clinical biomechanics_ mechanical concepts and terms

CHAPTER 2: MECHANICAL CONCEPTS AND TERMS

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CHAPTER 2:MECHANICAL CONCEPTS AND TERMS

This is Chapter 6 from R. C. Schafer, DC, PhD, FICC's best-sellingbook:Clinical Biomechanics: Musculoskeletal Actions and Reactions

Second Edition ~ Wiliams & Wilkins

The following materials are provided as a service to our profession. There is nocharge for individuals to copy and file these materials. However, they cannot besold or used in any group or commercial venture without written permissionfrom ACAPress.

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Energy and Mass Energy The Center of MassNewton's Laws of Mechanics The Law of Inertia The Law of Acceleration The Law of ReactionForce Moments Types of Force External Loads The Characteristics of Force Biomechanical DescriptionsStatic Equilibrium Statics EquilibriumLinear Forces Pressure Compression TensionConcurrent ForcesParallel Forces Lever Actions Wheel and Axle Mechanisms Pulley Systems Force Couples Bending Torsion

Chapter 2: Mechanical Concepts and Terms

All motor activities such as walking, running, jumping, squatting, pushing, pulling,lifting, and throwing are examples of dynamic musculoskeletal mechanics. To betterappreciate the sometimes simple and often complex factors involved, this chapterreviews the basic concepts and terms involved in maintaining static equilibrium.Static equilibrium is the starting point for all dynamic activities.
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Energy and Mass

Biomechanics is constantly concerned with a quantity of matter (whatever occupiesspace, a mass) to which a force has been applied. Such a mass is often the body asa whole, a part of the body such as a limb or segment, or an object such as a load tobe lifted or an exercise weight. By the same token, the word "body" refers to anymass; ie, the human body, a body part, or any object.

Energy

Energy is the power to work or to act. Body energy is that force which enables it toovercome resistance to motion, to produce a physical effect, and to accomplishwork. The body's kinetic energy, the energy level of the body due to its motion, isreflected solely in its velocity, and its potential energy is reflected solely in itsposition. Mathematically, kinetic energy is half the mass times the square of thevelocity: m/2 X V524. In a closed system where there are no external forces beingapplied, the law of conservation of mechanical energy states that the sum of kineticenergy and potential energy is equal to a constant for that system.

Potential energy (PE), measured in newton meters or joules, is also stored in thebody as a result of tissue displacement or deformation, like a wound spring or astretched bowstring or tendon. It is expressed mathematically in the equation PE =mass X gravitational acceleration X height of the mass relative to a chosen referencelevel (eg, the earth's surface). Thus, a 100-lb upper body balanced on L5 of a 6-ftperson has a potential energy of about 300 ft-lb relative the ground.

The Center of Mass

The exact center of an object's mass issometimes referred to as the object's centerof gravity. When an object's mass is evenlydistributed throughout, the center of massis located at the object's geometric center.In the human body, however, this isinfrequently true, and the center of mass islocated towards the heavier, often larger,aspect. When considering the body as awhole, the center of mass in the anatomicposition, for instance, is constantly shiftedduring activity when weight is shifted fromone area to another during locomotion orwhen weight is added to or subtracted fromthe body.

The term weight is not synonymous withthe word mass. Body weight refers to thepull of gravity on body mass. Mass is the quotient obtained by dividing the weight ofa body by the acceleration due to gravity (32 ft/sec524). Each of these terms has adifferent unit of measurement. Weight is measured in pounds or kilograms, while



mass is measured by a body's weight divided by the gravitational constant. Thepotential energy of gravity can be simply visualized as an invisible spring attachedbetween the body's center of mass and the center of the earth. The pull is alwaysstraight downward so that more work is required to move the body upward thanhorizontally (Fig. 2.1).

Newton's Laws of Mechanics

Sir Isaac Newton's three laws of mechanics apply in any movement or injury andserve as the basis for the science of mechanical engineering. They are appliedthroughout the study of biomechanics and deserve definition and explanation.

The Law of Inertia

NEWTON'S FIRST LAW

A body remains at rest or in a state of uniform motion in a straight line until actedupon by an unbalanced or outside force. When a body is at rest, the forces actingupon it are completely balanced. When the body or a part is in motion, it willcontinue to move until some force causes it to stop. All objects express inertia inthat they resist change whether at rest or in motion. The force necessary toovercome the inertia of a body depends upon the weight of the body and the rate atwhich it is moving. It is for this reason that more effort is required to put a shotthan throw a baseball the same distance.

An object does not move unless a force has been applied that is greater than theobject's inertia. A body at rest may have many forces acting upon it; and if theirmagnitudes and directions completely cancel one another, there is zero net force anda state of static equilibrium. If these forces are unbalanced and result in a net forceother than zero, movement (dynamics) occurs.

The Law of Acceleration

NEWTON'S SECOND LAW (PROPORTIONALITY)

The acceleration of an object is proportional to the unbalanced forces acting upon itand inversely proportional to the object's mass. In other words, the net force actingon a body gives it an acceleration that is proportional to the force in both directionand magnitude and inversely proportional to the mass of the body.

ACCELERATION MEASUREMENT

A forceful push moves a small object rapidly; a light push on a large object moves itslowly. Acceleration is a quantity, where changes in direction or magnitude mayoccur, which refers to the rate of change of linear velocity. It is measured by itsmagnitude in feet or meters per second per second. Mathematically, acceleration =force/mass, or final velocity minus original velocity divided by time.

The Law of Reaction



NEWTON'S THIRD LAW (INTERACTION)

For every action there is an equal and opposite reciprocal reaction. Inertia ismanifest as a reaction equal and opposite to the action that created the acceleration.Thus, forces are always in pairs that are equal in magnitude but opposite indirection. It is arbitrary which force is called the action and which the reaction, butusually in biomechanics we refer to internal body forces as actions and externalforces applied to the body as reactions (eg, weights, floor reactions).

EXAMPLES OF REACTION

Regardless what degree of force is induced upon a part, there is always acounteracting stress because for every action there must be a reaction. For instance,a downward pressure equals an opposing upward thrust (eg, as that of a rocket).When an individual pushes against or lifts up any object, the object pushes againstthe person or pulls down with equal force in a line directly opposite to that of theindividual's force. A force pulling right is equal to a pull toward the left, expressed interms of centripetal and centrifugal force. A spiraling force in one direction must beaccompanied by an equal twisting force in the opposite direction. A force permittinga part to slide downward must be resisted by an adequate upward force. And a forcetending to bend a structure along its axis must be resisted by a force equal toprevent such bending.

Force

Force, simply, is any push or pull produced by one object acting upon another. It isanything that tends to cause or change the yield movement acceleration of an object.For example, when an object at rest is pushed (or pulled), it moves in the direction ofthe push at a speed relative to the strength and time of the pushing force. Linearmovement without turning is called translation, and it is the result of the forcepassing through the center of mass. Some degree of rotation will accompanytranslation if the line of push or pull does not pass through the center of mass. Thefurther the line of force is from the center of mass, the greater is the rotationalcomponent.

Force is measured in gravitational units: pounds or kilograms. It has twocomponents: strength (magnitude of force) and direction.

Moments

The term moment in mechanics refers to the tendency, or measure of tendency, toproduce motion, especially about a point or axis. The moment of inertia is greatestin all axes of the body that go through the center of gravity of the body, and it is lessthrough axes which pass outside this center of gravity. Thus, it is easier to topple anupright object by striking it high or low than in the midsection.

It is easier to spin a person around by striking his outstretched arm than bystriking his shoulder. When a force produces rotation, the measure of this rotationaleffect is called a moment of force or torque. The rotation moment of such a force can



be computed by the force applied times the perpendicular distance from the centerof rotation.

Types of Force

LOAD AND STRESS

Forces and or moment (torque) external to a particular structure such as gravity,another muscle contraction, inertia, wind, water resistance, and surface reaction arereferred to as loads. The applied weight used in traction or an adjustment and theresistance offered to an exercise are external mechanical loads. Interior resistanceforces such as tendon tensile strength and muscle stretch which react to a load arereferred to as biomechanical stress.

NEWTONS

Loads are often measured by newtons, the universal measure of force based onNewton's second law of motion. A newton (N) is the quantity of force necessary togive a 1-kg mass an acceleration of 1 meter per second per second: 1 N = 0.2248poundforce; 1 poundforce = 4.48 newtons. Note that, unlike pounds and kilograms,a newton's definition does not depend on the earth's gravitational field.

SUBSTANCE MECHANICAL PROPERTIES

The mechanical properties of a substance determine how it will react to load andstress. If a substance's mechanical properties are identical in all directions such asa metal, it is isotropic. A sample portion of an isotrophic material shows the samecharacteristics of strength and elasticity as any other sample portion. As everyhuman tissue is specialized to resist customary loads, the human body contains noisotropic structures.

All body tissue is anisotropic; ie, its mechanical properties differ with varying areaorientations. As an example, a bone will vary in its strength and elasticity to a loaddepending upon whether the load is applied transversely, axially, at an angle, or witha twist.

External Loads

The resistance offered to the forces ofmusculoskeletal structures and joints iscommonly derived from gravitational pull,the resistance of a fixed structure, manualresistance, environmental factors (eg,swimming in water, running against wind),elasticity, and friction factors. Gravity isthe most common external force to whichthe body is subjected, and it always offers aforce directed in a straight line downward.In determining the effect of gravity, theweight and position of resistance must beconsidered (Fig. 2.2).



SAMPLE CLINICAL APPLICATIONS

Such factors have common applications in therapeutics. When the resistance ofgravity is not desired (eg, in weakness), the resistance of the body can be reduced byimmersion in water where the body is buoyed up by a force equal to the weight ofthe water displaced to balance the gravitational force on the body. Canes andcrutches also help to reduce gravitational forces on a weak or tender body part.

When resistance is desired, stationary or resistant structures and manual loads areutilized in developing isometric muscle contraction. In therapeutic exercise, forinstance, friction devices to offer load resistance against muscle contraction arepopular. A variety of elastic materials are used such as springs and tubes where theline of resistance lies along the length of the elastic material.

STRESS ON WEIGHT-BEARING JOINTS

Hollingshead/Jenkins point out that the pull of supporting muscles frequentlyincreases joint pressure in weight-bearing joints. For example, if a 200-lb personleans so that his weight is supported on one limb, the hip joint is subjected to all theperson's weight above the hip, plus the weight of the other limb, and it alsowithstands the pull of the muscles necessary to maintain equilibrium. As one lowerlimb is typically 15% of total body weight, this would mean the support of 170 lb ofbody weight plus 425 lb of balance force for a total force on the hip of almost 600 lb.This happens during quiet standing; running or holding a weight would greatly addto the stress.

SPINAL LOAD CONSIDERATIONS

Typical spinal loads offer another exampleof the effects of external forces on themusculoskeletal system. When the spine isloaded in lifting a weight, the lumbosacralarea is subjected to weight forces from boththe upper body plus the weight being lifted.It is also being subjected to the bendingtorque caused by these forces because they



are some distance from L5's center ofmass. The load on the lumbosacral disc isthe sum of the weight of the upper body,the weight held, the spinal muscle forces,and their lever arms respective to the disc.

The importance of spinal loads is underscored in such activities as lifting, bowling,rowing, and even in lordotic joggers. It has been estimated that when an object isheld 14 inches away from the spine, the load on the lumbosacral disc is 15 times theweight lifted. Thus, a mother lifting a 20-lb child at arms' length theoretically placesa 300-lb load on her lumbosacral disc.

Another example is a dead lift of 200 lb by a 170-lb person where it has been shownthat a 2000-lb force is exerted on the lumbosacral disc (Fig. 2.3). This load, ofcourse, must be dissipated, otherwise the L5 vertebra would be crushed. The load isdissipated through the paraspinal muscles and, importantly, by the abdominalcavity which acts as a hydraulic chamber to absorb and thus diminish the loadapplied.

These observations on spine loading emphasize the vulnerability of the spine to themechanical stresses placed upon it, especially in people with poor muscle tone. Bonycompression of the emerging nerve roots arises as a result of subarticularentrapment, pedicular kinking, or foraminal impingement due to posterior vertebralsubluxation.

STRESS ON NONWEIGHT-BEARING JOINTS

Even joints that do not bear weight can be subjected to tremendous pressure. Forexample, when the extended forearm is flexed, the flexors exert a line of pull that isalmost parallel to the the ulnar and radius. Thus, much of the muscular force isexerted at the elbow joint which compresses the articular surfaces. Because of thelack of complete articular reciprocity, this pressure isconcentrated onto an area farless than that of the whole apposed articular faces. If the hand holds a weightduring this flexion, the contraction must be of greater force, which in turn causesgreater pressure.

OTHER FACTORS

The total stress on the body during lifting is not completely determined bymechanical factors, however. It has been found that the combined effect ofbiomechanical and physiologic stresses leads to an overall measure of lifting- taskacceptability as expressed by the psychophysical stress involved. One study hasfound that there are conditions for which the acceptability measures of thecombined biomechanical and physiologic stresses and the psychophysical stressesinvolved were close to one another. (41)



The Characteristics of Force

The four features of a force are its magnitude, action line, direction, and point ofapplication. A force cannot be described unless these factors are known because anyvariation of one or more of these factors changes the result.

MAGNITUDE AND ACTION LINE

Magnitude is a scalar quantity such as time, speed, temperature, volume, andlength that has no direction. More factors must be known besides magnitude if aforce involving a stress is to be accurately described. For example, a 5-lb weight heldin a hand when the arm is held vertically produces a far different effect in theshoulder joint than the same weight held in the hand when the arm is heldhorizontally. Thus, the action line (line of force application) must be known.

DIRECTION AND POINT OF APPLICATION

Since a pulling force has a different effect than a pushing force, it is important toknow the direction of force along the action line. In addition, the site where the forceis applied must be known to complete the picture.

Biomechanical Descriptions

Many basic considerations in biomechanicsinvolve time, mass, center of mass,movement, force, and gravity --all of whichoperate in accordance with the laws ofphysics. However, while numerousparameters of movement are interrelated,no one factor is capable of completelydescribing movement by itself. Forexample, acceleration and velocity involvedisplacement and time, but they areinsufficient unless force and movement areconsidered.

VECTORS

Although force is usually applied over anarea, it is usually described inbiomechanical drawings as a summarizedpoint force by an arrow. Any quantity thatgives both magnitude and direction is avector (eg, a force) that can be described bya straight line. Quantities that involve onlymagnitude are referred to as scalars. Whenillustrating a force, the vector's lengthshould be proportional to the magnitude ofthe force. For example, if 1 inch is used torepresent a 10-lb force, a 2-inch line would represent a 20-lb force.



A vector can be used to define a force in a simple line drawing if the vector drawn toscale represents magnitude by the line's length, if the vector's tail indicates the pointwhere the force is applied on the object, and if the direction of force is indicated bythe vector's arrowhead. If the magnitude of a vector is known, it should be indicated(eg, 1 inch = 20 lb). If the magnitude is not known, it is indicated by the capital letterF (force) or P (pressure) to designate the unknown magnitude. Distances are usuallyrepresented by lower case letters.

The force of gravity is always directed toward the center of the earth. Thus, gravity'sline of action and direction are constants. In the upright "rigid" body, thegravitational force on the entire mass can be thought of as a single vector throughthe center of mass which represents the sum of many parallel positive and negativecoordinates (Fig. 2.4). If a weight is held in the outstretched hand, the quantity ofgravitational force is governed by the weight of the extremity plus the weight held.

SPACE

As a force may act along a single line in asingle plane or in any direction in space,this must be considered to provide anillustrative reference system. In a two-dimensional system, the plane is simplydivided into four quadrants by means of aperpendicular vertical ordinate line (Y axis)and a horizontal abscissa line (X axis). Thepoint of axial intersection is referred to asthe system's origin (Fig. 2.5). Abscissa (X)measurements to the right of the origin areconsidered positive, while those to the leftare negative. Ordinate (Y) measurementsabove the origin are considered positive,while those below the origin are negative.By this method, any point on the plane canbe given an X and Y value.

The term coordinates refers to specificpoint locations from the origin which havebeen given a value. For example, a pointlocated 5 units to the right of origin and 3 units down from the origin would bedefined as X = 5, Y = 3.

A third axis (usually titled Z) can be introduced to locate points in three dimensions.Such an axis crosses the origin and is perpendicular to the other two planes (X andY). All Z points in front of the X-Y plane are positive, while those behind are negative(Fig. 2.6). By utilizing X, Y, and Z coordinates, any point in space can be locatedand depicted. However, a minimum of six coordinates is necessary to specify theposition of a rigid body. Force and moment are three dimensional vectors havingthree components each; thus load may be considered a six-component vector.

In biomechanics, the body's origin is located at the body's center of mass which isusually just anterior to the S2 segment. When this point is known, gross body spacecan be visualized as being in the sagittal (right-left) Y-Z plane, frontal or coronal(anterior-posterior) X-Y plane, or horizontal or transverse (superior-inferior) X-Z



plane. With such a reference system, any movement of any body segment in theseplanes can be approximately described by placing a coordinate system at the axis ofa joint and projecting the action lines of the muscles involved.

Static Equilibrium

Statics

According to Newton's first law, a bodyremains at rest in static equilibrium whenits velocity is zero or remains in a state ofmotion (dynamic equilibrium) when itsvelocity is other than zero. The study ofbodies at rest, as the result of forces actingupon them simultaneously balance eachother so that the resultant velocity is zero,is referred to as statics. This balancedstate is one of translational equilibrium.That is, during motion, if a body moves in adirection in which a straight line in thebody always remains parallel to itself, themotion is called translation. It is a vectorquantity measured in feet or meters.

MAJOR PRINCIPLES OF STATICS

Two conditions of equilibrium summarizethe principles of statics: (1) For an object tobe in linear equilibrium, the total of all Xcomponents must equal zero and the sum of all Y components must equal zero. (2)For an object to be in rotatory equilibrium, the total of all torque forces that tend toproduce a rotation in one direction (eg, clockwise) must be counterbalanced by thetotal of torque forces that tend to produce a rotation in the opposite direction (eg,counterclockwise).

FREE-BODY ANALYSIS

Clinically, free-body analysis of statics is used whenever traction force is applied; eg,during a manual adjustment of the spine, extremities, or in the use of therapeuticequipment. Other applications are found, for instance, in determining stresses atparticular points during activity positions (Fig. 2.7). Freebody analysis is amathematical technique of utilizing equilibrium equations to determine the internalstresses at a structural point that is being subjected to external load. Suchequations can be used to calculate the magnitude of force and moments acting on avertebral area, for example, at a known position and load.

Equilibrium



While forces of all types may causesubluxations, dislocations, fractures,strains and sprains, etc, the biomechanicalmechanisms involved determine the typeand extent of the injury produceddepending upon the applications of forceand its resistance. For example, differentapplications of force may cause bending,stress, or compression fractures. When theexaminer understands how an injury wascaused, the tissues involved are morereadily located and the extent of injury ismore quickly ascertained.

Following is a brief discussion of linear,concurrent, and parallel forces, and theireffect upon equilibrium. However, forcesacting on a body are sometimes neither linear, concurrent, or parallel. Generalforces always include at least four forces to maintain equilibrium.

Linear Forces

Linear forces are those acting in the same straight line (Fig. 2.8). If two forces are tobe in equilibrium in a linear system, the forces must be equal in magnitude andexactly opposite in direction.

Pressure

Pressure refers to how a force is distributed over a surface. Pressure (P) can bedefined as the action of a force (F) against some opposing force distributed over anarea (A) as in the equation P = F/A, which gives the units of force per unit area suchas in pounds per square inch (psi).

PRESSURE DURING MANIPULATION

This principle of force is used throughout therapy. In manual adjustmentprocedures, for example, a patient can withstand a broad palm contact withconsiderable force without discomfort, yet the same force exerted by a thumbtip orpisiform contact becomes quite painful because the pressure per unit of surface areais now much greater. Thus, whenever pain or skin damage is the priorityconsideration, the contact forces should be applied over as large an area as possible.

PRESSURE OF SUPPORTS

The same principle must be applied in taping procedures to avoid circulatory andneural impairment, in applying traction slings to distribute force, and in fitting



supports if pressure sores are to be avoided. The noxious effects of continuouspressure can be reduced by using somewhat elastic materials such as felt or foamrubber padding as an underlay beneath supports to spread force from prominentbony areas. In large-area supports such as for scoliosis, an underlying water-inflated football bladder has shown to offer automatic pressure distribution andgood reciprocity to surface shape. The modern use of air splints duringtransportation of extremity fractures is another example of this principle applied inhealth care.

Compression

A pressure always results in a compression stress. Tensile and compression stresses(axial stresses) operate along the axis of a part without altering it. Both of thesestresses are measured in newtons. A compression force within the body tends topush substances closer together. When a muscle crossing a joint contracts, itproduces a compression force into the joint, and the bones must produce a reactiveforce to withstand the compression force. Within the spine, the vertebrae and theintervertebral discs are the major compression-carrying components which mustsupport the weight of the body above a particular disc, the initial tension in otherligaments, the additional tension in the muscles and ligaments that are necessary tobalance eccentric trunk weight, plus any added external load.

Tension

A pull causes a tensile stress that is an action directly opposed to compression.When tension is applied to connective tissue fibers, the fibers elongate to theirphysiologic limit somewhat like a stretched rubber band unless a cut or weaknessproduces a fracture. During torsion (shear) stress, fibers at 45* to the long axis areplaced in tension. When a long structure is subjected to bending stress, tension isexhibited in the fibers on the convex side of the curvature.

MOTION TENSION

Examples of tension are exhibited during all spinal movements. Anulus fibers of theintervertebral discs are placed in tension during disc torsion when the spine isrotated axially, and ligaments posterior to the instantaneous axis of rotation aretensed during spinal flexion. A spinal curvature in any direction involves a constantstate of abnormal tension and compression of bones, cartilages, and muscles.

During work, muscles do not maintain a constant tension, length, or move with aconstant rate of shortening. The strength of muscle action is affected markedly bythe amount of tension in the muscle at the start of movement, the degree of musclestretch at the beginning of contraction, and the rate at which shortening takes place.

POISSON'S RATIO

Similar to a piece of rubber, elastic connective tissue fibers thin during stretch andthicken during compression. In both cases, however, the volume remains constant.The ratio between axial strain in length from compression to transverse strain indiameter from tension is Poisson's ratio.



Concurrent Forces

In a concurrent force system, as contrasted to a linear system, the forces acting onthe body meet at a certain point rather than lie along the same line of action. Theseforces may be applied to the body from different angles so that their action linescross either interior or exterior to the body (Fig. 2.9). For example, if two coplanarnonparallel muscles are acting on a bone, a third concurrent force, passing throughthe point of intersection of the two original muscle forces, must act to maintainequilibrium and avoid rotation.

Parallel Forces

When parallel forces some distance from each other act upon a body, their forcesmust be completely nullified by each other if the body is to maintain equilibrium. Ifforces do not coincide at the same point, such as in a concurrent system, the resultis rotation around a stationary axis. A simple form of this action is a force systemwhere the forces lying in the same plane are parallel. Any force acting on an objectat a distance from a fixed point tends to rotate the object. Forces producingclockwise rotation are arbitrarily referred to as positive, while counterclockwiseforces are termed negative.

The distance from the point of force application (pivot point) to the point of rotationis called the moment arm or lever arm. When a force acts at a distance from apivot point, its effectiveness is determined by both its magnitude and its location.

The tendency of a force to cause rotation about an axis that is equal to themagnitude of the force times the perpendicular distance from the action line of theforce to that point is referred to as a moment (torque) of force. Mathematically, it isexpressed as moment = force X distance, and its unit of measure is in foot-pounds(ft-lb), kilogram-centimeters (kg-cm), or an equivalent measure.

Lever Actions

A lever system is a good example ofmoments developed by coplanar forces.Simply, a lever is a rigid bar turning aboutan axis. The three components of a leverare the fulcrum upon which the leverturns, the resistance or weight load whichis to be moved, and the effort which movesthe lever.

The articulating surfaces of joints areusually used as fulcrums, the rigid boneshafts extending from axis to axis serve aslever arms, and the source of effort to move



the lever arms are the muscles. That is, inthe body, we have an effort force and aresisting force acting around a pivot axis(fulcrum) which serves as a supportingforce (Fig. 2.10). When a muscle contracts,the bony lever arm to which it is fixed ispivoted about the fulcrum. Work is donewhen resistance is overcome by a leversystem. Here again is an example that theresistance to be overcome by the body isgenerally the sum of the load of the leversegment plus the load of the object to bemoved.

MECHANICAL ADVANTAGE

The force developed when a musclecontracts is determined by the mechanicaladvantage of the levers employed. Theposition of the attachment of the muscle in relation to the position of the center ofthe resistance and the position of the fulcrum are important in deciding themechanical advantage of any lever. Mechanical advantage is the ratio of output forcedelivered to the input force applied by a mover. If the resistance is placed near thefulcrum, the mechanical advantage is good. If the same resistance is placed furtherfrom the fulcrum, the mechanical advantage lessens and a greater effort is requiredto overcome the resistance.

Mechanical advantage is computed by dividing force into resistance: R/F. If a 150-lbindividual wishes to lift a 1200-lb weight by means of a lever, the mechanicaladvantage required of the lever would be R/F = 1200/150 = 8. Thus, the force armmust be eight times as long as the resistance arm of the lever.

TYPES OF LEVERS

At one time or another, every bone in the body, acting alone or in combination, actsas a lever, and the human machine offers many examples of first- and third-classlevers. Most of the joints of the body can be used as levers of more than one class.



First-Class Levers. An example of afirst-class lever where the fulcrum islocated between the applied load andthe resisting weight is seen in tappingthe toes on the floor and in the actionof the triceps on the ulnar when thearm is held over the head. Otherexamples are found (1) when thespleni act to extend the skull acrossthe atlanto-occipital joints (Fig. 2.11)and (2) when the soleus tendon forcebehind and the gravity force in front ofthe ankle fulcrum are utilized instanding erect. In a first-class leversystem, the longer the lever arm, theless force is required to move or resistthe applied load.

Second-Class Levers. A second-class lever has the resistance weightlocated between the applied force and the fulcrum. Since most of themuscles moving each joint are inserted near the joint and the resistance isusually at the long end of the body levers, levers of the first and thirdclasses are the most commonly used in the body. There are no positivesecond-class levers in the body because the length of the resistance armof the movement is always greater than that of the effort arm whenmovement is produced by muscle shortening. Some kinesiolo- gists referonly superficially to the action of the brachioradialis on the forearm duringelbow flexion and the action of the calf plantar flexors when one stands onthe toes as being second-class lever actions. A true second-class leversystem can be demonstrated, however, when muscle tension becomes aresistance to a reversal of joint action caused by an outside force so that athird- class lever system is reversed and becomes a second-class leversystem. In such cases, the eccentric muscular contraction is performingnegative rather than positive work. An example of this is seen when onestands on tiptoes where the fulcrum is located on the ball of the foot, andforce is applied through the gastrocnemius at the ankle to lift body weight.

Third-Class Levers. A third-class lever, where the applied force is alwayslocated between the fulcrum and the supported weight (resistance), is seenin the action of the biceps in flexing the forearm. The biceps insertsbetween the elbow and the hand; thus, when the biceps contracts, theelbow joint serves as a fulcrum. The same mechanism is seen in lifting aweight with the foot.

The resolution of the force of gravity or muscle contraction into components mustinclude a rotary component. Also, the distance from the point of application of therotary component to the axis of motion in the joint must be considered. The jointswhich serve as fulcrums also limit the range of movement of the body lever.

THE LEVERS PRINCIPLE

The mechanical advantage derived by the three different lever classes depend on the



about the axis between C1 and C2 bycontraction of the splenius capitis andcontralateral sternocleidomastoideusmuscles. Scapulohumeral rhythm and thedepression action of the rotator cuffmuscles on the humerus are two otherexamples of couple mechanisms. Aninterruption in either of these two couplescompromises shoulder girdle motion.Typical side-position lumbar and pelvicadjustments and cervical rotatoryadjustments incorporate twisting forces tothe spine in opposite directions by action of the adjustor's stabilizing and contactpoints.

A couple consisting of small forces with a large distance between them is just aseffective in producing rotation as one where the forces are great and the distancebetween them is small. For example, in a rotatory adjustment, a lesser force isnecessary to produce the same effect when contact is taken well on a transverseprocess than one taken closer to the spinous process.

COUPLING

A coupling is a device that serves to connect the ends of adjacent parts of objects toproduce a phenomenon of consistent association of one motion about an axis withanother simultaneous motion about a second axis. In the spine, for example, axialrotation is coupled with lateral bending, vertebral anterior translation is coupledwith flexion rotation, lateral scoliotic deformity is coupled with axial rotation torotate the posterior vertebral elements toward the concavity of the curvature, andvertebral movements toward and from the sagittal plane are coupled with associatedrotatory and translatory movements.

Bending

If a load is applied to a relatively longstructure that is not directly supported atthe point where the load is applied, theresulting deformity is called bending.During bending, the fibers on the concaveside of a connectivetissue structure arecompressed, while those on the convex sideare stretched.



Two effects are seen when a force acts onan object. First, the object tends to move inthe direction that the force is applied(translation). Second, the force will causethe object to rotate (bending moment).

BENDING MOMENT

A bending moment (torque) is a quantity,usually measured in newton meters, at apoint in a structure that is equal to theproduct of the applied force and theshortest distance from the point to theforce direction (Fig. 2.15). For example,think of the trunk of a person sitting as atree trunk and a laterally abducted arm as a branch of the tree. If a heavy book isplaced on an outstretched hand, the bending moment increases in magnitude fromzero at the hand to the maximum at the junction of the tree trunk and branch(shoulder). In the same manner, relatively small weights placed on horizontal limbsapply substantial bending moment at the thoracic and lumbar discs because of thelong lever arm. If equilibrium is to be maintained, this stress must be compensatedby the bending moment produced by large magnitudes of muscle and ligament forcebecause of the much shorter lever arms of these tissues.

Body weight acting through the center of gravity and the first class lever sytem of thehip tends to rotate the trunk toward the midline. To maintain equilibrium, thisturning effect about the hip from the force of body weight must be resisted by anequal and opposite turning effect produced by the abductors pulling the pelvisdownward. The bending moment is the product of force times the perpendiculardistance from the force to the center of rotation.

Spinal bending involves the multiple actions of tension, compression, and torsion.The amount of this fiber stress (S) equals the bending moment (B) divided by thesectional moment (I) of inertia times the fiber distance from the neutral axis (Y): S =B/I X Y. If the radius (R) of the curvature is desired, it may be computed by R = E/BX I, where E is the modulus of elasticity of the material.

The moment of inertia of an elliptical object is greatest for bending loads in thedirection that is parallel to its major axis. For this reason, the elliptical cross sectionof a vertebra's pedicle is seen to be most suitable for taking up bending loads in thesagittal plane where such loads are common.



MULTIPOINT BENDING

Both three-point and four-point bending occur within the body. Three-point bendingis a form of bending where one force is applied to one side of a structure and twoforces are applied on the other side. Examples are seen with a seesaw or a drawnbow string. In four-point bending, two transverse forces are applied on one side of astructure and two are applied on the other. If the forces are equal and symetrical,the structure between the inner two forces is constantly subjected to bendingmoment.

THE NEUTRAL AXIS

When a long fibrous structure is subjected to bending, the longitudinal line wherenormal axial stress is zero is referred to as the neutral axis (Fig. 2.16). The plane ofthe neutral axis is that area situated between the fibers under tension on the convexside of the curvature and the compressed fibers on the concave side. However, thereis usually shear stress along the neutral axis resulting from transverse forces eventhough the tension-compression stress is zero. In cases of torsion stress appliedabout the neutral axis, the fibers at the neutral axis will have zero shear stress.

Torsion

The mechanical internal moment or couple of restitution which arises in a cord orrod when twisted is referred to as torsion (Fig. 2.17). That is, torsion or torque is theload that is applied by force couples about the long axis of a structure. The momentof torque is the product of a force and its perpendicular distance from the fulcrum.Thus, torque (T) is synonymous with force (F) times the length of the lever arm (a): T= Fa.

If the torques on either side of the fulcrum are equal, the lever is in equilibrium. Asmentioned previously, when a lever is in equilibrium, the sum of the moments offorce or torques tending to turn it in one direction (eg, clockwise) about a given pointmust equal the sum of the moments of the torques tending to turn it in the oppositedirection (counterclockwise) about the same point.

APPLICATION PRINCIPLES

Practically all muscles pull obliquely and some pull with a slight twist. The obliqueinsertion of the pectoralis major into the humerus, for example, causes the humerusto be rotated as well as adducted during contraction of the muscle. In addition, allangles of pull against the bones change with each fraction of a degree of movement.For instance, the angle of pull of the biceps upon the radius changes with eachdegree of flexion of the elbow.

If torque is applied to the ends of a curved structure, each cross section of thestructure is subjected to both torsion and bending forces. Many researchers feel thatthis principle is responsible for the low-back pain from disc failure because simpleaxial rotation of the trunk (load) produces severe torsion and bending stress on thelumbosacral disc.

When considering rotational movement, torque fills the same role that force does formotion in a straight line. That is, the magnitude of the moment increases ordecreases the angular velocity of an object to produce acceleration or deceleration of



the rotation involved.

TORSION TERMS

Torsional Rigidity. Rotatory stiffness is called torsional rigidity inmechanics and represents the torque per unit, measured in newtonmeters per ra- dian, of angular deformation. This rotatory stiffness is acharacteristic of all body joints.

Area Moment of Inertia. According to Newton's first law,the terms mass and inertia canbe used interchangeably. Theterm "moment of inertia"describes the degree to which amaterial's shape influences itsstrength. There are two types:area and polar. The area momentof inertia refers to a measure, infeet or meters to the fourth power, of the distribution of material about itscenter which determines its bending and torsion strength (ie, its bendingresistance). It is for this factor that a hollow tube such as a long bone ismany times stronger in bending and torsion than a solid tube of identicalmass (Fig. 2.18).

Polar Moment of Inertia. This is that characteristic of the transversesec- tion of a long object that gives a measure of the distribution of thesubstance about its axis to increase its torsional strength (resistance). Itis also measured in feet or meters to the fourth power. The greaterdistance a mass is from its axis of torsion, the greater its polar moment ofinertia. The reason that the tibia spiral fractures most frequently at thejunction of its middle and distal third is because this site has a low polarmoment of inertia, even though the cortex is especially thick at this point.

Shear Stress. A force directed against a structure at an angle to its axisthat permits one part to slide over the other is called a shearing stress.Typical examples are that of the cervical and thoracic vertebral articularfacets and that occurring at the intervertebral disc and vertebral bodyjunction. In shear stress, both articulating parts may be movable with theparts sliding in opposite directions or one part fixed. Shear stressrepresents the intensity of force parallel to the surface upon which it actsand is measured in newtons/meter524 or pascals. Because bone isweaker in tension than in shear, torsional overstress produces spiralfractures in long bones.

Shear Modulus. Shear modulus is a material property that representsthe ratio of a substance's shear stress to its shear strain. As is shearstress, it is measured in newtons/meter524. Materials such as rubber andligamentous tissue with their low modulus of elasticity also have a lower,about 38% lower, modulus of shear.

With these concepts and terms in mind, we shall be able to proceed to those ofdynamics and stability.



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