Article.

Chapter 12

Biomechanics

GIDEON B. ARIEL

Biomechanics is an integration of the two disciplines of biology ("bio") and physics ("mechanics"). It recognizes that all bodies on earth, whether animate or inanimate, are affected in the same way by gravity, and it provides a better understanding of performance. In other words, a bridge, a car, a baseball player, and a'horse must all adhere to the laws of mechanics. The additional factors that must be - included to assess motion for the biological entities more accurately include such things as bone capacity, neuromuscular coordination, and physiologic attributes. From the understanding of each component comes a greater appreciation of the integrated result, which is called biomechanics.

Da Vinci once observed that, although drops of rain are in fact independent of one another, they appear to the human eye as "continuous threads descending" from the clouds, and that therein lies the truth of how the eye "preserves the impression of moving things which it sees."' Therein also lies the visual distortion that allows us to see motion pictures. Because of the properties of the human eye and the visual system, a series of separate images on film becomes a smoothly flowing image when projected onto a screen at a certain speed-a movie.

Movement of the human body is also a series of separate, individual actions. These actions begin with minute electrochemical processes that are infinitely swifter and more complicated than any set of film images trav

eling at 24 frames, or 1.5 feet, per second. Our muscles are thin strands of fibers which, when inactive, have all the strength of jelly. But when they contract or relax because of these electrochemical reactions, the result is movement of the body with a fluidity that prevents even the sharpest eyes from distinguishing the separate actions. For instance, the simplest of human movements, such as crooking a finger or raising an eyebrow, involves a complex of neuromuscular happenings that cannot be duplicated by artificial means. In fact, the best robot still moves in jerks and stops when compared with the subtle, flowing pace of a human.'

People fathom the nature of things by tracking their motion. All motion follows mechanical principles. Like the machines they make, people are a set of levers whose movements copy the geometry of classical mechanics. These levers are powered by muscles, whose actions can be as simple as their characters are complex. Each of the more than 600 muscles is abundantly supplied with nerves that link the muscles to the brain and spinal cord and that often follow labyrinthian circuits, humming with signals, to control the ebb and flow of muscular energy. Many muscles must work harmoniously together in order to perform even the simplest task.'

The study of biomechanics is an attempt to understand how these neuromuscular events occur and to analyze a series that the naked eye sees only dimly and the mind often fails to comprehend. Biomechanics is a science that

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depends on the known facts of biology, physics, and, to a lesser extent, chemistry. To reap the rich rewards of the more satisfying, fulfilling life this science can offer, a thorough understanding of both the "bio" and the "mechanics" of biomechanics must be gained.

NEUROMUSCULAR INTEGRATION

The "bio" part of biomechanics deals with the functioning living organisms or their parts. The smallest elements of the body, which maintain all the functions of life, are the cells. Furthermore, in the 500 million years that the human species has been on earth, the basic nature of the cells has remained relatively unchanged. Therefore, what was true for the cells of cave people continues to apply to modern human beings. Activities that produced fitness in the cells of prehistoric humans do the same today, because the human body has remained essentially unchanged over the eons. What has changed, and quite dramatically in Western civilizations, is the environment in which the body functions. Our cells have been forced to adapt to this fast-changing world.

The building or structural units of the human body are the bones, which are connected by ligaments. At the joints, cartilage cushions the shock of bone on bone, and the joint is lubricated by synovial fluid that can be pumped in and out of articular cartilage.

However, bones have no power to move. Like the frame of an automobile, they provide the basic structure on which the body rests. The engine that supplies the power to move comes from the muscles. It is the 600 muscles of the body, which account for about 40 percent of body weight, that do the work.4

Biomechanical engineers are principally concerned with the voluntary muscles. These are controlled by conscious and rather programmable routines that enable the skeletal system to move in a prescribed manner. The control programs are generated by the brain and can be modified by training. Muscles are caused to contract by signals from the central nervous system. The actions of the body can be likened to a link system in which those reciprocating engines, the muscles, move the bones of the foot, ankle, shank, thigh, and so on, under the

controlled stimulation of the central nervous system.

Consider some of the complexities of the simple act of walking. There must be a neurologic program and control of the nervous system pattern of firings and relaxations, chemical processes must be appropriately regulated, and muscular actions must be generated so that the activity is consistent with the laws of physics. Thus, muscle action is used to adjust the position of the body, keeping that center of gravity in line with the base. Each time this line of gravity is displaced out of the base, the body is in the act of falling. Muscles, in effect, act as cables pulling on bones. The tug of the cable makes motion possible, but it should be remembered that a muscle can only contract. Because muscles are paired, one contracting muscle pulls a bone forward, while the paired muscle can contract to pull the bone back in the opposite direction.

In all cases, the number of muscles involved in an action of the body is more than the eye observes.' The arms, hands, and fingers contain 52 pairs of muscles. The typesetting of this page employs all 52, although only the fingers and hands appear to shift positions significantly. The thighs, legs, and feet have 62 pairs of muscles. The back is composed of 112 pairs. Even when standing motionless, the muscles that are used in walking must be constantly at work to prevent falling. It is not possible for a corpse or skeleton to stand up, because there are no muscles to work at maintaining the proper distribution of body segments.

The three basic elements of the musculoskeletal system-bone, muscle, and connective tissue-normally perform with perfect teamwork. Their mission is to support the body, shield its delicate internal organs, and make it mobile. The coordination and interactions of these individual components is the responsibility of the nervous system.

In the 1700s, Galvani studied the movements of frog muscles and saw that they contracted when electrically stimulated. -He deduced that electrical current must be involved in the normal muscle contraction process. Both chemical and mechanical interactions affect muscular contractions, but any understanding of biomechanics requires an appreciation of biocybernetics, the study of control and communication in humans. The central nervous

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system consists of the brain and both the sensory and motor pathways that innervate the musculature. In the brain, 10 billion cells, about the same number as stars in our galaxy, engage in an electrochemical operation that, in conjunction with other body parts, permits us to see, hear, reason, imagine, create, love, hate, move, and be aware of exactly which process we are involved in, through the capacity to incorporate feedback.'

The building block of the system is a specialized nerve cell known as a neuron. Bundles of neurons are organized into larger entities, the nerves. Nerves serve as pathways for constant streams of information from eyes, ears, nose, and other areas, to the neurons of the brain. The brain evaluates the data in light of evolution and individual experience. In addition, nerves with receptor cells monitor such stimuli as pain, cold, touch, pressure, and even blood and body chemistry. Motor neurons within the brain and at the target sites control the movement of muscles. They not only trigger the chemicomechanical process of working muscles but also try to govern the actions.

The input for one neuron comes from other neurons and receptors by means of a synapse. Pathways for signals of motor neurons lie along the spinal column, which is why severe spinal injury can lead to paralysis of limbs. Motor neurons cause muscle fibers to contract. But the action in which a muscle fiber ceases to contract, in which it relaxes or lengthens, does not occur because of some signal to the motor neuron, Rather, it is the absence of a signal ordering the fiber to contract that allows the tissue to relax.

The intricate programming that coordinates this choreography of balance resides in the brain and central nervous system. This network relies. on continuous feedback in much the same way as control of today's modern automobile. No matter how frail he or she might be, the modern driver can control a vehicle with the flick of a wrist or ankle, because sophisticated mechanisms assist in steering, braking, and shifting. These mechanisms have sensors that measure some physical variable and use the "feedback" information to control the devices. In our bodies, there are numerous automatic feedback mechanisms of this kind controlling physiologic functions without any mental effort on our part. For example, blood pressure,

respiratory rate, and levels of insulin are regulated by feedback control between the brain and the receptor targets. Certain body sensors control muscle tension while others measure responses to changes in muscle length (Fig. 12-1).

These receptor, feedback, control center programs are actually extremely complicated and require continuous activity when smooth, normal, coordinated behavior is desired. For example, suppose a person is asked to flex an elbow steadily against a load. If there were a sudden unexpected increase in the weight, his elbow would have to extend, and a larger contraction of the biceps muscle would be needed to sustain the load. Conversely, a decrease in load brings a relaxation of the biceps. The control of muscular contraction is very sophisticated and highly programmed.

Consider another example, a person's signature. Whenever John Smith signs his name, it always looks the same (or enough so to be recognizable) and different from what any other person can write, even one who was trying to sign the name of John Smith. If Mr. Smith uses chalk and signs his name on a blackboard, the signature still appears the same, even though he used different muscles than those employed when writing on paper. The individuality remains. In this complex handwriting movement, there is a preprogrammed control mechanism. Optimum performance depends on the control efficiency, not on the strength of the muscles or the efficiency of the metabolism. The control of these processes is the most important factor. Most people believe the brain is primarily used for thinking, yet research shows it to be first and foremost a control system.

Some think that the brain is like a computer. However, the single computer element in the brain is the cell. Each cell acts like a computer, and we have 10 billion of them. Posture sensors detect the position of joints, tension in tendons, and the length and velocity of muscle contraction. Inertial sensors control rolling, twisting, turning, acceleration, and the position of the head with respect to gravitational attraction. Hormonal sensors, thermosensors, and blood chemistry analyzers report on the internal biological condition of the whole organism. All of this information is analyzed and processed in innumerable computing centers that detect patterns, compare incoming data with

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Figure 12-1 Feedback control of muscular contraction.

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stored expectations, and evaluate the results. Perhaps one of the more significant features of the brain is that many computations proceed simultaneously in many different places. The brain does not execute sequential programs of instructions like a computer; rather, it executes many parallel processes simultaneously.

The fineness of control depends upon the number of motor nerve units per muscle fiber.' The more neurons, the finer the ability to maneuver, as in the case of the muscles that operate the eye. When there are fewer motor nerve units involved, the action becomes less fine or precise. The individual muscle fibers that make up a muscle contract and relax in an elaborate synchronization. The arrangement permits all of them to arrive at a peak of action simultaneously. But certain diseases, such as polio or cerebral palsy, destroy the normal recruitment pattern of the muscle fibers. This causes weak or spasmodic muscle action.' In the absence of other symptoms, some diseases may therefore be diagnosed by analyzing the form of the aberrations in the sequence of muscle fiber firing.

Synchronization of muscle firing is critical for optimizing athletic performance. In the power events, such as throwing the discus or the high jump, it is extremely important that the muscle action be simultaneously activated to optimize the force. The central nervous system does this by sending signals to the individual muscle fibers. Lack of synchronization in power events results in less force and poorer performance. On the other hand, in events of endurance such as- long distance running, asynchronization is important, because fewer fibers are needed to maintain the action, thus permitting other fibers to "rest." It is a fact that the long distance runner who "over recruits" muscle fibers feels fatigue sooner.

Technique is important in achieving optimal performance. How does the brain adapt to the requirements? The answer relies on the great number of approximations that seem to add up to the correct signal. The brain achieves its incredible precision and reliability through redundancy and statistical techniques.9 Many axons carry information about the value of the same variable, each encoded slightly differently. The statistical summation of these many imprecise and noisy information channels results in the reliable transmission of precise mes

sages over long distances. In a similar way, a multiplicity of neurons may compute on roughly the same input variables. Clusters of such computing devices provide statistical precision and reliability in orders of magnitude greater than that achievable by any single neuron. The outputs of such clusters are transmitted and become inputs to other clusters, which perform additional analog computations. These computations result in fantastic numbers of signals terminating on the motor neurons that stimulate the muscles for movement."

Movement, then, could be used to differentiate between a dead thing and a live thing, and by this definition, human beings are obviously different from stones. But are they different from machines? Machines are often in restless movement; wheels spin, levers thrash, pistons pump, but clearly they are not "alive." What are two basic constituents of movement for a, biologically speaking, living thing? The first is muscle and the second, a signaling system that makes muscles contract in an orderly manner.

To begin with, although the molecular or cellular processes of each nerve or muscle cell may be similar, tasks and innervation ratios differ; because tasks differ, not all muscles work in the same way. Consider the operations required of the human eye and arm. Eye muscles must operate with great speed and precision in orienting the eyeball quickly to close or distant points of focus, as well as in tracking movement. At the same time, the eye muscle does not have to contend with such external demands as lifting weight. The fine control needed in eye movement calls for a high innervation ratio (the ratio of the number of neurons with axons terminating on the outer membrane of muscle cells to the number of cells in the muscle). For eye muscle, the innervation ratio is about 1 to 3, which means that the axon terminals of a single motor neuron release their chemical transmitter to no more than three individual muscle cells.

In contrast to this high innervation ratio, the axon terminals of a single motor neuron innervating a limb muscle, such as the biceps of the arm, may deliver a chemical transmitter to hundreds of muscle fibers. The muscle may, therefore, have a low ratio, one motor neuron to many hundreds of muscle cells. As a result,

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the output of the motor unit in limb muscle is correspondingly coarse.

One of the most elementary movements for humans is walking."-" All mammals and other land animals are born with the ability to walk and run. In experiments with babies between 4 and 6 weeks of age, infants started to walk when supported, raised to a standing position, and placed on a treadmill. It seems that a baby at this early age possesses and can utilize the built-in walking mechanism with which it was endowed by its genes. The nerve cells controlling the mechanism come from the spinal cord.

In order to understand complicated movement such as that of an athlete jumping or throwing or of a musician playing the violin, it is necessary to understand the brain, one of the few remaining frontiers to be explored. Humans' control of their movements comes from a system that is capable of novel and creative solutions to problems of movement.

Our movements are generated in different ways depending on the level of skill we are able to use. Athletes recruit their muscles in different ways depending on their level of acquired skill. The motor program is constantly changing in order to produce efficient movement. As mentioned above, each individual has a unique signature that appears approximately the same regardless of whether it was written with a pen on paper, chalk on a blackboard, or a stick in the sand. Yet for each of these signatures, a different set of muscles is utilized. Instructions to the muscles must come from the nervous system, but because the combinations of different muscles result in the same signature, the internal model is not simply a series of directives to a specific set of muscles. Somewhere in the nervous system a model of movement is formed that' ~s not related to its muscular means of achievement. In other words, the optimal motor control of skilled movement is generated by a program controlled in our central nervous system.

In addition to the control by the nervous system, the human body is composed of linked segments, and rotation of these segments about their anatomical axes is caused by force. Both muscle and gravitational forces are important in producing these turning actions, which are fundamental in bodily motions in all sports and

in daily life. Pushing, pulling, lifting, kicking, running, walking, and other human activities are results of rotational motion of the links, which consist of bones.

In motor skills, muscular forces interact to move the body parts through an activity. The displacement of the body parts and their speed of motion are important in the coordination of the activity and are also directly related to the forces produced. However, it is only because of the control provided by the brain that the muscular forces follow any particular displacement pattern. Without these brain controls, there would be no skilled athletic performance. In every planned human motion, the intricate timing of the varying forces is a critical factor for successful performance.'

The accurate coordination of the body parts and their velocities is essential for maximizing athletic performance. Muscular forces generated by the individual fibers must occur at the right time for optimum results. The strongest weight lifter cannot put the shot as far as an experienced shotputter, because although the weight lifter may possess greater muscular force, he has not trained his neuromuscular system to produce the correct forces at the appropriate time or speed.

Different athletic performances can be likened to a spectrum. On one side of the spectrum are the explosive activities, such as throwing, jumping, sprinting, and weight lifting. At the other end of the spectrum are the esthetic events, such as gymnastics, diving, and figure skating, in which success depends on the ability of the athlete to create movements that are pleasing to the judges. In the middle of the spectrum are the endurance activities, for which the athlete tries to maintain muscular contractions for long periods of time at submaximal intensity levels. Within this spectrum are events that demand that the athlete repeatedly shoot at a target with a high level of consistency and accuracy. Other activities, such as team sports, incorporate many overlapping characteristics. For example, football players need explosiveness, endurance, and accuracy.

In characterizing the movements of a person, we specify the particular activity, not the independent contraction of hundreds of thousands of muscle fibers. Walking, running, throwing, and jumping are movements that re-

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suit from contractions of muscles and their synergists in relatively standard patterns of coordinated activity.

The combination of muscle and bone forms a lever system that is one of the most basic mechanical systems for performing work. A lever is a machine by which force applied at one point does work at another."' Each joint in the human body is a fulcrum of a particular lever. There are different types of lever systems, and the human body uses all types. The forces on the different levers are applied by the muscular system. Muscles do all their work by contraction, or shortening. That means that they can only pull, never push. Although it may appear that the legs, arms, and body are used to push an object, nevertheless the mechanism that produces force is still muscles that are pulling. The explanation lies in the fine symmetry that characterizes so much of the human organism. Muscles, like so many other features of our anatomy, operate in pairs, agonists and antagonists. When a limb is flexed, the agonist muscle contracts while the antagonist lengthens. The two work together in a coordinated movement, with one assisting the other for desired optimal action.

For the body to regulate movement and muscular contraction, it must receive information about what it controls. In order to accomplish this, a servomechanism must be introduced. Many current concepts about the mechanisms of movement have evolved from the work of the British physiologist, Charles Scott ShQ'rrington.l' Early in this century, Sherrington studied the function of the motor neuron in certain reflexive forms of motor activity, such as scratching and walking. Signals from many different areas of the brain impinge on the spinal cord motor neurons, and Sherrington characterized motor neurons as the "final common pathway" linking the brain with muscle action. He studied muscle movements in animals whose spinal cords were severed, effectively separating the motor neurons from the brain. He found that within a few months after a dog's spinal cord was severed, a scratch reflex could be elicited by such mechanical stimuli as tickling the animal's skin or lightly pulling on its hair anywhere within a large, saddle-shaped region of the upper body. In describing these responses, he stated that the movements were

"executed without obvious impairment of direction or rhythm."

Sherrington's work led to today's concept of the "triggered movement" based on a "central program" involving a spinal rhythm generator. Not long after Sherrington, another British physiologist, Graham Brown, showed that rhythmic limb movements similar to those involved in walking were also possible in dogs deprived of connections between the brain and spinal cord. Evidently, spinal rhythm generators existed for walking as well as for

scratching. 17�'8

Many current investigations of the neurophysiology of locomotion are aimed at clarifying the interaction between what may be termed central programs from the brain and sensory feedback from outside the nervous system. Indeed, Sherrington's work was particularly concerned with the ways motor neuron activity could be regulated by sensory feedback. Sherrington introduced the term "proprioception" to describe sensory inputs arising in the course of centrally driven movements when "the stimuli to the receptors were delivered by the organism itself." Sherrington chose the prefix "proprio" (from the Latin, one's own) because he believed the major function of the proprioceptors was to provide feedback information on the organism's own movements.

These control mechanisms in the muscles and tendons themselves are governed by higher level mechanisms in the brain. In fact, the control of movement relies on a hierarchical structure. The sensory information in the muscle itself processes local information and transmits net results to higher centers. Feedback enters the hierarchy at every level.' At the lowest levels, the feedback is unprocessed; hence, it is fast-acting with very short delay. Thus, a simple patellar tendon reflex is executed more rapidly and with a shorter "program" than a complex task like hitting a golf ball off the tee 150 yards down the center of the fairway.

In more complicated tasks necessitating higher-level control, feedback data pass through more and more stages of an ascending sensory processing hierarchy. Thus, feedback closes a real time control loop at each level in the hierarchy. The lower-level loops are simple and fast acting. The higher-level loops are more sophisticated and slower. The combination gen-

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erates a lengthy sequence of movements that are goal directed and appropriate to the environment (Fig. 12-2).

Such behaviors appear to an external observer to be intentional or purposive. The toplevel input command is a goal, or task, which is successively decomposed into subgoals, or subtasks, at each stage of the control hierarchy until, at the lowest level, output signals drive

Thalamus

the muscles and produce movements. The success or failure of any particular task performance or goal-seeking action depends on whether the higher-level functions are capable of providing the correct mappings or information to maintain the output for the lowerlevel control in successful performance, despite perturbations and uncertainties in the environment.'

Large pyramidal cells of Betz

Fibers to lower extremity Fibers to trunk Fibers to upper extremity Genu of internal capsule

Ant. limb of internal capsule Corticospinal tract Temporopontine tract Frontopontine tract

Lenticular nucleus External capsule

Claustrum Extreme capsule Cortex of insula

Caudate nucleus (head)

Pyramidal decussation

Lateral corticospinal tract (crossed-axons of neuron t)

To motor endings C VIII in MM. of forearm and hand

To motor endings _� T IV Internuncial cell-neuron II in intercostal and

segmental back MM. Ventral root fiber

L IV

Anterior horn cell-neuron III

T

Anterior corticospinal tract (uncrossed-axons of neuron I)

To motor endings in gluteus medius and tibialis anterior MM.

To sacral segments of cord

Figure 12-2 Level of control.

Muscle action may involve sequential contraction or cocontraction, that is, the simultaneous contraction of the antagonistic muscles. If visible motion occurs, then the prime muscle mover has dominated, although motion should not be perceived as a contest but rather as a controlled effort. Cocontraction describes the muscle action involved in many stabilizing activities such as standing, handwriting, or slipping a key into a door lock. These types of movements require shortening of muscles and tension of muscle fibers in finely tuned or "motionless" activities.

On the other hand, ballistic movements involve a muscle action in which a burst of prime mover or agonist muscle activity is followed by relaxation, but the movement continues because of the momentum generated by the initial firing of the muscle fibers." When you kick or throw a ball or even walk at a normal pace, ballistic movements are used. If you attempt to duplicate the slow motion of a movie camera in these actions, the likelihood is that you are no longer engaged in ballistic activity or movement.

Muscular strength, endurance, and power

are important characteristics of skeletal mus

cles. Strength is the ability of a muscle to exert

force, which is static when no motion is pro

duced and dynamic when motion is produced.

Power is the strength of a muscle used over a

short period of time, and endurance is the abil

ity to use a muscle over a long period of time.

The body is developed like a system of links

in -a chain. In other words, movement and

strength in one region carry over to affect other

parts of the body. For example, proper postural

strength and alignment gained in the upper body

positively influence strength and postural align

ment in the trunk, lower back, and lower body.

f

MECHANICS

The second half of the science of biomechanics is concerned with the physical laws that can be applied to the human body, the "mechanical" consideration. Unlike the "bio" portion, which is affected by biological structure, anatomy, physiology, genetics, nutrition, activities, and environment, the mechanics portion is governed by mechanical laws, which are universal tenets throughout the earth.

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The Italian scientist Galileo Galilei (15641642) found experimentally that balls of different weights roll down an inclined plane at the same rate.21 If the plane were tipped more sharply, the balls would roll more rapidly, but all the balls would increase their rate of movement similarly; in the end, all would cover the same distance in the same time. This means that freely falling bodies fall through equal distances in equal times, regardless of their weight. A heavy body does not fall more rapidly than a light body. The importance of the falling masses experiment lies in an understanding of acceleration.

Galileo determined that the distance traversed by a body rolling down an inclined plane grows greater and greater in successive, equal time intervals. In other words, the rate of speed changes. Acceleration is the change in rate of speed or, more correctly, velocity. In the falling masses example, the velocity of the mass increased by the same amount each second. A change in velocity with time is called acceleration. On earth, the acceleration of free-falling bodies is a constant of 32 feet per second squared.

An understanding of acceleration was absolutely necessary in order for the English scientist Sir Isaac Newton (1642-1727) to formulate the laws of motion.22 As stated by the Newtonian law, acceleration produced by a particular force acting on a body is directly proportional to the magnitude of the force and inversely proportional to the mass of the body. In other words, the greater the acceleration, the greater the force, and if the mass is greater for the same force, the acceleration is reduced. From a practical point of view, the greater the mass or the weight of an object, the greater the force necessary to accelerate it. Also, to produce a greater acceleration with a given mass, a greater force is required.

The importance of discussing acceleration and forces lies in the fact that movement has to start with force. It is impossible to begin movement without applying force, whether it is external force, such as gravity, or an internal force, such as muscle. For example, the force applied to a hockey puck on the ice creates acceleration and sets the puck moving faster and faster as long as the force is applied. The length of time that force is applied to the puck is important. The muscular forces needed to swing

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the stick and skate down the ice are also forces that require consideration.

When external and internal forces that act on the body are measured, the mechanical models can be classified as static or dynamic. The static models are simpler, because no forces due to movement occur.

Consider a static model with a person standing motionless holding an iron weight in his hand, as in the shotput event, and assume that the shot has a 10-kg mass. In this case, the force acting on the shot is vertical. The gravitational attraction of the earth creates the weight of the mass, and its magnitude is proportional to the mass times the gravitational factor, which is the gravitational acceleration in meters per second squared. In other words, the weight (W) of the shot is equal to the mass (m) of the shot times the gravitational acceleration (a).

W= ma

One should bear in mind that forces (including weight) are vector quantities and therefore have a magnitude, a direction, a line of action, and a point of application. In Figure 12

3, the magnitude of the force is 10 kg times 9.8067 meters per second squared, or 98 newtons. A newton is a unit of force rather than of mass. Because this is a static analysis without motion, the direction of the force is vertically down, and the line of action is vertical. The point of application of the gravitational force is at the center of the mass. The center of the mass (also known as center of gravity of the mass) is the place where the mass can be considered to be in gravitational balance, so that if one were to hang the mass at this point, it would be in balance regardless of its orientation in space.

In Figure 12-3, the load is stationary, because the person holding the shotput is motionlesss Therefore, the downward force has to be cancelled by an opposite and equal upward force. The force, in this situation, is provided by the hand supporting the mass or shot. The upward force cancels the downward force, and the load is said to be in equilibrium. The opposite force is called a reactive force, and it is designated in Figure 12-3 as "R." Because the forces act along the same line of action, no rotation occurs at the wrist, elbow, or shoulder joints.

This example can be described using the engineering analytic concept called a free-body diagram. In a free-body diagram, a graphic representation is given including the magnitude of forces. In this example, the system is in equilibrium, so the summation of forces must be equal to zero.

IF =0

The force in the downward direction is equal to -98 newtons. (The reason for the neg-, ative sign is to indicate the downward direction.) The force in the upward direction is equal to 98 newtons. Thus:

-98 newtons + 98 newtons = 0

From this simple equation, it can be de

termined that the hand has to apply 98 new

tons of force in order to keep the shot from faI1ing down.

A more complicated problem is to calculate the static force at the elbow. For this calculation the length, weight, and the center of mass of the forearm must be known. Calculations using this information yield the forces at the elbow joint that resist, or are exerted against, the combined forces of the load, the forearm, and the hand. If the forearm and hand segment are assumed to weigh 15 newtons, then the combined effect at the elbow joint is as follows:

-98 newtons - 15 newtons plus the counterforce at the elbow equals zero

(-98N - 15N + R elbow = 0)

This means that the resultant force R at the elbow is equal to 98 N + 15 N or 113 newtons in the positive direction (upward) in order to cancel the force of the shot, the forearm, and hand, which are in the negative or downward direction.

In the above example, the forearm and the hand were considered as one segment for simplicity. A more thorough analysis would divide this into two segments, consisting of the hand segment with its center of mass and the forearm with its center of mass.

Where does the force at the elbow joint come from to counteract the weight of the shot with the forearm and hand segment? The an-

*0 AJ

JVK

1[141~

N

Moment

of Force

17 cm

Figure 12-3 Analysis of forces. F - force, R - reactive force, M - moments at elbow (ME) and shoulder (Ms), W weight of forearm (W,) and upper arm (W�), I, = the perpendicular distance from the center of the elbow joint to the vector of force from the center of the mass at the hand, I, = the perpendicular distance from the center of the elbow joint to the center of mass of the forearm.

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swer is that this reactive force is generated by the muscles around the elbow joint, with some additional force provided by the ligaments and connective tissue around the elbow joint.

In mechanics, one must consider not only the force(s) but also the product of force and time, which is called an impulse. For a given mass, a given impulse results in a particular velocity. The heavier the object, the greater the impulse needed to achieve the same velocity. Thus, it is obvious that velocity and mass are related to each other and, in fact, the product of mass and velocity is referred to in physics as momentum. This law of momentum is most important in contact sports in which different masses collide at different velocities. This law is what allows a smaller football player with greater velocity to block a heavier football player with lesser velocity.

In a hockey game, the puck, which possesses a certain mass and speeds across the ice at a given velocity, has momentum equal to its mass times its velocity. If along its travels another hockey puck of the same mass, moving at the same speed but in the opposite direction, collides with it, they would come to an instant stop. One momentum would cancel the other. This principle of conservation of momentum is an important component in the game of billiards, in which solid balls hit others at different velocities.

In running and jumping activities, the forward force applied to the body depends on the force of the foot applied to the ground and the amount of time that this force was applied. In other words, the product of the two or the impulse determines the energy applied to the performance. The combination of greater velocity, magnitude of force, and time of contact with the ground are the essential factors that determineYthe speed of an athlete in the horizontal or vertical direction.

These linear movements, in which objects displace all their dimensions at the same rate, are important in biomechanical considerations. However, the anatomy of the human body dictates that the parts move primarily in a rotational fashion. A good example of rotational movement is the wheel, in which the center remains stationary while the other parts move around it.

To understand rotational movement one must understand torque. A force that gives rise

to rotational movement is called a torque. the amount of torque or, as it is also called, moment, depends on the force and its distance from the center of the rotational object. The product of force and distance is equal to torque. More specifically, the moment of force around a joint is equal to the product of a force and the perpendicular distance from its line of action to the point of rotation. In the example given above, the force on the hand and forearm create a moment around the elbow joint, forcing it to rotate. In Figure 12-3, the moment around the elbow joint is equal to the perpendicular distance (12) from the elbow joint center to the vector of force from the center of the mass at the hand (designated as F,) times the combined static force, calculated before as 113 newtons. Thus:

12 X 113 N = moment '

When 12 equals 25 cm, the moment around the elbow joint is as follows:

25 cm x 113 N = 2,825 Ncm

Moments, like forces, are vectors; therefore, direction about a point of rotation as well as magnitude must be considered. Moments of force are very significant around the body joints, because the human structure consists of long bones and, the further from the center of rotation the force is applied to these long segments, the greater are the moments around the joints of the body.

In the previous example, we considered the static equilibrium of forces, or the first condition of equilibrium. When considering the equations for moments of force, the second condition of equilibrium is assumed, which states that the sum of the moments around a joint in static analysis is equal to zero. This means that the moment around the elbow caused by the load and the weight of the forearm and hand must be balanced by a moment exerted by the muscles around the elbow to keep the arm from rotating at the elbow because of gravitational force. Specifically in this example, the moment caused by the forearm and hand (the perpendicular distance, 13, from the elbow joint to the center of mass of the forearm times the weight of the forearm), plus the moment caused by the load in the hand (the perpendicular distance, 12, from the elbow joint to

Biomechanics / 283

the line of force times the force-load) must equal the countermoment created by the elbow flexor muscles (ME) in order for the elbow to remain still. In equation form:

(13 X -WF) + (12 X -WE) + ME = 0 or (I3 X WF) + (I2 X WL) = ME

To describe this example numerically, the weight of the shot is assumed to be 98 newtons of downward force. The force due to the weight of the forearm and hand is assumed to be 15 newtons. The distance from the center of mass of the forearm to the center of the elbow joint is assumed to be 17 cm. The perpendicular distances to the lines of force are calculated below.

The perpendicular distance from the elbow joint center to the line of force from the center of mass of the forearm is calculated as the product of the cosine of the elbow angle times 17 cm, which yields approximately 15 cm�. The perpendicular distance from the elbow joint center to the line of force of the mass at the hand is calculated as the total forearm and hand length times the cosine of the elbow angle and is found to be approximately 25 cm. Using this information, it is possible to calculate the moment around the elbow joint as follows:

-(15 cm x 15 N) + -(25 cm

x98 N)+ME=0

therefore

ME = 2,675 Ncm

The muscles around the elbow joint must exert 2,675 Ncm of torque to keep the arm from rotating because of gravitational force.

The importance of the concepts presented thus far is,that there are two types of forces acting on the joint in a static analysis. The translational force affects the tendency to move along the line of action of the force. The second force is the moment or the torque that tends to rotate the segments about the supporting joints. To combat the first effect, the joint has to counteract both the translational force (with tensile forces in ligaments and muscles to hold the joint together) and the shearing and compressive forces, which also act on the joint contact surfaces. An executive can develop "tennis elbow" by holding a briefcase, because the ten

rile force at the joint may cause microscopic tears in the connective tissues at the elbow joint.

On the other hand, the rotational moment is a function of the strength of the muscle to move or rotate the joint. When a person plays tennis, the muscles move the racket at the same time as ligaments and tendons react to the shearing forces. These shearing forces, which occur during movement and impact, can result in tissue injury.

Thus far, consideration has been limited to analysis of forces around one segment, the hand and forearm. The problem becomes more complicated when additional segments are considered. It is possible to treat each segment separately and then add the effects of the previous segments to the present segment. In this way, a kinetic chain from one segment to the attached segment is created. The analysis begins - at the point of application of the external load and proceeds in sequence, solving the equilibrium equations for each body segment, until reaching the segment that supports the body, which is usually the feet.

To analyze the forces on the upper arm, all of the external forces and moments operating on the arm must be considered. In this case, the weight of the upper arm and the resultant elbow force and moment caused by the weight of the forearm and hand link must be considered. Thus, it is possible to calculate the static equilibrium equations at the shoulder that result in a reactive force (Rs) and a moment (Ms) for the person analyzed.

The principle of momentum that applies to linear movement also applies to rotational movement, and the conservation of angular momentum is one of the key principles in athletic performance. Angular momentum is a function of the mass and the rotational acceleration and is calculated as the square of the distance from the center of rotation. In rotational motion, therefore, the quantity of mass times the square of the distance from the center of rotation is analogous to mass alone in linear motion.

These basic physical concepts are essential to the understanding of human movement and the principles of physical performance. The fact that it is harder to hold a weight further from the center portion of the body is related to torque. The fact that a ballet dancer on toes and a figure skater on ice can generate high

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rotational speed is related to the fact that both performers are affected by the conservation of angular momentum.

The product of a turning body's moment of inertia and its angular velocity is called its

angular momentum. According to the law of

conservation of angular momentum, a turning body, isolated from external forces, has a constant angular momentum; that is to say, the product of moment of inertia and angular velocity about the axis of rotation is constant. If, for example, a man is standing on a revolving turntable without friction, he may increase his resistance to turning three-fold by stretching his arms sideways (Fig. 12-4). By the same token, if a man rotating on the same frictionless turntable pulls his hands toward his body, the rotational velocity increases three-fold, because the moment of inertia has decreased.

A figure skater makes use of these laws on ice. At first, as rapid a spin as possible is produced with arms extended. The arms are then brought down, and the body spins on the point of one skate with remarkable velocity. The same principle allows discus throwers or shotputters to generate higher speed across the circle of throwing.

These laws of motion are critical when applied to the muscles and bones of the body. To understand the application of motion, we must first understand the use of a basic tool, the lever.

The lever is one of the most basic mechanical systems for performing work. Each joint in the human body is the fulcrum of a particular lever. There are different types of lever systems and the human body uses all types. The forces on the different levers are applied by the

Figure 12-4 Conservation of angular momentum.

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muscular system. Activity occurs because the muscles contract or pull the various bones, which constitute the levers employed in the mechanical properties of motion.

As mentioned above, muscles operate in pairs known as agonists and antagonists. Bending the arm at the elbow, for example, requires the biceps to contract while the extensors, the triceps, relax. In order to stop this bending motion, the biceps must stop contracting at the appropriate time and the triceps must begin to contract in order to slow and subsequently stop the action. The neural coordination of this system was previously discussed in the "bio" section.

Physics divides levers into three classes,14 In the first of these, force is applied at one end of the lever and the resistance to be overcome or the work to be done lies at the other end. The fulcrum, or pivotal point, lies between. Two children bouncing up and down on a playground teeter-totter exemplify a class one lever.

In the second class, the force is applied at one end but the resistance is located above the pivot or fulcrum. A crow bar underneath a tree stump is an example of class two leverage.

In the third type, force is exerted between the pivot point and the resistance, and this is the common lever system within the human body. When you lift a weight with your arm, the pivot is the elbow joint, the force is exerted between your elbow and your hand by your biceps muscle, and the weight in your hand is the resistance (Fig. 12-5).

� . A lever may either increase the amount of work that can be done with a given input of force or it may cause the work to be done at a faster rate than the application of the force. Ar-chirnedes once bragged that he could move the world if given a long enough lever." To perform the feat, Archimedes would have used a second class lever, with his fulcrum very close to earth; he himself would have dangled on his elongated lever somewhere deep in outer space.

A mechanical advantage is gained with use of a lever. The amount of force is multiplied many times over to produce greater output at the other end. Note that this is true if the fulcrum is situated closer to where the force is applied than to where it is executed. If the reverse is true, and the fulcrum is nearer to the point where the force is executed than to the point

of force application (a class three lever), the result is a mechanical disadvantage.

For humans, the fulcrum usually falls closer to the point where the force is executed or initiated than to where it is applied, or where the

k is done. The biceps attaches to the radius bone quite close to the elbow. Therefore, to lift a 1-lb weight with your hand, your biceps operates at a mechanical disadvantage of approximately seven to one: To lift 1 lb requires a force of 7 Ib.

However, the same principle that governs mechanical advantage and disadvantage has its compensations. The hand at the end of the lever of the arm moves seven times faster than the point at which the biceps attaches to the radius. It is easily seen that only a slight movement upward of the forearm near the elbow causes the hand to move several inches during the same time interval. Obviously, the hand travels considerably faster than the elbow.

For most human joints, the length of the lever does not produce a mechanical advantage. Nonetheless, there is still more potential for production of speed if the human levers are longer. The knees are particularly vulnerable to injury, not only because of their limited range but also because, in some instances, the whole body becomes one long lever applying its force at the knees. A sport that illustrates this point is skiing. If the boot does not release when the shear forces are excessive, the long skis and the body can create an exaggerated and destructive lever, ultimately resulting in injury.

While Archimedes would have required a very long lever to move a very large ball (the earth), Hannibal needed a shorter lever to throw large balls from his catapult. Individuals concerned with much smaller spheres, such as golf and baseball, can apply still more force to the object of their intentions with a longer lever. Golfers should play with the longest clubs they can comfortably manage, as should batters in baseball.

However, the longer the lever, the less fine the control, and the greater the requirement for muscular force. Thus, the putter, the club used for a deft, accurate stroke, is the shortest in the bag. Many good golfers further reduce the potential margin for error by shortening up on the putter and holding it lower on the shaft.

In addition to some of the important com-

286 /Scientific Foundations of Sports Medicine R

T

F

R

F

Figure 12-5 Levers: F - applied force, R - resistance, A= fulcrum.

ponents of mechanics, it is also essential to understand the other laws of motion. Newton neatly encapsulated these laws into three principles. The first states that an object remains at rest until some force acts upon it. If the object is already in motion, it continues at a constant speed unless some outside force is brought to bear. In other words, until the levers of foot and leg are applied to a soccer ball, it remains at rest on the ground. However, once it is kicked, the ball continues to roll at a constant rate until it is acted on by the outside force of friction from ground or air, or by contact from another system of levers in the form of an opposing soccer player.

When two or more forces act on an object, the subsequent force is known by physicists as the resultant force. If player A kicks a soccer ball due north simultaneously with player B's kick of the same ball due west, the ball will travel northwest along a path determined by which athlete delivered the most force. The route taken by the ball and its velocity are the resultant force supplied by players A and B.

Newton declared that the main task of mechanics was to learn about forces from observed motions. The physics behind movement is related to the law of momentum, which is part of Newton's second law. Momentum is a concept that consists of velocity multiplied by the mass of the moving object. Momentum, in terms of physics, is distinguished from force, which is defined as mass multiplied by acceleration, or the rate of change in velocity. Alteration of momentum, or a change in motion, declared Newton, is governed by the force brought to bear upon the object, which then follows the straight line in which the force acts.

Consider the problem of a man leaping over a small puddle. He runs toward the puddle, creating many forces including horizontal ones. Fps he nears the water, the central nervous system, the movement coordinator, orders the muscles of the feet and legs to contract, generating a vertical force for the jump. The height depends on the man's ability to generate enough force to exceed gravitational force temporarily. If the man weighs 150 pounds and produces only 140 pounds of vertical force, he will have wet feet. Once airborne, he can no longer add any force to the jump. The force of momentum, the velocity at take-off multiplied by the man's weight, must be enough to overcome the

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demands of gravity in order to jump over, not into, the puddle. The vertical force combines with the horizontal force for the leap. That is to say, the body does not travel in either a purely vertical direction or a solely horizontal one. Rather the path becomes a combination of horizontal and vertical forces, a direction that physicists call a resultant.

Newton's third law is that for every force that acts upon an object, the object itself exerts an equal and opposite amount of force. When you kick a ball with your bare foot, the painful sensation in your big toe confirms Sir Isaac's third law. The recoil of a fired rifle is also an example of equal and opposite reactions. A car striking a bridge abutment at 60 miles per hour is demolished, while one that nudges the wall at 5 miles per hour remains intact. The wreck is an example of a much greater degree, of equal and opposite force.

Another principle affecting the body is derived partly from theories of Einstein. An old bedroom farce joke uses the punch line, "Everybody's got to be someplace," and Albert Einstein said that energy can be neither created nor destroyed. In other words, energy or a visible manifestation of it in the form of force also always must "be someplace."

This means that when one generates a force by swiveling the back and then suddenly tries to stop the movement of the back, the force developed in the trunk of the body does not simply disappear. It must go someplace. The secret to efficient use of a body for work or sport, for fitness or injury prevention, depends to a great extent on where these forces go or how well they are exploited.

In the human body, the bones, or levers, move in a rotational manner. These angular movements create linear movement for the total body. The same laws that govern linear motion also govern angular motion. The only difference is that the length of the lever also plays an important part. If the body begins a rotation, it continues to turn on its axis until the movement is altered either by a change in body position or by the application of some other force. Imagine that the ice skater mentioned above begins a spin with the arms abducted or outstretched, building up angular momentum by the maneuver. If this athlete suddenly drops the arms to the side, the velocity of the spin increases, because the momentum that was ini-

288 /Scientific Foundations of Sports Medicine

tially generated is constantly maintained around the axis. The change in the arms' distance from the center of the body transfers this angular momentum to the body itself.

Angular momentum can be redistributed throughout the body. When a long jumper leaves the ground, he is propelled forward, and angular momentum is developed. However, unless that momentum can be redirected, the jumper will land flat on his face. Such a disaster is prevented by transferring some of the angular momentum to the arms, which explains the wild flailing exhibited by long jumpers (Fig. 12-6).

Angular momentum can be expressed in terms of two other important parameters of rotation: angular velocity and moment of inertia.

Angular velocity is represented by the bo. rotational speed and direction. For example a diver performs a forward double somers in 1 second, the magnitude of his average gular velocity is two revolutions per secon.

The moment of inertia of a body abou axis is the body's tendency to resist change angular velocity about that axis. It is obvi that massive and extended bodies have a la moment of inertia than do lighter and smz ones. In fact, the contribution of each part or segment in a body to the total momen inertia about an axis is equal to the mass of segment times the square of its distance fi the axis of rotation. For example, a typical ver with his body straight and his arms at sides has a moment of inertia of 14 kg per

Figure 12-6 Transfer of angular momentum.

Biomechanics / 289

ter squared about his somersaulting axis, but a moment of inertia of only 1 kg per meter squared about his twisting axis.

Angular momentum is the product of the angular velocity and the moment of inertia about a specific axis. In the case of the diver, that is the sum of angular velocities around the two axes and the moment of inertia around these axes.

The analogy between angular momentum (moment of inertia times angular velocity) and linear momentum (mass times linear velocity) is not perfect. The reason is that the body can change its body segment lengths while performing angular movement, such as the diver moving from a tuck position to a straight body. That changes the moment of inertia about his somersaulting axis. In linear momentum, this change does not occur.

Any mechanical phenomenon created by the human body must be initiated by the energy produced by the skeletal muscles. This energy allows the rotational movement of a body segment to create movement. The faster the movement, the more powerful is the motion.

' There are some limitations to any analogy between power created by muscles and that produced by an engine. An engine is rated as having a certain amount of horsepower, meaning that it can produce a specific amount of work each second that it is in operation. It lifts or pushes a number of pounds a certain distance. We can measure sustained human efforts the same way. A woman pedaling a bicycle can be rated.for the horsepower she produces in transporting her weight and that of the bike over a certain distance within a certain amount of time. This type of power rating is valid for a rhythmic and sustained amount of force. But it does not serve as a useful description for impulsive actions.

Consider for a moment what happens when one fires'a rifle with the barrel pointed straight up into the sky. Most of the power to speed the bullet on its way is produced before the bullet is actually moving. Because of the confines of the rifle barrel, there may be some power added as the explosive charge pushes toward the muzzle behind the bullet. There is no way to compute an accurate value for the amount of horsepower generated. The force is not con

stant, and gravity and friction constantly alter the velocity.

The same is true for an impulsive action by a human, such as a high jump. It may be said that one jumper actually generates more force than another jumper but still does not leap as high, because of a failure to coordinate all of the force into as large a single impulse. The key measurement, therefore, is not how much "horsepower" was developed as the athlete sprinted to the launching point and hurled himself into the air, but how much ultimate ballistic muscle force was generated for the actual lift-off.

Another factor needed to understand movement is appreciation of the classification of mechanical energy, which is defined as the capacity to perform work. Kinetic energy is that which the body possesses by virtue of its motion. During the windup of a pitch, the arms of the baseball pitcher contain kinetic energy. Potential energy exists in the position of the body. Likewise, a diver at the edge of the platform possesses a certain amount of potential energy through the imminent application of gravity.

Sometimes the types of energy can be totally separate aspects of a movement. For example, the instant that a person begins to rise from a trampoline, the kinetic energy begins to diminish and the potential energy increases. At the highest point of the maneuver, the instant of zero velocity when the gymnast is neither ascending nor descending, the kinetic energy is zero and the potential energy is at its maximum. During the descent, the potential energy in effect is transformed to kinetic energy. At the deepest penetration of the trampoline bed, the strain energy reaches its maximum.

These mechanical, physical precepts are useful in the analysis of human movement, because they permit examination of the forms of energy, forces, directions, or speeds that constitute an activity. Quantification can also assist in determining the most efficient use of effort, that is, the optimal way to do something.

BIOMECHANICS

The field of biomechanics can be divided into kinematics, which describes the motion of the

290 /Scientific Foundations of Sports Medicine

body and its segments without reference to the forces that cause the motion, and kinetics, which describes the forces that cause the movement. The kinematic parameters include linear and angular displacement, velocity, and acceleration. The kinetic parameters include the external and internal forces that act on the body segments.

In order to measure the kinematic and kinetic parameters, it is necessary to make a few assumptions. If it were possible to disassemble and reassemble the human body like other machines, measurements could be taken more accurately. However, this is obviously impossible. Therefore, some of the measurements are derived from cadavers, and additional assumptions are made based upon the linkages of the human body. This is not different from any other field involved with living bodies. In the field of physiology, for example, many assumptions are made about the ability of the body to consume oxygen. In the conversion of energy measurements from external measurements to internal measurements, many reasonable assumptions are made. In determining the composition of different muscles and their classification into fast and slow twitch muscles, many assumptions are made about the chemical staining methods and the counting methods. Of course all statistical methods, which are the basis for most behavioral research, utilize assumptions about the normality of the populations and the distribution of the data samples.

Therefore, to view the human as a machine Made of links is an oversimplification, but it is possible to create a representation of the body in'a humanoid model made of rigid segments. This model facilitates quantitative analysis of movement. The links that represent the body's limbs are a series of interconnected rigid segments that Flemonstrate independent motion.

This system can be applied more accurately if we realize that there are different body types. It is clear that body differences in shape occur between ages and sexes, and within individuals. The field which deals with the measurement of size, weight, and proportions of the human body is anthropometry. 3

Anthropometric data are fundamental to biomechanics, because some of the assumptions made in the calculation of movement parameters are based on them. When a scientist

performs a biomechanical analysis of any movement, the human body is considered to be a system of mechanical links, with each link of known physical size and shape according to anthropometric measurement (Fig. 12-7).

After adapting the anthropometric measurements to the different body segments, the next assumption is that this link system is connected at identifiable joints. Because the body landmarks or the body segments are covered by muscle, fat, and skin, it is sometimes difficult to identify joints such as the hips and shoulders. However, with the aid of statistical and numerical methods, some of the errors can be filtered out.

Some of the pioneers in the field of anthropometry are Braune and Fischer, Dempster, and Snyder, Chaffin, and Schulz."-" They have made tremendous contributions by dissecting cadavers and measuring the location of joint centers. Using cinematographic techniques, it is possible to trace the intersections of the long axes of the segments during movement. Some of the landmarks used in the field of biomechanics are illustrated in Figures 12-7 and 12-8.

In addition to landmarks required for biomechanical tracing, it is important to predict

Figure 12-7 Anthropometric measurements of the human body.

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the segment mass and location of the center of the mass (see Fig. 12-8). The National Aeronautics and Space Administration has made detailed measurements of human body composition and the relative mass for segments such as arms, legs, and hands, given the overall height and weight of the individual. The specifications may not be exactly accurate for each individual, but they are close enough to humans in general for the purposes of even the most exacting scientists. Body segment mass and volume are related to the density of the segment. Density can be determined by immersing cadaver body segments in water and measuring the volume of water displaced. The equation used is D = M/v, where D equals average density, M equals the mass of the segment, and v equals the volume of water displaced. The values thus obtained for the different body segments are available in various biomechanics textbooks.

In addition to the segment mass and volume, the distribution of the mass within the segment is necessary in order to compute the kinetic information. From this distribution of the mass, it is possible to calculate the mass center or the center of gravity of the segment. There are a few methods to calculate the segment center of gravity. One method determines the distribution of forces when a person is suspended between two force platforms by calculating the change in vertical forces created by moving various segments to different angles. Another method involves submersion of the segment in water. Regardless of the method used, a sufficient data base exists from various investigations that have calculated the center of mass for different segments and for different populations, so that these parameters need not be recalculated for each analysis.

Knowledge of the center of gravity of each segment ,and its weight and length allows the calculation of the static force and torque at each body joint for a given posture as described in the mechanics section of this chapter. However, in athletic performances and in normal human life, we are seldom concerned with static posture. More realistic are the dynamic performances in which the forces caused by motion plus the forces caused by gravity act upon the body.

For these dynamic analyses of the human body, it is necessary to know the inertial property of the segment. This property is referred to

Biomechanics / 291

W e

Figure 12-8 Coplanar link system: R = reaction force, M = moment, CM = center of mass, W = weight.

as the moment of inertia. The formula that describes the moment of inertia follows:

I= M x R x R

That is, the moment of inertia of the segment is equal to the mass of the segment times the square of the perpendicular distance from a given axis. There are different methods for calculating the moment of inertia of the individual body segments. These are described in various biomechanics textbooks.

It is also important to calculate the place on the body segment at which the moment of inertia affects the segment. This point can be der-

292 / Scientific Foundations of Sports Medicine

ived by knowing the radius of gyration. The radius of gyration is equal to the square root of the moment of inertia divided by the mass of the segment.

According to Drillis and Contini, the radius of gyration is "the distance from the axis of rotation to an assumed point where the concentrated total mass of the body would have the same moment of inertia as it does in its original distributed state."27 This information is necessary to quantify the dynamics of human motion in conjunction with other parameters.

It should be remembered that all of these estimated parameters are used in calculating the dynamic forces rather than merely in describing movement in qualitative terms. These parameters are available in numerous sources, and the normal analysis of human movement does not require the individual calculation of all of these parameters. The information resides in tables and charts that can be accessed at will. The normal analysis of movement relies on this information, in the same way that physiologists depend on the tables presenting characteristics of different gases and their coefficients at various temperatures and pressures.

Quantification of an action, whether to evaluate it or to attempt t-) improve it, can be accomplished through biomechanical analysis. Biomechanical assessments normally begin with quantification of the kinematic portion. This is usually accomplished by utilizing high-speed cinematography or videography, which allows careful. scrutiny of even the fastest movements of huans or animals. The films or videos are traced, and the resulting data are stored in a computer that calculates the results by applying the principles of physics and mechanical engineering. Tables and graphs can then be generated, giving a precise profile of what actually occurred during the execution of the movement. The researcher then carefully examines this output in order to understanding the motion and, in the case of an athlete, to determine which patterns are most important in distinguishing championship from average performances.

Biomechanics is a science still in its adolescence with many discoveries yet to be made. Hand analysis of high-speed films is a slow and tedious process, and it is only recently that the computer has been harnessed to make the pro

cess more efficient. Development of this technology in the United States has meant that many complex analyses can now be executed in a relatively short time.

In the past, athletic achievement depended mainly on the individual's talent, although skill was often enhanced or ruined by existing facilities, equipment, and, undeniably, coaches. Athletes with superior genetic compositions who successfully interacted with the available facilities dominated the list of world records. Continual improvement of equipment and techniques has complemented raw talent.

However, with the advent of new measurement tools and knowledge in the field of sport science, athletic achievement has attained a new dimension. The athletic teams of the United States, which for years dominated amateur sports, are no longer the leaders. Countries such as those of Eastern Europe and Cuba, which have relatively small populations, have achieved a spectacular level of success in athletic events. Current evidence suggests this trend may continue through the remainder of the 1980s and 1990s. Such domination stems from the application of science to the realm of athletic performance.

Modern coaches can use biomechanical means to optimize the human body in each event. Because the human body obeys the same physical laws as all other earthly objects, the laws of motion govern its performance. In order to throw, run, or jump, physical laws must be obeyed. It is impossible to throw the shot 20 meters if the shot velocity and angle of release do not attain certain values. These values do not differ for different athletes, because for each particular shot velocity, there is one specific optimal angle.

For the jumper to leap 8 meters, it is necessary to produce certain forces on the ground to propel the body with a specific reaction force at a particular angle. This force is unique, and it is impossible to cover the same distance with only a fraction of the force because gravitational pull acts uniformly regardless of the jumper.

The concept to be reemphasized here is that all bodies, athletes, implements, or machines are affected by and must adhere to the laws of motion. The science of biomechanics deals specifically with motion of the body and

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the resultant forces. A number of scientists have long recognized these facts of force and motion and their relationship to humans, but the kind of equipment that could measure and analyze the motion and forces involved was lacking. Thus, further research was impeded.

Without a computer to store information, retrieve it, and perform the myriad computations, such calculations can place the scientist in an impossible position. But before a computer can perform its job, whether it is to guide a robot, print a check, or retrieve a space vehicle, it needs a program, a sequence of instructions that tell it how and what to do.

Programming a computer involves hundreds and, at times, thousands of hours of work. But once the instructions have been fed into the computer, it can automatically execute the hundreds of steps without any need for further instructions, and the execution may only take a few seconds. The beauty of a computer is that it can play the great game of "what if?" In sports, one could ask, "What if I hold the shot down here and then whirl in this fashion?" The computer can calculate the distance the shot would travel, applying the amount of force developed in previous analysis. Through use of the computer, then, biomechanics can write equations and construct models to obtain optimal performances.

Another critical element is the camera, either a high-speed movie or sufficiently fast video system. It provides sequences of the body in motion. Knowing the speed with which film .orlvideo tape travels through the camera allows calculation of the velocity and acceleration of body segments using the joints as points of referepce. For example, if the shutter speed on the camera is 200 frames per second, one can identify the location of the right knee at the start of a sprint, compare the position of the right knee ,in frame 20 of the film, and learn how far the right knee has moved in one-tenth of a second. The data can be further utilized to determine velocity, acceleration, and, with some additional information, even the forces involved. The forces can be calculated by measuring the length of the leg, for example from knee to ankle, and, by using the NASA specifications, determining the mass of that segment and the center of gravity. Using these values, quite reasonable estimates of the exact forces

and torques around the joint center can be calculated (Fig. 12-9).

Along with analyses based on films taken during actual events, highly sensitive force plates have been developed for precise impact measurements. These allow controlled laboratory testing of forces, such as when an object like the human foot strikes the plate during a sprint, or when a monkey leaps from the plate onto a table. The plate is capable of recording three different components of forces-vertical, horizontal, and sideways or lateral-as well as the moment or torque.

Any kind of athletic movement or work action that can be photographed with a high-speed motion picture or video camera can be fed into the computer. Forces can be plotted for each segment of the body as the accelerations and lengths of the segments are measured. ,Themaximum amount of force that can be generated using a particular approach in an activity can be calculated.28 For instance, it is feasible to calculate how high a jumper might go if he changed from his customary form of the roll to the flop style, assuming he was able to generate the amount of force for the flop as he did for the roll. Analyses have shown that the flop happens to be a more efficient use of forces for athletes who do not possess extremely powerful legs.

It is important to remember that because of both gross and subtle variations in the neuromuscular system of each human, the biomechanical actions of individuals are as unique as their fingerprints. The shades of difference from one person to another are, in fact, great enough to permit the development of a foolproof method for guaranteeing a signature. A person could file his or her signature in a computer bank. The information in the computer would contain not only the shapes of the letters, but the amount of force the individual applied to every loop, line, and curve. With this device, a buyer in a store need only sign the chit on a force plate or use a pen with a forcesensitive transducer that transmitted the information directly to the computer. The patterns of force would be compared instantly and, if not the same, the new one would be rejected.

Similarly, detection of variations or errors in human movement has always been one of the most difficult problems facing coaches,

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Cull Graphing module

A = UEL_MAGLi. FOOT v = VELMAG-R. ANXLE a = UELMAG_R. XNEE o = VELMAG_R. HI P o = VELJMAG L.HIP

= VEL MAGL. KNEE

Figure 12-9 Computed performance analysis.

Biomechanics / 295

trainers, and physicians in athletic situations. If the error detection is inaccurate or nonspecific, the quality of correction is poor. Failure to recognize the causes of error stems from an inadequate understanding of the mechanisms of human motion. Impact in sports, automobile accidents, falls, and other movements involving forces can be acccurately quantified through biomechanical applications.

The designer of protective equipment for sports such as hockey and football must have an understanding of biomechanics, because it is necessary to comprehend before the equipment is designed how the human head reacts to impact forces or how a skier's leg reacts to twisting forces. The forces produced by the human body cause a change in acceleration or speed. The change might involve the entire body, as in sprint starting, skating, or volleyball (in a vertical jump to block). It may also be a body segment or combination of segments, as with a boxer's upper arm and forearm, a golfer's arms, or a soccer player's thighs and lower legs. Through use of biomechanical analysis, it is now possible to detect errors scientifically that are beyond the visual capabilities of the human eye.

To enhance the understanding of biomechanics, we should now consider a few physical terms that refer to muscular activity. When a muscle contracts, it produces force. This force moves the limb and may move an external object to perform work. This work is executed in a certain time to produce power.

A muscle may contract in various ways. If the movement involved is of a constant speed, the movement and the contraction are called isokinetic. When muscular force development results in no change in length for the muscles and in no skeletal movement, the contraction is termed isometric. If the force generated by the muscles results in a shortening contraction, the contraction is called concentric. If the force generated by the muscles results in an elongation of the muscle, the contraction is called eccentric.

When the muscle contracts and there is a change in limb position, work is performed. When time is required to perform the physical work, then units of power measurement are employed, because the rate of work is power. In human performance, striving for excellence

on the athletic field or in recreation, it is important to be able to sum the forces exerted on the various joints. This principle is called the summation of joint forces.

For example, in swinging the golf club in the drive, the amount of force exerted by the club on the golf ball depends on how much of the total force exerted by the body actually reaches the club. If there is any Toss of force due to bad timing, the golf club head will not move at the same velocity. Any violation of the principle of summation of joint forces can result in too small a force being exerted by the golf club.

Another important biomechanical principle is that of continuity of joint forces. This is illustrated by the fact that the golfer not only must use all body joints efficiently, but also must time their use so that the motion begins at the larger segment (such as the thigh) and then continues and is overlapped by motion of the hip and trunk. There must be no pauses in the flow of motion from the legs to the trunk and to the club. It must be continuous. A violation of this principle results not only in too small a force but also in bad timing and a poor "feel" on the golf club.

Because club speed is determined by the force applied and the length of time of force application, the best combination of force application should be determined-a large force in a short time or a small force for a longer time.

There is an optimal combination for each activity. The size of the force multiplied by its time of application is called "impulse" and it is actually this force-time combination that produces the golf club velocity. Therefore, the impulse in any activity should be determined to result in optimum efficiency. Although compromises in the size of force and duration of application often have to be made in sports to achieve an optimal combination, one such combination to be avoided is a small force applied for a short time.

The size of the force an athlete can produce is determined by his or her ability to comply with the principles of summation and continuity of joint forces. In the absence of measuring devices, assessing whether the force application time is as great as possible presents yet another problem. In general, if each joint has gone through a complete range of motion,

296 /Scientific Foundations of Sports Medicine

one can be assured that the maximum time available has been used.

It was previously pointed out that not only must the range of motion of the joint be complete, but the joint must straighten fast and the combined joint motion must be continuous. The concept of the combined effect of force and duration of application in producing speed changes is called the principle of impulse. Violation of this principle causes further errors in performance.

Direction of force application is another important principle. The direction of the application of force to the golf club is vital, but, so is the direction from the club head to the golf ball. In an optimal situation, the force is exactly 90 degrees to the club, and the club head hits the ball exactly at its center. However, some deviation is at times necessary if the flight of the ball has to be changed in a predetermined pattern. Incorrect direction of force can be disastrous in events such as gymnastics and diving. A good technique implies that the principle of direction of force has been followed.

A final principle is the summation of body segment speeds. Especially in any throwing, kicking, and striking events, it is important to obtain as high a hand, foot, stick blade, racket head, or club head speed as possible at the instant of impact or release. The speed of the last segment in the chain is built by adding the individual speeds of all the preceding segments with appropriate timing. If any of the segments contributes. low or negative values, the resultant measured for the last segment is less than optimum. This principle is similar to summation of joint forces and is closely related to it.

In summary, any motion should obey the principles of summation of joint forces, continuity of joint forces, impulse, and the direction of joint forces. Thropgh the use of biomechanics, all of these principles can be quantified and optimized so that better and safer results can be obtained.

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Scientific Foundations of Sports Medicine ISBN 1-55664-081-1 0 1989 by B.C. Decker Incorporated under the International Copyright Union. All rights reserved.