ED 092 494

AUTHORTITLEINSTITUTION

NOTEAVAILABLE FROM

EDRS PRICEDESCRIPTORS

IDENTIFIERS

nnrnmvum uvcnmv

SP 008 083

Hay, James G., Ed.Kinesiology IV.American Association for Health, Physical Education,and Recreation, Washington, D.C.62p.AAHPER Publications Sales, 1201 16th Street, N.W.,Washington, D.C. 20036 (Stock No. 245-25548,$4.50)

MF-$0.75 HC Not Available from EDRS. PLUS POSTAGEAnatomy; College Curriculum; Exercise (Physiology);*Health; Human Body; Kinesthetic Methods; Kinetics;*Physical Education; *PhysiologyKinesiology

ABSTRACTThis is a collection of significant papers by leading

authorities, compiled by the American Association of Health, PhysicalEducation, and Recreation's Kinesiology Committee of the PhysicalEducation Division. The following papers are included in thiscollection: "Supporting Biomechanics Subject Matter in theUndergraduate Curriculum "; "Laboratory Exercises in Biomechanics forUndergraduate Students"; "Preaxial and Postaxial NeuromuscularRelationships in the Upper Extremity: A Method of Teaching MuscleInnervation": "Biomechanical Analysis of Human Motion"; "Moment ofInertia of the Human Body"; and "Assessment of Forearm Position uponUpperarm and Shoulder Girdle Strength Performance." (JA)

KINESIOLOGY IVPublished by the Committee on Kinesiologyof the Physical Education Division

(k).

AMERICAN ASSOCIATION FOR HEALTH,PHYSICAL EDUCATION, AND RECREATION

1201 Sixteenth St., N.W., Washington, D.C. 20036

Contents

Supporting biomechanics subject matter in the undergraduate curriculum, David L.Kelley 1

Laboratory exercises in biomechanics for undergraduate students, Doris I. Miller 12

Preaxial and pa taxial neuromuscular relationships in the upper extremity: A methodof teaching m Bele innervation, Donald J. Hobart and Joseph R. Vorro 24

Biomechanical analysis of human motion, James G. Andrews 32

Moment of inertia of the human body, James G. Hay 43

Assessment of forearm positions upon upperarm and shoulder girdle strength perform-ance, John Pisropo 53

Committee on Kinesiology1973-74 Officers

Chairperson:ANN ELIZABETH ATWATER, Department of Physical Education for WomenUniversity of Arizona, Tucson, Arizona

Chairperson-Elect:DAVID L. KELLEY, nepartment of Physical EducationUniversity of Maryland, College Park, Maryland

Past Chairperson:MARLENE ADRIAN, Department of Physical Education for WomenWashington State University, Pullman, Washington

Secretary:ERNEST DEGUTIS, Department of Physical EducationWestern State College of Colorado, Gunnison, Colorado

Editor of the Kinesiology Column in the A AHPER Journal and of Kinesiology IV:JAMES G. HAY, Department of Physical Education for MenThe University of Iowa, Iowa City, Iowa

Headquarters Staff:WILLIAM L. COOPER, Director of Publications

RITA KOPANIC, Research Editor

iv

DAVID L KELLEY

Supporting Biomechanics Subject Matter in the

Undergraduate Curriculum

PROGRAMS OFFERING the opportunity tospecialize in the emerging subject matter areaknown as biomechanics have begun tomaterialize at the graduate level in theUnited States. An increasing number of uni-versity physical education departments areestablishing within their faculty, teachingposts which carry the responsibilities of de-veloping courses and programs in biome-chanics as well as supervising graduatetheses. One might be tempted to call thisnotable trend a "Biomechanics Bloom," forit is real and is beginning to demonstrate itsinfluence quite broadly. It is interesting tonote that this development is almost certainto carry with it the gradual establishment ofintroductory biomechanics courses at theundergraduate level, a phenomenon whichhas shown itself to be operative in manyother disciplines in the past.

Although this downward drift of subjectmatter content is to be expected, there islittle likelihood of widespread developmentof degree programs in biomechanics at theundergraduate level in the immediate future.It would be possible to cite a number of rea-sons to support such a contention, but it isenough to say at this point that the twinrequisites of qualified faculty and costlyfacilities to support such programs arc simplybeyond the resources of presently constituteddepartments of physical education.

David L. Kelley is associate professor ofphysical education of the University ofMaryland. College Park, Maryland.

Kinesiology IV

Traditionally, physical education under-graduate majors have been introduced tomatters akin to biomechanics through re-quired kinesiology courses. The content andscope of these courses have and still do varywidely from school to school. So much so,that it is not uncommon to find enteringgraduate students virtually bereft of experi-ences dealing with the scientific foundationsof motion study which would allow themunfettered passage into graduate courses inbiomechanics without repeating the under-graduate kinesiology course or courses at thenew institution.

It is to be expected that among themissing ingredients of such kinesiologycourses were matters primarily mechanicaland mathematical in nature. It is to be ex-pected also that undergraduate kinesiologycourses will adually evolve to the pointwhere more and more biomechanics subjectmatte' will be included on an introductorybut rigorous level in addition to the staple,applied anatomy. In this way, those who feelit unwise to relinquish the venerated term,kinesiology, can make a number of simpleadjustments in their traditional kinesiologyofferings which can improve the scope of thestudy of human motion under their tutelageand, at the same time, set the stage for subse-quent course work under the heading ofbiomechanics,

This article was presented to the Kinesi-ology Committee Section meeting, NationalAAHPER Convention. Minneapolis, Minn.,Spring. 1973.

1

The combination of kinesiology and bio-mechanics subject matter then could be con-strued to represent a very important arm ofthe broader subject matter of physical edu-cation, and those of us who have strongfeelings about retaining kinesiology as aworkable and descriptive term in the under-graduate curriculum would be served. Forinstance, this subject matter arm could carrya name which is a contraction of the twoterms to become kinesiomechanics. Sincewriters often become enamored with terms oftheir own invention, kinesiomechanics willbe used hereafter to represent the under-graduate subject matter combination withinwhich separate emphases on kinesiology andbiomechanics may be pursued as courses.

Discussions of the desirable contents ofbeginning biomechanics courses for theundergraduate course are inevitable. How-ever, it is not the purpose of the presentdiscussion to deal with course content excepton the broadest of levels. The purpose atpresent is to deal with those matters whichact to undergird the development and opera-tion of undergraduate courses, inviting ourattention to discussions of: (1) programconsiderations, (2) facilities and equipmentsupport, (3) supporting organizations, and(4) faculty.

That which follows should be receivedwith the understanding that the first under-graduate course in biomechanics is con-ceived as following a prerequisite kinesiologycourse which is structured as noted in thepreceding paragraph. Furthermore, this dis-course is, by no means, an exhaustive cover-age of all the elements involved in estab-lishing a new subject matter area. What itcan be, is a simple discussion of everydaymatters which may assist instructors in thetasks of launching new courses in bio-mechanics and, hopefully, encouragement forthose with such aspirations to make theefforts necessary to the success of thosecourses.

PROGRAM CONSIDERATIONS

Like human beings, programs developedby them tend to show many of the same

characteristics of aging. A tendency whichis seen now and again in physical educationteacher training curricula is that of inordinateclutter. Requirements which at one timewere logical and defensible, remain in thecurriculum although evidence for their beingretained as requirements is meager. Theymay be kept more as a matter of administra-tive convenience, with each requirementbolstered by its advocates who lobby forcontinued inclusion of their pet. Nearly allof our physical education programs requirea solid block of professional educationcourses which are designed to meet statecertification requirements for public schoolteachers.

Concurrently, pressures build to introducenew subject matter which has developedfrom recent scholarly thrusts in our dis-cipline. Short of adding extra semesters toencompass the growth, the outcomes of thesestresses are programs which can be and oftenare: (1) rigid as to elective flexibility, (2)deficient in providing for innovative curricu-lum options, and (3) outmoded for theirtime.

Under such circumstances, students oftenfind it difficult to schedule anything beyondtheir major programs and find that practi-cally every minute of their student careers iscontrolled by requirements of one sort oranother. It is possible to find well-knownmajor programs in the United States whichrequire the undertaking of 17 credit hoursper semester in order that the degree andteaching credential can be obtained within a4-yr. course of study, accumulating as manyas 136 credit hours in doing so.

We, as physical educators, appear todemonstrate a propensity for collection whichis not mitigated by a very clear understand-ing of space and time limitations. Fortu-nately, we are generally open to trying newthings, but often the necessary awareness ofthe arithmetic of additions and subtractionscomes as a surprise. Clutter is, indeed, oneresult of such faulty arithmetic and is seento run counter to the needs of an environ-ment which encourages the development ofnew subject matter areas such as bio-mechanics.

2 Kinesiology IV

In common with many other emerginginterests within physical education, bio-mechanics courses at the undergraduate levelwould, at first, he expected to serve anelective tenure. However, as noted earlier,for elective courses to be patronized, it isnecessary to have clutter-free programs.Such programs come about by design andserious efforts in the service of electiveflexibility and are likely to carry with them aheaping spoonful of painful experienceswhen some faculty members find that theirspecialties have been transplanted to elec-tive status if the surgery is not skillful.

Yet, it is probably in the best interests ofboth faculty and students to require of allstudents only those courses which constituteundeniably the elemental parts of our dis-cipline. Those which remain more peripheralmust settle for being offered periodically aselectives. Fortunately, those courses whichdemonstrate real substance and are continu-ally well-taught, will survive and thus servethe needs of the department and studentsalike. Consequently, one of the prime pro-gram requisites to establishing undergraduatecourses in biomechanics is to support thedevelopment of greater elective flexibility.It may just come to pass at some future timethat biomcchanics will have achieved a statuswhich could justify its inclusion as a re-quirement for all students.

The needs of today's students with theirmore diversified interests and backgrounds,and the rapid expansion of knowledge in thefield of physical education are placingincreasing responsibilities on college anduniversity departments to meet the challengeof preparing students with a more advancedknowledge of their discipline. One means ofachieving this end is to develop curriculumoptions to serv., the emerging and broaderdemands of th t growing group of individualswho do not see their future in public schoolteaching but are, nevertheless, intenselyinterested in understanding the multifacetedplace of motor performance in the dailyexistence of mankind.

A basic question unders,ying this sort ofdevelopment deals with whether or not pro-grams should be limited to the task of pre-

Kinesiology IV

paring students for a specific employment.In the past, public school teaching hasusually been the sole, clearly identified placeof future employment. With the demand forteachers now on the decline, placement is farfrom guaranteed, and graduating seniors arebeing forced to investigate other means ofearning a living. This state of affairs is beingrecognized earlier by succeeding students,which tends to focus their attentions favor-ably toward curriculum options which, ifavailable, can provide more-than-adequatecredentials for competing for employmentin a variety of areas in our society.

Although numerous sites of satisfyingvocations could be listed here, it would Kernadvisable to see the prime function of non-teaching programs in physical education asproviding an education which will allow thegraduate sufficient background to pursuewhatever courses meet his/her interests.This aim is, therefore, not unlike thatespoused by many other college departments(i.e., English, foreign languages, history, finearts, etc.) who welcome students, not on theassumption of guaranteeing some specificfuture employment, but on the basis of amutual and abiding interest in the subjectmatter involved. Herein lies a stimulatingmeans of securing a place for undergraduatebiomcchanics course work, for it is withinthis sort of educational climate that theintroduction of new and influential practicesmay take root. It is certainly not beyondcredibility to suggest that a first course inbiomechanics might be included as a re-quirement of all students within such anundergraduate curriculum option.

With the development of new programoptions comes the opportunity to investi-gate briefly an assumption which has beenwith us so long a time that it has becomepractically axiomatic. That is, specializationwithin the subject matter domain of physicaleducation cannot profitably take place otherthan at the graduate level. For example, if astudent should develop an intense interest inthe kinesiomcchanics arm of our broadersubject matter as a result of experience withhuman anatomy and kincsiology early in hisundergraduate career, very few avenues will

3

be found available to him to advance hisknowledge in that area until after graduation.

Serious attention to the matter of expect-ing students to specialize to some extent, avery natural urge for most of us, in estab-lished areas of their interest within our fieldis a concept whose time appears to havearrived, particularly within nonteaching cur-riculum options. Certainly one of the areaswhich can be singled out for additional stu-dent emphasis is kinesiomechanics. Studentsselecting this path would be encouraged toelect courses outside of their department aswell as from within to enrich their back-grounds further. In this way the problem ofstaying current with the advancing knowl-edge in certain, selected areas could beefficaciously pursued along with attendingto the more general knowledge of the otherareas provided by single courses in thecurriculum.

If students were expected to identify andthen pursue to additional depth, let us say,two concentrations (perhaps kinesiome-chanics and exercise physiology might serveas an expected zombination) from a groupof those established by the department, a listof courses which were deemed appropriateto support those concentrations could be pre-pared to aid students in making correctchoices in light of their backgrounds. For astudent whose background was noticeablyweak in mathematics, a rather commonoccurrence within physical education stu-dents, suitable courses leading to adequateworking knowledge of such areas as analyticgeometry and calculus could be prescribed.Similarly, if additional work in mechanicsseemed appropriate where an adequatemathematics background was in evidence,courses selected from physics and engineer-ing departments might be counseled. In sucha program, the stimuli for offering additionalin-house experiences for interested studentswould be high, and courses such as bio-mechanics could run parallel to those takenoutside the department.

In most physical education degree pro-grams, but particularly in those where dif-ferent curriculum options are not available,it is most i:nportant to initiate and offer

4

"Independent Studies" courses where inter-ested students can work on a one-to-onebasis with a faculty member in an area suchas biomechanics where no formal courseexists. Courses with this sort of purpose arefound under different names in differentinstitutions. It is not important what namethe course has been given, but to provide avehicle where experiences beyond that avail-able from established courses in the catalogmay he pursued. Under the auspices of theseofferings, many valuable experiences can bemade availabl; that cannot be included inregular classes because of the large numberof students serviced. Even with these de-sirable possibilities available, it is surprisinghow few students take advantage of theseone-to-one services.

The problem probably hinges. upon threecontributory circumstances. First, specialstudies offerings are seldom advertised veryadequately on a department level. Second,when known to exist, requirements clutteroften interferes with the students electing thecourses. Third, faculty members interestedin supervising these experiences do not offerenough encouragement to those studentswhom they feel could handle such situationsto advantage. It is our good fortune thatthese experiences materially benefit facultymembers by providing new ideas, methods,and approaches for present or proposedcourses. Thus, one means of developing anongoing program and interest in the studyof human motion topics is to encourage yourable students to try their hands at inde-pendent studies and urge them to plan theirschedules in advance to provide the time forthem later.

Most colleges have, within their coursenumbering systems, a means for trying outnew course offerings without first goingthrough the tangled procedures wIkh placea new course in the catalog with an officialtitle and course number. These may be desig-nated generally as "Special Problems" or"Seminars" where faculty members mayoffer and students may elect to study matterswhich are of special interest or just cominginto prominence. On occasion, the subjectof these trial courses may even be centered

Kinesiology IV

around a faculty member's personal researchprograms which may have accumulated aconsiderable cache of interesting findings tobe compared and integrated with materialsfrom the literature. When that research hasbeen focused upon kinesiomechanics studies,it is natural that it could contribute well to atrial course in biomechanics. If, upon one ormore trials of the course, it is clear thatdepartment and student needs are beingserved, the course can then be submittedformally for regular course status with apermanent catalog number designation. Itis through procedures such as these thatmajor curricula make great strides to avoidbecoming outmoded, as well as encouragingthe development of new courses in emergingsubject matter areas such as biomechanics.

To summarize briefly revarding programconsiderations, it would appear helpful torecommend working toward or encouraging:

1. A reduction in the magnitude of re-quirements clutter, particularly in our pres-ent teacher training programs.

2. The development of broad electiveflexibility in present programs as well asproposed programs.

3. The development of nonteaching cur-riculum options in programs, where noneexist at present, so that an increase in subjectmatter depth may be offered.

4. The investigation of the possibilities ofrequiring students to specialize to some ex-tent in nonteaching curriculum options.

5. 'The initiation and use of "IndependentStudies" courses to enrich the usually limitedofferings available in kinesiomechanics.

6. The development and use of trialcourses which could, if proved effective onsuch a trial basis, become regular course of-ferings in the program.

FACILITIES AND EQUIPMENT SUPPORT

Few would argue against the value of in-cluding laboratory experiences in an under-graduate biomechanics offering. There is noavoiding the fact that biomechanics courses

Kinesiology IV

which include a substantial helping of labo-ratory demonstrations and experiments willbe costly to initiate if certain facilities andequipment arc not available at the outset.Further, if each student enrolled is expectedto complete an investigative project of somesort as a course requirement, the cost of be-ing adequately equipped will be higher still.So it becomes necessary to make some deci-sions as to what might be advantageouslyemployed and to establish a general under-standing of priorities in the acquisition ofequipment for existing facilities.

An assumption underlying the discussionswhich follow is that the means of demonstrat-ing and experimenting with biomechanicsphenomena in a first course would beachieved best through the use of graphicalmethods of data acquisition, analysis, andpresentation. It is quite likely that some im-portant pieces of equipmen": are alreadyavailable in most physical t.ducation depart-ment laboratories and if they are not, simplebeginnings usually may be undertakenthrough the assistance of other departmentswithin the college or university which dealwith similar matters.

Examples of such are the departments of:(1) mechanical, civil, and electrical engi-neering; (2) physics, (3) dramatic arts andcommunications; (4) educational technol-ogy; (5) industrial ethication; and (6) au-diovisual services. When it becomes clearthat certain important support facilities andequipment are not going to be obtainedby your department for some time to come,step out and get acquainted with your col-leagues in o'her departments and work outarrangements to us: their facilities on a tem-porary basis. Yeti will be pleasantly sur-prised to fins' now receptive they can be tothe needs of someone such as yourself inorganizing a first course in biomechanics.So, make acquaintances and see what isavailable for your use.

Devices for the simple demonstration ofmechanics phenomena, those that have be-come so familiar to us from beginning phys-ics courses, are not difficult to obtain and putto use. However, a distinct problem in bio-mechanics situations is that of demonstrating

5

these same phenomena unambiguously withhuman beings acting as the subjects underscrutiny. Because of the complexity of hu-man movement functions, the process of cap-turing elements of a complicated task forimmediate as well as subsequent study underconvenient circumstances is of utmost im-portance and it is clear that devices ancillaryto our own observational faculties are neces-sary. Those which are deemed within thereach of present physical education depart-ments are listed below, and it will be seenthat each is essentially a graphic process.Please note that they are listed in order ofgreatest value without regard to cost. Theyare: ( 1 ) Photographic, (2) Elect:omyo-graphic, (3) Kinctographic,2 and (4) Goni-ographic.

Insofar as one can predict general usage,the first priority with respect to equipmentand facilities support is to provide the meansof obtaining photographic records of tran-sient events. The permanent records pro-duced by a photo system may be convenientlystored and then utilized later in a mannerwhich can provide for adequate data reduc-tion, both qualitative and quantitative. Sincesome means of recording serial events (andthus provide a time base) is mandatory to bio-mechanics study, the use of cinematographyis called for. Facilities to support even themost basic of cinematographic work dependupon two factors, namely, adequate lightingand sufficient space to accommodate thephotographed act and the optical require-ments of the system in use.

If the work is to be done indoors, suffi-cient light is a decided problem and artificiallighting, both horizontal and from above,must be provided in quantities far larger thanmost people imagine, particularly when largespaces such as gymnasiums are involved. It

This term has been taken from Morton,D. J., The Human Foot, (New York: TheHafner Publishing Co., 1964) p. 154. in whichthe term, kinetograph, was used as the name ofa device for recording foot imprints duringstanding and, ambulation. As used here, kine-tographic processes of data acquisition refer tothe use of force registering devices, the mostsophisticated of which are force platforms.

6

is of some importance to point out how com-mon it is to find that existing electrical wiringcapacities are not able to cope with the de-mands of indoor lighting over extended peri-ods, and the inevitable searches must beginto find and replace blown fuses or to re-actuate tripped circuit breakers, The mes-sage carried by this common occurrence is toknow your facilities well and make plans tocircumvent these perplexing and time-con-suming difficulties. When filming outdoors,lighting problems are seldom insurmount-able.

After the latent photographic record hasbeen processed, at least two pieces of datareduction equipment are mandatory and itwould be ideal if these could have their ownarea for use by students, undisturbed by theother activities of a laboratory. The firstserves to support qualitative analysis in addi-tion to everyday classroom teaching uses. Itis a sturdy motion picture projector whichprovides both single-frame operation as wellas motion projection. WitIrthis device, themore superficial but still important featuresof the photographed act may be studied overand over until they can be described withhigh accuracy. The second device is a filmreader of some sort (they may be had in awide range of sophistication) which alloy'sconvenient extraction of quantitative coordi-nate and time data from single-frame images.From these kinematic elements, numerousother mechanical quantities may be derived.

If suitable camera gear is not available,the ,cqu pment, film, and a photographer canusual;y be obtained to serve your temporaryneeds from the audiovisual services depart-ment of your college. With some care paidto informing the photographer of your specialrequirements, satisfactory records may beobtained, both for classroom use as well asfor student projects. One cautionary note isessential here. These services may not bee-itirely gratuitous, and it is wise to investi-gate all costs and the procedures for inter-departmental billing that are used so thatrequests for adequate monetary support canbe settled well in advance. Better still, askfor a sum of support funds to cover all course

Kinesiology IV

costs as a part of the department's yearlybudget and be sure to plan for the inevitableincrease in costs of services and supplies asyour course develops in complexity.

Next in importance is the ability to moni-tor and record acticn potentials from activemuscles of the body during some event,either dynamic or static in nature. Henceelectromyography is called for with a mini-mum capacity for monitoring two differentmuscles simultaneously at the outset, and abuilding capacity for at least four channelstotal!), for futu..? use. If limited to monitor-ing but one muscle at a time, much of theinformative interplay between muscles is

made most difficult to obtain. If it can bemanaged, purchase equipment that providesfor integrated as well as direct recordingmodes of operation. In this way, both quan-titative and qualitative analytical needs canhe handled conveniently.

In the beginning, it should be satisfactoryto limit the use of electrode types to the sur-face kind, and consequently, to the monitor-ing of surerficial musculatures. After pro-ficiency has been gained using surface tech-niques, an investment in and use of "indwell-ing," electrodes could be attempted after firstinvestigating the medical and liability re-strictions involved. Then, the movementcontributions of deeper and smaller musclescan be demonstrated and studied. In addi-tion, it would be wise to plan to include anoscilloscope to assist in the search for anddemonstration of electrical artifacts and forsome mcins of transducing the muscle actionpotentials into audible sounds through a

loudspeaker.One of the truly valuable advantages of

electromyography in laboratory situations isits ability to have interpretable informationat hand immediately. Because of this imme-diate record of monitored events, it servesthe needs of laboratory demonstrations in away that few other systems provide. Forexample, an original set of circumstances canbe included in a demonstration and beforethe monitored act is performed, hypothesesmay be advanced regarding expected out-comes. After studying the recorded evidence,additional hypotheses can be offered as to

Kinesiology IV

what should occur when a variable is added.This, too, can be tested immediately, leadingto more tests under other circumstances, andso on.

When electromyography is combined withcinematography to record a movement eventover a common time base, a synergistic effectis obtained where the totel information ob-tained is greater than the sum of the indi-vidual system outputs. The combination ofqualitative and quantitative features pro-vided with such a combined system is literallyoverwhelming, to the point where a singlerecorded event can provide demonstrationmaterial of nearly endless biomechanicalphenomena.

Kinetographic gear is usually one of themost commonly encountered equipmenttypes found in physical education labora-tories. Because of their use in conjunctionwith concerns of exercise physiology andkinesiology courses and studies, devices suchas weight scales, dynamometers, cable ten-siometers, and even more elaborate instru-ments to measure strength, parametersutilizing strain gauges and load cells areoften found in plentiful supply. These maybe put to advantageous use in biomechanicssituations when the direct measurement ofapplied forces is preferred to derivation.Under controlled conditions, forces exertedvolitionally through our musculoskeletallever systems and registered on devices suchas the cable tensiometer, can serve nicely tostudy the changing effects of lever armlengths, muscle lengths, and joint posi-tions. When combined with simultaneouselectromyographic monitoring of muscleactions, we again find outcomes which cm,-tribute more than would be expected to anunderstanding of the intricacies of anatomicalmechanics.

The force plate of platform, a complicatedinstrument which can register concurrentforce magnitudes in more than one dimen-sion, is gaining advocates rapidly eventhough it is not inexpensive. It may be putto excellent use in verifying force magnitudesderived through cinematographic methodsor in conjunction with cinematography toestablish forces with the exact positions

7

where they occurred. It is unlikely thatinstruments of this sort will be broadly avail-able as the result of a simple purchasealthough they have immense value in thestudy of human movement. When they areobtained, they are usually fabricated on aspecial design basis from a small "develop-ment" company or by some to the largemechanical and electronic shops servinglarge engineering or science departments atmajor universities.

A search for one already in use on yourcampus, particularly within engineering de-partments, might well be profitable; if notfor continuous use purposes, perhaps forperiodic demonstration purposes. Again,step out and see what your institution has tooffer. In any case, it would be wise to keepinstruments of this sort in mind and gradu-ally move toward developing the capacity toutilize them as an adjunct to your under-graduate biomechanics offerings, especiallyin those departments where graduate work inbiomechanics is already established. For anintroductory source of information concern-ing the force platform aitd its uses, readersare referred to Payne."

Goniographic techniques for angularmeasurement of joint positions and move-ment have been in use for quite a long time.More recently, provision for continuous re-cording by electrical means have resulted inthe electrogottiotneter (elgon). As has beenthe case with otiv.-.r specialized devices foundin physical education laboratories, in-housefabrication to meet specific needs has beencommon. Consequently, the ability to under-take goniographic investigations and demon-strations is not inordinately costly to im-plement. For those who are unfamiliar withthis instrument, attention is directed to thefirst issue of this publication.4

" A. H. Payne, "The. Use of Force Platformsin the Study of Physical Activities,- Tire Uni-versity of Birmingham Review, Autumn, 1966,Birmingham, England.

4 Marlene J. Adrian, "An Introduction toElectrogoniometry," Kinesiology Review, 1968.

8

Just as the force platform may be usedwith and to check the accuracy of cinemat-ographic determinations, the same holds truefor the combination of goniographic andcinematographic methods of measuring jointmovement over a common time base. Also,in common with the other kinds of equip-ment discussed previously, goniographicmethods place the investigative emphasisdirectly upon the use of human subjects, acircumstance which can too often be over-looked with the result that the "mechanics"in biomechanics can be emphasized to adegree where the "bio" is neglected.

SUPPORTING ORGANIZATIONS

The intent of this section is quite simpleand can be attended to without undue labor-ing. The faculty member who finds himselfor herself the only person with an intenseinterest and background in a subject matterarea within a department, can lead a ratherlonely existence inasmuch as there may be noothers with whom special interests may bediscussed. It has been a common tactic forphysical education departments across thenation to employ one faculty member toserve the department as their resident expertin kinesiomechanics matters. Others may beasked to teach sections in undergraduatekinesiology so that the required number ofmajor students may be served; but on mostoccasions, these faculty members have otherspecialties and duties which consume theirinterests and time. Consequently, the oppor-tunity to exchange ideas, practices, methods,and new developments with others of simi-lar interests are relished whenever theymaterialize while attending such gatheringsas conferences, clinics, and workshops. Itwould .be most beneficial if this kind ofstimulating interaction could occur moreoften than on a once yearly basis. Hence, thethrust of this discussion is to encourage theorganization and development of commoninterest groups which can meet regularly todiscuss kinesiomechanics topics.

Since the author has been involved re-cently in that kind of task, the incorporation

Kinesiology IV

of a specific organization as a case in pointappears to be justified. Figure 1, presentsthe mark or emblem of the MarylandKinesiological Society, a new, common in-terest organization which has developedspontaneously as the result of the interactionof diversely placed faculty members withinthe University of Maryland. At present,members of the Society come from thefaculties of the departments of anatomy andphysiology of the School of Dentistry,anatomy and physical therapy of the Schoolof Medicine, and physical education, as wellas tinm the United States Public HealthService in Baltimore, Maryland.

Recently, invitations to attend monthlymeetings have been extended to interestedcolleagues in other state and private collegesfrom the relatively small state of Maryland.Therefore, what was in the beginning anorganization populated primarily by facultymembers of one institution, now is in theprocess of expanding to embrace a larernumber of interested specialists throughoutthe state.

Organizations of this sort need not bestructured only along state lines. In largestates such as Texas or California, smaller,regional groups would be more advisable formonthly meetings while statewide gatheringscould be set up on a once yearly basis.Whatever the organizational structure turnsout to be, the opportunities provided to share

Figure 1. Emblem of the Maryland KinesiologicalSociety.

ideas is the true goal and our experience hasbeen one of growing enthusiasm. Agendasfor forthcoming meetings are prepared anddistributed in advance, which announce re-ports and presentations from members con-cerning their research projects and findings,discussions of proposed projects and theusual soliciting of assistance in the planningof projects and courses to be taught.

For example, one recent meeting includedun interesting and candid evaluative report ofa Biomechanics Workshop course given at amidwestern university which was attended bya member. The following month, a slidepresentation by another member, entitled"Application of Neuromuscular Function toDetermine Occlusion and Rest by VisualizingMasticatory Muscle Potentials," generated alively discussion. Because the meeting placewas located in the facility where the researchhad taken place, demonstrations of some ofthe procedures were also presented.

Plans are afoot to invite prominent indi-viduals outside our membership to speak oftheir studies and findings which relate to thepurroses of the gatherings. In addition, itLas oeen most gratifying to be able to invitestudents to attend these meetings and to findthat they thoroughly enjoy the experienceand hope to be invited again. Efforts are inthe planning stage to cultivate additionalmemberships from the disciplines of engi-neering and orthopedics. C. .sequently, itseems reasonable to say that the time andefforts required to organize such groups arewell worth the investment since the oppor-tunities to "go to the well" for scholarly andprofessional refreshment are just cause forsuch an undertaking in support of the devel-oping subject matter area of kinesiorne-chanics.

FACULTY

Although this discussion category is themost important of them all, it was left for lastto provide for extra emphasis. For, if ade-quately prepared faculty members are notavailable to handle present and proposed

Kinesiology IV 9

courses in biomechanics and kinesiology,little of what has preceded this final categorywill be very useful. It is the view of thiswriter that at present there is a dearth ofproperly trained people to handle bio-mechanics courses within the present pool ofundergraduate kinesiology teachers in ourcolleges and universities. Far too often,courses of this sort are serviced by theexpedient known as "pressing into service ofthe ill-prepared." This situation needs to beremedied, and it is hoped that the followingdiscussion will aid in identifying some areaswhere positive changes may be accomplishedas well as identifying some means for doingso, short of resigning one's position andreturning to full time graduate student statusin biomechanics.

Among the areas of weakness which areoften found in the backgrounds of many ofthe ill-prepared is that of an insufficientunderstanding of mathematics. Mathematicsacts as the common language of the sciencesand provides the means of going beyond thequalitative into the quantitative. Most ofthose who are limited in this manner arecompelled to confine their treatment of bio-mechanics topics to coverages which may bedescribed as bounded by intuition. Beyondthese mathematical limitations, and relatedto them, are additional background defi-ciencies in basic physics and mechanics,anatomy which includes the diss:':ction ofhuman cadavers, comfortable acquaintance-ships with technological hardware and theprinciples of its operation, and finally,knowledge of the research and professionalliterature involved with these matters. It iseasy to see how several of these deficienciescan be related to one another.

For those readers who may consider theforegoing as a case of overstatement, thefollowing anecdote may be useful. Onemember of this writer's summer term, under-graCuate kinesiology course identified him-self as a graduate student who had chosenthis area of study to be one of several inwhich he hoped to be examined prior toadmittance to candidacy for the Doctor ofPhilosophy degree, His interest and progresswhile pursuing the course of study indicated

10

an aptitude commensurate with his intent.However, during an impromptu discussionwith the student, he let it be known thatalthough he had never before completed asingle undergraduate course in the kinesio-mechancis area, he was employed by a statecollege department of physical education andwas their resident instructor of kinesiologyfor their undergraduate majors. The preva-lence of such circumstances could be thecause of much argument, but it is likely thatan occurrence of this sort is not nearly asimprobable as we might prefer to imagine.

Another area of faculty concern whichbears upon these discussions is that it appearsthat only a small number from the presentpool of kinesiology teachers is demonstratingevidence of research productivity in the formof published reports. Consistent outputseems to emanate from a few individuals whomay, by the goad fortunes of their employ-ment, find it both personally stimulating aswell as professionally rewarding to be pro-ductive in the scholarly pursuits of researchendeavors and the public dissemination oftheir findings. The rather consistent publica-tion of the results of student proiects such asgraduate theses is not to be confused withwhat has just been stated.

What is important is that faculty withavowed interests it teaching kinesiome-chanics subject matter should see, as anatural adjunct to that kind of employment,the responsibility to contribute new knowl-edge to the area of their dedication. Forthere is no more exciting and satisfying ex-perience in teaching than to be able to say toa class "... now, let us see how the resultsof some recent work of mine bears upon thetopics we have just been discussing." "Bythe way, this project is not yet completed,and I was hoping to find several studentsinterested in lending a hand two or threeafternoons a week." The reactions to suchinvitations are usually most responsive andvery productive in boosting the interests ofmany of your students because they aresearching for involvement beyond the realmof the clzssroom.

To identify problems is valuable, whileto offer suggested means for remedying those

Kinesiology IV

problems is helpful. The concluding para-graphs are involved with suggestions forimproving present circumstances, dealingmainly with encouragements to: (1) begina program of studying basic areas in back-grounds where important gaps are in evi-dence, (2) ask for help when it becomesnecessary, and (3) get busy with researchprojects in areas of your interest.

All of us are cognizant of gaps in oureducational backgrounds that we woulddearly prefer to be filled, if only the timeand means would present themselves. It isnot reasonable to expect such means to comeabout spontaneously. They materialize be-cause they are made to happen on the basisof careful planning and identification of thedesired course of action. It makes littledifference whether the study of mathematicsand mechanics, for example, is pursueddependently or in formal institutional set-tings. The important consideration is thestrength of the will to improve the power ofyour background. If it is preferable to studyanalytical geometry and review algebra inde-pendently, purchase suitable books and ma-terials and dig into it until the need for expertconsultation becomes necessary. When thisoccurs, seek help from within your institu-tion; possibly in the form of periodic tutoringfrom a colleague in another department orfrom the person whose office is just down the

hall from your own in your department whohas a command of such matters. There is nobetter time than the present to get started.

Lastly, on your way to your office on thefirst day of the new semester, stop in for avisit with your department Chairman andmake it clear, diplomatically that is, that youare in the process of formulating the meansof logically studying a kinesiomechanicsphenomenon which has needed attention forsome time. Further, let it be understoodwithout equivocation that you expect certainadjustments to transpire in order that yourproject may begin and be carried through toits reasonable conclusionthat being theidentification of and plans for attacking re-lated matters that surely must come to lightas a result of the original study, and the pub-lication of the original results. You areprobably in for a surprise to find your plansaccepted as reasonable and desirable alongwith a promise to facilitate them. Withthis outcome residing firmly in your mind,and knowing that one of the most difficulttasks is in just getting started, it will becomforting to realize that most worthwhileendeavors take a while to mature and thatthe optimistic declaration of unknown originthat is becoming popular among busy, pro-ductive people can help you as well. That is--"Inch by inch, it's a cinch."

Kinesiology IV 11

DORIS I. MILLER

Laboratory Exercises in Biomechanics for

Undergraduate Students

WHENEVER POSSIBLE, laboratory experi-ments in undergraduate biomechanicscourses should afford the student an oppor-tunity to apply the laws of mechanics toactual situations in sport. Such applicationsnot only provide meaningful experiences,but also reinforce the student's knowledge ofthe fundamental principles and increase hisunderstanding of the related concepts. Thetwo laboratory exercises presented here areexamples of an attempt to achieve theseobjectives.

KINEMATICS AND KINETICS OF A COMINGROCK AFTER DELIVERY

The sport of curling, specifically themotion of the rock after delivery, provides anappropriate vehicle for the experimentaldetermination of linear and angular posi-tion, velocity, and acceleration as functionsof time; the relationship between linear andangular velocity; as well as kinetic frictionand coefficient of friction. When the curlerreleases the rock (Figure 1), he imparts toit both a linear and a rotary motion. In the

Doris I. Miller is an assistant professor inthe School of Physical and Health Educa-tion at the University of Washington,Seattle, Washington. The article is basedupon a presentation given at the AAHPERNation& Convention in Minneapolis Min-nesota, April 13, 1973.

12

case of a draw shot, the granite curling stonetravels about 100 ft before coming to restin the "rings" or "house" at the opposite endof the rink (Figure 2). During this 15- to20-sec interval, the rock completes up tothree or four turns which can be readilyobserved by watching the motion of thehandle.

As it slides down the ice, the rock is underthe influence of two external forces (Figure3). Its weight ( W), which may vary from40 to 44 lb, acts vertically downward. Theground reaction force (R) is expressed asthe vector sum of the normal component(N) directed upward at right angles to theice surface and the kinetic friction com-ponent (FrA ) acting along the ice surface tooppose the motion. Air resistance can beconsidered negligible in this situation. Asthe rock decreases in speed and approachesa condition of rest, the friction experiencedby the edge on the outside of the turn may besmaller than that encountered by the insideedge. This unbalance in the friction forcewith the inside edge approaching a staticcondition while the outside continues to slidehas been suggested as the reason why therock "curls" or deviates from its initial linearpath (2, 3).

The laboratory exercise designed to studythese phenomena involves large groups ofstudents and requires a minimum of equip-ment (Table ' ). It has proven to be a par-ticularly enjoyable experience for the stu-dents and yet, at the same time, stresses anumber of fundamental mechanical prin-ciples. The following outline is distributedto the students before the laboratory.

Kinesiology IV

t-

to

Figure 1. The curling delivery.

Laboratory outlineIntroduction. The purpose of this labo-

ratory is to investigate the kinematics andkinetics of a curling r )ck in a draw shotfrom the time the rock is delivered until

it comes to rest in the "house." The linearposition, velocity, and acceleration andthe angular position and velocity of therock will be determined as functions oftime. The kinetic friction force and thekinetic coefficient of friction will be calcu-lated. Attempts will also be made torelate the theory of an "unbalanced fric-tion force" to the curl of the rock.

Application. Each group should have15 to 20 members including one fairlyconsistent curler who will serve as thesublet,;. The subject should select aparticular draw shot and repeat it 3 times.The rock should not be swept.

The information to be recorded foreach trial is listed on the laboratory rec-ord form (Table 2). The items markedwith an asterisk (*) must be o,,+ainedduring the actual trial while the othervariables can be determined later. Spe-cifically, the following information mustbe recorded:

1. The time for the rock to travelfrom:

(a) Release on the hog line(b) The hog line to the center of the

rink (the latter must be marked since nocenter line exists on the rink).

(c) The center to the hog line(d) The hog to the tee line or until the

rock comes to rest.(e) The tee line until the rock comes to

rest (if applicable).2. The distance covered by the rock

between the designated lines. Since therock may not be traveling paraiiei to the

TABLE 1. EQUIPMENT REQUIRED FOR THE CURLING LABORATORY

Number Item Comments

2-4/group8-10/group8-10/group

8-10/group

1/group1

1

Regulation curling rocksStop watchesRed poker chips

Blue poker chips

100-ft measuring tapeWeigh scale

Thermometer

Fewer are required if split timers are availableTo indicate the location of the rock at designated

distancesTo indicate the initiator and completion of each

half turn of the rock

An inexpensive bathroom scale will serve thepurpose

One may be located in the curling rink. This isnot an essential item

Kinesiology IV 13

BACKLINE

TEE HOGLINE \LINE

2 1 72'Figure 2. Diagram of curling rink.

restraining boards, it is important toplace a marker at the point where itcrosses a given line and then to measurethe distance between the markers.

3. The time required for each halfturn of the rock. Start when the handleis parallel to the length of the rink afterrelease. Also note the location of eachhalf turn on the rink by placing markerson the ice at the beginning and end ofeach half turn.

Figure 3. Kinetics of a curling rock.

=

Frk =

14

in a,, F, = m awni, N W = 0g

N = W

Frk = i1 x. NFrk

;-Lk = N

4. The place at which the rock beginsto curl.

5. The weight and radius of the rock.

Calculations. Determine the following:I. The linear velocity and linear ac-

celeration of the center of the rock duringthe distance intervals specified in Part I.of the previous section. Plot linear posi-tion-time, velocity-time, and acceleration-time graphs. (Remember that distanceand time intervals are not equal). Includethe information from all three trials oneach graph.

2. The angular velocity of the rock.Plot angular position-time and velocity-time graphs. Include the informationfrom all three trials on each graph.

3. The linear velocity of the inside andoutside edges of the rock each time thehandle is perpendicular to the length ofthe rink (Figure 4). Assume that 11(,, VI,and V, the linear velocities of the centerof gravity, inside and outside edges of therock, respectively, are acting in the samedirection. The value of Vo must be ob-tained from the linear velocity-time graphat the time corresponding to the midpointof the half-turn being considered, (Donot forget that in all linear-angularvelocity relationships, the angular velocitymust be expressed in radians per second.)

4. The normal and tangential (fric-tion) components of the ground reactionforce acting upon the rock. To do this,first construct a free body diagram of therock as it moves along the ice. Considerthe rock as a particle. Then apply theforce-mass-acceleration relationship (New-ton's second law).

Kinesiology IV

INSIDE

VI

Figure 4. Linear-angular velocity relationship.

V0 = VG + 1.01V, = VI; "" rto

F --= ni a

Draw a friction-velocity graph with ve-locity plotted along the horizontal axis.

5. The kinetic coefficient of frictionfrom the relationship.

Frk N

Discussion of results. When interpret-ing the results of this laboratory, the fol-lowing questions should be considered.Was the subject consistent in his per-formance? What are possible sources oferror in obtaining the results? What isthe relationship between the linear ve-locity of the rock and the friction force?How do the results compare with thoseobtained by Harrington (2) and McMil-lan (3) ?

CommentsExamples of the type of position, velocity,

and acceleration relationships commonlyfound in this laboratory are presented inFigures 5 and 6. The coefficient of kineticfriction can be expected to be in the .01 to

Kinesiology IV

.04 range. Theoretically, the kinetic frictionshould be independent of velocity until therock slows considerably and approaches thecondition of rest. At this time, it shouldbecome larger as it nears the higher staticfriction value. This increase, however, isdifficult to show in the experimental resultsbecause of the gross nature of the measure-ments.

Since considerable flexibility is afforded bythis laboratory, the instructor may want tolimit the calculations to linear velocity andacceleration or he may choose to follow theinstructions as presented. On the other hand,he may decide to go beyond these basicprinciples and use the information collectedin the laboratory as the basis for consideringthe inherent error in the differentiation ofexperimental data and methods of curvefitting.

FLUCTUATIONS IN THE GROUND REACTION

FORCE DURING JUMPING TAKE-OFFS'

The concept that the ground reaction forcefluctuates above and below body weight inresponse to changes in the acceleration of theperformer's mass center is difficult for moststudents to fully comprehend. The purposeof this laboratory, therefore, is to focusupon this problem in an attempt to increasethe student's understanding of the basicprinciples involved. It actually consists ofthree exercises which may be presentedeither as a series or independently at thediscretion of the instructor. For the sake ofsimplicity, most of the analysis is limited tothe vertical components of the force andmotion. The influence of air resistance is

disregarded.

Theoretical calculationsThe students are first given a chart (Table

3) listing the vertical coordinates of the mass

A detailed discussion of this concept is pre-sented in Miller and Nelson (4:53-61).

15

TABLE 2. CURLING LABORATORY RECORD

Subject* Skill Level* Temperature*

Shot Attempted* Pebble Conditions*

Rock Weight* lb Mass slugs Radius*

Linear velocity of center of rockI. Release to hog line

*a. Distance*b. Timec. Velocity

2. Hog line to center*a. Distance*b. Timec. Velocity

3. Center to hog line*a. Distance*b. Timec. Velocity

4. Hog line to tee line*a. Distance*b. Timec. Velocity

5. Tee line to rest*a. Distance*b. Timec. Velocity

Trial 1

Linear acceleration of center of rock,kinetic friction force, and coefficient offriction

L -2. a. Change in velocityb. Change in timec. Accelerationd. Kinetic friction forcee. Coefficient of friction

(Repeat the same information for intervals 2. 3.. 3. 4.. and 4. 5.)

Angular velocityI. First half turn

*a. Timeb. Angular velocity

*c. Location(Repeat the same information for each subsequent II:Until-n:1'

Linear velocity of inside and outside edgesof the rock

I. First half turna. Angular velocityb. Linear velocity of centerc. Linear velocity of outsided. Linear velocity of inside

(Repeat the same information for each subsequent half turn.)

Trial 2 Trial 3

16 Kincsiolouy 1V

100

z

v) 75oa. 4)

..-cra 50

25

0

15

10 15

TIME (sec )20

0

V4) 54)

cc I. 0

WZ_

1.50 5 10 15 0 5

TIME (sec ) TIME ( sec )

Figure 5. Linear kinematics of a curling rock after delivery.

Kinesiology IV 17

TABLE 3. CALCULATION CHART"

From the time and vertical coordinates of the mass center of a 144-lb jumper, calculate the verticaldisplacement, velocity, change in velocity, acceleration and ground reaction force component. Tofacilitate calculations, assume the acceleration due to gravity to be -32.00 ft/sec/sec. Using a singlegraph with a common zero line, plot the vertical position, velocity and acceleration of the mass center;ground reaction force component; and body weight as functions of time.

Change in ReactionTime Position Displacement Velocity velocity Acceleration force(sec) (ft) (ft) (ft/sec) (ft/sec) (ft/sec) (lb)

0.00 3.400.05 3.390.10 3.370.15 3.340.20 1290.25 3.210.30 3.070.35 2.900.40 2.710.45 2.550.50 2.430.55 2.360.60 2.360.65 2.450.70 2.670.75 3.030.80 3.550.85 4.150.90 4.720.95 5.211.00 5.62

Miller and Nelson (4:56)

5 10

TIME (sec)

>- 1.5

5O w_J (r)

> 1.0CC

acnz 0.5fr

15 0 5 10 15

TIME (sec)Figure 6. Angular kinematics of a curling rock after delivery.

18 Kincsiology IV

center of an athlete during a standing jumptake-off. These data, modeled after a studyon vertical jumping reported by Gerrish (1),are used to determine the vertical com-ponents of position, velocity, acceleration,and ground reaction force as functions oftime. All of these parameters along withbody weight are plotted on a single graphwith a common zero line (Figure 7) and in-terpretations are made. The students aredirected to pay special attention to themaxima and minima of the curves as well tothe points at which the curves intersect thezero line. For example, a careful examina-tion of Figure 7 should indicate the fol-lowing:

I. While the body is moving downward,the velocity remains negative; while the bodyis moving upward, the velocity is positive.

2. A negative acceleration correspondswith a decreasing velocity and a positiveacceleration with an increasing velocity,

3. When the acceleration is equal to zero,the velocity is at its minimum or maximumand the ground reaction force is equal tobody weight.

4. The jumper can be moving downwardand yet experiencing upward or positiveacceleration.

5. The vertical component of the groundreaction will always exceed body weightwhen the acceleration of the jumper's masscenter is positive (upward) and will fallbelow body weight when the acceleration isnegative. This fact should be verified by anexamination of the free body diagram andthe equations of motion (Figure 8),

6. Once free in the air, the jumper'svelocity continues to decrease, his accelera-tion is a consatnt 32 ft /sec /sec (the ac-celeration due to gravity) and the groundreaction force is zero.

Experimental dataThe second portion of the laboratory is

devoted to collecting experimental data toillustrate the same principles. The equipmentrequired for this phase includes a PolaroidGraph-Check Sequence Camera, a timingdisplay, a weigh scale with a dial indicator,

Kinesiology IV

and some object of known length whi,:h canbe used for converting film dimensions toactual distances. A piece of masking tape isplaced on the hip of the subject to approxi-mate the location of the center of gravity.The subject stands on the scale to have hisbody weight recorded. He then performs amovement of a nonexplosive nature such asdescending to or ascending from a crouchposition. This action is photographed by theGraph-Check Camera which is fastenedsecurely to a tripod and aligned to an angleto the face of the scale so that the subject'shead does not obstruct the view of the dialindicator (Figure 9). The plane containingthe mark on the hip of the subject and theconversion object must be at right angles tothe optical axis of the camera to avoid per-spective error in estimating the linear posi-tion of the hip.

From the Polaroid picture which containsa sequence of eight images of the action, thestudents can read the vertical component ofthe ground reaction directly from the scale,the vertical position of the hip marker ap-proximating the mass center location, andthe time intervals. These data along with theresulting velocity and acceleration can beplotted on a graph similar to the one shownin Figure 7. It is readily admitted that thescale is by no means as accurate as a forceplatform and is not suitable for investigatingexplosive types of movements. The sequenceof pictures, in conjunction with the scale.

readings, however, provides first-hand evi-dence of the fluctuations of the groundreaction force above and below body weightin response to the acceleration of the centerof gravity of the body.

Linear impulsemomentum relationshipsThe theme of this laboratory can be ex-

tended to include a consideration of linearimpulse and momentum related to jumpingperformance. The first point to be made isthat forces acting over a time interval cause achange in momentum. The force-time curvesof the long jump take-off presented byRamey (7) can be used to illustrate thisconcept. They can be enlarged by an Ludio-

19

6 12 -

I 1

5 10 -

GROUND9 REACTION

FORCE

4 8 -.. /

POSITION7 z.... I- - - ...... /

cu 6 r-..' /

tn .%...

... 5-..-

21- 4 -ccBODY WEIGHT

3 -111

1

0

2II- I .a./

120 600

/ 110 550

100 500

- 70 450

- 80 400

1%

4.

:111

-4

VELOCITY

- 70 Q 350

- 60U

- 50 (11

- 40...-

300 -1::

20 -W

o uu)

0 -

-10

- -20ACCELERATION - -30Jill

0 .10 .20 .30 .40 .5040

.60 .70 .80 .90 1.00

TIME ( sec )Figure 7. Vertical kinetics and kinematics of a standing jump take-off.

visual department and transferred to a spiritmaster so that dittoed copies of the curvesare available for each student.

While the long jumper is in contact withthe board, two external forces act upon him:his body weight and the reaction of the

20

300

250' -°

200 wc.)

150 0

100

50

0

ground. The latter is expressed in terms of ahorizontal and a vertical component, R, andR,,, respectively. The impulses which theseforces generate in the horizontal and verticaldirections must be treated separately sincethey are vectors (Figure 10) .

Kinesiology IV

1 RFigure 8. Free body diagram and equations ofmotion.

= nt a.,R., = m a.,

F, = mR, W = nt a,

R, = W a,

Impulse is represented by f F dt in which

F is the vector sum of all the external forcesacting upon the body. Thus, in the verticaldirection, Fy = Ry W while in the hori-zontal direction, Fr = R. The integral

Kinesiology IV

simply specifies the area beneath the force-time curve. In the case of a force such asthe ground reaction which fluctuates withtime, this curve is irregular. The areabeneath it, however, can be approximated bydividing it into small rectangles or squares ofknown area and then summing these com-posite areas. If the curve is traced ontograph paper, this task can be accomplishedwith reasonable accuracy. Since the bodyweight is constant, the impulse of theweight is simply equal to the area of therectangle with a base equivalent to the timethe jumper is in contact with the board andheight equal to his body weight.

From force-time curves recorded during ajump take-off, information on the per-former's weight and his velocity at the begin-ning of the take-off, the horizontal andvertical components of the velocity of hismass center at the instant of projection canbe determined. An example of the necessarycalculations is shown in Figure 10.

When interpreting the significance of theforce-time relationships, the students shouldconsider: th° influence of body weight; theimplications of spending less time in contactwith the take-off board (characteristic ofgood performers); and how the accelerationof the individual segments contributes to theacceleration of the mass center of the totalbody. References (5), (6), (7), and (8)are recommended reading for this laboratoryand will help to provide an in-depth under-standing of the application of linear-impulsemomentum concepts to situations in sport.

ReferencesI. GERRISH, PAUL H. A dynamical analysis of the

standing vertical jump. New York: ColumbiaUniversity, 1934.

2. HARRINGTON. E. L. An experimental study ofthe motion of curling stones. Transactions ofthe Royal Society of Canada 18:247-59, 1924(section III).

3. McMILLAN, R. For curlers only. The Roundel13 : 11-14, (Jan.-Feb. ), 1961.

4. MILLER, DORIS I., and NELSON, RICHARD C.Biomechanics of sport: A research approach.Philadelphia: Lea & Febiger, 1973.

5. MURRAY, M. P.; SEIREG, A.: and SCHOLZ, R. C.Center of gravity center of pressure, and sup-portive forces during human activities. Journalof Applied Physiology 23:831-38, 1967.

21

Figure 9. Sequence photograph.

6. PAYNE, A. H.; SLATER, W, J.; and TELFORD, T.The use of a force platform in the study ofathletic activities. A preliminary investigation.Ergonomics 11:123-43, 1968.

7. RAMEY, MELVIN R. Force relationships in the

running long jump. Medicine and Science inSports 2:146-51, 1970.

8. RAMEY, MELVIN R. Effective use of forceplates for long jump studies. Research Quar-terly 43:247-52, 1972.

22 Kinesiology IV

500

400

300

200

100

VERTICAL HORIZONTAL

0 .05 .10

TIME (sec

itc(Ry W) dt =

cR dt `W dt =

Vi = 21 ft /sec

.15 0 .05 .10 .15

TIME (sec 1

fFdt =0 my

1.1) ( Vf V1 )15032.2 (Vf Q1

88 x .5 i 50 x .15 = 4.66 Vf

44.0 22.5 = 4.66 Vf

Vf = 4.61 ft /sec

=150

R

t R

Rx dt = m (VfVi )

SR x d t - ( Vf 21)150

20 x .5 =4.66 Vf 97.86

87.86 = 4.66 Vf

Vf = 18.85 ft /set

Figure 10. Linear impulse-momentum relationships during a long jump take -'ff.

Kinesiology IV 23

DONALD J. HOBART

JOSEPH R. VORRO

Preaxial and Postaxial Neuromuscular Relationships in the

Upper Extremity: A Method of Teaching Muscle Innervation

KINESIOLOGY STUDENTS normally are re-quired to learn osteology and muscle actionsand attachments in their study of the humanorganism. They are also asked later, tocombine their knowledge of anatomy withmechanics to study various human move-ments. Consequently, a good comprehensiveknowledge of the human body is needed sothat kinesiological analysis can become auseful classroom tool. It is reason7'ile toassume then that in order to make theirknowledge of anatomy lasting and useful,general principles must be taught whereverpossible.

The purpose of this article is to present ageneral embryologien1 principle of muscleinnervation and to offer a plan to teach thespecific innervation of the upper extremity.The use of this plan generally eliminates theneed for detailed memorization of specificinnervations and aids in future recall ofgeneral muscle actions. Thus, this methodoffers a different and possibly more effectivemethod of organizing and studying the basicmusculature.

In order for this plan to he an effectivetool certain basic ideas mast be presentedand understood, The embryological basis is

Donald J. Hobart is assistant professorand Joseph R. 'v'orro is graduate assistantin the Department of Anatomy of iiieSchool of Dentistry at the University ofMaryland, Baltimore, Maryland.

24

presented first, then a discussion of thetypical spinal nerve and its relationship tothe brachial plexus, and finally a set of state-ments presented according to osteologicalrelationships, movement relationships, aidexceptions.

EMBRYOLOGY

In the developing human embryo, limbbuds emerge laterally from the trunk.Within these buds a bony axis is formed,thus, separating the developing muscles intoanterior and posterior compartments (FigureI ). Later, these muscles become the flexors(anterior muscles) and the extensors (pos-terior muscles) of the limb. With time, theinnervating nerves enter the limb also asanterior and posterior branches; the anteriornerves innervate the anterior muscles and theposterior nerves innervate the posterior mus-cles. Once this neuromuscular relationshipis established, it is maintained into adult life.

Since the anterior or flexor muscles arelocated in front of (i.e., 'pre') the skeliqalaxis they are generally labeled as preaxialmuscles and are innervated by preaxial (an-terior) nerves. The posterior or extensormuscles are behind the skeletal axis (i.e.,`post') and are generally labeled as post-axial muscles. The innervating posteriornerves are also called postaxial nerves.

Kinesiology IV

SPINAL NERVE

DORSAL PRIMARY RAMUS

VENTRAL PRIMARY RAMUS

POSTERIOR DIVISION OF VENTRAL RAMUS

DEVELOPING POSTERIOR(EXTENSORPOST AXIAL) MUSCLES

DEVELOPINGANTERIOR(FLEXOR- PRE AXIAL)

MUSCLES

DEVELOPING SKELETALAXIS OF UPPER EXTREMITY

ANTERIOR DIVISION OF VENTRAL RAMUS

Figure 1. A cross section of the developing human limb-bud.

Postnatally the limb remains divided intoanterior and posterior compartments (Figure2). In the arm these compartments areseparated by the humerus and one lateral andmedial intermuscular septa. The anteriorcompartment contains the biceps, brachialis,and coracobrachialis, flexors at the shoulderand elbow joints, while the posterior com-partment houses the triceps, an extensor.In the forearm the radius, ulna, interosseousmembrane, and the lateral and medial inter-muscular septa form the dividing line be-tween the flexors at the wrist. M -P', and I-P2joints in the anterior compartment and theextensors at the wrist, M-P and I-P joints inthe posterior compartment (Figure 2) (4).

' Meta carpophalangeal joint.Interphalangeal joint.

Kinesiology IV

TYPICAL SPINAL NERVE

The preaxial and postaxial nerves arebranches of one of the 31 typical spinalnerves emanating from the various spinalcord levels. There are 8 ceruical, 12 tho-racic, 5 lumbar, 5 sacral, and I coccygealnerves, each composed of a dorsal root whichreceives all of the sensory or afferent im-pulses, and a ventral root which transmitsmotor or efferent neurons. The two rootscombine to form the mixed (sensory andmotor) trunk of the spinal nerve. This partof the nerve is very short and divides into adorsal and ventral primary ramus almost assoon as it emerges from the intervertebralforamen (Figure 3). The dorsal primaryramus immediately penetrates into the mus-culature of the back and supplies motor in-

25

MedialIntermuscular Septum

Triceps

ARM

PRE -AXIALMusculocutaneous N

XORS

Biceps

Brachtahs

Humerus

_P_re-Awai jPu,l-Axial

Lateral InlermuSCularSeptum

EXTENSORS FOREARM

PRE -AXIALMedian NUlna, N

os

POST- AXIALRadial N

InterosseusMembrane

Ulnar

LPre-ArealrPoSt-Axial

POST-AXIALRadial N

Lateralinteernuscuiar

Septum

Figure 2. Cross sections of the arm and forearm :thawing the flexor and extensor compartments.

nervation and cutaneous sensation to thisregion. The ventral primary ramus on theother hand provides motor and sensoryinnervation to the lateral and anteriorregions of the torso (1, 2, 3, 4).

At certain levels of the spinal cord, theventral primary ramus of one level willcombine with the ventral primary ramus ofone or more other levels to form plexuses.These plexuses are areas for the intercom-munication of the ventral primary rami. Theresulting terminal branches may then carryneurons from various spinal cord levels.Several plexuses of this type are found alongthe spinal cord, i.e., cervical plexus, brachialplexus, lumbar plexus, and sacral plexus,each providing the innervation for a specificarea of the body. The discussion here willhe limited to the brachial plexus.

26

BRACHIAL PLEXUS

The brachial plexus is formed from theventral primary rami of the last four cervicalspinal nerves (C5, C6, C7, C8) and the firstthoracic spinal nerve (T1). The ventralrami from C5 to C6 combine to form thesuperior trunk after posterior fibers havebranched from C5 to become the dorsalscapular nerve and the long thoracic nerve(which also received contributions from C6and C7). Additionally, two small nervesoriginate from the superior trunk. One, thesuprascapular nerve, is composed of pos-terior fibers, and the other, the nerve to thesuhclavius, is zomposed of anterior fibers.The middle trunk is created by the ventralprimary ramus of C7 alone, while the

Kinesiology IV

Spinal CordDorsal Root

(sensory)Dorsal Root

--Ganglion

DorsalPrimary Ramus

Muscular( Actor)

BranchesVentral Primary

RemusSpinalNerve

AnteriorCutaneous(Sensory)Branch

Ventral Root(Motor)

Muscular(Motor) Branches

Figure 3. Typical spinal nerve.

inferior trunk is formed from a combinationof C8 and T1.

F:!ch of the three trunks then divide intoanterior and posterior divisions. All of theposterior divisions combine to form theposterior cord. Thus, all branches originatingfrom this cord will contain only posteriorfibers. The anterior divisions from the su-perior and middle trunks join to make thelateral cord while the anterior division ofthe inferior trunk becomes the medial cord.Thus, all remainir: branches from the lateraland medial cords will contain only anteriorfibers. Five small nerves are derived fromthe cords at this point in the plexus. Thelateral and medial pectoral nerves branchfrom the lateral and medial cords, respec-tively. while the upper and lower subscapularnerves aild the thoracodorsal nerve ;middle

LateralCutaneous(Sensory)Branch

subscapular) originate from the posteriorcord.

After giving off these branches the cordscontinue distally to approximately the infero-lateral border of the pectoralis minor wherethey divide, intermingle, and unite again toform the terminal nerves of the plexus. Thelateral and medial cords divide with one halfof each combining to form the median nerve.The remaining part of the lateral cord con-tinues as the musculocutaneous nerve, whilethe continuation of the medial cord is theulnar nerve. The two terminal branches ofthe posterior cord are the axillary and radialnerves (Figure 4).

The important aspect of the brachialplexus, from the standpoint of this discus-sion, is the division of its terminal branches

Kinesiology IV 27

Spinal nerve

Dorsal rootDorsal PrimaryRamus

N tO Subclavius

Swrascapular N

Superior Trunk

Anterior Division

Lateral Cord

Lateral Pectoral NAnteriorDivision

POsleriorDivision

Middle TrunkMusculocutaneous

N

Interior Trunk

Aailary N

Anterior Division

LongThoracic N

Medial BrachialCutaneous N

Radial N

Medial AntebrachialCutaneous N

Ulnar N

Figure 4. The brachial plexus. The shaded area indicates postaxial nerves.

into preaxial and postaxial groups. Thisdivision is summarized below:

Prea.via!

I. Nerve to sub-clavius

2. Medical pectoralnerve

3. Literal pectoralnerve

4. Musculocutancousnerve

5. Median nerve

6. Ulnar nerve

Postaxial

1. Dorsal scapularnerve

2. Suprascapularnerve

3. Lower subscapularnerve

4. Thoracodorsalnerve

5. Upper subscapularnerve

6. Axillary nerve

7. Radial nerve

8. Long thoracicnerve

Median N

PRE- AND POSTAXIAL RELATIONSHIPS

Within the preceding sections, importantfacts have been discussed: (1) the muscula-ture of the developing limb-bud is dividedinto a flexor (anterior) and an extensor(posterior) compartment by the limb skele-ton, (2) the developing flexor muscles areinnervated by the anterior divisions of theventral primary rami while the extensormuscles receive their innervation from theposterior divisions, (3) these neuromuscularrelationships are maintained throughout de-velopment, and (4) the brachial plexus iscomposed of five ventral primary rami, whichdivide into anterior and posterior divisions,intermingle, and eventually unite to formthe terminal preaxial and postaxial nerves ofthe plexus.

28 Kinesiology IV

Through the application of the abovefacts, it is possible to develop a set of generalstatements that can be used to define thespecific innervation of the muscles of theupper extremity. This can be accomplishedby: ( I ) pointing out how osteology can beused, (2) a discussion of movements otherthan flexion and extension, (3) presentinga functional breakdown of the terminalnerves of the brachial plexus, and (4) notingthe exceptions.

Osteology. Observation of embryologicaldevelopment has revealed that in the upperextremity the clavicle has exclusively pre-axial muscles attached to it and the scapula(excluding the coracoid process) has onlypostaxial muscle attachments. Thus, thesebones can be considered preaxial and post-axial, respectively. The remaining bones ofthe upper extremity have both preaxial andpostaxial muscles attaching to them (I, 3, 4).

The coracoid process of the scapula de-veloped as an anterior bone and consequentlyhas preaxial muscle attachments. It main-tains its preaxial status although it later be-came attached to the body of the scapula.The clavicle is also a preaxial bone with pre-axial muscle attachments. Muscles originat-ing from the coraeoid process and theclavicle; the pectoralis minor, biceps brachii,coracobrachialis, pectoralis major, and sub-clavius, are al! preaxial muscles. Those mus-cic5 attaching to the scapula proper: therhomboid major and minor, supraspinatus,infraspinatus, subscapularis, serratus anteri-or, deltoid, triceps, latissimus dorsi, teresmajor and teres minor, are all postaxialmuscles. This information may be sum-merized in three statements:

Statement 1. Muscles attaching to thecoracoid process of the scapula are preaxialmuscles.

Statement 2. Muscles attaching to thescapula proper are postaxial muscles.

Statement 3. Muscles attaching to theclavicle are preaxial muscles.

The order of the above statements must bemaintained to permit the student to deter-mine the hierarchy of muscle attachments.For instance, is the biceps brachii a preaxial

Kinesiology IV

or postaxial muscle? The answer would bepreaxial, as the coracoid process origin over-rides the scapular origin. Similarly, thedeltoid muscle is considered a postaxialmuscle as its scapular origin takes preferenceover its clavicular origin.

Movements. It has been determined thatmovements other than flexion and extensionare related to preaxial or postaxial organiza-tion. These additional movements are pre-sented below and except where noted applyto the glenohumeral, elbow, wrist, MP, and1P joints. Each muscle that has one ofthese movements as their prime action willfall into the appropriate preaxial or postaxialcategory.

Preaxial:I. Flexion (with the exception of the

brachioradialis)2. Adduction3. Pronation4. Abduction at the MP joints5. Opposition of the thumb

postaxial:1. Extension2. Abduction3. Supination4. Rotation of the humerus

Statement 4. Muscles that have postaxialmovements as their prime action arc inner-vated by postaxial nerves.

Statement 5. Muscles that have preaxialmovements as their prime action are inner-vated by preaxial nerves.

Now that the osteological and motion rela-tions to the preaxial and postaxial concepthave been examined, the terminal branchesof the brachial plexus can be discussed anda functional classification of the above nervesoutlined (see Tables 1 and 2):

Exceptions. Within any system of classi-fication there exists exceptions and this sys-tem is no different. The exceptions include:( ) The brachioradialis is an elbow flexor(preaxial movement) but is innervated bythe radial nerve which is postaxial, (2) Thetrapezius is innervated by a cranial nerve(XI, accessory nerve) which does not fit intothis classification.

29

TABLE I. OUTLINE OF THE BRANCHESOF THE TRUNKS AND CORDS OF THE

BRACHIAL PLEXUS

Postaxial nerves and musclesI. Dorsal scapularRhomboid major and

minor2. SuprascapularSupraspinatus and infra-

spinatus3. Long thoracicSerratus anterior4. .Upper subscapularSubscapularis5. ThoracodorsalLatissumus dorsi6. Lower SubscapularSubscapularis and

teres major

Preaxial nerves and musclesI. Nerve to subclaviusSubclavius2. Lateral pectoralPectoralis major3. Medial pectoralPeeioralis major and

minor

SUMMARY

The innervation of the upper extremitycan be summarized by 9 statements which,when applied in order, can be used to deter-mine the specific innervation of each muscle:

1. Muscles attaching to the coracoidprocess are preaxial.

2. Muscles attaching to the scapularproper are postaxial.

3. Muscles attaching to the clavicle arepreaxial.

4. Since in the area of the shoulder thenumber of muscles innervated by each nerveis minimal, no general concepts can bedrawn. However, the three statements listedbelow should help to avoid rote memoriza-tion of the innervation of each muscle:

a. Postaxial nerves associated with thescapula are: dorsal scapular, suprascapular,long thoracic, upper and lower subscapularnerves.

b. Postaxial nerves associated with shoul-der movements are the axillary, long thoracicand thoracodorsal nerves.

c. Preaxial nerves associated with shoul-der movements arc pectoral nerves, nerve tosubclavius, and musculocutaneous nerves.

30

5. Preaxial muscles are flexors, adduc-tors, and pronators.

6. Postaxial muscles are extensors, ab-ductors, supinators, and humeral rotators.

7. Muscles located in the hand are pre-axial.

8. Preaxial muscles located in the fore-arm and hand are innervated by the medianor ulnar nerve. Except for 1'/ muscles, themedian nerve innervates all of the preaxialforearm muscles as well as five muscleslocated in the hand (the thenar muscles andthe two lateral lumbricals). The ulnarnervc innervates 11/2 preaxial muscles in theforearm (flexor carpi ulnaris and the medialtwo heads of the flexor digitorum profundus)and all muscles located in the hand not in-nervated by the median nerve.

9. Postaxial muscles located in the armand forearm are innervated by the radialnerve.

As an aid in using the above statements todetermine the specific innervation of amuscle the following steps are offered:

I. Does the muscle attach to the scapularor clavicle? If not, continue.

2. Where is the muscle generally located:Anterior thoracic wall, arm, forearm, orhand?

3. What is the prime action of the muscle?Is it a preaxial or postaxial movement? If itis located in the forearm and is preaxial, is itthe flexor carpi ulnaris or the flexor digi-torum profundus? If it is located in thehand, is it a thenar muscle or the 1st or 2ndlumbrical?

With the answers to these questions and agood understanding of the above statements,the student should be able to determine thespecific innervation of any muscle in theupper extremity.

ACKNOWLEDGMENT. The authorswish to thank Carol Fairchild for herexcellent art work in the preparation of thismanuscript.

Kinesiology IV

TABLE 2. OUTLINE OF THE TERMINAL BRANCHES OF THE BRACHIAL PLEXUSAND THE MUSCLES THEY INNERVATE

Axillary nerve: Postaxial, innervates an abductor of the shoulder joint and a humeral rotator:1. Deltoid2. Teres minor

Radial nerve: Postaxial, innervates extensors of the elbow, wrist, M-P, I-P joints, supinator ofthe forearm, and an abductor of the thumb (it innervates no muscles located in thehand):

I. Triceps 7. Extensor digitorum2. Anconeous 8. Extensor indicis3. Supinator 9. Extensor digiti minimi4. Extensor carpi radialis longus 10. Extensor pollicis longus5. Extensor carpi radialis brevis II. Extensor pollicis brevis6. Extensor carpi ulnaris 12. Abductor pollicis longus

13. Brachioradialis-Exception

Musculoemaneous nerve: Preaxial, innervates flexors of the shoulder and elbow joints:I. Coracobrachialis2. Biceps brachii3. Brachialis

ilvfoilian nerve: Preaxial, innervates flexors of the wrist, M-P, and I-P joints, pronators of theforearm and thumb opposers:

I. Palmaris longus 5. Pronator teres2. Flexor digitorum superficialis 6. Pronator quadratus3. Flexor digitorum profundus 7. Flexor carpi radialis

(the two heads that insert in 8. First and second lumbricalesthe second and third digits) 9. Flexor pollicis brevis

4. Flexor pollicis longus 10. Abductor pollicis brevis1 I. Opponens pollicis

Ulnar nerve: Preaxial, innervates 11/2 flexors at wrist joint; abductor, adductor and flexor of last fourM-P and I-P joints; and adductor of thumb:

I.

2.

Flexor carpi ulnarisFlexor digitorum profundus (two heads

that insert in the fourth and fifth digits)3. Third and fourth lumbricales

4. Dorsal interossei5. Palmar interossei6. Adductor pollicis7. Opponens digiti minimi

ReferencesI. GARDNER, ERNEST; DONALD, J. GRAY; and

RONAN. CRALILLY. Ann/only. 3rd Ed., Phila-delphia: W. B. Saunders Company, 1969.

2. GRAY, HENRY. Anatomy of the human body.Charles Goss, Ed.. Philadelphia: Lea & Febiger,1973.

Kinesiology IV

3. HOLLINSLEAD, HENRY W. Textbook of allow-my. 2nd Ed., New York: Harper & Row Pub-lishers, 1967,

4. WOODBURNE, RUSSELL T. Essentials of humananatomy. 4th Ed., New York: Oxford Univer-sity Press, 1969.

31

JAMES G. ANDREWS

Biomechanical Analysis of Human Motion

BIOMECHANICS IS A scientific discipline con-cerned with the application and extension ofthe principles and methodology of me-chanics, to the analysis of biological systems.In the general biomechanical analysis of anyhuman motor activity, we seek to relateobservable configurations or motions of thebody, to the forces which must be acting inorder to maintain those configurations orproduce those motions.

The development of valid and usefulforce-motion relationships requires that thebody be represented by a simple yet realisticmechanical model. Subsequent investigationsof the force-motion equations describing thebehavior of that model are of considerablepractical interest, not only to physical edu-cators, coaches, and activity participants, butalso to physicians, surgeons, physical thera-pists, and the handicapped and disabled.These investigations should lead to a betterunderstanding of how physical activities areactually accomplished and should help toestablish how to teach and train people toperform them more effectively and efficiently.

MODELING

Human body segments, with the exceptionof the hands and feet, may often be realistic-ally idealized as rigid bodies for the pur-poses of a biomechanical analysis. The bony

James G. Andrews is associate professorof Mechanics and Hydraulics at the Uni-versity of Iowa, Iowa City, Iowa.

32

internal structure of any anatomical segmentconforms closely to the idealization of a rigidbody. The surrounding tissues, althoughdeformable, usually undergo relatively smallchanges in size and/or shape during segmentmotion. These factors, coupled with themathematical simplicity associated with thedynamic analysis of rigid as opposed to de-formable bodies, have been used to justifythe representation of body segments as rigidbodies for the purpose of performing bio-chemical analyses.

The human body may therefore be re-garded as a mechanical system composed ofN rigid bodies B, (i = 1, 2, ... , N) inter-connected by anatomical joints. The charac-teristics of these joints vary from onelocation to another in the body, and theprecise mechanical nature of most normalhuman joints is unknown. Consequently, inorder to model these joints properly, we arenormally forced to represent them as smoothbut slightly loose ball-and-socket joints. Theassumption' of joint smoothness appears rea-sonable, particularly for normal subjectswhere an adequate supply of synovial fluidfurnishes an excellent lubricating film be-tween articular surfaces that have no discon-tinuities. For subjects with abnormn1 (e.g.,arthritic) joints, however, such an idealiza-tion must be used with caution.

The concept of letting slightly loose ball-and-socket joints represent the anatomicaljoints between body segments is a useful one.Most normal human joints appear to exhibitsome degree of looseness and allow for somesmall amount of general, three-dimensionalrotational motion. By utilizing a mechanicalball-and-socket joint model, where the ballcenter is allowed to displace slightly relative

Kinesiology IV

to the socket center, we allow not only for allthree possible rotational degrees of freedom,but also for all three possible translationaldegrees of freedom.

ANALYSIS

Each body' segment B if idealized as arigid body, will move in accordance with theprinciples of Newtonian (nonrelativistic)mechanics. These principles specify that themotion of B, in an inertial reference frameR is governed by two vector equations.These equations are the translational equa-tion, referred to as the principle of themotion of the mass center, or center ofgravity, G, of B, in R, i.e.,

F, = m,aG' (1)

and the rotational equation, referred to as theprinciple of angular momentum of B, aboutG, in R, i.e.,

MG, HG;(2)

In equation (1), F, is the resultant externalforce acting on B m, represents the mass ofB,, and aG' denotes the acceleration of G, inR. In equation (2), MG' is the resultantmoment about G, of all external forces andcouples acting on B and A' is the time-derivative of if' , the angular momentumof B, about G, in R. (Symbols set in italic,such as mi, represent scalar quantities,whereas, symbols set in boldface, such as Fdenote vector quantities.)

SIMPLIFICATIONS FOR PLANE MOTION

Many human motor activities are es-sentially two-dimensional, with all points inthe body moving in planes that are fixed inR and parallel to each other. Normal gait,for example, is essentially planar in nature,and the body segments are often regarded asmoving in the midsagittal plane. If weidealize body segments as rigid laminas, andconsider their two-dimensional motion in

Kinesiology IV

an (x, y) plane fixed in R, then the twovector equations of motion (1) andreduce to the three scalar equations

=- ,n a.

(2)

(3)

Fr; = Miav (4)

m? = /G. (5)

On the left-hand sides of equations (3) and(4), F,, and F,., represent the x and y com-ponents of F respectively; in (5), M.-G. de-notes the z component of MG'. On the right-hand sides of (3) and (4), a5' and aGi arethe x and y components of aG' , respectively,while m, denotes the mass of B,, in (5), 1 .represents the moment of inertia of B, abouta z-axis through G and an. denotes thescalar angular acceleration of B, in R.

FORCE AND MOMENT FACTORS

The left-hand sides of the equations gov-erning the motion of B, in R contain theforce and moment factors. The resultant ex-ternal force F, acting on Bi is the vector sumof all external force distributions acting onB. The resultant moment acting on B, aboutGi, MG', is the vector sum of all momentsabout G, due to each individual externalforce distribution acting on B,.

The external force distributions contribut-ing to 1F, and MG' may be classified into twobroad categories. The first category (I) in-cludes all remotely applied force distributionssuch as the distributed weight force. It canbe shown that the system of parallel dis-tributed weight forces acting on I influencesthe equilibrium or motion of that rigid bodyin exactly the same way as (i.e., is equipol-lent to) a single force W the weight force,acting downward at the center of gravity ormass center point G, and B,. The magnitudeof this resultant weight force, as well as theapproximate location of point G1 where itmay be regarded as acting, can be estimatedwith reasonable accuracy using the tech-niques and data recommended by Hay (1).

The second broad category (II) of ex-ternal force distributions acting on B, in-

33

eludes all directly applied force distributionsarising due to contact of the segment with theexternal environment. This category may beconveniently divided into (a) those contactforce distributions acting at the proximal anddistal joints due to the presencc of adjacentbody segments (e.g., the compressive effectsof the neighboring cartilage and bony stric-tures, and the tensile effects of the musclesand ligaments, etc., which are theoreticallyseparated when each body segment is iso-lated by passing an imaginary sectioning sur-face through the proximal and distal joints);and (b) those other contact force distribu-tions acting on the body segment (e.g., theeffects of segment contact with an externalobject such as the ground or a piece of equip-ment, and the effects of contact with otherbody segments on the surface area betweenthe proximal and distal joints).

It can be shown that any general forcedistribution is equipollent to the resultantforce of that distribution applied at anarbitrary point Q plus a single couple withmoment equal to the resultant moment ofthat force distribution about Q,. In per-forming a biomechanical analysis of a typicalbody segment during any human motoractivity, we normally make a sketch of thatsegment called a free body diagram or FBD(Figure 1). This sketch shows all externalforce distributions acting on B,.

For the sake of simplicity, however, in-stead of showing the weight as a distributed(category I) force, we normally show onlythe equipollent resultant weight force W1acting downward at the center of gravity,G,. Similarly, instead of showing the com-plicated force distributions at the proximaland distal joints (category Ha), we normallyshow only the equipollent resultant force andmoment corresponding to these distributions,arbitrarily referred to or acting at the jointcenter point (P, for proximal, and D, fordistal, respectively). Finally, instead ofshowing the sometimes equally complexforce distributions acting on the segmentsurface between the proximal and distaljoints (category Hb), we normally show onlythe equipollent resultant force and the re-sultant moment corresponding to these dis-

34

tributions, acting at some arbitrary butappropriately located point Q.

Category Ha force distributions are trans-mitted by internal anatomical structures inthe neighborhood of the body joints, and it ispresently impossible to measure these forcesdirectly and accurately in live human sub-jects. Category lib force distributions, onthe other hand, can be directly and ac-curately measured using force plates andother appropriately instrumented pieces ofexperimental equipment.

It is indeed unfortunate that category Haforce distributions cannot be measureddirectly and reliably, because these forcesare of major interest to us if we wish tothoroughly understand a particular motoractivity and devise and develop suitablemethods for training and strengtheningpeople to perform it more efficiently andeffectively. The equipollent resultant forceand moment at any body joint, since theydepend directly on the individual forcedistributions in the various anatomicalstructures, are thus also impossible toreliably measure at present. These resultantsmay be determined indirectly, however, if allother terms in the equations of motion areknown. This indirect approach to the deter-mination of the resultants of all category Haforce distributions is characteristic of thebiomechanical analysis of human motoractivities, and it has been referred to as theindirect dynamics problem of biomechanics(2). Additional comments on this generalmethod, and an example problem illustratingits use, are included in the last two sectionsof this paper.

INERTIA FACTORS

The inertia factors ini and LG.' which affectthe two-dimensional motion of B, in R ap-pear on the right-hand sides of equations(3), (4), and (5). The mass m, is a scalarmeasure of the body's resistance to accele-rated translational motion (i.e., motion ofB, such that no rotation takes place relativeto R). Mass is related to body weight W, by

Kinesiology IV

Figure 1. Free body diagram (FBD).

g, the local acceleration due to gravity (g isapproximately equal to 9.8 mps2, or to 32/fps =), through Newton's second law. For afreely falling body subjected to only theweight force acting downward in the positivey-direction. equation (4) becomes

W, = ni,g (6)

The moment of inertia term LG.' is a meas-ure of the body's resistance to acceleratedrotational motion. Moment of inertia apoint property of the body Bi (indicate ..y

the superscript letter G,), and it is also asso-ciated with an axis through that point (indi-

Kinesiology IV

cated by the subscript letter z). Thus,is the moment of inertia of body B, about az-axis through Gt. We can always expressL.G.' as the product of the mass mi of B, andthe square of a characteristic length kG,`,where k.G.: is called the radius of gyration forB, about a z-axis through Gi. Thus, we havethat

nii(k?')2 (7)

In order to determine appropriate valuesfor and e' for any particular body seg-ment of a live human subject, we again must

35

Figure 2. Location of G, at time t and at time t'.

use anthropometric measurements and dataand procedures that yield at best only ap-proximate values. Segment mass values canbe determined using equation (6) if theweight force Wi is estimated with reasonableaccuracy as recommended by Hay (1), andif the local value of g is known. The situa-tion regarding the determination of rea-sonably accurate moment of inertia (orradius of gyration) values is considerablyless satisfactory. For a review and critiqueof the data and procedures currently avail-able, see the survey article by flay (3).

36

KINEMATIC FACTORS

X

The acceleration components of point Giin R appear as right-hand side terms in equa-tions (3) and (4), and in order to developan understanding of these terms, it is usefulto review the basic definitions in two-dimen-sional p, rticie kinematics. Let point Gimove on a curve Ci fixed in the (x, y)-pianeof the inertial reference frame R:Oxyz withorigin 0. At time t, Gi is at point Ui on Ci;at a later time t' = t + At, Gi is at point V,on C, (Figure 2).

Kincsiology IV

The vector locating G, relative to 0 attime t is denote,' (t), and the vectorlocating G, relative to 0 at time t' is de-noted by r G' ° (t'). We define the displace-ment of G. in R during the time-intervalAt t' t by the symbol ArG,, where

rG,(t')

rG, 0 (8)

The average velocity cf G, in R during At isdenoted by vaGv'g, where

G,V

G. A r /At (9)

The velocity of G, in R at time t, denotedby VG. (t), is defined in terms of a limit as Atgets very small, or as t' approaches t:

G,, limit ( G,V 0') kVavg) (10)

The direction of vG, (t) is tangent to thecurve C, at U, since the direction of ArG, asAt approaches zero, gets closer and closer tothat tangent line.

The average acceleration of G, in R duringAt is denoted by aaGv'g, where

tvG'(t') vG.(t)liAt (11)

The acceleration of G, in R at time t, denotedby aG' ( t), is also defined in terms of a limitas At gets very small:

G, limita (t) = (aavG, g) (12)

If we take movies of a particular humanmotor activity ;Ind identify the anatomicaljoint center points in each film frame, thenwe can locate the center of gravity of eachindividual body segment in each film frameby using appropriate center of gravity loca-tion data. If the developed pictures showthe base reference frame R in the back-ground, then we can locate each segment'scenter of gravity G, in R at each instant oftime t when a film frame is exposed. Theseposition vectors G. ° (t) can then be used toobtain the frame to frame displacement vec-tors Jr G', which can in turn be used to deter-mine average velocity values vaGi'g If thenumber of film frames exposed per second islarge enough so that the points G, do notmove too much from one frame to the next,

Kinesiology IV

then we can use the calculated averagevelocity values as approximate values forthe actual velocities. These approximatevelocity values can then be used to generateaverage acceleration vectors, which in turncan be used to approximate the actual ac-celeration values. In this way, we can experi-mentally measure the location history of theapproximately located center of gravitypoints for each body segment, and deduceapproximate values for and duringthe time period when we wish to study themotion of the various body segments 13, in R.

The scalar angular acceleration of B, in R,«B', appears as a right-hand side term inequation (5). In order to assure a properunderstanding of this quantity, it is useful toreview the basic definition in two-dimen-sional rigid body rotational motion. Let therigid lamina B, move in the (x, y)-plane ofthe inertial reference frame R:Oxyz withorigin 0. Let points Pi and D, be fixed inB and let B, move in R so that at time t,B, is in configuration I, and at a later time t'

t + At, B, is in configuration II (Figure 3).The scalar angular displacement of B, in

R during At is denoted by a, where

1=-- 02 01 (13)

The average scalar angular velocity of B, inP during At is denoted by 4,, where

(dal3,:g = A 0/A t (14)

The scalar angular velocity of B, in R attime t, denoted by (,,B. (t), is defined in termsof a limit as At becomes very small:

B limit ((,) kr') At,0 ,,avg) (15)

The average scalar angular acceleration of13, in R during At is denoted by aaBv, where

2aB4 = [(,)B(t') (.)Th(t)11-1t (16)

The scalar angular acceleration of 13, in R attime t, denoted by aB' (t), is defined by alimit as At becomes very small:

B, limit ( b.; \2 (t) At,0 k2avg) (17)

If we take movies and identify two char-acteristic points (Pi and Di) on each seg-

37

Figure 3. Location of B. at time t and at time t'.

ment in each film frame, then we can meas-ure the angle between the straight linesegment PP. and any fixed line (e.g., thex-axis of R) in each film frame. For suf-ficiently fast frame rates, we can use theaverage scalar angular velocity (,aB,',, to ap-proximate the actual scalar angular velocity

B,(,) (t). Similarly, we can obtain the averagescalar angular acceleration, ceav,g, and use itto approximate the actual scalar angularacceleration (I) . In this manner, we candetermine approximate values for the scalarangular acceleration of B. in R throughout

38

the time period when we wish to study themotion of the various body ss-4,nents.

SOLUTION PROCEDURE

In performing a biomechanical analysis ofany human motor activity, we normally wishto determine the unknown category IIa forcedistribution resultants which act on the indi-'vidual body segments in the neighborhoodof the joints to maintain or change the jointcon figuration. These resultants cannot be

Kinesiology IV

measured directly in live human subjectswith present-day technology, and they musttherefore be calculated indirectly if they areto be determined at all. The procedurenormally used to determine these unknownresultants is to solve for them using the equa-tions governing the motion of the systemelements. Equations (3), (4), and (5)describe the two-dimensional motion of atypical rigid body segment B1 moving in the(x,y)-plane of the inertial reference frameR. Although these three scalar equations aredifferential equations, they are valid at anyinstant of time t, and they can therefore beused to determine instantaneous values of theunknown category IIa force and moment

1

resAltnts if all other terms in these equationsarc known.

In order to adequately describe the gen-eral solution procedure, let us expand theleft-hand sides of equations (3), (4), and(5), using the two-dimensional FBD for atypical body segment B1 shown in Figure 4.We obtain

+ Fax + F0,. = nliaG:i (18)

Fl + F(20, W1 = iniaG' (19)

M0;: + Ahiz13FQq 14F0;.r I5Fpix InFpiy=1G,' 213q20)

y

1-4E-4Figure 4. Two-dimensional

Kinesiology IV

free body diagram for a typical body segment B1.

39

Using movies of the motor activity, welocate points P, and D, in each body segmentat each instant of time t when a film frame isexposed. Using anthropometric measure-ments and suitable data and procedures, wealso determine approximate values of seg-ment weight, mass, center of gravity location,and moment of inertia. From this informa-tion, we can then deduce approximate valuesfor a G,', a vG' and «B' as functions of timc t,and thereby evaluate the right-hand sides ofequations (18), (19), and (20) completely.

By devising suitable instrumentation(force plates, etc.), we can also determinethe category lib force distribution resultantsF 12,V; F (1)., and MQ,,) and the points Q,

where they act on B. We therefore knowsome of the terms appearing on the left-handsides of equations (18), (19), and (20).

The only unknowns that remain in thethree scalar equations of motion are the xand y components of the proximal and distaljoint resultant forces (FP;,., Fp,,, and F D,, ,F D,y, respectively), and the z components ofthe proximal and distal joint resultant mo-ments (MP;, and M respectively). Inorder to solve for these six scalar unknowns,we begin by considering the extremity (arm,leg, head) that either contains or is closest tothe body segment or joint of interest. Weinitially focus our attention on the most distalof the body segments in that extremity, since,for this most distal segment (Bv), the re-sultant joint force and moment at the distaljoint are both known. If these three scalars(FD,r, FDiv, and MD,.;) are not each identi-cally equal to zero, then By is loaded at Dvby some external category lib force dis-tribution whose resultants can be measuredexperimentally. Consequently, for Bv, equa-tions (18) and (19) each contain only onescalar unknown (Fp,.x and FP,v, respec-tively) which can therefore be determineddirectly. If we substitute these calculatedvalues for FP,,,and F P,.y into equation' (20),then this equation contains only one un-known (Mp.) which can therefore be deter-mined directly.

We then proceed to the adjacent andnext most distal body segment (Bx.,), and

40

use Newton's third law of action and reactionto determine the resultant force and momentacting on the distal joint of B. _1 due to thepresence of Bv. Newton's third law impliesthat the category Ha force and momentresultants acting on the distal joint of Bv-idue to By must be equal in magnitude butopposite in direction to the correspondingresultants acting on the same (proximal)joint of BA due to the presence of BA' -1.Hence, for segment B. -1, we 0-lain a situa-tion similar to the one we had for BN, wherewe now know the resultants of the force dis-tribution acting on the distal joint of BN-We therefore proceed as for segment BN,using the associated three scalar equationsof motion to calculate the two unknownforce components and the unknown momentcomponent acting on BA at the proximaljoint Pv We repeat this process, movingproximally from one body segment to thenext, until we have solved for all unknowncategory Ha force and moment resultantsacting on all intermediate body segments atthe anatomical joints.

EXAMPLE PROBLEM

In order to illustrate the general procedureused in the biomechanical analysis of humanmotor activities, we shall briefly consider theessentially two-dimensional activity of run-ning on a straightaway. For the sake of con-venience, let us suppose that we wish todetermine the forces transmitted by theanatomical structures in the neighborhood ofthe knee joint during foot contact with theground.

We begin the associated biomechanicalanalysis by considering the most distal bodysegment in the extremity (leg) which con-tacts the ground and contains the region ofinterest. This segment is the foot enclosed ina shoe which we decide to model as a singlerigid body (B!). The foot plus shoe segmentB., is isolated from the adjacent lower legsegment B1 by an imaginary sectioning planepassing through the ankle joint A. The FBDof B at the typical instant of time during

Kinesiology IV

segment contact with the ground, is shown inFigure 5. The ground reaction force dis-tribution (category 11b) acting on B, hasbeen replaced by a simple equipollent force-couple system consisting of the resultantforce components FQ, and FQ acting atpoint Q, and the resultant component MQ:.The distributed weight force has been re-placed by the resultant weight force W.acting downward in the negative y directionat the center of gravity, G.. The complexcategory IIa force distribution acting onB, at A has been replaced by a simpleequipollent force-couple system consisting ofthe resultant force components F.L. and FAA,acting at A, together with the resultantcouple M

The three scalar equations of motioncorresponding to equations (18), (19), and(20) now take the form

W''FAx FQy

gar' (21)

W'' GFay FAY W: = ay' (22)

MA: MQ: SaFQx SIFQy

x17.G22:S2FAy S4FA =

Using an instrumented force plate, we candetermine the horizontal and vertical com-ponents of the ground reaction force (FQand FQ,,,, respectively), and the momentcomponent Mg, about an arbitrary point Qin the contact region. By attaching twomarkers to B. at points A and H, and byidentifying these points in each film frame,we can measure the angle between the linesegment AH and the fixed x axis, and usethis varying angle to determine «"2. If pointG. can be approximately located relative to

QyFigure 5. Free: body diagram of B2 during segment contact with the grou

Kinesiology IV 41

points A and H in each film frame, then wecan also deduce values for a,6,:' and aG,'

Finally, if we can obtain a reasonably ac-curate value for /.', then we can solve equa-tion (21) for solve equation (22) forF.,, and then substitute these values intoequation (23) and solve it for

We now proceed to the adjacent and nextmost distal body segment, the lower leg(B1), and analyze it in a similar manner.The force and moment resultants acting onB1 at A Fill; MA,) are nowknown from the previous analysis of the footplus shoe segment B. The three scalar

equations governing the motion of B1 in Rcan therefore be used to solve for the desiredwiknown force and moment resultants actingon BI at the knee, due to the presence ofthe neighboring thigh segment,

Bibliography

I. HAv, J. G. The center of gravity of the humanbody. Kinesiology III, 1973.

2. 0110, E. Y., and K. Rim. Analysis of humangait by means of optimization technique. Pro-ceedings of the 241h Annual Conference onEngineering in Medicine and Biology, LasVegas, 1971.

3. Hew, J. G. The moment of inertia of thehuman body. Kinesiology IV, 1974.

42 Kinel,iology IV

JAMES G. HAY

Moment of Inertia of the Human Body

INFORMATION CONCERNING the inertialcharacteristics of the human bodythemass, center of gravity location, and momentof inertia or radius of gyrationis a neces-sary prerequisite to the conduct of detailedquantitative analyses of human motion.

Although numerous attempts have beenmade to obtain appropriate data concerningthe mass and center of gravity location of thehuman body and each of its various segments(10), relatively few efforts have been di-rected toward obtaining appropriate data forthe corresponding moments of inertia orradii of gyration.

The purposes of this paper are: (1) toreview the work of the major contributorsto knowledge in the area of moment ofinertia determination; and (2) to suggestguidelines which might be followed in decid-ing which method or set of available resultsshould be used in a given analysis of humanmotion.

Several methods of determining themoment of inertia (or the radius of gyration)have been proposed but only two of thesereferred to here as the compound pendulumand the mathematical modeling methodshave been used with any frequency.

COMPOUND PENDULUM METHOD

Basically, this method consists of sus-pending the body from some fixed point,

James G. Hay is associate professor ofphysical education at The University ofIowa, Iowa City, Iowa.

Kinesiology IV

setting it in motion by shifting it a few de-grees from its equilibrium position, anddetermining the period of oscillation (i.e.,the time taken for the body to swing from thelimit of its motion in one direction to itslimit in the other direction, and back again).The moment of inertia is then obtained usingthe following equation (based upon the be-havior of a body which experiences suchsimple harmonic motion):

r=

Wh

472

where I= the moment of inertia of the bodyabout an axis through the point of suspen-sion, 0; W = the weight of the body; h= thedistance from the center of gravity to point0; and T = the period of oscillation.

Two other equations:

10 =

where m = the mass of the body and k = theradius of gyration relative to the axis through0, and:

10 = I

where I, = the moment of inertia of thebody relative to an axis through its center ofgravity and parallel to the axis through 0,are then used to obtain, respectively, k andI,..

Fischer (8) and Dempster (5) used thecompound pendulum method to determinethe moments of inertia of selected segmentsof cadavers.

Fischer dissected a small cadaver [150.0cm (59.3 in.), 44.057 kg (97.1 1b)1, in-serted parallel steel rods, one at each end ofeach segment, suspended each segment from

43

each rod in turn and determined the periodsof oscillation. From the data thus obtainedand previously obtained data on segmentmass and center of gravity location, he thencomputed the moment of inertia and radiusof gyration of each segment relative to atransverse axis through its center of gravity.[Note: Fischer also reported values forthese same parameters relative to a longi-tudinal axis through the center of gravity ofeach segment. However, the manner inwhich he arrived at these values is not clear.]

Dempster followed a very similar pro-cedure using eight, white, male cadavers of"medium build" (Table 1). Each segmentin turn was supported on knife-edges fixedto the ends of a .5-in. pipe placed trans-versely through the proximal end of the seg-ment. (In the case of the head, neck, andtrunk segment, the rod was placed throughthe centers of the acetabula.) "The body wasthen allowed to swing freely on the knife

edges through an arc of approximately 5'. .

Ten measurements, each, of 10 periods ofoscillation, were taken with a stop watch;from these an average period was determinedand recorded" (5, pp 50-51). The resultsobtained by Dempster are presented InTables 2 and 3.

Santschi, DuBois, and Omoto (14) usedtwo large, compound pendulums, to deter-mine the principal moments of inertia of theliving human body in eight different posi-tions (Figure 1). Sixty-six males, selectedon the basis of stature and weight to repre-sent the Air Force population stature andweight characteristics as described by Hertz-berg, Daniels, and Churchill (11) were usedas subjects. The procedure involved strap-ping the subject into the first pendulum inthe required position, setting the pendulumto oscillate through ± 1° and determiningthe period of oscillation. ("At least two 10-

TABLE 1. CADAVERS USED IN DEMPSTER'S STUDY

No.

Somato-type

(Sheldonsystem)

Age')yr

Supineheight"'

cm(in.)

Weight'(kg)lb Cause of death Embalmed

14815 4-5-2 1/2 67 168.9 (51.2) Unknown yes(66.5) 113

15059 3-5-3 52 159.8 (58.3) Cerebral hemorrhage no(62.9) 128.5

15062 4-2 4 75 169.6 (58.3) General arteriosclerosis no(66.8) 128.5

15095 4-3-4 83 135.3 (49.5) Unknown no(53.3) 109.25

15097 4 -5 -3 73 176.4 (72.3) Esophageal carcinoma no(69.4) 159.5

15168 3-3 4 61 186.6 (71.2) Coronary thrombosis no(73.5) 157

15250 3-3-4 180.3 (60.3) Acute coronary occlusion no(71.0) 133

15251 4 -4 -2 158.5 (55.8) Chronic myocarditis no(62.4) 123

° Determined from front, left side, and rear view photographs of suspended cadaver.With regard to the physical characteristics of his subjects, Dempster observed that "all the available

cadaver material represented individuals of the older segment of the population. The specimens weresmaller then either the average white maiL population or the military populations of special interest, and theweights were below those of average young individuals. Physically, however, the subjects were representativespecimens for their age level" (5. p. 47).

44 Kinesiology

TABLE 2. MOMENTS OF INERTIA OF SEGMENTS ABOUT TRANSVERSE AXESTHROUGH THEIR CENTERS OF GRAVITY

(after Dempster)Moments of inertia in gm-cm= X 106

Cadavernumber

Entireupper

extrem-ity Arm

Fore-armandhand

Fore-arm Hand

Entirelower

extrem-ity Thigh

Leg andfoot Leg Foot

Left side14815 1.10 .122 .187 .059 .005 4.90 0.26 0.82 .321 .021

15059 0.78 .118 .051 .004 5.70 0.64 0.73 .330 .02515062 0.96 .115 .155 .043 .005 6.05 0.82 0.55 .308 .02915095 0.79 .079 .128 .035 .005 4.60 0.65 0.73 .260 .02615097 0.98 .222 .287 .055 .009 9. ' 0 1.14 1.58 .650 .03715168 1.42 .191 .188 .072 .002 10.00 3.29 1.66 .560 .04315250 1.35 .155 .218 .074 .003 9.80 1.22 1.29 .560 .03515251 1.02 .112 .14( .050 .003 5.60 0.61 0.94 .340 .033

Right side14815 0.90 .190 .220 .058 .007 4.60 0.21 0.81 .307 .01815039 0.78 .130 .137 .041 .005 6.70 0.70 0.85 .340 .02515062 0.99 .102 .180 .055 .004 5.67 0.76 0.86 .298 .02815095 0.58 .062 .128 .059 .003 5.20 0.69 0.75 .275 .01315097 1.10 .220 .298 .072 .011 9.20 1.27 1.65 .620 .04015168 1.40 .145 .197 .061 .003 8.60 3.12 1.64 .620 .03815250 1.57 .166 .232 .068 .004 9.50 1.44 1.40 .620 .03515251 0.91 .120 .152 .054 .03 5.20 0.61 0.96 .360 .032

TABLE 3. MOMENTS OF INERTIA OF TRUNK SEGMENTS ABOUT TRANSVERSEAXES THROUGH THEIR CENTERS OF GRAVITY

(after Dempster)Moments of inertia in gm-cm= X 10-6

Cadavernumber

Trunkminuslimbs

Trunkminus

shoulders

ShouldersHead and

neck Thorax

Abdomino-pelvicregionLeft Right

15059 15.5 14.0 0.355 0.378 0.22 0.4515062 23.7 15.9 0.500 0.32415095 13.4 13.0 0.417 0.421

15097 22.1 21.0 0.800 0.700 0.31 1.19 3.24

15168 24.3 23.1 0.520 0.800 0.23 2.18 9.70

15250 14.9 16.4 0.425 0.425 0.32 0.96 2.44

15251 14.9 14.0 0.480 0.420 0.39 0.99 1.96

cycle-period averages were taken . . . to en-sure that reproducibility was achieved").The "suspension axis" of the pendulum wasthen changed and the process repeated.Finally, the subject was strapped into thesecond pendulum in the same position andthe entire process repeated.

Kinesiology IV

The moments of inertia relative to thethree principal axes of the body were thencomputed (Table 4). A multiple regressionanalysis of moment of inertia vs. stature andweight was conducted for all positions andprincipal axes. In all but three instances themultiple correlation coefficients exceeded 0.9

45

1. Standing

4. Sitting

2. Standing, ArmsOver Head

3. Spread Eagle

5. Sitting, Forearms Down 6. Sitting, ThighsElevated

7. MercuryConfiguration

Figure 1. Body positions used in Santschi et al. study.

(Table 5). Santschi et al. concluded, there-fore, that: "These large values of R indicatea very strong dependence of moment ofinertia on stature and weight, which com-

46

bined with the relatively small values ofstandard error of estimate and the iargesample size, demonstrate the usefulness ofthe regression equation as a predictive tool."

Kinesiology IV

TABLE 4. ARITHMETIC MEANSAND STANDARD DEVIATIONS OFSAMPLE MOMENTS OF INERTIA

(after Santschi et al.)

A-cis°

Moment of inertia(lb -in.- sec.')

Mean SD

1. Standing 115.0 19.3

y 103.0 17.911.3 2.2

2. Standing, arms 152.0 26.1over head 137.0 25.3

11.1 1.93. Spread eagle 151.0 27.1

114.0 21.336.6 7.9

4. Sitting 61.1 10.3y 66.6 11.6z 33.5 5.8

5. Sitting, forearms 62.4 9.7down 68.1 12.0

33.8 5.96. Sitting, thighs 39.1 6.0

elevated y 38.0 5.826.3 5.1

7. Mercuryconfiguration x 65.8 10.3

y 75.2 14.034.2 5.6

8. Relaxed x 92.2 13.3(weightless) . y 88.2 13.3

z 35.9 5.4

The z-axis if formed by the intersection of thesagittal plane and the frontal plane; the y-axis, bythe intersection of the frontal and transverse planes;and, the x-axis, by the intersection of the sagittaland transverse planes.

Drillis and Contini (6) outlined severalmethods which might be used to determinethe moment of inertia of a human bodyand/or its individual segments. Thesemethods were also discussed in earlier arti-cles by Contini, Drillis, and Bluestein (4)and Drillis, Contini, and Bluestein (7) andin a subsequent article by Contini (3).Among these was one which they eventuallyused to gather data on the mornents of inertiaof the limb segments of 20 adult males aged20-40 yr. [Note: Although the authors

Kinesiology IV

refer to a test sample of 20 subjects (6, p.15), results are reported for only 12 sub-jects (6, p. 49 et seq.)]

In this method, castings of plaster of Parisor dental stone were made of the limb seg-ments of each subject. These were thenmade to oscillate about a fixed suspensionpoint and the period of oscillation deter-mined. This period was then correctvi onthe basis of the relative weights of the actualsegment and the cast replica and the momentof inertia of the segment was computed. Themean values obtained are presented inTable 6. [Note: Drillis and Contini reportedthese results in "gr2" (6, p. 86). However,since they compared their values directlywith those of Dempster, it is assumed thatDrillis and Contini intended that the samegm-cm= unit used by Dempster be reportedfor their own results.] Table 6 also con-tains mean values for the radii of gyrationexpressed as a function of segment length,for eight subjects.

These data on radii of gyration have alsobeen reported by Contini (3), who, in addi-tion, reported average values for radii ofgyration for various populations-normals,amputees, and hemiplegics, both male andfemale. However, whether these values wereobtained using the casting-compound-pendu-lum method or, more simply, by measuringsegment lengths and using ratios previouslydetermined (see Table 6) is not clearlystated.

MATHEMATICAL MODELING METHOD

In this method, each segment of the bodyis represented as a regular geometric solid ofknown mass and its moments of inertia(and/or radii of gyration) are determinedusing the appropriate :omputational tech-niques.

Amar (1), one of the first to use thisapproach, considered the trunk as a cylinderand the limbs as frustra of cones and com-puted segmental moments of inertia for anadult male of 65 kg (143 lb) .

Kulwicki, Schlei, and Vergamini (12)

47

TABLE 5. CORRELATION OF MOMENT OF INERTIA WITH STATURE AND WEIGHT(after Santschi et al.)

Axis SE t, Regression equations"

1. Standing x 0.98 4.18 232.0 +3.77S +0.512Wy 0.96 5.27 212.0 +3.43S ±0.460W

0.93 0.84 -0.604 -0.098S +0.112W2. Standing, arms over head x 0.98 5.63 -328.0 +5.36S +0.652W

Y 0.96 6.89 -332.0 +5.34S +0.589Wz 0.89 0.87 1.4 0.085S +0.094W

3. Spread eagle x 0.98 4.90 -353.0 +5.63S +0.677Wy 0.96 6.24 270.0 +4.30S +0.516Wz 0.93 2.82 -101.0 + 1.52S +0.191W

4. Sitting x 0.92 4.01 -91.6 +1.43S +0.322Wy 0.92 4.51 -135.0 +2.26S +0.268Wz 0.97 1.45 -52.8 +0.76S +0.201W

5. Sitting, forearms down x 0.91 3.98 -78.7 +1.29S +0.309Wy 0.92 4.67 -127.0 +2.05S +0.321Wz 0.97 1.36 -53.7 +0.765S +0.206W

6. Sitting, thighs elevated x 0.89 2.79 -33.8 +0.543S +0.212Wy 0.77 3.66 22.2 +0.434S +0.180Wz 0.92 2.00 -30.4 -1-0.3285 +0.204W

7. Mercury configuration x 0.93 3.75 -94.3 +1.57S +0.308WY 0.94 4.96 -175.0 +2.85S +0.318Wz 0.96 1.64 -45.0 +0.668S +0.197W

8. Relaxed (weightless) x 0.96 3.71 -106.0 + 1.77S +0.452Wy 0.94 4.54 139.0 + 2.43S +0.352Wz 0.96 1.54 47.2 +0.776S +0.176W

1 and SE in lb-in.-sec'S in in.W in lb

developed a model consisting of six rightcircular cylinders (two arms, two legs, torso,and head) in order to evaluate the effective-ness of certain movements in producing rota-tion while in a weightless state. The lineardimensions of the model were based on the50th percentile data of Hertzberg, Daniels,and Churchill (11) and the mass of eachsegment was based on the correspondingmear. for Dempster's (5) cadavers. Theprincipal moments of inertia were computedusing the standard equations:

6 = 1/2 mr2

where 1, = the moment of inertia about thesegment's long axis, m = the segment mass,and r = the radius of the segment, and

to = f-2m (3r2 + 12)

TABLE 6. SEGMENT MOMENTS OFINERTIA AND RADII OF GYRATION OF

SEGMENTS ABOUT TRANSVERSEAXES THROUGH THEIR CENTERS

OF GRAVITY(after Drillis and Contini)

Segment

Momentof inertia(gm-cm2X 10')

Radius ofgyration

Segmentlength

Entire upper extremity 1.33 0.24Upper arm 0.138 0.26Forearm and hand 0.247 0.25Forearm 0.073Hand 0.0059Entire lower extremity 7.49 0.24Th.gh 0.895 0.23Shank and foot 1.120 0.29Shank 0.495 0.27Foot 0.020

48 Kinesiology IV

where 1 = the moment of inertia about thesegments frontal or transverse axis and 1 =the length of the segment. The results ofthese computations are shown in Table 7.

Whitsett (16) developed a 14-segmentmodel of the human body for the purpose ofpredicting "man's mechanical behavior insome selected conditions associated withweightlessness." The 14 segments and thegeometric solids used to represent thes-., seg-ments are shown in Figure 2. The lineardimensions of the model were based on the50th percentile data of Hertzberg et al.(11); the masses of the limb segments weredetermined using the regression equationsdeveloped by Barter (2); the center of masslocations for the limb segments and theaverage density for all segmentsthe latterused, among other things, for obtainingvalues for the masses of the head and torsowere based on Dempster's work withcadavers (5). The principal moments ofinertia of each segment were computed usingthe standard equations for the correspondinggeometric solid (Table 8). These data werethen used to determine the princiol mo-ments of inertia of the whole body for threeselected positions.

ELLIPSOID

ELUPTICAL

CYLINDER

FRUSTUM OFA RIGHTCIRCULAR

CONE

HEAD andNECK

TORSO

SPHERE

°FRUSTUM OF

A RIGHTCIRCULAR

CONE

RECTANGULAR

PARALLELEPIPED

UPPER

ARM

LOWER

ARM

HAND

UPPER LEO

LOWER

LEG

FOOT

Figure 2. Whitsett's 14segment model.

TABLE 7. PRINCIPAL MOMENTS OFINERTIA

(after Kulwicki et al.)

Moments of inertia(slugs -ft"-)

TransverseLongitudinal and frontal

Segment axis axis.

Head .012 0.043Torso .324 1.118Arm .002 0.086Leg .017 0.512

Since the segments were symmetrical about theirlong axes, the computed moments of inertia for thetransverse and frontal axes were identical.

Hanavan (9) designed a 15-segmentmodel (Figure 3) in order to predict theinertial properties of the human body in anyfixed body position. The dimensions andproperties of the segments were calculatedusing a total of 25 anthropometric meas-urements taken on the individual subject.The weights of the segments were computedusing the regression equations derived byBarter (2).

To determine the validity of his model,Hanavan used anthropometric raw data ob-tained by Santschi et al. (14) and com-puted the principal moments of inertia ofeach of their 66 subjects for each of thefirst seven positions shown in Figure 1. Hethen compared the results obtained in thismanner with those obtained experimentally,by Santschi et al. For frontal and transverseaxes, one half of the predicted values (i.e.,the values obtained using the model) gen-erally fell within 10 percent of the experi-mental values. Markedly greater errors wereobtained in computing the moments ofinertia relative to the longitudinal axisonehalf of the predicted values generally fellwithin 20 percent of the experimental data.Hanavan attributed these greater percentageerrors to the fact that the moment of inertiarelative to the longitudinal axis is generallyof a much smaller magnitude than the other

Kinesiology IV 49

TABLE 8. PRINCIPAL MOMENTS OFINERTIA OF BODY SEGMENTS

(after Whitsett)

Moments of inertia (slugs-ft')

SegmentFrontal

axisTransverse Longitu-

axis dinal axis

Head 0.0183 0.0183 0.0124Torso 1.0000 0.9300 0,2300Upper arm 0.0157 0.0157 0.0018Lower arm 0.0056 0.0056 0.0008Hand 0.0004 0.0004 0.0004Upper leg 0.0776 0.0776 0.0154Lower leg 0.0372 0.0372 0,0037Foot 0.0028 0.0028 0.0006

principal moments of inertia and thus "asmall numerical error becomes a much largerpercentage error."

Finally, Hanavan used his mathematicalmodel to develop a design guide which couldbe used to establish preliminary designspecifications requiring knowledge of theinertial properties of the human body inselected body positions. For this purpose heused the anthropometric dimensions for fivecomposite subjects (5th, 25th, 50th, 75th,and 95th percentile) obtained in the surveyof Air Force Personnel conducted by Hertz-berg et al. (11) and 31 different body posi-tions which could be assumed in a full pres-sure suit. The inertial properties of these fivecomposite subjects were computed for eachof the 31 body positions.

OTHER METHODS

A niimber of otbt.r methods have beenused to determine the moments of inertia ofthe human body and/or its component parts.

Liu, Laborde, and Van Buskirk (13) useda torsional penduluma device which twistsback and forth after being released from atorsional stress initially imposed upon ittodetermine the principal moments of Meal-.of serial transverse sections of the trunk or amale cadaver. The principal moments ofinertia for each of the 24 transverse sections

(each of which contained roughly onevertebra) are shown in Tabir, 9.

Weinbach (15) described a method fordetermining the moment of inertia of anerect human body about a transverse axisthrough the soles of the feet. This methodinvolved the construction of a "volumecontour map" based on data gathered fromfrcnt and side view photographs of thesubject (or from anthropometric measurestaken directly from the subject) and thedetermination of the area under one of thederived curves making up the "map." Themoment of inertia concerned was then com-puted using the relationship:

H5I A cu deem -mm --

where H = the actual height of the subject(in cm), h = the height of the subject as

Right

LI

0

Figure 3. Hanavan's 15-segment model.

Left

50 Kinesiology IV

TABLE 9. PRINCIPAL MOMENTS OF INERTIA OF TRUNK SEGMENTS(after Liu et al.)

LevelMass

(Ib-sec2/in)

Moment of inertia (Ib-sec2-in.)

Frontal axis Transverse axis Longitudinal axis

C I .00182 .0047 .0055 .0097C 2 .00162 .0037 .0047 .0070C 3 .00089 .0029 .0023 .0038C 4 .00117 .0013 .0033 .0050C 5 .00154 .0053 .0043 .0127C 6 .00129 .0018 .0047 .0086C 7 .00348" .0311" .0089" .0385"T 1 .00348" .0311" .0089" .0385"T 2 .00558 .0516 .0175 .0758T 3 .00558 .0472 .0222 .0764T 4 .00478 .0508 .0212 .0716T 5 .00720 .0789 .0295 .115T 6 .00669 .0762 .0428 .115T 7 .00890 .0987 .0618 .148T 8 .00623 .0666 .0428 .105T 9 .00704 .0784 .0494 .115TI0 .00573" .0636" .0482" .107"TIl .00573" .n636" .0482" .107"112 .00856 .0837 .0637 .144L 1 .0113 .122 .0626 .174L 2 .0100 .01498 .0542 .147L 3 .0119 .124 .0542 .162L 4 .0101 .108 .0408 .141L 5 .0125 .133 .0588 .181Pelvis .0354 .383 .454 476

Averaged with adjacent slice due to bad cut.

depicted (in mm), and A = the area underthe derived curve (in sq mm).

DISCUSSION

Which of the available methods or sets ofdata should be used in a given investigationdepends on a number of factors including thenature of the proposed investigation, theaxes about which m)ments of inertia arerequired, and the characteristics of the sub-jects involved.

In some instances the appropriate choicefrom among the available methods or setsof data is fairly obvious. For example, if aninvestigation requires the deicimination of

Kinesiology IV

one or more of the principal moments ofinertia of a subject (or subjects) in any ofthe positions depicted in Figure 1, the 'logicalprocedure is to obtain the required meac,ures of height and weight and use these inconjunction with the appropriate regressionequation(s) in Table 5.

However, where an investigation calls forthe determination of moments of inertia of abody in orientations other than those con-sklered by Santschi et al. a choice must bemade between (a) using the segmental dataof Dempster (5), Drillis and Contini (6),Hanavan (9), or Whitsett (16),' and (b)

I The data of Kulwicki et al. (12) is prob-ably too gross for most applications and is ex-cluded from this list for that reason.

51

undertaking a study similar to that ofSantschi et al. in order to d ermine therequired values. Since the latter of thesetwo alternatives constitutes an undertakingof considerable magnitude, it would seemlogical to ftsure that the possibilities af-forded by the first alternative had been quiteexhausted before seriously considering thesecond.

The nature of the segmental data availablefrom the four sources listed above varies intwo important respects:

1. Only two (Hanavan and Whitsett)provide segmental moments of inertia rela-tive to all three principal axes. The othertwo sources contain data for segmentalmoments of inertia relative to the transverseaxis only-a fact which severely restricts theuses to which these latter data can be put.[Note: If it is only the moments of inertiarelative to the transverse axes that are re-quired, data from the studies of Dempsterand Hanavan are probably to be preferredto those reported by DrilliS and Contini,Contini (both of which reports were incom-plete at critical points) and Whitsett (whosemodel took no account of individual differ-ences in physique).]

2. The characteristics of the subjects onwhom segmental data has been gathered, orupon whose dimensions the mathematicalmodels have been based vary considerably.Thus, since Santschi et al have demonstratedthat the principal moments of inertia aregreatly influenced by the physical dimensionsof the individual, it would seem reasonableto suggest:

a. If Dempster's cadaver data is to beused, the data gathered on the cadaver whosestature and weight most nearly approximatesthat of the subject concerned would be themost appropriate.

b. If a mathematical model is to be usedto derive the requil.,:d segmental data and thesubjects involved ale available for the pur-pose of obtaining anthropometric measure-ments, the model of Hinavan would prob-ably be more appropriate than that ofWhitsett because it is based on the physical

52

dimensions of individual subjects rather thanon mean values.

2.

3.

4.

5.

6.

7.

8.

s.

10.

11.

12.

13.

14.

D.

16.

ReferencesAMAR, JULES. The human motor. New York:E. P. Dutton & Co., 1920.BARTER, JAMES T. Estimation of the massof the body segments. WADC Technical Re-port 57-260, Wright-Patterson Air ForceBase, Ohio, 1957.CONTINI, RENATO. Body segment parameters,part II. Artificial Limbs 16(1):1-19, 1972.CONTINI, RENATO; DRILLIS, RUDOLFS, J.; andBLUESTEIN, MAURICE. Determination of bodysegment parameters. Human Factors 5(5):493-504, 1963.DEMPSTER, WILFRED T. Space requirementsof the seated operator. WADC Technical Re-port 55-159, Wright-Pattersoa Air Force Base,Ohio, 1955.DRILLIS, RUDOLFS, and CONTINI, RENATO.Body segment parameters. Office of Voca-tional Rehabilitation, Department of Health,Education, and Welfare, Technical Report1166.03. New York University School ofEngineering and Science, 1966.DRILLIS, RUDOLFS; CONTINI, RENATO; andBLUESTEIN, MAURICE. Body segment param-eters. Artificial Limbs 8 ( 1 ) :44-66, 1964.FISCHER, OTTO, Theoretische Grundlagen fureine Mechanik der lebenden Kiirper mitSpeziellen Anivendungen auf den Menschen,sowie auf einige Bewegungs-vorgiinge anMaschinen. Berlin: B. G. Teubner, 1906.HANAVAN, ERNEST P. A mathematical modelof the human body. AMRL Technical Report64-102, Wright-Patterson Air Force Base,Ohio, 1964.HAY, JAMES G. The center of gravity of thehuman body. Kinesiology III 20-44, 1973.HERTZBERG, H. T. , DANIELS, G. S.; andCHURCHILL, E. Anthropometry of flying per-sonnel-1950. WADC Technical Report 52..321. Wright-Patterson Air Force Base, Ohio,1954.KULWICKI, PHILIP V.; SCHLEI, EDWARD J.; andVERGAMINI, PAUL L. Weightless tnan: Self-rotation techniques. AMRL Technical Docu-mentary Report 62-129, Wright-Patterson AirForce Base, Ohio, 1962.Liu, Y. KING; LABORDE, J. M.; and VANBUSKIRK, WILLIAM C. Inertial properties of asegmented cadaver trunk: Their implicationsin acceleration injuries. Aerospace Medicine42(6):650-57, 1971.SANTSCHI, W. R.; DU BOIS, J.; and OMOTO, C.Moments of inertia and centers of gravity ofthe living human body. AMRL TechnicalDocumentary Report 63-36, Wright-PattersonAir Force Base, Ohio, 1963.WEINBACH, A. P. Contour maps, center ofgravity, moment of inertia and surface area ofthe human body. Human Biology 10:356-71,1938.WHITSETT, CHARLES E. Some dynarn:c re-sponse characteristics of weightless man.AMRL Technical Documentary Report 63-18,Wright-Patterson Air Force Base, Ohio, 1963.

Kinesiology IV

JOHN PISCOPO

Assessment of Forearm Positions upon Upperarm and

Shoulder Girdle Strength Performance

FLEXION AND EXTFIsstON of the elbow jointin the sagittal plaae, well illustrated by pull-ups or chinning, continues to predominateas a popular exercise for testing upperarmand shoulder girdle strength. Flexing theelbow against resistance primarily entailsstrong contractions of the biceps brachii,brachialis, and brachioradialis. Along withsit-ups, pull-ups are usually an integral ele-ment in standardized physical fitness tests(2, 6, 7, 9, 13). Most physical educatorsagree that isotonic movements of elbow flex-ion and extension are fundamental motionsin manipulating objects, and, perhaps moreimportant, essential for controlling neuro-muscular coordination and body weight.

Germane to the performance of pull-upsis the position of the hands. Various kinesi-ologists have reported the effects of forearmposition on elbow flexion efficiency; how-ever, differences in opinion continue (4, 10,11, 12, 14). Is the pronate i grasp superiorto the supinated grip? What advantage doesthe semipronated forearm have over thepronated or supinated position? Two inves-tigators describe the midpoint (semipro-nated) position as the most efficient methodfor mechanical and electromyographicalstandpoints (4, 12). Other researchers rec-ommend the supinated grasp (3, 6, 14, 15).One researcher suggests that little justifica-tion exists for requiring any certain positionof the hands while chinning (8).

John Piscopo teaches at State Universityof New York at Buffalo, Buffalo, New York.

Kinesiology IV

Recent studies have been conducted ex-ploring hand positions and elbow flexion. Asynthesis of these investigations appears todiscredit the pronated (palms forward) handgrasp as an efficient method of pull-up per-formance for boys, and the flexed-arm hangfor girls (3, 15). Notwithstanding, certainphysical fitness tests continue to specify thepronated grasp as a prescribed manner inexecuting the pull-up (2, 9).

Electromyographical analysis and per-formance testing reveal significant findingswhich question the rationale of the pronatedhand position as an acceptable technique inperforming the traditional pull-up exercise.

ELECTROMYOGRAPHICAL ASPECTS

Studies by Basmajian (4) point out thefine isotonic flexion interplay among the bi-ceps brachii, brachialis, and brachioradialis,and suggest that a wide rAnge of individualpatterns of myographic activity exists in el-bow flexion. It is significant to note that thebiceps brachii is generally active during flex-ion of the supine forearm under all condi-tions as well as in the semiprone forearmwhen a load of 2 lb is lifted (4). However,action potentials with the forearm prone re-veal little, if any, role in flexion of the elbow.This phenomenon may be partially explainedby the change in the line of puii from pro-nated to supinated in the chinning action( Figures 1 a and 1 b) . Rasch and Burke (10)

53

describe the inability of the biceps to recordstrong electromyographic potentials due tothe wrapping of the tendon of the bicepsmore than half-way around the bone (ra-dius) with contraction of the muscle tendingto unwrap itself and thus supinate the hand.Wells (14) concludes that the pronatedforearm pull-up cannot be justified from akinesiological viewpoint, since the bicepsbrachii is least active with the hand in pro-nation.

The forearm position does not appear tolessen the brachialis and brachioradialis con-traction. Basmajian (4) states that thebrachialis is a flexor of the supine, semiproneand pronated forearm in slow and quickmovements and designates this muscle as the"workhorse" among the elbow flexors. Elec-tromyographically, the brachioradialis re-cords greater action potentials in the semi-prone and prone positions than with thesupine hand grasp. Although these primeelbow flexors differ in their flexor activity invarious forearm positions, all three musclesact maximally when a weight is lifted during

Figure 1. (a) Supinated forearm (direct line ofpull); (b) Pronated forearm (twisting line of pull).

54

flexion of a semiprone forearm (4). Itshould be noted that the above postulationsare based on lifting weights with the hand,and not the traditional pull-up of lifting bodyweight on a chinning bar.

MECHANICAL ASPECTS

The elbow articulation is a typical uniaxialginglymus (hinge) with an average 146°range of motion ( I ). Figure 2 illustrateselbow flexion as an internal lever of the thirdclass. The prime flexors originate from thetip of the corocoid process and glenoid fossaof the scapula (short and long heads of bi-ceps), lower two-thirds on front of the hu-merus (brachialis) and lower two-thirds ofthe outer condyloid ridge of the humerus(brachioradialis). Insertion of these power-ful flexors attach to: (a) the medial aspectof the radial tuberosity (biceps); (b) thelower part of the coronoid process and tuber-osity of the ulna (brachialis): and (c) thelateral side of the radius above the styloidprocess (brachioradialis) (5).

Mechanically, elbow flexion is a classicexample of the body's structure demonstrat-ing a long resistance arm and short force armarrangement (Figure 2). Short force arms(distance from joint to muscle insertion)and a long resistance arm (distance fromjoint to point of resistance) simply requiremore muscular strength to produce move-ment. The internal skeletal and musclar ar-rangement does not favvi muscular advan-tages in the pull-up action of chinning. Thebiceps brachii is not only a flexor of theelbow but a prime supinator as well, and inthis writer's view it is this factor which causesthe position of the forearm to affect pullingefficiency in elbow flexion.

The insertion of the biceps on the tuberos-ity of the radius lies behind the longitudinalaxis of the latter so that the tendon windsaround the ulna border of the radius (11).It is this supinatory effect which prohibits thefull mechanical advantage of the muscle'sdirect line of pull upon the biceps brachiiwhen the forearm is pronated.

Kinesiology IV

Figure 2. Flexion of the elbow joint (third class le' er).

Figure 1b illustrates the twisting line ofpall of the biceps when the elbow is flexedwith a pronated hand.

Mechanically, the semiprone (one-halfway between supination and pronation) is acompromise grasp. In this pull-up position(palms facing each other), the biceps tendonhas started to wrap around the radius. Somerotational power is present and the biceps isnot utilized to its fullest potential as com-pared with the supinated position, but itsstrength is greater than in the pronated posi-tion.

Kinesiology IV

RECENT STUDIES AT SUNYAB

Two recent studies completed at the StateUniversity of New York at Buffalo, underthe supervision of the writer, support thesuperiority of the supinated hand grasp overthe pronated grip in the performance of pull-ups and flex-arm hang among elementaryand junior high school boys and girls (:35

15). Williams (15) investigated the supi-nated, pronated, and semipronated forearmpositions among 123 fifth and sixth gradeboys using each of the three positions. Pro-

55

nated and supinated grasps were performedin the traditional chin-up fashion on thehorizontal bar. The semiprone grasp wasexecuted on a modified horizontal ladder rig-ging, shown in Figure 3. Reliability coeffi-cients of .93, .90, and .94 were establishedfor each position, respectively, indicatinghigh consistency scores.

Means of 4.02, 3.56, and 2.38, respec-tively, were calculated for the supinated,semipiunated and pronated grasps. Meanscores for each group revealed that the su-pinated grasp was superior to the othergrasps tested, while use of the pronated fore-arm was least productive in performance(15). Analysis of variance indicated that asignificant difference among the three gripswas significant at the .01 level of confidence(15). Although the semipronated grasp wasnot as efficient in pull-ups achieved whencompared with the supinated grasp, Williams(15) suggests that this style should be inves-tigated further because the traditional grasphad the advantage of familiarity among thesubjects. Most students found the semi-pronated grip strange, and this variable mayhave elicited lower scores in the semipro-nated position as compared with the supi-nated grasp.

Ash ( 3 ) analyzed forearm grasps in asimilar study among 151 ninth and tenth

4

(V

Figure 3. The semipronated position.

grade girls. The flexed-arm test (AAHPERmethod) was administered in each of the fol-lowing forearm positions: pronated, supi-nated, and midpoint (semipronated). Relia-bility coefficients ranged from .84 to ,89.Analysis of variance disclosed differencessignificant at the 1 percent level among thethree positions. The t test was applied to thepronated and supinated grasps, with meanscores of 8.70 and 21.08 sec, respectively.

Results supported the performance supe-riority of supinated grasp as compared withthe pronated position. Mean scores of 22.15(midpoint) add 21.08 (supinated position)did not elicit a significant difference at the 1percent level between these two grasps. Thisinvestigation is congruent with the Williamsdata, which reveal the inefficiency of thepronated grasp as compared with the supi-nated position. As in the Williams study, themidpoint grasp was new and unfamiliar tothe girls tested. This factor may have influ-enced the results, lessening the scores withthe semipronated grasp.

DISCUSSION AND IMPLICATIONS

Evidence appears to support the supinatedforearm grasp as the most effective methodof performing pull-ups. Mechanically andelectromyographically, the biceps brachii,one of the most powerful elbow flexors, canexert its greatest force in the supinated posi-tion with the mechanical aspect favoring thenontwisting tendon advantage over the pro-nated forearm.

The pronated forearm position cannot bedefended kinesiologically as an efficient graspin performing pull-ups, yet certain arm andshoulder strength tests specify this style.

Some question still remains concerning thesemipronated grasp. It is this writer's viewthat the newness and unfamiliarity of themidpoint grip does have the effect of de-creasing the number of pull-ups performed:however, more research is needed at thistime to analyze the semipronated forearmspecifically as an effective position.

The correct hand grasp has important im-plications for physical educators and allied

56 Kinesiology IV

health specialists interested in human move-ment proficiency.

Individuals with low strength decrementsmay achieve greater pull-up performancethrough the improved mechanical efficiencyof the supinated forearm by delaying theonset of fatigue.

Standardization of forearm grasps willallow measurement and evaluation specialiststo compare pull-up norms validly.

Coaches and performers in such sports asgymnastics and swimming have a special in-terest in hand grasp where correct hand posi-tion is essential for maximum pulling power.

Corrective rehabilitation exercise thera-pists can apply the direct line of pull prin-ciple of the supinated hand for greater elbowflexion in restoring normal range of move-ment.

Bioengineers may well utilize kinesiolog-ical implications of forearm grasps in thedesign of hand tools, appliances, and pro-thestic instruments.

Tasks requiring elbow flexion are innu-merable in human movement. Whatever thetask may be, efficient body mechanics addsquality to everyday living as the individualmoves in his/her work and recreational en-vironment.

References

I. AMERICAN ACADEMY OF ORTHOPAEDIC SUR-GEONS Joint motion: Method of measuringand recording. Chicago: The Academy, 1965,p. 83.

2. AMERICAN ASSOCIATION FOR HEALTH, PHYS-ICAL EDUCATION, AND RECREATION. Youth fit-ness test manual. Rev. ed. Washington, D.C.:The Association, 1965.

3. Asti, SUSAN G. The effects of three forearmpositions on arm strength of ninth and tenthgrade girls. Master's project, State Universityof New York at Buffalo, 1971.

4. BASMAJIAN, J. V. Muscles alive. Baltimore:Williams & Wilkins Co., 1967, pp. 173, 177.

5. DUVAL, ELLEN NEALL. Kinesiology: The anat-omy of motion. Englewood Cliffs, N.J.:Prentice-Hall, 1959, p. 15.

6. FLEISHMAN, EDWIN. Examiners manual forthe basic fitness tests. Englewood Ciins, N.J.:Prentice-Hall, 1964.

7. JOHNSON, BARRY L., and NELSON, JACK K.Practical measurements for evaluation in phys-ical education. Minneapolis: Burgess Publish-ing Co., 1969.

8. MCGRAW, L. W. Effects of variations of fore-arm position in elbow flexion. Research Quar-terly 35:504-10, Oct. 1964.

9. PRESIDENT'S COUNCIL ON YOUTH FITNESS.Youth physical finless: Suggested elements ofa school-centered program. Washington, D.C.:Superintendent of Documents, U.S. Govern-ment Printing Office, 1961.

10. RASCH, PHILIP J., and BURKE, ROGER K.Kinesiology and applied anatomy. 4th ed.Philadelphia: Lea and Febiger, 1971, p. 189.

11. STEINDLER, ARTHUR. Kinesiology of the hu-man body under normal and pathological con-ditions. Springfield, 111.: Charles C Thomas,1955, p. 503.

12. THOMPSON, CLEM W. Manual of structuralkinesiology. 7th ed. St. Louis: C. V. MosbyCo., 1973.

13. UNIVERSITY OF THE STATE OF NEW YORK,STATE EDUCATION DEPARTMENT. New YorkState physical fitness test. Albany, N.Y.: TheUniversity, 1966.

14. WELLS, KATHERINE. Kinesiology. 5th ed.Philadelphia: W. B. Saunders Co., 1971, p.224.

15. WILLIAMS, ROGER J. The effects of three fore-arm positions on turn strength of fifth andsixth grade boys. Master's project, State Uni-versity of New York at Buffalo, 1972.

Kinesiology IV 57

ALSO AVAILABLE FROM AAHPER

KINESIOLOGY III (1973)

A collection of significant papers by leading authorities, compiled by theAAHPER Kinesiology Committee. Some of the topics treated are: in-herent movement patterns in man; a laboratory design for under-graduate kinesiology; the center of gravity of the human body; threedimensional cinematography; and web graphics and the qualitativeanalysis of movement.

KINESIOLOGY REVIEW 1971

A review of studies dealing with various aspects of kinesiology, includingsuch topics as computer movement analysis, kinetic energy and movement individuality, study of muscle action, sequential timing of movement patterns, cinematographical analysis, somatotype methodologyand kinesiology research.

ABSTRACTS OF RESEARCH PAPERS

Abstracts of research papers and research symposiums presented atAAHPER National Conventions:1974 (Anaheim)1973 (Minneapolis)1972 (Houston)1971 (Detroit)1970 (Seattle)

COMPLETED RESEARCH IN HEALTH,PHYSICAL EDUCATION, AND RECREATION

Annual compilation of research published in over 100 periodicals andabstracts of master's and doctor's theses in these areas:1973 (Vol. 15)1972 (Vol. 14)1971 (Vol. 13)1970 (Vol. 12)1969 (Vol. 11)1968 (Vol. 10)1967 (Vol. 9)

RESEARCH METHODS IN HEALTH,PHYSICAL EDUCATION, AND RECREATION

An uptodate, authoritative reference and basic textbook written bynationally known research specialists. Presented in dear, direct styleand set in easy-toread type, it deals with all phases of research fromselecting a problem to the final writing of the report. An invaluable toolfor the experienced researcher and teacher of graduate courses, as wellas the student working on his first project. It is indexed and has extensive bibliographies for each subject treated. Completely revised, 3rd ed.,1973.

For a current price list and order instructions, write:AAHPER, 1201 16th Street, NW, Washington, DC 20036.