion that a body continues to move with the same velocity when no unbalanced force is acting on it. On the basis of everyday experience of motion of objects around us, it is very easy to understand Galileo's conclusion. When we apply a small push to the wheelchair, we find that the wheelchair (Fig. 1.8) moves through some distance and then stops.
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Fig. 1.8: Movement of wheelchair
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It does not keep moving forever. Similarly a tricycle on the road continuously needs to be peddled to keep it in motion.
 
NEWTON'S LAW OF MOTION
After Galileo, Sir Isaac Newton (1642-1727) of England made a detailed and systematic study of motion of the bodies and formulated the three basic laws of motion. These laws after his name are called Newton's Laws of Motion.
 
First Law
A body continues in its state of rest or of uniform motion in a straight line until it is acted upon by an unbalanced external force.
 
Second Law
The force on an object is directly proportional to the product of the mass of the object and its acceleration and it acts in the direction of acceleration produced.
 
Third Law
To every action there is an equal and opposite reaction. Action and reaction act on different bodies but they act simultaneously.
These laws are based upon human experience about nature and are true everywhere in the universe.
The Newton's first law of motion contains following important points:
  1. Inertia is the basic property of all material bodies in the universe.
  2. It gives a qualitative definition of the force. It defines the force is that external influence which is necessary to change the state of rest or of uniform motion of the body.
  3. It also explains that only an external force can change its state of rest or of uniform motion in a straight line.
The Newton's second law of motion explains the relationship between force, mass and acceleration.
If ‘f’ indicates the force, ‘m’ stands for the mass and ‘a’ for acceleration, then as per second law of motion.
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Where k is constant of proportionality and its value depends upon the unit chosen for measuring force.
For one unit of force.
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Alternatively
The law states that the acceleration of the body is directly proportional to the unbalanced forces acting on it and is inversely proportional to its mass. The direction of acceleration is the same as that of force, i.e.
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Combining the above two equations
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where k is the constant of proportionality.
Whenever, two bodies interact the force exerted by anyone of them is called action and that exerted by other is called reaction.
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Fig. 1.9: KAFO (Lateral view)
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Fig. 1.10: A patient of PPRP wearing KAFO (Different views)
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Fig. 1.11A and B: Patient wearing dorsolumbosacral orthosis showing three-point pressure points
When a patient with postpolio residual paralysis is wearing a knee ankle foot orthosis with ischeal weight bearing design the weight of the upper part of the body is born by the ischeal seat through the 11ischeal tuberosity. The stability achieved during walking with such orthosis is a good example of equal and opposite forces acting at the point on ischeal seat (Figs 1.8 to 1.11). However, some of the body weight is also borne circumferentially on the thigh bands.
The Newton's third law of motion deals with the interaction between pair of bodies and is explained as follows:
To every action there is an equal and opposite reaction. Action and reaction always act on different bodies.
According to this law whenever a body exerts force on a body, the second body also exerts force on the first body, a force of equal magnitude but opposite direction. Thus we see that Galileo's discoveries and those of others contributed to Newton's laws of Motion that form the current basis for mechanics and biomechanics.