Biomechanical Analysis of Vertebrate Skeletal Systems 6-Glase

5/25/2018 Biomechanical Analysis of Vertebrate Skeletal Systems 6-Glase

Chap ter 6Biomechanical Analysis of VertebrateSkeletal Sy stems

Jon C Glase, Melvin Zimmerman, andStephen C Brown

Jon Glase received his B.S. and Ph.D. degrees from Cornell Uni-versity in the areas of vertebrate biology and behavioral ecology,respectively. In 1974, after two years as Assistant Professor ofbiology at Siena College, he assumed his current position as SeniorLecturer, Section of Neurobiology and Behavior, Cornell Univer-sity. He serves as Coordinator of Laboratories for a two-semesterintroductory biology laboratory course for science majors. His re-search interests include the behavioralecology of bird social systemsand orientation behavior and sensory physiology of the honey bee.Melvin C. Zimmerman is an Assistant Professor of Biology at Ly-coming College, Williamsport, PA. He received his B.S. in biologyfrom S.U.N.Y.-Cortland (1967) and his M.S., Ph.D. in zoologyfrom Miami University Ohio; 1977). After completion of hisPh.D., he spent 2 years as a teaching post-doctoral fellow with theintroductory biology course at Cornell University. In addition tointroductory biology, he also teaches ecology, invertebrate zoology,parasitology and aquatic biology at Lycoming. His research dealswith the bioenergetics and ecology of aquatic invertebrates.Stephen C. Brown received his Ph.D. in zoology from the Universityof Michigan in 1966. He is an Associate Professor in the Depart-ment of Biological Sciences, S.U.N.Y -Albany, where he teachescourses in invertebrate zoology and comparative animal physiology.His research interests include biomechanics of invertebrates andthe regulation of salt and water balance in lower vertebrates, es-pecially amphibians.

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122 Biomechanical AnalysisI. Introduction

This laboratory presents the structure function concept, certainly one ofthe most important recurring themes in biology. The skeletal system (andassociated muscular-nervous system) of a species represents natu ral selectionsbest efforts in producing an arrangem ent of jointed levers to deal with th ephysical stresses imposed by the environment and allow the total behaviorrequired of t ha t species. Another major objective is to exam ine some of therules of the gam e with which natu ral selection has had to deal. Specifically,Newtons laws of motion and force and their impact on the evolution ofskeletal systems are considered. Upon com pletion of t he labo ratory, stud entsshould understand the physical concepts of torque, work, and mechanicaladvantage, and their application in analyzing skeletal systems from a struc-ture-function viewpoint.This laboratory was developed in response to the recognition th at studentslack much understanding for how vertebrate skeletal systems function andwhy they have evolved into their present diverse forms. That the bumps,ridges, and depressionson bones have significance n th e attach men t of musclesand their functioning in lever systems escapes most students as they exam inea skeleton. Th at the diversity of form in vertebra te skeletal systems is under-standable from a function viewpoint and can be studied a nd explained usingsimple concepts from physics ar e importa nt ideas not usually app reciated bythe underg raduate studen t. We have developed these exercises to help studentsgain some experience with the physical realities tha t govern the evolution ofskeletal systems.These exercises can be used in a standa rd, instructor-led laboratory ses-sion, as they have been used a t S iena College and L ycoming College and forsix years in the introductory biology laboratory course a t Cornell University.The exercises could also be adapted for use in a n autotutorial format. Thislaboratory topic would be appropriate in various biology courses, includingintroductory biology, zoology, comparative v ertebrate anatomy , and evolution.In conjunction with this laboratory, we assign the article by Hildebrand, HowAnimals Run (1 960).

II Student MaterialsIntroduction*

Vertebrates and arthropods have shown remarkable plasticity of designin successfully adapting to aquatic, terrestrial, and ae rial life. Unquestionably,one major fac tor contributing to each groups success has been the independentevolution of skeletal systems (the endoskeleton of vertebrates and the exo-skeleton of arth ropo ds) organized a s a series of jointed levers operated by*Adapted from Chapter 13 in the laboratory text Investigative Biology. Glase et al. 1980


Biomechanical Analysis 123specific muscles. Analysis of the mechanical properties of skeletal systems(or parts thereof) can yield much biologically relevant information on thecharacteristics and potentials of movement in the animal as a whole. Suchanalyses are particularly useful in evaluating the stru cture/fu nction relation-ship of animals with regard to locomotory or feeding behavior.Before beginning your analyses of certa in verte bra te skele tal units, it willbe useful to recall the basic laws governing motion and force (courtesy of SirIsaac Newton, circa 1675) .I. A body remains at rest (or moves at a constant velocity) unless a forceacts upon it.

II A force gives a body a n acc eleration in th e direction of the force whichis directly proportional to that force and inversely proportional to themass of the body.III If body A exerts a force on body B, body B exerts an e qual an d oppositeforce on body A.

Whe n expressed in biological terms, Law I states that if an animal (orparts thereof) is a t rest relative to its environm ent, it can only be set in m otionby the application of a force, and consequently, if a n ani ma l is to move by itsown unaided efforts, it must elicit a force against its external environment.Law II states that when an animal elicits from its environment an externalpropulsive force, the velocity imparted to th e anim al is directly proportionalto the m agnitude of th e force and the period of time during which it acts; atthe sam e time, it is inversely porportional to the animals m ass. Law IIobviously has implications when considering the amount of muscular forcenecessary to move heavy and light objects of equal size. Translated into bio-logical terms, Law an be expressed by saying tha t when subjecting itsbody to a forward propulsive force, an anim al must simultaneously exert anexactly equal but opposite backwa rd force against its external environment.Th e animal moves forward because the environment resists the movement ofthe fins, legs, or wings relative to the body.With respect to the third law, it is useful to consider its application tomuscular action in general. A typical skeletal muscle has three basic areas.Th e muscles ends (origin and insertion) are usually attached to some skeletalpar t (e.g., bone or cartilage via tendons). The origin is attached to a stationarybone and is therefore relatively non-movable, whereas t he insertion is attachedto a more movable part. The enlarged center section of the muscle (belly)contains many muscle cells (fibers),which contract and pull the bone attachedto the muscles insertion. When a muscle develops tension, the force th at itexerts on the bone a t its insertion is exactly equal in m agnitude, and oppositein direction, to that which it exerts on the bone at the muscles origin. Itshould be noted that the final movement caused by muscular contraction is


124 Biomechanical Analysisdetermined not only by the origin and insertion of the muscle, and th e typeof bone joint, but also by the antagonistic muscle group. Muscles typicallywork in antagonistic groups. For example, one muscle group (biceps group)causes an upward movement (flexion) of the forelimb, and an antagonisticgroup (triceps group) causes a downward m ovement (extension) of the lim b.

All bone/muscle systems are machines. A machine is a mechanism tha ttransmits force from one place to another, usually also changing its magn itude.It is useful to designate any force applied to a machine as an in-force (Fi ) ,and any force derived from a machine as an out-force (Fo). In the body, in-forces are applied by th e pull of tendons or tensed ligaments resulting frommuscle contraction; useful out-forces are ultimately derived a t th e teeth, feet,digits, and elsewhere. For th e most p art , we will consider only simple m achineshaving one in-force and one out-force.Bone/Muscle Systems As Lever Machines

An in-force may be transm itted to an out-force by a crank shaft, hydraulicdevice, pulley, lever, or som e other m echanism. M ost feeding and locomotorsystem s of the body transm it fo rces by levers, and only thes e will be consideredhere. A lever (F igure 6.1) is a rigid structu re, such as a crowbar or bone, thattransmits forces by turning (or tending to turn) at a pivot or fulcrum .Our childhood experiences with seesaws can help us be tter understand thefunctioning of lever systems . Successsful use of a see saw depends on its beingbalanced with respect to the two participants. In order to obtain a balancedseesaw, the two individuals (A and B) must adjust their positions from thefulcrum in accordance with their body weights, Lets consider why this is true.In Figure 6.1, FA nd F, are the forces exerted on the lever by the weight ofindividuals A and B, respectively. Each force is spaced from the fulcrum bya segment of the lever called a lever arm or moment arm. The distanceseparating A from the fu lcrum is As lever arm, or SA.Bs distance from thefulcrum is the lever arm S . FAcauses the lever to turn in a counterclockwisedirection. F causes it to turn in a clockwise direction. A measurement of theturning power tha t a force exerts on a lever system is called torque (T) andequals the m agnitude of the force times the length of its lever arm . IndividualA creates a counterclockwise torque on the lever equal to F AS A. s torque isclockwise in direction an d equ al to BSB In general, if FASA > FBSB,he leverrotates in the direction of FA;when FASA< FBSB, the lever rotates in thedirect ion of F,. A lever is said to be in a sta te of equilibrium when the algebraic


Biomechanical Analysis 125

sum of all the torques acting upon it equals zero. That is, a lever is in equi-librium when the sum of all the torques tha t produce counterclockwise rotationequals the sum of all the torques tha t produce clockwise rotation. T his generalstatement is called the law of the lever:At equilibrium, counterclockwise torque = clockwise torque,

or

FulcrumFigure 6.1. A simple lever system (see text for discussion).

Therefore, in order to obtain a balanced seesaw, the two participants mustadjust their positions from the fulcrum so that the clockwise and counter-clockwise torques they produce are equal. If both individuals are of ab out th esame weight, then they should be about equal distances from the pivot inorder to achieve a balanced lever system. That is, if their weight forces areequal (FA = FB), hen their lever arms must also be equal (SA= SB) f theclockwise and counterclockwise torques are to be equal (FASA= FBSB).Clea rly, if individual A is heavier than individu al B (FA> FB), then A's leverarm must be proportionately less than B's lever arm if FASAs to still equalFBSB.Now let's consider how levers are used as machines in the vertebrateskeletal systems (Figure 6 . 2 ) . Atypical skeletal lever system involves twobones: bone 1 serves as the actual lever upon which forces ar e exerted; bone2 provides the fulcrum about which bone 1 can turn. A muscle inserted onbone 2 at a distance from the fulcrum contracts, producing the in-force (Fi)on the lever system. Th e in-lever arm (Si) is the distance separating Fi fromthe fulcrum. The muscle's effort produces a clockwise in-torque (Ti) whichequals FiSi.Where bone 1 contacts the environment a n out-force is developed.The distance separating Fo from the fulcrum is the out-lever arm ( S o ) .Theout-torque (To) equals FoSo. Since Fi transmitted through Si produces F,transmitted through So, in all cases Ti and To are equal in both m agnitudeand direction.

in-torque = out-torqueFiSi= FoSoTi= To


126 Biomechanical Analysis

RFigure 6.2. A skeletal lever system see text for discussion).

Fo can now be used to move against some environmental resistance (R)such as a weight. As the m uscle contracts and Fi increases, F, also increasesproportionately. Newtons Third Law states that as force is applied by thelever system against R, an equal (in magnitude) and opposite (in direction)force is applied by R against the lever system. Fr increases directly with F,and sets up a counterclockwise torque equal to the FrSo tha t keeps the leversystem in equilibrium. As predicted by th e law of th e lever,at equilibrium, clockwise torque = counterclockwise orque,

orFiSi = FrSo

However, when o equals the force required to move R, bone 1 moves in aclockwise direction and the lever system has done useful work.It is important that the student of biomechanics be able to solve theequation for the law of the lever for any of the variables, and to understandthe relation of each to the others. If more than two forces tend to turn thesame lever, then the net direction of rotation is determined by com paring thesums of all the clockwise and the counterclockwise torques.The three recognized classes of lever, together with examples of theiroccurrence in the body, are illustrated in Figure 6.3. When examining theillustration it is important that you do not attempt to memorize diagrams,but learn to identify the pivot and the in- and out-forces. The distinction tobe drawn between them is one concerning the relative position of the pointsof application of the in-force or effort (i.e., th e muscle force operating th e


Biomechanical Analysis 127lever) and the load or resistance w hich the out-force has to balance if itis to hold the lever arm steady, or has to overcome if it is to start the leverdoing useful work. In levers of the first class, the input an d ou tput forces areapplied on opposite sides of the fulcrum, whereas in levers of the second andthird classes, they a re applied on the sam e side of t he pivot point. Th e classof lever employed often depends upon the type of movement intended. Forexample, all three types of levers may be found in the m ovements of th e foot.Tapping the toes involves the use of a first class lever; standing on the toesinvolves a second class lever when we focus on the action of the calf m uscle;and lifting a w eight with th e foot involves a th ird c lass lever when we conside rthe action of the muscles located on the front of the leg. A vast majority ofthe levers of the body are of th e third class. First class levers are few, but a restill more numerous than the second class levers. Can you think of somereasons why this is true ?

Firstclasslever

Secondclasslever

Thirdclasslever

Out-force

ROut-force In-force

(Fo) (Fi)

Figure 6.3. Illustration of three classes of levers as found in the movements of thearm and foot. R represents the resistance, against which the out-force is applied andthe fulcrum is at (Adapted from M. Hildebrand Analysis of VertebrateStructure. Copyright 974 by John W iley and Sons, New York. Reprinted withpermission.)



The Kinematic Modell.* The physical model that you will use in these exercises is called a kine-matic model, because kinematics is the study of motion, and we areultimately concerned in this laboratory with unde rstanding th e basis formovement in organisms. Initially, consider the simple lever system of t hekinematic model (Figure 6.4 . dentify the components Fi, Si, F,, and So.

Figure 6.4. A diagram of the kinematic model left) and the human lower leg andfoot right). An eye-ring is attached at position a. ositions 1 and 2 representattachment points for the gastrocnemius muscle, whose contraction produces an in-force on the calcaneus. Positions 3, 4. and 5 represent points on the front of the footwhere an out-force can be measured.

Use of the Kinematic Model and Spring Scales1. The model should be used in a horizontal position relative tothe benchtop, with the top bar (with hooks) firmly bracedagainst som ething.2 The spring scales should be hooked into the paper clips attachedto the foots eye rings, and the cord looped over the top barhooks, but not tied.3. Since you will be working in pairs, the following arrangem entworks best (see Figure 6.5). While one person holds the modeldown by the leg piece and also holds stationary the scaleattached to position 3, 4,or 5, the other person applies forceon the other scale, attached to 1 or 2, by pulling its cord. The

*Note: Answers to im portant questions in th e following section and sample d ata collected withthe model are included in III N S T R U C T O R S M A T E R I A L S



Figure 6.5. The suggested arrangem ent of two individuals manipulating and makingmeasurements with the kinematic model.magnitude of this in-force is measured by the lefthand scale.The righthand scale measures the out-force m agnitude. M ea-sureme nts should be made w hile keeping the foot roughly per-pendicular to the leg.

4. Frictional resistance within the scales and a t the pivot joint ar ethe main sources of error. In making measurements these canbe minimized a s follows: (a) be sure t ha t th e pivot bolt is onlyloosely attached; (b) while watching the righthand scale, pullon the left-hand scale until the desired weight force (2 pounds)is just reached on the righthand scale. Slowly release tensionon the lefthand scale until the indicator on the righthand scaleis j u s t affected. The reading on the lefthand scale representsthe best measurem ent of th e in-force required to produce a 2-pound out-force.a. With the spring scales attached to positions 2 and 3, verifv thatthe foot is stationary relative to the leg (i.e., t is at equilib-rium) only when the two forces exert equal but oppo site torquesabout the axis of the joint.


130 Biomechanical Analysisb. Is this true fo r any angle forme d between foot and leg?c. Is the magnitude of the forc e necessary fo r producing a balancingtorque at position 2 changed if the forc e exerted on the f ron t ofthe foo t is moved to insertion point 4? Are the torques (F X S)still equal? Rulers are available to measure distances.d. Ne xt , examine the compression force s developed at the pivots

(points of articulation) of skeletal lever systems. T o do this ,move the pivot bolt at the ankle ioint and atta ch a third scale tothe eye-hook (a in Figure 6.4) . W hile one person firm ly holdsstationary both the leg and the upper two spring scales (le fthan dscale attached t o position I or 2, righthand scale attached toposition 3, 4 , or 5) . the other person pull s down on the thirdscale. Simulta neou sly read all three scales. Th e third scale meas-ures the compression forc e (Fc) tha t Fi and Fr develop at th e pivotpoint. Recall that when t he lever is in equilibrium, Fo = F,. Whatis the relationship between Fc, Fi, and F,7 Is this relationship stillobserved if Fi and r are applied at other positions on the model?Try it2. Now consider the kinematic model i n relation to the anatomy of your

own leg/ankle/foot (Figure 6.4) .Positions 1 and 2 represent two pos-sible points of insertion of the Achilles tendon from th e gastrocnem iusmuscle into the heel bone (calcaneus). P ositions 3, 4, and 5 representpoints along th e foot where forces are exerted, corresponding to posi-tions at the proximal and distal ends of the m etatarsa l bones, and th eends of the toes, resp ectively. Alternatively, positions 3, 4, and 5 canbe considered the ends of feet of different lengths.The purpose of w alking is to propel the body forward , and althoughwalking involves the muscles and joints of the whole body, the footprovides the pivot about which the body turns. That is, although theforce exerted by your weight acts at the same point (the ankle joint)as you take a forward strid e when walking, the fulcrum shifts forward,as does the foots distrib ution of body weight (see F igures 6.6 an d 6.7.)Examine Figure 6.6 and attempt a stride yourself (a stride is fr o mheel-strike to heel-strike by the same foo t). T ry to identify how m anyof the lever classes are involved (see Figure 6 .3 ) . At what point(s)along the stride does the gastrocnemius counteract t he weight force ?For the foot of the walking huma n, all the param eters of the lever laware variable: both Si and So change as the fulcrum changes position;Fo varies during the stride as th e distribution of to tal body weight isshifted from one foot to the other; Fi varies a s Fo, Si, and Sovary. Inactuality, because the model cannot duplicate the variable positioning



Figure 6.6. The striding sequence. The sequence starts as the right leg black)swings in front of the body and the heel makes contact with the ground. Bodyweight is progressively distributed from the back to the front of the foot until it isborne by the toes principally the big toe). At this moment the left leg white),which has been swinging forward ready to take its turn in the walking cycle, hits theground in the heel-strike position. The right leg, with a final strong propulsive drivethe toe-off), breaks free and starts to swing forward for the next step; and so it goeson, and the ground is covered by a smooth, rocking, heel-toe motion of one foot afterthe other. From J. R. Napier: Primate Locomotion. Copyright 1976 by OxfordUniversity Press, Ely House, London. Reprinted with permission of CarolinaBiological Supply Company.)

Figure 6.7. A diagram showing distribution of weight in the human foot. Whenindividual is motionless left), the foot divides its load one-half the body weight)between the heel and ball, along axis A-B, and equally on both sides of the C-Daxis. When striding right) the load is distributed smoothly from I through 4 .From J . R. Napier: The Antiquity of Human Walking. Copyright 1967 byW. H . Freeman and Co., San Francisco, California. Reprinted with permission.)

From J. R. Napier: The Antiquity or numanW. H . Freeman and Co., San Francisco, California. Reprinted with permission.)

From J. R. Napier: The Antiquity or numanW. H . Freeman and Co., San Francisco, California. Reprinted with permission.)



of the fulcrum, the kinem atic model func tions on ly as a first classlever. Th e in-force can be applied to either position 1 or 2 (see Figure6.4 nd produce a n out-force at position 3 4,or 5.

3. Let us now consider the fo ur parame ters of th e lever law for differentspecies of animals. Species can vary in reference to bone lengths andinsertion points of m uscles.a. For a species with its gastrocnem ius inserted at position I , mea-sure the muscle force s required to cause a 2-pound out-forc e tobe exerted at po sitions 3, 4, and 5. Enter these data in Table 6.1.b. For a species with its gastrocnem ius inserted at position 2, m ea-sure the musc le force s required t o cause the 2-pound out-force atpositions 3, 4, and 5. Enter these data in Table 6.1.

Table 6.1. The force exerted by gastrocnemius (Fi) to produce a constant out-forceof 2 pounds (Fo) at position 3, 4 or 5.Fo at Position3 4 5

2Gastrocnemiusinsertionposition

c. At what position does the gastrocnemius exert the most force toproduce the 2-pound out-force? T he least? Based on your results insection I d, estimate the co mpression force (Fc) exerted on the pivotpoint fo r each of the in-force and out-force positions in Table 6.1.What structural adaptations would be useful in dealing with thesecompression orces at the point s of articulation in real skeletal leversystems? W hat material covers the actual surfaces of articulation ina vertebrate?4. W e can gain insight into the force conversion efficiency of th e leg footlever system by roughly estimating the force mechanical advantage

(FMA) of the m achine. This is done by dividing the out-force (in thiscase the constant force of 2 pounds) by the in-force exerted by the gas-trocnemius, or:out-force ==FMA = in-force Fi

Note: We can consider skeletal lever systems force-efficient ifF M A > 1.0, because the muscle involved is producing more out-forcethan the in-force it generates. If F M A < 1.0 the skeletal lever systemis force-inefficient in th at the out-force is less than th e in-force tha t th emuscle generates. With F M A = 1.0, the muscle neither gains nor losesmechanical advantage since Fi = F,.

------I

------I


Biomechanical Analysis 133a. From your m easurements above, calculate the F M A fo r a specieswith its gastrocnemius inserted at position 1 Enter these data inTable 6.2. Do the sam e fo r a second species with i ts gastrocnemiusinserted in position 2.

Table 6.2. The force mechanical advantage at various gastrocnemius insertionpositions and output force positions.Fo at position3 4

2GastrocnemiusInsertion

Position

b. In each case, at what point along the fo ot is the greatest F M A ob-served (i.e., position 3, the proximal metatarsals; position 4, thedistal m etatarsals; or position 5 , the toes)? Does this agree with you rexperience with your own leg and foot? To answer this, suspend oneleg in mid-air, and pull up with a rope at points along the foo tcorresponding t o positions 3, 4, and 5. Wh ile contracting your gas-trocnemius, use the tension developed on the rope as an estima te ofthe out-force magnitude produced by the muscle at these positionson the fo ot . Does you r leg/foot lever system agree with the kine-matic model? Are these results understandable in terms of th e lawof the lever?c. Which of the two species (species I = gastrocnemius inserted inposition I ; species 2 = insertion at position 2) has the greatest forc emechanical advantage?

5 . The maxim um effectiveness of a particular m uscle/bone lever systemis achieved when the distance moved by the m uscle is small com pared tothe distance moved by the business end of the bone (the end of themoment arm m oving the load). Speed mechanical advantage ( S M A )equals the distance moved by the business end of the bone (B) divided bythe distance of muscle contraction (M) , or:

BS M A =Note that M is equivalent to the dis tance moved by the heel bone at themuscles insertion point.a. To obtain estimates of S M A , we need to measure the arcs describedby po ints corresponding to the tw o muscle insertion positions and th ethree foo t lengths. The arcs can be ma de by placing the mo del on asheet of paper and, with ive pencils positioned in holes located along



the foot , move the foot through the fu l l extent of its rotation. Also,carefully mark the position of the pivot point. Care fully measurethese arcs, to the nearest mm , and also the lever arms for all fivepoin ts (see Figure 6.8).M and M 2are the contraction distances orgastrocne mius muscles inserted at distances S ,and S fr om the pivot .B,, B,, and B are the movements of the ends of feet of lengths S3,S4, and S5 respectively.Results similar to the following should be achieved.

II

Figure 6.8. Diagram showing the relationship between the lever arms (S1-S5) a tvarious position 1-5) in a simple lever system, and the distance of musclecontraction (M1-M2) and bone movement (B,, B,, B3) at these positions.Calculate th e following speed mechanical advantages from your m ea-surements:

BM1

BM 1

Note: We can consider skeletal lever systems speed-efficient ifSMA > 1.0, since the muscle is moving the bones end through agreater arc than its own contraction distance. If SMA < 1.0, thelever system is relatively speed-inefficient since the distanc e moved bythe muscle is greate r than the movem ent of the other en d of the bonecaused by its contraction. With SMA = 1 .O the muscle neither gainsnor loses mechanical advan tage since the contraction distance eq ualsthe bone movement.



How do the above SM A values compare with:

W hy should a relationship exist between SMA and t he correspondinglever arm ratios? Compare the SMA values fo r th e two m uscle in-sertion positions and fo ot lengths.b. How does the SMA of a species with its gastrocnemius inserted atposition I compare with that of a species whose muscle insertion isat po sition 2?c. Suppose w e examine two species whose gastrocnemius musc les insertat an equal distance ro m the ax is of rotation, but whose fe et are ofdifferent lengths. Wh ich species would have the greater SMA?d. Wh at part of your foo t contacts the ground when yo u want speed (asin running)? Does yo ur leg/foot lever system agree with w hat w ould

be predicted fr o m your measurements with the kinematic model?6. The work of a muscle (W) is equal to the force exerted by the muscle(F) times the distance moved by the muscle (M), i .e., the amount ofshortening during contr action. Thu s, if m uscles A and B exert equalforces, but muscle A contracts by lc m and m uscle B by 2 cm, muscle Bhas done twice as much work as A.Using your data on t he muscle force Fi)eeded to produce a 2-poundout-force (Table 6.1) and your data on distances moved by muscles atpositions I and 2 (M1and M2; section 5 , calculate th e work performedby muscles (W = F M ) at positions one and tw o in the skeletal leversystem. Enter these data in Table 6.3, expressed a s centimeter pounds.*Are th ese data reasonable?Table 6.3. The work (centimeter pounds) performed by muscles at insertionpositions 1 and 2 on the calcaneus bone.

Fo at Position3 4

2GastrocnemiusInsertionPosition

*Ide ally both measurem ents should be in metric units. W e deviate fro m this because the onlyeconomical spring scales we could obtain measure force in pounds.



7. How does the FMA compare with the SMA at the various points alongthe foot/leg lever?OF W H A T C O N S E Q U E N C E I S T H I S I N P R E D I C T I N G T H EPRO PERTIES OF S K E L E T A L D E S I G N F R O M L O C O M O T O R YCH A RA CTERISTICS??

Analysis of Articulated Vertebrate Skeleton sNow t ha t you have developed some insight into the physical considerationsimportant in the evolution of endoskeletal systems, you have the opportunityto apply this knowledge to a variety of organisms. The article by MiltonHildebrand (How Animals Run) should provide some additional back-ground information. The articulated skeletons of a number of different ver-tebrates: man; fish; frog; snake; turtle; bird; cat; salam ander; etc.; ar e availablefor study.Select one of th e specimens f o r detailed an alysis. Note that you are notrequired to learn the names of the bones for a particular skeleton; bones ar enamed on the figures simply for the purpose of orientation and comparisonbetween organisms. Carefully examine the lengths and arrangements of theskeletal bones. Al so note the prominent bumps and knobs on each of

the bones. These protuberances serve as attach ment points (origins and in-sertions) or th e skeletal muscles. Consider what you know about the loco-motory and feeding behavior of the species you are studying and thebiomechanical principles yo u have ju st learned. For example, a mam mal th atdigs needs to produce a large out-force (Fo) at the forefoot when the tricepscontracts. Since F, = FiSi/So, the animal can increase Fo by increasing Fi orSi or decreasing So.What bone movements are necessary to produce the simple behavioralmovements typical of the organism you are examining?How would you arrang e the skeletal muscles in your anim al to producethese movements? Be specificStimulation of a Frog Skeletal Muscle

Another method useful in studying the relationships between skeletalsystems, muscle arrangements, and m ovement is to directly stimula te an in tactmuscle and observe its effects on the animal. Obtain a fro g that has beendoubly pithed. Remove the skin ro m a fore- and hindlimb. A layer o f externalconnective tissue (fascia) is evident on the surf ace of each m uscle. With thehandle of a dissecting needle, carefully free the gastrocnemius m uscle alongits entire length. Be careful not to break the origin or the insertion. In thefrog, the gastrocnemius has its origin on the distal end of the f e m u r and onthe triceps fem or is muscle. It inserts by the tendon of Achilles, which runsalong the ankle, to the side of the foot. Free the Achil les tendon fr om i ts



fascia and note the extreme length of the insertion. The antagonist of thegastrocnemius is the tibialis anticus longus, which is on the front of the ca lf.Your teaching assistant will aid you with the electrical stimulation of themuscle preparation.Examine the other muscles of the frog. What changes in the orientationof th e frogs bones ar e implemented by contractions of the muscles you ex-

amine?Attempt to understand the integrated contraction of m uscle groups nec-essary to enable the frog to turn around, walk, jum p, or swim .Examination of an Exoskeletal Mu scle System

Arthropods, with exoskeletons, have their muscles attached to the insideof the skeletal system. Would the same mechanical principles that you ob-served in reference to vertebrates also hold for an arthropod? Observe thearthropod on dem onstration, and diagram in the worksheet an e xoskeletonlever system with an extensor and flexor muscle correctly positioned andlabeled.


138 BiomechanicalAnalysis

BIOMECHANICSWORKSHEET Name

Lab day and timeLab instructors name

You are now in a position to predict and analyze the properties of l eg la nk le lfoot lever systems in vertebrates which have become modified during the courseof evolution for: (1) producing powerful pushing forces vs. (2) providing rapid lo-comotory movements.

1. Diagram the foot/leg lever of an animal that has evolved maximum forcemechanical advantage FMA).

2. Diagram the foot/leg lever of an animal that has evolved maximum speedmechanical advantage (SMA).

3 Can one animal show skeleta l and muscle adaptations for maximizing bothforce and speed at the same time? Why and how?


Biomechanical Analysis 1394. Can animals functionally convert their leg /foo t lever systems from high force

to high speed systems? How? Give an example.

5. Estimate the SMA for the gastrocnemius/foot lever systems of the threevertebrates shown in the Hildebrand article, using their lever arm ratios. Dothese SMA values agree with predictions for these organisms in terms of theirrequirements for force and speed efficiency? Show your calculations.

6. Diagram an exoskeleton lever system with a labeled extensor and flexormuscle shown and an arrow indicating the direction of movement during flex-ion.


140 Biomechanical AnalysisIII nstructors Mate rials

A. Suggestions for an Introduction to the LaboratoryOu r general approach to teaching this laboratory has involved a learn-by-doing strategy. T hat is, we do relatively little pre-lab lecturing but, rather,directly involve the stude nts with the m aterials. Although the w ritten stude ntmaterials (see previous section) and the article by Hildebrand 1970) shouldinitially provide adequa te background for stud ent understanding of this lab-oratory se quence, it is useful to review several simple concepts. Fir st, since wewill be treating skeletons as the simple lever systems t ha t they are , applyingsome simple concepts from physics will have relevance and give some insightinto their evolution. Second, it will be useful to discuss the following terms[with reference to a see-saw (Figure 6.1) to give some added relevance]: in-force, out-force, in-lever arm, out-lever arm, torque, and the law of thelever. W ith these basic ideas discussed, students can begin work, althoughit will be necessary to also present th e conc epts of mechanical advantage and

work ater in th e session. As d ata are collected, the instructor leads a consid-eration of it, making explicit its biological implications, and helps studentsanswer the questions posed in the laboratory han dout. T he following sectionprovides suggestions for this phase of th e labor atory session.Note: The work with the kinem atic model introduces students to essentialconcepts. The other sections of the article (Analysis of Skeletal S ystems a ndStimulation of Frog M uscles) are extensions of this work and allow studentsto use some of the concepts developed with the model. The instructor candecide on the am ount of em phasis to place on these sections. Our experienceshows that about two hours is required for a thorough session doing theexercises with the model and discussing the results. A bout one hour can beproductively devoted to the skeletal system analysis or stimulation of frogmuscle groups.B. Suggested Laboratory Activities Involving the Kinematic Model;Answers to Questions Posed in the Student Ma terials

After a brief review of the physical concepts (as outlined in the precedingsection), students should receive their kinematic m odels (one model per stu-dent pair) an d begin the procedure section of the stud ent materials.Answers to questions posed in the procedure section of th e stude nt ma -terials are as follows:1. a. Equilibrium in a lever system occurs when all opposite torques aboutthe joints axis are equal. Since the moment arm s from the axis topositions #2 and 3 are eq ual, the forces required to produce equilib-rium should be approximately equal.



b. Yes. They should verify this.c. Yes. The force needed at position #2 to produce a balancing torquewill be considerably greater if the load force is applied at position#4. Students should carefully measure forces involved, measure themoment arms, and determine that the two torques are approximatelyequal.

F i t #2F, at 3 Fi at #2F, at 4Fi = 2 pounds Fi = 4.25 poundsSi = 5.1 cm Si = 5.1 cmF, = 2 pounds F, = 2.0 poundsSo= 5.2 cm So= 10.3 cmFiSi= FoSo FiSi= FoSo(2)(5.1) (2)(5.2) (4.25)(5.1) (2)(10.3)10.2 10.4 21.7 20.6

d. This exercise demon strates tha t the compression forces developing a tpoints of articulation (i.e., base of tibia and fibula) are equal to thesum of the forces on either side of the axis producing equilibrium.Thus, with a persons weight over the toes and a balancing forcegenerated by the gastrocnemius and other calf m uscles, the compres-sion force generated on the ankle joint may be several times thepersons weight. Of course, there are two ankle joints, each bearingonly one half the total. This also explains why the articulating endsof limb bones are enlarged and strengthened (you m ight point this outlater when they are examining skeletons). The following diagramshould clarify the arran gemen t of three scales in this exercise.The easiest way to m ake me asurem ents is to place the m odel flat withthree scales in position and with the bolt removed. While one personfirmly holds the upper pa rt of th e m odel down, the other person pullson the lower scale (C) and reads the three forces generated.Fc = Fi F,.2. With reference to Figure 6.3, the comparison between the kinematicmodel and the leg/ankle/foot system should be evident.



ASpringscale

I \1 2 3 4 5 PositionsPivot bolt removed

3. a. See the following da ta (in lbs).b. Se e the following da ta (in lbs).Fo at Position3 4 5

Gastrocnemius 1InsertionPosition 2 2.00 7.25

c. Position 5, for both species.Position 3, for both species.As indicated in Table 6.1 the force developed by the gastrocnemiusto obtain equilibrium increases directly as the distance from the an klejoint ax is to the force position increases. Again, the compression or ce swhich joints are subject to are equal to the su m of the force s oneither side of the joi nt. In the above example, with Fi at position 1,and 2 pounds at position 3, the compression force would be



M1

4.

a .

b.C.5.

B3

1.25 2.00 = 3.25 pounds. With Fi a t #1, and 2 pounds at #5, thecom pression force would be 4.75 2.00 = 6.75. Cartilage is locatedbetween the points of articulation of bones, particularly a t joints sub -ject to high compression forces. Because of the elasticity and com-pressibility of this material in comparison with bone, cartilage helpsreduce wear and aids in the absorption of shock.Mechanical advantage is here viewed as a relative m easure of input versusoutput, or w hat you get for what you give. Students will discover later,when they calculate muscle work output, that you dont get somethingfor nothing If a species evolves to maxim ize force mec hanical adv antag e,a proportional decrease in speed mechanical advantage is simultaneouslyaccrued, and vice versa.See the following da ta.

F, at Position3 4 5Gastrocnemius 1InsertionPosition 2

Greatest FM A is achieved with F, a t position 3 for both species.The species with its gastrocnemius inserted a t position 1 has the greatestFMA.a. It is important to carefully m ark the location of the pivot bolt whenmaking the tracings, since this is needed to determine the momentarms. T he following measure ments, in cm, an d calculations are typicalof those collected with our models.

Ankle joint 15.37.7


144 Biomechanical AnalysisB

B 1.34 ; 2.00B = 3.03= 2.03 .

M 1 M11M2 M2 M2

B = 0.68B1 = 1.03

S5 = 3.004 = 2.02S = 1.02 ;S S2 S2Since the radius (the Ss or moment a rms ) of a circle determines thelength of the arc (the Ms and Bs), dividing B, by M y will producethe same quotients as th at obtained by dividing Sx by Sy. The conceptis important since it allows us to calculate speed m echanical advan-tages for different skeletal units as moment arm ratios without thenecessity of dealing with arcs. S M A is greatest with Fi at #2 and Foa t 5 . SMA is least with Fi a t 1 and Fo a t #3.b. Toes. Yesc. The species with its gastrocnemius inserted at position #2 has g reater

d. Species that, under these conditions, have longer feet will have gre aterSM A than the species with its insertion a t l .SMA .6 . Consider the following da ta (in cm-lbs).Fo at Position3 4 5

GastrocnemiusInsertionPositionWith a fixed weight force, muscles inserted a t 1 perform the same workas muscles inserted at #2. Muscles with insertion at #1 are minimizingthe force needed to counterbalance a weight force, but must contractthrough a greate r distance, therefore proportionately increasing M in thework equation F X M = W). These muscles are efficient in terms ofFM A, but a re less efficient in terms of S M A. M uscles with their insertionat #2 are m inimizing the contraction distance required in order to coun-terbalance a weight force, but must contract with greater force in orderto do so. This proportionately increases the F component of the workequation. Therefore, these muscles are efficient in terms of SMA, butinefficient in terms of F M A.


Biomechanical Analysis 1457 . F M A increases and SM A decreases with an increa se in the distance fromthe pivot point to the muscles insertion. FMA decreases and SMA in-creases with an increase in the distance from th e pivot point to the locationof the weight force. We wou ld, therefore, predict that species requiringrapid locomotion should have their locom otory muscles inserted closeto the pivot points of the leg joints and also that these species should

have relatively long leg bones. In referen ce to the first point, bony pro-cesses for the insertion of locomotory muscles (such as the calcaneus)should be relatively short. The reverse should be true for species notrequiring rapid locomotion, but instead needing the ability to m ove heavyobjects (such a s their own weight). These anim als should have long bonyprocesses for muscle insertion and relatively short limb bones. .C. Sugge sted Approach to Analysis of Articulated Vertebrate Skeleton s

In this part of the laboratory, students are asked to examine severaldifferent skeletal systems and consider the sizes, shapes, and arrang em ent ofbones in reference to what they know about the feeding behavior and loco-motory behavior of the animal. Extensive interaction with student groupsduring this section is required. O ur labora tories usually have a minimum offive different vertebrate skeletal systems on display: (1) human, (2) frog,(3) cat, (4) chicken or pigeon, and ( 5 ) snake, bat, salam ander, turtle, fish, orhorse. As an aid to students in their com parison of different skeletal systems,supplemental diagrams of the main vertebrate bones are provided in theirlaboratory text or on posters in the laboratory.Although we explain that attem pts to apply m echanical principles to thebody based only on an examination of skeletal systems must be done withcaution, we ask stude nts to consider a specific movem ent (i.e., walking, jump-ing) and speculate on what muscle arrangement would be required by theanimal in order to perform the behavior. In addition, we explain that adap-tations of the whole organism are involved in its locomotory ability. As dis-cussed in H ildebrand, the speed of the ch eetah depends not only on its long(digitigrade or fingerwalking) feet, but also on a supple, flexible spine androtational ability of the pelvic and pectoral girdles. In preparation for yourdiscussions, the references listed in the bibliography, and specifically the bookby Gans (1 974), titled Biomechanics-an Approac h to Vertebra te Biology,should be helpful.A good approach to this phase of t he laboratory is to assign stude nt groupsto th e various skeletons and to ask them to prepa re an end-of-the-lab presen-tation discussing adaptations shown by their skeleton in relation to concepts



learned with th e kinematic model. We have found that this approach stim u-lates students to thoroughly analyze their skeletal system and helps them linkthe physical concepts learned with the m odel to th e biology of locomotion andfeeding behavior.D. Electrical Stimulation of Muscles of a Skinned Pithed Frog

This segment of the laboratory work can be very useful in helping stude ntsappreciate the complex, integrated action of muscle groups needed to producesimple movements. It can be done as a demonstration by the instructor inabout 15-20 minutes or more actively involve students for one hour. One frogand stimulator per pair of students are adequate in the latter case. Becausethe muscles ar e bigger, larger-size frogs ( at least 3 inches, snout-to-vent) m akeit easier to stimu late specific muscles without cross-stimulating ad jacent mus-cles.After the frog is doubly pithed, th e skin should be carefully removed fromone fore- and hind-leg. We use a Grass Instruments stimulator (model S5)but any similar square-wave stimulator is adequate. W e have found tha t astimulus of 10 to 40 volts (depending on the preparation) w ith a duration ofabout 10milliseconds and a frequency of 10 pulses per sec is best. Th e stim-ulator can be used to determ ine the action of specific muscles (flexor, extensor,adductor, abductor) and to identify which muscles form synergist and antag-onist groups relative to a bone lever system. A detailed examination of theactions of the many small muscles of the foreleg and forefoot ar e particularlyimpressive. Students should consult an articulated frog skeleton to understandwhere the muscles they stimu late have their origins and insertions and mak epredictions on their actions. To better see the action of a muscle when i t isstimulated, hold the bone on which it has its origin in a fixed position. Thiswill allow the muscle to produce maximum movem ent of the bone on whichit inserts. Keep the frog well moistened with frog Ringers solution (7.5 gNaCl, 0.35 g K C l, 0.21 g CaCI2 in 1.0 liter water).E. Examination of an Exoskeleton Muscle System*

A preserved, dissected crayfish, lobster, or c rab w ith som e labeled extensorand flexor muscle groups is placed on demonstration. Good preparations canusually be made of the muscles in the abdomen and/or cheliped. For a com-prehensive description of the biom echanics of chelipeds, see Brown et l 1979.*(for methods to use in stimulating hindleg flexor and extensor muscles of a live grasshopper seethe Chapter in this volume by Carlson, et al-eds. note).



1.

2.

IV. Biomechanics Worksheet Answers

Foot

Long calcaneusshort foot

Short calcaneuslong foot

Foot3. Yes. In theory, by having two sets of muscles, each inserted on differentpar ts of the sam e bone, one could have the best of both p ossible worlds.In fact, this is quite common (see the article by Hildebrand and hisdiscussion of the vicuna). The speed efficient muscle would have its in-sertion close to the joint. T he force efficient muscle would be inserted a ta greater distance from the joint. This ar range me nt allows gear shifting.4. The lever arms are measured directly from the figure in the Hildebrandarticle (1 970).

5.927.1 cm =SMAs: D e e r = 1.2 cmD o g = cm = 5.00S, 0.9 cm

The deer, being a fast-running mammal, should possess limbs showinggreater S MA. This would be true, to a lesser extent, for the dog. Thebadger, being a digging mamm al, requires a certain am ount of FMA andthus a reduction in SMA.



6 .

5 . Yes, by varying the location of the fu lcrum fro m directly under the ankleto the toes. Th e kangaroo is a good example of an a nima l tha t loafs andwalks on the flat of its feet (functionally plantigrade). While running,only the tips of the toes touch the ground (functionally digitigrade).

Extensor Flexor

Insertions

Note: The position of extensors and flexors in endoskeletal systems isreversed from th eir position in exoskeletal systems . Arrow shows directionof segment movement when flexor contracts.References

Alexander, R. McN. Animal Mechanics. London; Sidgw ick and Jackson; 1968.An interesting readable text on biomechanics which covers both vertebratesBrown, S. C. ; Cossuto,S. R.; Loos, R. W. Biomechanicsof Chelipeds in some decapod

One of the ew recent studies on the biomechanics of organisms with exos-and invertebrates.crustaceans. J . Zool. Lond. 188:143-159; 1979.keletons.Gray, J. How Animals Move. Cambridge, MA: Cambridge University Press; 1953.A classic review of animal locomotion. More elementary than his next book.(see below).Gray, J. How fishes swim. Scientific American 197(2): 48-54; 1957.

Gray, J . Animal Locomotion. New York: W .W . Norton; 1968.A general comparisonof swimming in ish. whales, and dolphins.An updated more comprehensive review of the application of mechanics tolocomotion. Excellent sourceon ishes. amphibians, snakes and birds. Extensivebibliography.Gans, C. How snakes move. Scientific American 222(6): 82-96; 1970.

Gans, C. Biomechanics, A n Approach to Vertebrate Biology. Philadelphia, P A J . B.Lippincott Co.; 1974.Good review of principles. Mos tly a detailed coverage of the biomechanicsof locomotion and food gathering of reptiles, espec ially snakes.Glase, J. C. and Zimmerman, M. C. Mechanical analysis of vertebrate skeletal sys-tems. Glase, J. C.; Ecklund, P. R.; Houck, M. A. eds Investigative Biology.Denver, CO: Morton Publishing Co; 1980: 317-348.An introductory biology laboratory tex t with an investigative approach.

An interesting description of locomotion without appendages.



Hildebrand, M. How animals run. Scientific American 202 5): 148-1 57; 1960.Especially good background material fo r this laboratory. Discusses adap-tions of the skeleton and muscles that increase speed of running in mamm als,notably horses and cats. We require our students to read this article before theycome to the laboratory.Hildebrand, M . Analysis of Vertebrate Structure. New York John Wiley and Sons;1974.An excellent readable test in comparative anatomy. Contains eight chapterson locomotionof vertebrates.Napier, J . R. The antiquity of human walking. Scientific American 216 4): 56-66:1967.Includes some of the classic photographs of human movement by the pho-tographer Eadweard Maybridge.Napier, J . R. Primate locomotion. Oxford biology Reader 41. London: Oxford Uni-versity Press: 1976.Available fr om Carolina Biological Supply Co.Pennycuick,C. Animal flight. Studies in biology 33. London: Edward Arnold Publ.;1972.Good comparisonof bird and bat fligh t.

APPENDIX IConstructionof the Kinematic ModelThe kinematic model is constructed from three pieces of 2 3/16 x 3/4 pine seeFigure 6.9). Both the top and foot are 10 long and connected by a 163/4leg.The top is fitted to the leg by two nails after a 2 3/16-x-3/8 section is cut out. Thefoot is connected to the leg by a 1 1/2-x-1/4bolt.Five holes are drilled into the foot at a height of 3 4 and distances from theheel of 1 2 11/2 51/2, 7 and 9 1/2 respectively. To allow mobility of the footin the ankle region, a 3/8-deep, V-shaped ( 1 1 4 bottom, 3%top) groove is cutfrom the back. The toe and heel ends of the groove are cut at angles of 30 and20 , respectively.In order to fit the foot, the lower end of the leg is rounded anda 3-x-3/8 piece cut from the front. When operational, five 2 paper clips are fastenedto the eye screws. To perform the exercises described in the laboratory, three ZebcoDe-Liar Model 208; obtained from Fredon WholesaleCo. , 1912 Teall Ave., Syracuse,NY 13206, phone 315-463-0464) fish weighing scales are required per model. Thehook of a fish scale is connected to a paper clip and force applied by pulling on a

piece of string connecting the scale to a hook in the top piece of the model. Werecommend that each pair of students have access to a model.



Figure 6.9. Plans for construction of the kinematic model.

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Biomechanical Analysis of Vertebrate Skeletal Systems 6-Glase