information to users

INFORMATION TO USERS

This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter free, while others may be from any type o f computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality

6

” x 9” black and white

photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.

UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.


Locomotor Energetics and Limb Length in Hominid Bipedality

by Patricia Ann Kramer

A dissertation submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

University of Washington

1998

Approved by_ Chairperson of Supervisory Committee

Program Authorized x to Offer Degree__________ A

Date

ij

I

O p g > i Q 0 Lj

I3.M oh J_5%6


UMI Number: 9836201

Copyright 1998 by Kramer, Patricia Ann All rights reserved.

UMI Microform 9836201 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

UMI

300 North Zeeb Road Ann Arbor, MI 48103


© Copyright 1998 Patricia Ann Kramer


Doctoral Dissertation In presenting this dissertation in partial fulfillment of the requirements for the Doctoral degree at the University of Washington, I agree that the Library shall make its copies freely available for inspection. I further agree that extensive copying of this dissertation is allowable only for scholarly purposes, consistent with "fair use" as prescribed in the U.S. Copyright Law. Requests for copying or reproduction of this dissertation may be referred to University Microfilms, 1490 Eisenhower Place, P.O. Box 975, Ann Arbor, MI 48106, to whom the author has granted "the right to reproduce and sell (a) copies of the manuscript in microform and/or (b) printed copies of the manuscript made from microform."

Signature'

Date


University of Washington Abstract Locomotor Energetics and Leg Length in Hominid Bipedality by Patricia Ann Kramer Chairperson of the Supervisory Committee: Professor Gerald G. Eck Department of Anthropology Bipedality is the defining characteristic of hominids, yet during decades o f study, little attention has been given to the quantifiable energetic aspects of bipedality as a unique locomotor form. Hominid bipedality is, presumably, a solution to some unique problem for the early hominids, one that has much to do with energy usage. Locomotion is interesting because it is a task in which most creatures frequently engage and as such is subject to strong selective pressure. Human walking has been characterized as pendular and as optimized to take advantage of the changing levels of potential and kinetic energy that occur as the body and limbs move throughout the stride. Although this optimization minimizes energy use, some energy is required to maintain motion. This energy can be quantified by developing a dynamic model that uses kinematic equations to determine energy expenditure. Though the origins of bipedality remain clouded, two discernible forms of locomotor anatomy are present in the hominid fossil record: the australopithecine and hominine configurations. The australopithecine form is best represented by AL 288-1, a partial skeleton of Australopithecus afarensis, and is characterized as having short legs and wide pelves. The hominine form can be represented by modem humans and has long legs and a narrow pelves. By representing both configurations with a dynamic model, I can compare their energy usage and begin to explain why these two forms are present in the hominid line. Because AL 288-1 was a female and because females with the costly energetic demands of gestation, lactation and juvenile support might have especially benefited from greater efficiency in the morphology of their locomotor anatomy, the anatomy of a modem human female is used in the hominine configuration. When the results of modelling the two configurations are compared, two things are immediately apparent. First, the australopithecine configuration is significantly more energetically efficient than the hominine version. This finding holds for comparisons made


from both a time specific (J/kgs) and distance specific (J/kgm) perspective. Secondly, although the australopithecine configuration is energetically efficient at slow walking velocities, it limits the day range of the individuals that exhibit it. The day range o f the hominine configuration is greater than 2 0 % larger than the day range o f the australopithecine configuration. These findings have implications for the behavior of Australopithecus and Homo. Australopithecus seems to be adapted for slow speed walking in an environment of relative plenty. Homo, on the contrary, seems to be adapted to higher speeds and longer distances in an environment in which resources are more dispersed.


TABLE OF CONTENTS

List o f Figures List o f Tables Chapter One: Introduction 1.0 Introduction 1.1 Background 1.2 Overview o f the analysis details 1.3 Energetic efficiency as an important selective pressure 1.4 Efficiency and its measurement 1.5 Context and relevance of this research Chapter Two: The fossil record, the data on extant species, and their relevance to this project 2.0 Introduction 2.1 Hominid fossils in review 2.2 Reconstructing fossil hominids 2.3 The lower limb 2.4 The pelvis 2.5 Comparison o f Australopithecus and Homo 2.6 Effect of anatomical differences on movement profiles 2.7 Stride characteristics o f Australopithecus 2.8 Summary Chapter Three: Theory behind energy used in and for movement 3.0 Introduction 3 .1 Energy calculations in locomotion 3.2 Human bipedal movement 3.3 Modelling a bipedal hominid 3.4 Metabolic energy usage versus locomotor energy usage 3.5 Cost of transport 3.6 Empirical research on the effect o f the relevant body parameters of the model 3.7 Gait transition 3.8 Equivalent velocity 3 .9 Interindividual variation Chapter Four: Application of theory to this problem 4.0 Introduction 4.1 Development of segment parameters 4.2 Development of movement profiles 4 .3 Development of angular velocities 4.4 Joint degrees of freedom 4.5 Justification for selection of segments


Page iii v 1 2 5 7 9 10

12 13 15 17 22 25 26 41 43 45 45 46 48 52 59 60 61 64 66

67 68

72 85 88

89

TABLE OF CONTENTS (Cont.) 4.6 Male versus female anthropometries 4.7 Sources of error Chapter Five: Results 5.0 Introduction 5.1 Joint Displacements 5.2 Variation in horizontal velocity 5.3 Vertical acceleration 5.4 Variation in potential and kinetic energy 5.5 Energy required as input 5.6 Maximum velocity 5.7 Equivalent velocity 5 . 8 Cost o f Transport 5.9 Energy savings 5.10 Comparison with empirical data Chapter Six: Interpretation of Results 6.10 Introduction 6.1 Two bipedal styles 6.2 Using this model to predict movement and energy usage 6.3 On a "kinematically different form" o f bipedality 6.4 On an "energetically...different form"of bipedality 6.5 Foraging niches Literature Cited Appendix A: List of Terms and Abbreviations Appendix B. Thetas and Omegas (0-100% SC) Appendix C: FORTRAN Program Listing Appendix D: EXCEL Spreadsheets Appendix E: Derivation o f Equations E.l Derivation of the equations used to compute the displacement of a point in the model E.2 Calculation of the velocity of each point E.3 Calculation of potential energy E.4 Calculation of kinetic energy E.5 Calculation of energy change and total energy E . 6 Calculation of the mass moments of inertia E.7 Detailed development of link parameters

ii


89 89 91 91 97 100 101 103 105 107 108 110 113 115 115 116 117 120 123 126 139 143 153 162 172 172 174 174 175 176 177 181

LIST OF FIGURES

Number 2.3.1 Femoral length vs. time before present 3.2.1 Stance and swing phase in human bipedality 3.3.1 Sketch o f model indicating joints and links 3.3.2 Pelvic swing 3.3.3 ^bcxz a>bcxz as a function of time 3.3.4 Determination o f the velocity of a point 3.4.1 Energy use vs. velocity for mammals, primates and humans 3.4.2 Human energy use vs. velocity 3.5.1 Cost of transport vs. velocity 4.0.1 Sketch of model indicating joints and links (repeated from 3.3.1) 4.2.1 Definition o f angles in Winter (1987) 4.2.2 Angular excursion in degrees vs. percent o f stride cycle. Knee, hip and ankle angles are shown at three cadences (slow, natural and fast) 4.2.3 Angular excursion in degrees vs. percent o f stride cycle. Foot, leg and thigh angles are shown at three cadences (slow, natural and fast) 4.2.4 Definition o f angles used to compute energy usage 4.2.5 Angular excursion in degrees vs. percent o f stride cycle. 0ae, 0a£j and 0 db angles are shown at three cadences (slow, natural and fast) 4.2.6 Angular excursion in degrees vs. percent of stride cycle. Corrected 0ae, 0 acj and 0 (jb angles are shown at three cadences (slow, natural and fast) 4.2.7 Leg movement during walking 4.2.8. Angular excursion in degrees vs. percent o f stride cycle. ©bcxz *s shown for three cadences (slow, natural and fast) 4.2.9. Angular excursion in degrees vs. percent of stride cycle. 0bcyz *s shown for three cadences (slow, natural and fast) 4.3.1 Angular velocity versus % stride cycle for o a(j, ©jb and coae 4.3.2 Angular velocity versus % stride cycle for ©bcxz and ^bcyz 5.1.1 Progression of hominine and australopithecine configurations at fast cadence 5.1.2 Progression of hominine and australopithecine configurations at normal cadence 5.1.3 Progression of hominine and australopithecine configurations at slow cadence 5.2.1 Variation in horizontal (x-axis) velocity of joints on the stance leg for an input velocity of 2 m/s


Page 19 47 49 49 50 51 54 56 60 67 77 78 78 79 80 81 82 83 84 86

87 92 92 93 98

LIST OF FIGURES (cont.)

5.2.2 Variation in horizontal (x-axis) velocity o f joints on the swing leg for an input velocity o f 2 m/s 5.4.1 Variation in kinetic and potential energies with % stride cycle for Homo (fast cadence) 5.4.2 Variation in kinetic and potential energies with % stride cycle for Australopithecus (fast cadence) 5.5.1 Energy added vs. velocity 5.6.1 Ankle angular velocity vs. % stride cycle 5.8.1 Cost of transport vs. velocity 5.8.2 Cost of transport vs. adjusted velocity 5.10.1 Comparison of predicted metabolic energy usage with model generated energy usage for modem humans E. 1.1 Sketch of model indicating joints and links (repeated from 3.3.1 and 4.0.1) E.6 .1 Unfactored distances from x and z axes E.6.2 Differential block masses for modem humans and A. afarensis E.6.3 Mass moments o f inertia for modem humans and A. afarensis

iv


99 101

102 104 106 109 110

114 172 179 180 180

LIST OF TABLES Number Page 2.3.1 Femoral and tibial samples of Australopithecus, Homo and Pan 21 2.3.2 Femoral and tibial lengths of Australopithecus, Homo and Pan 22 2.4.1 Pelvic dimensions of Australopithecus, Homo and Pan 23 2.5.1 Relative body proportions 26 4.1.1 Lengths o f segments for modem humans and A. afarensis 69 4.1.2 masses o f segments for modem humans and A. afarensis 70 4.1.3 Mass moments o f inertia of segments for modem humans and A. afarensis 72 4.2.1 Final adjustments to movement profiles 85 4.3.1 Final adjustments to angular velocity profiles 88 5.1.1 Conformation of model displacement to expectations 93 5.1.2 Stride lengths for Homo and Australopithecus 95 5.1.3 Vertical displacements of HAT 97 5.2.1 Variation in input versus average velocity 98 5.3.1 Maximum vertical acceleration 100 5.5.1 Esum totals for all cadences 105 5.7.1 Dynamically equivalent velocities 108 5.7.2 Esum totals for all cadences using dynamically equivalent velocities 108 5.9.1 Effect of difference in energy usage on total body fat 111 5.9.2 Average day and year range of Homo and Australopithecus 112 E.6 .1 Mass moments o f inertia for limb segments 177 E.6.2 Body dimensions for modem humans and australopithecines 181 E.7.1 Determination o f long bone lengths 182 E.7.2 Values for determination of I3 and I4 183

V


ACKNOWLEDGMENTS I wish to acknowledge the help and friendship of several individuals. First and foremostly, I thank Dr. Gerald G. Eck, my mentor and the chairman of my committee, for countless hours of discusion, for unbounded enthusiasm for this project, and for unfailing support of my work. Without Gerry, this effort would have been impossible. I also want to thank the other members of my committee—Dr. Peter E. Nute, Dr. Donna L. Leonetti, and Dr. Thomas L. Daniel. Each has been asked to cross the boundaries o f their own particular discipline to allow me to synthesize a holistic approach to this problem. I also gratefully acknowledge the help and support of the other faculty and the students o f the Biocultural Program in Anthropology of the University of Washington.

vi


DEDICATION This dissertation is dedicated to Mother, who gave me the strength to stride forward with confidence, to Brian, who showed me that a little meandering never hurt anyone, and to Stephen, who taught me that life is all one big circle anyway.

vii


Chapter One: Introduction 1.0 Introduction This dissertation concerns the amount of energy that hominids1 use to walk in their native habitat. Locomotion is interesting because it is a task in which most creatures frequently engage and hominid locomotion is particularly interesting because it is a unique form o f bipedality—reciprocal bipedal gait without the use o f a balancing tail. Hominid bipedality is, presumably, a solution to some unique problem for the early hominids, one that I believe has much to do with energy usage. The origins o f bipedality remain clouded but two discernible forms o f locomotor anatomy are present in the hominid fossil record: the australopithecine and hominine forms. By representing both configurations with a dynamic model, I can compare their energy usage and begin to explain why two forms are present in the hominid line. This research exploits the notion that females with the costly energetic demands of gestation, lactation and juvenile support might have especially benefited from greater efficiency in the morphology of their locomotor anatomy. Six chapters constitute the body of this work. Chapter 1 introduces the main ideas and details the background upon which the research rests. Chapter 2 describes the hominid fossil record and the interpretations that researchers have formed from it. Chapter 3 discusses the theory behind the calculation of the energy used in locomotion and the dynamic modelling techniques used in the analysis, while Chapter 4 details the inputs to the model. The results are summarized in Chapter 5 and Chapter 6 presents the conclusions that can be drawn from those results. Several appendices are provided to amplify the discussions presented in the main text.

1 Throughout this report, "hominid" refers to bipedal hominoids including the genera Australopithecus, Parcmthropus and Homo and not to the quadrupedal forms (Pan and Gorilla). Following Gregory and Heilman (1939), "australopithecine" refers to east and south African early hominids (Australopithecus and Paranthropus) while "hominine" refers only to Homo. These semantic differentiations allow for linguistic simplicity and precision and are not intended to spark taxonomic debate.


2 1.1 Background Bipedality is the quintessential characteristic of the hominids, yet its origins and adaptive significance remain obscure. Despite decades o f debate and volumes of published research, the cause of the rise of bipedality is as questioned today as at any time in the past 100 years. Although there are many causes for this confusion and recent finds of Ardipithecus ramidus (White et al., 1994; White et al., 1995) and Australopithecus anamensis (Leakey et al., 1995) may help lead to resolution, presently all that is clear is that some form o f arboreal hominoid changed into a habitual terrestrial biped. As interesting as understanding the origin of bipedality might prove, it now seems intractable. "Bipedality" is not, however, one mode of locomotion, rather it is a class of possible locomotor styles. Just as there are a myriad of types of anatomical and facultative quadrupedality, adapted to various locomotory niches, so too can there be different kinds of bipedality, presumably adapted to their niches as well. Within the hominid clade there are two distinct anatomical configurations (Zihlman, 1978; Rak, 1991; Foley, 1992; Jungers, 1991; McHenry, 1991b) that might correspond to different adaptations: the australopithecine and the hominine configuration. Historically, two schools of thought have existed about hominid bipedality (McHenry, 1983; Duncan etal., 1994). One school maintains that australopithecines are transitional forms, not fully adapted to bipedality, potentially due to a continued reliance on arboreal resources (Robinson, 1972; Zihlman, 1978; Zihlman and Brunker, 1979; Jungers, 1982; Stem and Susman, 1983). The other school holds that australopithecines were fully bipedal and that their gaits were virtually indistinguishable from those of modem humans (Lovejoy et al., 1973; McHenry, 1975; White, 1980; Latimer et al., 1987; Lovejoy, 1988; Latimer and Lovejoy, 1989). Rak (1991:283) offers a third alternative to which I subscribe: "Lucy's pelvis [AL 288-1, A. afarensis]...does not represent simply an intermediate stage.... Although clearly bipedal and highly terrestrial,


3 Lucy evidently achieved this mode of locomotion through a solution all her own." McHenry and Jungers concur with this position indicating that, although australopithecines like A. afarensis "became specialized for bipedal locomotion", their form of bipedality "was kinematically and energetically different from that of modem humans" (McHenry, 1991b: 133). This difference created a "fundamental difference in some aspects of the locomotor repertoires" of the two groups (Jungers, 1991:222). Rak (1991) characterizes A. afarensis as having short legs and a wide pelvis while Homo is configured with long legs and as narrow a pelvis as is practical to allow for the birth o f an infant. Jungers (1991) also suggests a distinction between the australopithecine and hominine body shape. The fossil record, though sparse, supports this claim. The partial skeleton AL 288-1 (Johanson et al., 1982) best characterizes the locomotor anatomy o f A. afarensis and its anatomy is typical of the australopithecine configuration. Both H. erectus and H. sapiens typify the hominine pattern although H. habilis is questionable. At first glance, the ideas of the transition school make intuitive sense. If the last common ancestor between Pan, Gorilla and the hominids is presumed to be a quadruped, then the sequence o f locomotor forms would read: Miocene hominoid quadrupedality, australopithecine compromise bipedality, hominine bipedality. But upon reflection, this sequence needs revision. Australopithecines existed as terrestrial bipeds for at least 2 million years (4.0-2.0 million years ago) before Homo emerged with its new body configuration. The robust australopithecines arose at the same time as Homo but they maintained the typical short-legged and wide-hipped australopithecine configuration (Robinson, 1972; Grausz et al., 1988; McHenry, 1991b; Jungers, 1991). At a minimum, the australopithecine "compromise" configuration existed for 3 million years. In addition, the robust australopithecines, who are distinct enough to merit at least their own species and potentially their own genus, maintained this "inefficient compromise" in locomotor anatomy while making significant cranial adaptations. It is unlikely that any primate genus


4 would be able to thrive for 3 million years with a significant locomotor handicap. It is, therefore, probable that the australopithecine form o f bipedality was efficient in its particular time and place. Since the robust australopithecines and Homo were contemporaneous and sympatric for a million years, the question then arises: why did Homo develop long legs while the australopithecines did not? Though hardly a novel suggestion (Foley, 1992; McHenry, 1991b; Jungers, 1991), I propose one possible explanation for this change in locomotor anatomy: the two groups occupied different foraging niches. I hypothesize that Homo needed long legs and narrow pelves to move with greater energetic efficiency at higher speeds, while the australopithecine configuration was designed to be more efficient at lower speeds. This hypothesis devolves from the idea that australopithecines were primarily vegetarians (Kay and Grine, 1988) while early Homo was more omnivorous—utilizing hunted or scavenged meat (Hill, 1982; Blumenschine and Cavallo, 1992). After the Miocene cooling that prompted the rise of the family Hominidae, the climate was relatively stable with a mosaic environment of riverine forests, open woodlands and grasslands. Resources were less abundant and more widely distributed than in the early and middle Miocene tropical rain forests that had given rise to the hominoids (Foley, 1992). Australopithecine bipedality was adapted to this more variable ecological setting. As the late Pliocene climate in East Africa became ever cooler, drier and more seasonal, high-density resource patches became more widely distributed (Foley, 1992). Hominids could adapt to low-quality resources and maintain their locomotor style or continue to utilize high-quality resources and change their locomotor system. Robust australopithecines followed the first path. Homo, in contrast, changed its locomotor style in order to forage over longer distances (Foley, 1992) or to pursue animals to hunt (Hill, 1982) or scavenge (Blumenschine and Cavallo, 1992). Both foraging over long distances and pursuing game animals require high speeds.


5 This scenario of an australopithecine adaptation to low speeds and a hominine adaptation to higher speeds is suggested by Jungers (1991) and will be tested in this research. If the australopithecine configuration is optimized for low speeds and the hominine configuration for higher speeds, then a critical velocity may exist where it becomes energetically efficient or anatomically necessary to change body configuration. O f course, no creature locomotes solely at a single velocity and what is of interest is the habitual velocity range. If the range changes from below this critical velocity to above it, then the body configuration might change to accommodate this change in habitual speed. If no critical velocity exists, several intriguing questions obtain. Why do the combinations of wide hips-short legs and narrow hips-long legs exist, but not those of wide hips-long legs or narrow hips-short legs? If the analysis indicates that the australopithecine configuration was efficient at all speeds, then why did narrow hips and long legs develop in Homo? Alternately, if the hominine configuration is most efficient at all speeds, then why did the australopithecines exist for 3 million years with a wide pelvis and short legs? This dissertation seeks to answer these and other related questions. 1.2 Overview of the analysis procedure In order to answer the questions asked in the previous sections, I have constructed a dynamic model of a walking biped. Although Chapter 3 details the modelling process and mechanical analyses that I performed, a few introductory comments are in order at this point. Bipedal walking is defined as a gait in which one foot is on the ground at all times. When viewed from the perspective of one leg, it can be broken into two parts, the stance phase and the swing phase. The stance phase starts with heel strike, continues as the body rotates over the stance leg, and then ends with toe off. When one leg is in the stance phase the other leg is in the swing phase. The swing phase begins as the toe leaves the ground, continues as the leg is swung under the body and ends with heel strike of the next cycle. The body's center of gravity moves vertically as the legs move and the body


6 progresses forward. These movements use energy. Moving the body’s center o f gravity up and down and swinging the limbs require that muscles contract and contractions require the expenditure of energy. I have captured these movements of the body’s center of gravity and legs and estimated the energy used by modelling the head-arms-trunk as a mass and the pelvis, thigh, leg and foot as rigid links. The "model" is simply a set of equations developed from the basic principles of dynamics, a branch of mechanics. The model allows for the inputs to the model to be varied so that I can use the same model to gather data on both the australopithecine and hominine body plans. As indicated in Section 1.1, the australopithecine configuration is short legged and wide hipped while that of Homo is long legged and narrow hipped. The model is the same for the two configurations but the inputs are specific to the two different body plans. The inputs for the model are of two types. The first type of input needed is movement of the biped in time and space. I call these "movement profiles" and they are simply the angular movement of a specific link in the model measured against time. Section 4.2 describes in detail how these movement profiles were developed. The movement profiles are the same for both configurations. The second type of data needed for the model is the segmental parameters of the biped. This includes such things as the length o f each link in the model and the distribution o f each link's mass along its length. Using the data from the fossil record for australopithecines and from current research on modem humans, I create each body plan. What this means is that for the australopithecine version, for instance, the link representing the thigh can be 280 mm long, while that for the modem human can be 400 mm. In a similar manner, all the other links and the other necessary data can be varied to arrive at versions that represent a particular body configuration. Chapter 2 and Section 4 .1 detail the development of these inputs. Different inputs of the segmental parameters result in different amounts of energy required to cause the movements. This energy difference can


7 be computed for various velocities and the energy used by the australopithecines can then be compared to the energy used by the modem humans. This comparison is the crux of the research. 1.3 Energetic efficiency as an important selective pressure Axiomatic to this research is the concept that a creature that minimizes its energy expenditure on locomotion while still accomplishing its required tasks will leave more descendents than one that "squanders" energy in inefficient locomotion. This is basic to the classic theory of evolutionary biology. In other words, the constraints of resource allocation are the mediators of survival and successful reproduction o f an individual. A resource is a limited commodity and energy to survive and procreate is one of the most essential resources. An adaptation that allows a creature to devote less energy to a necessary task will experience tremendous selective advantage because that energy can then be apportioned to another requirement. In the environment of evolutionary adaptedness, there are always more tasks to perform than energy to perform them. Locomotion is necessary to any primate and affects all aspects of its life. An explanatory framework that posits an understanding that an "adaptation" may be more or less advantageous at various points in an individual's life is necessary to fully appreciate the importance of locomotion in shaping anatomy. Life history theory, one such framework, is an appropriate paradigm from which to view changes in locomotory anatomy and their energetic consequences because Locomotion is fundamental to foraging and feeding and to predator avoidance, to mating and caring for offspring. Locomotion, therefore, compels consideration of the whole animal throughout its life cycle.... [LJocomotion is central to an individual's ability to survive, to mate and to ensure the survival of its offspring, and therefore to the broader framework of life history theory and reproductive success (Zihlman, 1992:315). Although a daunting task, to me this means that all phases of the life cycle and both sexes must be considered in any complete evaluation of the biomechanics of hominid bipedality.


This research, however, attempts to shed light on only one facet of this problem—the adult female—since the best fossil evidence for the australopithecine configuration is from specimens that have been diagnosed as female (Johanson et al., 1982; Grausz et al., 1988). In addition, adult primate females may be particularly energetically constrained because they must provide for offspring that are highly energetically demanding for long periods of development (Kaplan, 1996). Gestation and lactation demand significant energy expenditures and maternal energy depletion can affect interbirth intervals (Tracer, 1991 and 1996). Infant transport is another significant maternal investment (Kramer, in review). Energy is a fundamental constraint on the species that has been documented in modem humans and in the great apes (Kaplan, 1996). Since male reproductive success is dependent on females and female reproductive success is dependent on energy stores, the locomotor anatomy of females should experience strong and direct selective pressure for efficiency (Kaplan, 1996). Ultimately, "the principal cost of any locomotor system is energy" (Foley, 1992:139). A locomotor system can facilitate other behaviors, but these are secondary. Interestingly, hominids have a unique locomotor system that includes only the hindlimbs, freeing the forelimbs for other tasks. Having unoccupied forelimbs can be a useful thing, as can be the various other results of bipedality, but they will develop only if locomotor function is reasonably unimpaired by the change. In the extreme example, if freeing the forelimbs for other roles left the creature unable to locomote, bipedality could not have developed because the cost to a basic hominid function—moving—would be too high. It is certainly possible that some short term impairment in locomotor function would be tolerable if the benefits o f free hands (or some other secondary benefit) simultaneously were large, but the selective pressures to develop a more efficient system would also be intense. In other words, the origin of bipedality might have a strong non-locomotor component, but the development of an efficient system would be rapid. Since I will be


9 evaluating two locomotor styles that each existed for millions of years, I think that it is reasonable to conclude that both were optimized for locomotor efficiency in their environmental niches. 1.4 Efficiency and its measurement Theoretically, efficiency is a measure of how much of a quantity must be added to a system relative to how much is gained from it. Efficiency is typically thought of in terms o f a ratio or percentage; for instance, a system that is 100% efficient delivers as much as it requires. Economy is a completely different measure that involves only the amount required and is unrelated to the amount delivered. Consequently, a system can be efficient without being economical or economical without being efficient. An example of the relevance of these concepts to this research is as follows: two resource patches are available, one that contains 50 joules (J) of food resources and costs 50 J o f locomotor energy to attain and one that has 100 J of food and costs 75 J to attain. The first patch has an efficiency of 100% [= 50/50*100%] while the second has an efficiency of 133% [= 100/75* 100%]. If efficiency is the only constraint, then the second patch is the better choice; however, if you are economically limited in that you only have 60 J of locomotor energy available to you, then the only choice is the first patch. The important point is that comparing efficiencies between two systems without controlling for the economy o f the situation can be misleading. In addition, other constraints may prohibit the selection o f the most efficient system. Particularly germane to this research is the constraint of either time or distance that comes from including velocity in the analysis. Returning to the previous example, the second patch might be unfeasible because it takes too long to arrive there or is, in other words, too far away. For this research, the question is how much metabolic energy must be delivered to the system in order to move a given body mass at a certain velocity. By specifying the body mass and the (relative) velocity, I constrain the analysis of my systems (the configuration of the locomotor anatomy). I am not saying that a


10 particular velocity is "best," rather I am saying that at a given velocity, one system can be labelled "better" or more efficient, i.e. requires less energy to attain that velocity. If a species "chooses" an energetically inefficient path, however, that does not mean that the species was transitional or compromised. It probably simply means that the species had important constraints other than energetic efficiency with which to contend. 1.5 Relevance of this research I hope that this research sheds some light on the habitual locomotory profile o f the extinct genus Australopithecus. The uniqueness o f the australopithecine locomotor anatomy has prompted much discussion in the literature and claims for locomotor efficiency (Lovejoy et al., 1973; McHenry, 1975; White, 1980; Latimer et al., 1987; Lovejoy, 1988; Latimer and Lovejoy, 1989) or lack thereof (Robinson, 1972; Zihlman, 1978; Zihlman and Brunker, 1979; Jungers, 1982; Stem and Susman, 1983) have abounded; however, these arguments have not been based on quantitative data. I should like to fill, at least partially, that data gap. This research is particularly important in light of recent research that concludes that limb length is not a "structural indicator o f design for efficiency" and that body mass alone is important (Steudel, 1994). I want to show that there is a velocity range in which australopithecines were more efficient than modem humans. I suspect that there is such a range and that the australopithecines were efficient in their locomotory niche—slow speeds—and that the increasing leg length in Homo is a response to the need for higher walking speeds. This research, however, has broader implications than solely the examination of australopithecine locomotor efficiency. It provides a technique for modelling other anatomical configurations (like that of the neandertals) and for exploring questions of body configuration among modem humans. In addition, the conclusions reached herein may help place the australopithecines and Homo in their appropriate ecological niches. In the next chapter, I shall turn to a description of


the fossil record and the controversy concerning the transitional nature of australopithecine bipedality.


Chapter Two: The Fossil Record, the Data on Extant Species and Their Relevance to This Project 2.0 Introduction In this chapter, I explore the hominid fossil record and, in particular, what is known about the locomotor anatomy o f australopithecines, early Homo and modem humans. I also detail why this information is relevant to my research and in doing so address two basic questions: was the australopithecine body plan different from that of modem humans and does this difference, if present, indicate a kinematic difference between the two forms? Discerning the answer to the first question is a matter of evaluating the fossil record, no small task, while understanding the second is much more subjective because it involves not only interpreting the physical shape of the fossil but also interpreting what functional significance, if any, that shape had. Despite difficulties in understanding the fossils, I think that reasonable answers to the two questions can be obtained. First, does evidence for an australopithecine locomotor configuration exist and, if it does, are australopithecines different from modem humans? I believe that the answer is yes, or in other words, that the evidence indicates that australopithecines as a genus exhibit a particular form of locomotor anatomy and that the australopithecine form is different from the hominine version. To support this contention, I will provide estimates for femoral length, tibial length, interacetabular distance, femoral neck length and body mass. All o f these body parameters are o f importance in developing the inputs for the dynamic model that is the data gathering device for this project. Some data on chimpanzees (Pan troglodytes) and bonobos (P. paniscus) are also provided for reference. The second basic question that can be addressed from evaluation of the fossil record is: do the details of the australopithecine configuration support the assumption that australopithecines were kinematically similar to modem humans? Again, I think that the answer to this question is yes and I will provide descriptions o f the fossil evidence to


13 support this claim. That australopithecines are kinematically similar to modem humans is fundamental to this research because I must use the human movement profiles (detailed in section 4.2) for both groups. Kinematic similarity implies that the two groups moved in similar ways but does not imply that they used similar force or energy (kinetic similarity) to do so. Because the fossil record is sparse and individual specimens are almost always fragmentary, some ambiguity inevitably exists in determining the characteristics of the relevant parts of the locomotor anatomy. I, therefore, first discuss the historical context of fossil reconstruction of locomotor anatomy and then give the specific details. At the end of this chapter, I summarize the findings and place them in the context of my research. 2.1 Hominid bipedality in review Darwin (1872) first recognized that bipedality was a meaningful distinction of humans from the great apes when he began to explore the idea o f the descent of humans from an apelike ancestor. Although Dart found the first evidence o f bipedal australopithecines in South Africa in the early part of this century, it was not until Robinson's work (1972) that a thorough and systematic study o f hominid bipedality was undertaken. Since that time, two schools of thought have existed about hominid bipedality (McHenry, 1983; Duncan etal., 1994). One school maintains that australopithecines are transitional forms, not fully adapted to bipedality perhaps due to a continued reliance on arboreal resources (Robinson, 1972; Zihlman, 1978; Zihlmanand Brunker, 1979; Jungers, 1982; Stem and Susman, 1983). Robinson (1972) characterizes the South African robust australopithecines (which he designates Paranthropus robustus) as transitional but the gracile forms (Homo africanus in his scheme) as modem. Stem and Susman (1983:312) describe A. afarensis as lacking in "some o f the fundamental qualitative traits of modem human locomotion." Zihlman (1978) and Zihlman and Brunker (1979) speak of "an australopithecine adaptation" while Jungers (1982:676 and


14 1991:220) states that "kinematic identity and functional equivalence with the bipedal gait of modem humans seems highly improbable." A particularly troubling aspect o f this first school of thought is that many of its proponents take "different from modem humans" one step further and conclude that since australopithecines were different from modem humans, they were less efficient at bipedality. Little analytical support for this contention is provided. The other school holds that australopithecines were fully bipedal and that their gaits were virtually indistinguishable from those of modem humans (Lovejoy et al., 1973; McHenry, 1975; White, 1980; Latimer et al., 1987; Lovejoy, 1988; Latimer and Lovejoy, 1989). Lovejoy et al. (1973:757) and Latimer et al. (1987:173) use phrases like "no feature.. .was found to distinguish" and "fully adapted to bipedalism equivalent to that o f//, sapiens." McHenry (1975:45) found "that there is little fundamental difference in gait among them [australopithecines and modem humans]" but has since changed his mind (McHenry, 1991b). White (1980:175) suggests "that the Laetoli hominid trails...do not differ substantially from modem human trails made on a similar substrate." Both schools of thought use the same fossil data to support their cases and despite numerous, and oftentimes acrimonious, debates no resolution has been reached, although such has been offered by Jungers (1991) and Rak (1991). Jungers' view is more comparative and theoretical, while Rak's is more specific. After examining body shape and size, Jungers (1991:222) concludes that there is a fundamental difference in some aspects of the locomotor repertoires of Lucy (and probably other australopithecines) versus modem humans (and probably early Homo). Both groups can be characterized as bipeds, but their solutions to terrestrial bipedality are sufficiently different in mechanical terms to have been reflected in major differences in many features of skeletal design. Rak (1991:283) asserts that "Lucy's pelvis [AL-288, A. afarensis]...does not represent simply an intermediate stage.... Although clearly bipedal and highly terrestrial, Lucy


15 evidently achieved this mode of locomotion through a solution all her own." Rak goes on to suggest that the reason for the wide pelves o f australopithecines was to increase stride length by pelvic rotation. This is the only functional explanation that is given for the difference in body shape. My research takes the idea of the adaptation o f body shape to a particular locomotor regime (different walking speeds) and tests it with a dynamic model. 2.2 Reconstructing fossil hominds If fossils were found intact, associated with other parts o f the same individual, and together with other individuals of the same species in a coherent, uniform temporal sequence and if osteological remains could unambiguously inform the investigator on body mass and mass distribution, then this section would be unimportant. Unfortunately, in most cases none of these conditions is met and, most frequently, the researcher is left to use her judgment to recreate even the most basic of osteological dimensions. It is this judgment that often confounds the efforts of paleontologists. Paleontology in general and hominid paleontology in particular have gone to great lengths to develop objective techniques to discern a myriad of body dimensions using mostly comparative methods. Unfortunately, objectivity is often an impossible position to maintain. As Smith and Harrold (1997) note in a recent critique of the debate on the origins of modem humans, Background preparation and individual experiences can have large effects on interpretations.... These convictions may be based on a great deal of study and knowledge, but reasons accessible to others who have not had one's own particular experience must be presented, for others may have had equally salient impressions incompatible with one's own. Despite the fact that human judgment is inherently subject to human perspective, as long as researchers keep in mind that this bias is present, fossil reconstructions that rely on judgment can be useful. With this caveat in mind, I will now turn to a discussion of several "objective" techniques for the reconstruction of osteological dimensions. Only the


16 techniques that are used to arrive at estimates of bone lengths and body mass are of importance to this research so only these two approaches will be examined. The basic comparative method uses regression formulae to estimate one unknown character from data on another known character. In order to make this estimation, data on intact specimens (where all the character states are known) are gathered from individuals that are believed to exhibit a similar relationship between the characters. For instance, femoral length in hominid fossils can be estimated from femoral head size, femoral shaft diameter and acetabular size (McHenry, 1991a), to name just a few possibilities. Data gathered from modem humans, chimpanzees, bonobos, and other closely related species have been gathered and used to create various regression models. Using these models, knowledge o f one dimension, like acetabular size, allows the researcher to estimate another dimension, like femoral length. As long as the model that is used was developed from a population that has the same relationship between the characters, then this method is excellent. Unfortunately, this is exactly where the method breaks down. How do you know that the model population and the fossil specimen have a similar relationship when you do not have a population of fossil specimen from which to determine the relationship in the first place? For example, the only truly "intact" femur of Australopithecus is AL 288-lap and the relationship of its femoral length and other osteological parameters is different from (outside the variation of) the extant groups to which it has been compared. The femur is 280 mm long (Johanson et al., 1982). Vancata (1991) uses four models (pongid, monkey, hominid and an average of the three) to estimate femoral length and obtains estimates of 300 mm, 290 mm, 345 mm, and 310 mm, respectively, for AL 288-lap. Using the known lengths of AL 288-lap and several hominine femurs, he suggests that the average model is "most reliable because there is only slight overestimation in A. afarensis and slight underestimation in Homo. .." (Vancata 1991:148). Interestingly, this is exactly what you would expect if australopithecines were


17 short legged and Homo long legged. This also emphasizes the quandary in which anyone who attempts to reconstruct australopithecine anatomy finds herself. There simply is not enough fossil data to construct a population and australopithecines are sufficiently different from those populations from which we do have data to cast much doubt on extrapolations from extant groups. Fortunately, AL 288-1 is a partial skeleton and the bones of its lower limb are reasonably intact as are its innominate and sacrum. Reconstruction of the bony dimensions relevant to this research is, therefore, relatively unambiguous and bounded. Reconstructing body mass from osteological measurements is even less certain than determining femoral length from acetabular size. In the case of body mass, however, some estimate must be used because body mass does not leave a fossil record and no australopithecines have ever been weighed. For my analysis, I will use McHenry (1991 and 1992) for estimates o f femoral length and body mass along with Vancata (1991) and Webb (1996). 2.3 The lower limb Despite the inaccuracies that are possible in reconstructing bone lengths from incomplete fossils, researchers often compare the ratio of humeral to femoral length (humerofemoral index) of various extant and extinct primate groups and conclude that, though still shorter legged than modem forms, AL 288-1's legs were longer than what one would expect in her immediate non-hominid ancestor. For reference, AL 288-1's humerofemoral index is 85, while that of bonobos is approximately 99 and of modem humans is approximately 73 (Jungers, 1982). Because AL 288-l's index is intermediate, researchers often assume that her legs were longer than those of her non-hominid ancestor. Using humerofemoral indices to compare changes in hindlimb length is, however, particularly problematic because it ignores the potentially confounding effect of selective pressure on the length of forelimbs. The conclusion that the leg of A. afarensis


18 was longer than that of her immediate ancestor is, therefore, a potentially misleading one because it is equally possible that AL 288-1's arms may have been shorter while her legs remained the same length as those o f her Miocene hominoid ancestor (Jungers, 1991) or that both hindlimb and forelimb length may have changed. Even though there are problems associated with comparing humerofemoral indices, it seemed clear until recently that A. afarensis was short legged when compared to modem humans and that leg length has steadily increased from the time of A. afarensis to that of modem humans. Recent re-evaluation of the evidence has, however, shown that leg length may not have increased gradually from/I. afarensis to H. sapiens, but instead may have remain constant in australopithecines and then abruptly jumped to modem levels with the advent of Homo (Jungers, 1991). Webb (1996:518) takes yet another view and says "femur length, and therefore probably lower limb length, increased rapidly during the first 2 Ma [4-2 mya], then changed little thereafter." Figure 2.3.1 shows the femoral length of all fossils that have been assigned a length in the literature plotted against time before present and is adapted from Webb (1996, Fig. 3 and Table 1^). Although one interpretation of Figure 2.3.1 is that femoral length gradually increased from 3.5 to 2 million years ago, an equally likely, and I think more correct, interpretation is that australopithecines exhibit one range of femoral lengths while Homo

2 Webb (1996) uses data from (Vancata, 1991) on four femoral fragments—AL-3 33-3, AL 333-4, TM 1513, and KNM-ER 999. Webb attributes the first three to Australopithecus and ER 999 to H. habilis. Other work indicates that ER 999 is H. sapiens. Vancata evaluates four models (monkey, pongid, hominid and an average of the three) for determining femoral length and suggests that the average is the "best." Following this advice, Webb uses the estimate of femoral length from the average model. This average model, however, causes a "slight over-estimation in A. afarensis specimens and slight under-estimation of the length of Homo habilis femora" (Vancata 1991: p. 148). This pattern is exactly what I would expect if australopithecines maintained an apelike leg length while Homo experienced leg lengthening. For that reason, I choose to use Vancata's pongid model to estimate femoral length for the australopithecines and his hominid model for ER 999.


19 has another range of longer lengths. This interpretation is in agreement with Jungers (1991). Indeed, because australopithecine legs are remarkably similar in absolute length to

femoral length (m) 0.5 T A A

0.45 -0.4 -0.35 0.3 -0.25 --

■ australopithecines 0.2

A Homo

--

0.15 -

OH 62

0.1

0.05 -time before present (million years) -3.5

■3

-2.5

2

1.5

1

-0.5

0

0.5

Figure 2.3.1 Femoral length vs. time before present.

those of bonobos and chimpanzees and their estimated body mass is in the same range (see Table 2.3.2), it seems most parsimonious to conclude that this limb length is plesiomorphic. Interestingly, most of the early data are inferred from reconstruction of length from femoral shaft diameter, femoral head size or acetabular diameter. Only 7 complete or almost complete femora exist from prior to 1.5 mya—AL 288-lap, KNM-ER 1472, KNM-ER 1481a, KNM-ER 1808, KNM-WT 15000g, KNM-ER 737 and KNM-ER 736 These seven are indicated in Figure 2.3.1 by arrows. The conclusion that there was an abrupt shift in leg length with Homo would be further strengthened if OH 62 was considered an anomaly and removed from the data for Homo. The femoral data from the OH 62 partial skeleton include a left shaft and neck. Femoral length was reconstructed


20 based on shaft diameter (Johanson and Shreeve, 1989) and may well be misleading since erosion of the shaft is evident and reconstruction of length from diameter is problematic (Ruff, 1984). (See discussion in Section 2.1 of the problems associated with reconstructions.) Korey (1990) finds that OH 62's humerofemoral index, of which femoral length is a primary contributor, could lie anywhere between that o f modem humans and that of gorillas. In addition, the data from WT 15000g must be treated with some caution because the individual was a juvenile at the time of death (Walker and Leakey, 1993). At this point it is important to note that I am not including neandertals (Homo neanderthalensis) in this data set because, although they have an excellent record by paleontological standards, they may exhibit a locomotor anatomy different from that of the other species of Homo and I do not want to confound the two. In order to avoid the many problems associated with reconstructions of fossil fragments, I have chosen to include in my analysis only those fossil femora and tibiae that either are part of a partial skeleton or include at least one end (usually the proximal) and a substantial portion o f the shaft. The relevant details for the fossils I have selected are shown in Table 2.3.1. Table 2.3.2 shows the femoral and tibial lengths and the body masses of Australopithecus, Homo and Pan. Although most of the fossil data shown in the following table required some reconstruction, the femora of Sts 14 and ER 1500 are fragmentary and are included only because both femora are part of a partial skeleton. Partial skeletons are important because they can inform about the relationship of several osteological dimensions within the same individual. The most important observation that can be made about the data is that they are consistent within genera. For instance, the three australopithecines match each other rather well. As can be seen in Table 2.3.2, femoral length for Australopithecus ranges from 280 to 310 mm while the tibial length estimates are 245 and 250 mm. For Homo,


21

Table 2.3.1 Femoral and tibial samples Australopithecus, Homo and Pan. Taxa A. afarensis A. africanus A. boisei

Specimen ID AL 288-1 Sts 14 KNM-ER 1500

Location Hadar, Ethiopia Sterkfontein, SA Koobi Fora, Kenya

Age (mya) 3.2 2.5-3.0 1.9-2.0

H. habilis H. habilis H. habilis H. erectus H. erectus H. erectus H. erectus H. erectus H. habilis H. erectus H. erectus H. sapiens H. sapiens

KNM-ER 1472 KNM-ER 1481a OH 62 KNM-ER 736 KNM-ER 737 OH 34 Trinil 3 KNM-WT 15000 KNM-ER 3228 OH 28 KNM-WT 15000 modem sample modem sample

Koobi Fora, Kenya Koobi Fora, Kenya Olduvai Gorge, Kenya Koobi Fora, Kenya Koobi Fora, Kenya Olduvai Gorge, Kenya Java Koobi Fora, Kenya Koobi Fora, Kenya Olduvai Gorge, Kenya Koobi Fora, Kenya North America North America

1.9 1.9 1.8 1.7 1.6 ~1 © oo « ^ m is o vi ^ N in ov *1 © m - o t'mm © 2 2 >r' 2 S 10 w"' so" '® '® **■'" rn" “

• s «Tfn © f s Io © m' o» -mo on© c00^ © inr \ © N oJ oOc N t ' -0^ 'otoN©9r ~'

r- oo" ©’ © © ©" ©" ©’ ©’ ©’ ©' ©’ ©" ©' ©" oo' oo' r~- r~ ©' ©' ©' ©’ ©' w>

r25) M ' r ' C o o o N ' t o o e oMNf' N f oNi oNo N ( Nn ' nt on on onoT( S f ^' »i 't © ^ o^ oi no xj


168

Um r - m* © s m 00 0 © NO

m Ki CN *n r-* 0 00 © M 00 CN m °N rn © © 00 V> 0 ©* N Gf 1 1 1 1

o - f l ’ OONa c o Of i O' O' f l i n o o n v i i f l

*s

~I o o p o © o © © o © — —■

0 *T

3

•o * •O

9 9

9 ’ 9 ’ O

9 ' 9 ' Gf

o ’

O

O O

s O ' O '

^ r r - © m r * - ^ P r> ^ , v o ' O r * - \ © v o < N © © < N f n —*©~- - *©soc©\ so m 'oOoN©h © o o0 n 0- o0 s -M- r- iNh M ^ O« ' nh o o—n— - n'0 ^r i ^ f —' o v o o o m m o m —< r- m cN©m IO N ■ io ^ oi o n n in \o © v 0 i« v j c \ cn \ 0 © ' 0 ’ —" CN CN CN CNCN CN CN CN CN —’ —’ o’ o’ — o' o’ o' o’ o’ —' —’ — —’ —’—
m —’ —'—’ o’ o’ o' o' o' o' o' o’ o' o' o’ o' o' o’ o' o’ o’ o' o' o’ o' o' o'

CO B O O O O O O O OOOOOOOOOOO OO O O OO OOO O O—ONOC' — m - £» o oO oO oO oO oO oO O o o o o o o o o O o o O o O o O o e o o o o2 o 2 o' o' o' o' o' o' o' o' o' o' o' o' o' o' o’ o' o’ o' o' o' o’ o’ o’ o’ o’ o'

CJ C — rf r~ m o o o o o o o o o o o o o o o o o o o o o o o o o o

U CN If IO 00 O CN 00

— —

OOOON^'OOOON^^OOOMtOOOO

0s-


&>

55

170

—1 s i r~ o

mm

n

on

n o - o o c N T f v o r ^ o s ■Nf-v-ii/i —' o o o t ' - o o o o m ' * —

— —— c N m m c N — ©

—© — CTNr~moc 0 ' m v —' r N t N t N c s l O O O O O o ’ o ’ o’ o ’ o ’

(

0

9 9 9

— © o 9

—

9 ' o ’ o ’ o ’ o ’ o ' 9 ’ 9 ’ 9'

o ’ o'

s o o o o o o o o o o o ^ O O O O O O O O O O T f - O O O O O O O O O o' o ’ o' o ’ o ’ o' o ’ o ’ o ’ o ’

— r n v » >o v> o o — —• —« — O O O O o ’ o ’

—O s e o t S O \ t S V ) O O v o \ O o O O

. © mvOfNVi © r s t ^ v—c o0 o0t n0o 0t s rO ^Oi O Nv©v © © —~ O O O O O O O O 9

o O O o'

9 ’ 9'

o O O o’

o'

o'

o'

o o o ’ o'

o o o 9* o ’ 9 '

r-'J ^ frn t'-T fv o 0

0

— ts©

' f N f N O O —

0

0

o ’ o'

-

0

9 ’ o'

© 9'

0

0

0

■

9’ 9’ 9’

o o o o o o o r ^ r - t ^ — O p O O p p p t ' i m v O O v — O O O O O O O O — © © © —« o ’ o' © o' o' © © o ’ 9' 9' 9' 9' 9'

iP -nO o—ot SS '«t-CTst^

9'

o’ 9’ 9’ 9’ 9’ 9’

9'

9'

o ’ o'

o ’ o ’ o ’ o ’ o ’ o'

o'

o' o '

o ’ o ’ o'

ooootSTtvooootSTpvoooocs'^-ooo

o ’ o'

o

ts

o ’ o ’ o'

o’

vo

o VI

00

v> rS

t— 00 o’—

N= S'


II e

Appendix E: Derivation of Equations

E.l Derivation of the equations used to compute the displacement of a p o in t After the angular excursions and angular velocities are developed (see Chapters 3 and 4 and Appendix B), the displacement of each joint in the model can be determined. Angles are given in degrees and lengths in meters. All displacement variable names begin with "d" and are followed by the letters representing the (axis) direction and the point of interest.

HAT

HAT Joints: e/1 a/h d/g b/f c Links: ea/ih ad/hg db/gf bc/fc

= head, arm, trunk = = = = =

ball of foot ankle knee acetabulum center of pelvis

= foot = leg = thigh = 1 / 2 of pelvis

Figure E.1.1 Sketch of model indicating joints and links (repeated from 2.3.1 and 3.0.1)

Referring to Figure E. 1.1, the equations for displacements are:


173

0-40% o f stride cvcle:

dxe = l4COs(9foot-180)

dye = dxb+ l3 sin(0 bcyz)

dye = l4 sin(0 fool- 1 80)

d x f = dxc+ l3 sin(0 bcxz)

dxa = 0

d y f = dxc+l3 sin(0 bcyz)

dya = 0

d x g = dxf+l2 sin(0 thigh -9O)

dxd = 1j sin(0ieg-9O)

dyg = dyf-l2 COs(0 th jg h -9O)

dyd = licos(0ieg-9O)

dxh = d xg+ 11sin(0 ieg -9 O)

dxb = dxd-l2 sin(0 tj1jgj1-9 O)

dyh = dyg-1 ] c o s(01e g -9 O)

dyb = dyd-l2 COs(0 thigh-9 O)

dxi = dxh+l4 c o s (0 fo o t- 180)

dxc = dxb+^sinfObo^

dyi = dyh-l4 sin(0 fo o t- 18O)

40-50% of stride cycle:

dxe = 14 dye = 0

All of the other angles are the same as

dxa = dxe-l4 cos(0 foot-l 80)

those for 0-40% of the stride cycle.

dya= dye+l4 sin(0 foot- 1 8 O)

As is apparent in Figure E. 1.1, the heel is on the ground from 0-40% of stride cycle (heel strike to heel-off) and since the right heel is the zero reference point, i.e. all displacements are relative to point a, all other displacements are calculated from that point. The displacement of both e and d can be calculated directly from a. The other displacements are calculated relative to the preceding point in the model in a chainlike fashion. Between


174

40-50% of the stride cycle, the heel begins to rise off the ground, so the toe, point e, becomes the start o f the chain for calculating displacements. E.2 Calculation of the velocity of each point. Velocity is distance moved per unit time; therefore, the displacements calculated from the equations shown in the previous sections can be used to calculate a velocity of each point for each increment of time. I have used 2% of stride cycle as the increment because Winter's movement profiles were given in 2% increments. Total time to complete a stride (tmax) can be calculated from the total distance moved in a stride and the average velocity of the body (represented by the HAT). Total distance moved is simply the difference in x axis displacement between the position of point b (right hip) at time = 0 % and at time = 50% of stride cycle times 2 [dmax = (dxc(0) - dxc(50))*2]. As an example, vax = (dxa(i)-dxa(i-l))/tinc

where: tine = tmax/number of increments

vay= (dya(i)-dya(i-l))/tinc The velocities for all the other points are calculated in a similar manner. E.3 Calculation of Potential Energy Potential energy is the energy associated with position in space and is always related to a reference line, in this analysis, the ground. Potential energy is the weight o f a link times its distance from the ground [PE = mgh]. Since the mass of each of the links in the legs is located at the link's center, displacements for those positions must be developed from the displacement of each end of the link. The mass of the body (HAT) is applied at point c so no additional calculation is necessary. If the right and left legs and the pelvis are treated separately, this gives the following equations where "Ep-" refers to the potential energy and the last letter refers to the body part (right, left or pelvis).


175 Epp = mg(dyc) Epr = mdbg(dyd+dyb)/2+madg(dya+dyd)/2 +maeg(dya+dye)/2 Epl = m£jbg(dyff dyg)/2+ma£jg(dyh+dyg)/2+maeg(dyh+dyi)/2 where:

g = acceleration of gravity m = mass o f HAT (applied at point c) mdb = mass of links db and fg mad = mass of links ad and gh mae = mass o f links ae and hi

E.4 Calculation of K inetic Energy Kinetic energy is the energy of motion and it has two components, rotational (in a circle) and translational (in a straight line). As shown in Eqn. 2.1.2, the equation for one link when the link only rotates in one plane is

KE = ,5mv2 + .5Imco^

where: m = mass of the link v = velocity o f the link Im = mass moment of inertia of the link to = angular velocity of the link

This equation is appropriate for the thigh, leg, and foot but not for the pelvis. The KE equation for the pelvis is KE = ,5mv2 + ^(Imbcyy^bcxz 2 + ^mbcxx^bcyz2) " ^mbcxy^bcxz^bcyz Multiple links can be summed to form equations for the right and left legs and the pelvis. These equations are shown below. Note that subscripts indicate link identifiers while the variables for the HAT are represented by an absence o f subscripts as is detailed in section E.3. Ekr=. 5 *[(macjvadc2 +Ima£i(cDacl)2 )+(maevaec2 +Imae(a)ae)2 )+(mdbvdbc2 +Imdb(a>db)2)]


176 EkI=.5*[(madvghc2+Irna(i(fflgh)2)+(maevhic2+Imae((ahi)2)+(mdbvfgc2+Imdb((0fg)2)] Ekp=.5mvc2 + ^(IjubcyyOJbcxz2 + ^mbcxx^bcyz2) " ^mbcxy^bcxz^bcyz E.5 Calculation of energy change and total energy. Once the potential and kinetic energies have been determined from the equations shown in the preceding sections for the right and left legs and the pelvis at each time increment, then the change in energy can be determined. This change, dE—, is simply the differences between two consecutive time increments. dEpl(i) = Epl(i)-Epl(i-1) dEkl(i) = Ekl(i)-Ekl(i-1) dEtotall(i) = dEpl(i)+dEkl(i)

dEpr(i) = Epr(i)-Epr(i-1) dEklr(i) = Ekr(i)-Ekr(i-1) dEtotalr(i) = dEpr(i)+dEkr(i)

dEpp = Epp(i)-Epp(i-1) dEkp = Ekp(i)-Ekp(i-1) dEtotalp(i) = dEpp(i)+dEkp(i) Changes in energy are only summed for each major component (right and left leg and pelvis) because there can be no energy transfer between the legs and the body. (See section 3.3 for a complete discussion of this issue.) The total energy that must be added to each major component for the complete stride is the summed of all the positive dEtotal-'s. A positive dEtotal- indicates that energy was added to the system while a negative dEtotal- indicates that there was "extra" energy that was dissipated.


177 Esuml = Z dEtotall(i)

when, dEtotall(i) > 0

Esumr = Z dEtotalr(i)

when, dEtotalr(i) > 0

Esump = Z dEtotalp©

when, dEtotalp© > 0

The variation in these three outcome variables as the velocities and configurations change is the crux of this research project. E . 6 Calculation of the mass moments of inertia. The moments of inertia given in Table 3.1.3 were developed in two ways. First, the limb segments were calculated using the formula (NASA, 1971, p. IV-50-51): Im = mass*length*factor

where: Im =

mass moment of inertia for a segment

mass = the segment's mass length = the segment's total length factor = factor developed from cadaver studies Table E.6 .1 gives the relevant values.

Table E.6.1 Mass moments of inertia for limb segments. Configuration modem human

segment

calf (ad/gh) leg (db/fg) foot (ae/hi) australopithecine calf (ad/gh) leg (db/fg) foot (ae/hi)

mass (kg) 3.00 5.64 0.84 1.65 3.10 0.46

length (m) 0.390 0.373 0 .1 1 0

0..265 0.252 0.080

factor .282 .282 .250 .282 .282 .250

Im (kgm2) 0.0363 0.0624 0.00064 0.0092 0.0157 0.00019

The calculation of the mass moments of inertia (Im) for the HAT are more complicated because no simple method exists in the literature for the determining the mass moments of inertia of the HAT. (Whole body moments of inertia do exist, however, and


178 can be used as an upper bound check for this calculation.) Consequently, an approximation based on the definition of the mass moments of inertia must be used. If the HAT were allowed to rotate in all three planes and it was not symmetric in any o f them, six total moments of inertia would be required. Fortunately, only three moments o f inertia are needed, one for rotation in the xz (horizontal) plane, one for rotation in the yz (frontal) plane and a cross product term. The terms for the xz and yz planes (Im^cyy and Imbcxx) are needed because the HAT rotates in both o f these planes, i.e. ffl^cxz and ©bcyz exist. The cross product term (Im^cxy) is necessary because the body is not symmetric about the z axis. Note that the standard nomenclature for mass moment of inertia is "Im ^" for rotation in the yz plane or, in other words, about the x axis. The cross product term is then "Iniyz" because the body is non-symmetric in the yz plane. The formulas for calculating the necessary mass moments of inertia are Inibcxx = J(z 2 + y 2)dm

where: x =

x distance from centroid

Inibcyy = | (x 2 + z2 )dm

y=

y distance from centroid

Imbcxy = J xydm

z=

z distance from centroid

dm = differential segment o f mass While theoretically useful, these formulas require that an equation that describes the shape of the object in 3 dimensions be available which, in this case, it is not. An approximation o f the integral can be determined, however, by dividing the body into small (pseudo differential) elements and calculating each element's mass and distances from the centroid, and, then, summing over the entire body. I used this technique and it is demonstrated below for Imbcyy. Figure E.6 . 1 shows a idealized view looking down on the HAT. Note that this is a schematic and is not drawn to scale. The large rectangular outline represents the body, the smaller interior rectangle the head, and the two small rectangles the arms. The x axis divides the body into symmetric left and right sides while the z axis divides the


179 body into an anterior and posterior portion. The centroid is assumed to be located at the center of the body rectangle.

distance from x axis

21 1 0 1 2l

2 1 0 1 2

3l 2|

distance from z axis

2

1 0

1 0

1 21

1 2

2 1 0 1 2

X --------- ►

2 2 2 2 2

1 1 1 1 1

ol 01 ° ° ol °1 _o|

1 1 1

1

1

2 2 2 2 2

Distances are used for both configurations. z

Figure E.6 . 1 Unfactored distances from x and z axes.

The distances shown Figure E.6 .1 are relative, or unfactored, so that the same values can be used for any body configuration. For modem humans, the z distance values are factored by 47.2 mm/block while for A. afarensis the factor is 28.8 mm/block. For the x distance, one factor is used for both, 53.4 mm/block. The mass that each block represents is shown in Figure E.6.2. A. afarensis has smaller values; although they were approximately the same width (left-right), they were shorter and narrower and, consequently, weighed less.


180 differential mass of each block

1.2 1.7 1.7 1.7 1.2

1.2 1.7 1.7 1.7 1.2

1.6 1.2 1.7 1.7 1.7 1.2 1.6

1.2 1.7 1.7 1.7 1.2

1.2 1.2 1.2 1.2 1.2

X

---------►

0.6 0.9 0.9 0.9 0.6

0.6 0.9 0.9 0.9 0.6

1 0.6 0.9 0.9 0.9 0.6 1

0.6 0.6 0.6 0.6 0.6

A. afarensis

Modem Human

1

0.6 0.9 0.9 0.9 0.6

z

Figure E.6.2 Differential block masses for modern humans and A. afarensis.

mass moment of inertia for each block: 0 . 04|

0.02 0.02 0.01 0.02 0.02

0.02 0.01 0.00 0.01 0.02

0.011 0.02 0.001 0.01 0.00 0.00 0.001 0.01 0.011 0.02

0.02 0.01 0.01 0.01 0.02

X --------------►

0 .04|

z

V

Modem Human sum = 0.41 kgm2

0.01 0.01 0.00 0.01 0.01

0.01 0.00 0.00 0.00 0.01

0.02 0.01 0.00 0.00 0.00 0.01 0.02

0.01 0.00 0.00 0.00 0.01

0.01 0.00 0.00 0.00 0.01

A. afarensis sum = 0.17 kgm2

Figure E.6.3 Mass moments of inertia for modern humans and A. afarensis.

The mass moment of inertia represented by each differential element is obtained by adding the square of the distances shown in figure E.6 .1 and multiplying by the differential mass shown in Figure E.6.2. in accordance with the integral formula for Im^cyy. The total mass moment of inertia is the sum of all the individual blocks. This technique was used to develop the other two moments of inertia (Imfocxx and Im^cxy). All the relevant


181 dimensions required for this analysis are shown in Table E.6.2 while the values used for mass moments of inertia are shown in Table 3.1.3.

Table E.6.2 Body dimensions for modern humans and australopithecines.

stature head breadth head length head height biacromial breadth chest breadth mid shoulder height, sitting bust depth biceps circumference/diameter 1. 2. 3. 4. 5. 6. 7.

Modern Human 1 (mm) 1604 145 184 276 355 2002 580 236 273/59

Australopithecines 1 (mm) 10507 145 2003 1804 355 267 3 535 1446 273/59

NASA (1971) Section HI, pp. 22-58, unless noted otherwise. Decreased to account for waist. Increased over modem humans. NASA*stature ratio [NASA* 1050/1604], Stature-leg length-head height [1050-(265+252)-180]. NAS A* sitting shoulder height ratio [NASA*353/580], McHenry 1991.

One check of these numbers is to make sure that the sum of the differential masses add to the total HAT mass. In all cases the sum of the differential masses is within 5% of the actual value, which for this level of sophistication is acceptable. E.7 Detailed development of link parameters The lengths of the links that represent the body segments in the australopithecine model are derived from AL 288-1 (Tables 2.3.2 and 2.4.1), while those for modem humans are an average of the adult female data presented in Tague (1992) and NASA (1971). The long bone lengths presented in section 2.3 are combined with factors given in


182 NASA (1971) to determine the length of thigh and lower leg link. These factors (Table 3, p. IV-13) convert bone lengths into biomechanical lengths. The biomechanical length takes into consideration the effect o f cartilage and synovial fluid present in the joints as well as the potential offset between anatomical landmarks and joint centerlines. Table E.7.1 gives the bone lengths, factors and segmental (biomechanical) lengths.

Table E.7.1 Determination of long bone lengths. configuration

A. afarensis modem human

bone length (mm) femur (I2 ) 280 414

factor

link length (mm)

0.90 0.90

252 373

bone length (mm) thigh Ol) 245 360

factor

link length (mm)

1.08 1.08

265 390

The total pelvic widths are determined by adding the femoral neck length o f each side to the interacetabular distance as shown in Table 2.4.1. The length of link bc/cf (I3 ) is one half the pelvic width. The length of the foot (I4 ) is the distance from the intersection o f the tibia with the foot to the ball of the foot. I approximate this distance in modem humans as the distance instep length minus the distance from the lateral malleolus to the heel (NASA, 1971). For australopithecines, I used a similar technique. I measured the distance from the posterior edge of the heel impression to the deepest part of the ball of the foot in the three best preserved Laetoli footprints (Jones 1987, Fig. D. lb-d, footprints G-l-33, G-l-35, and G-l-36). I averaged these values to obtain an instep length for australopithecines. From instep length, I subtracted the ratio of the stature of AL 288-1 to my modem human female times the distance from heel to lateral malleolus in modem


183 humans [foot length aa = instep aa - (stature AL 288-1/ stature modem human)*distance heel to malleolus]. Table E.7.2 summarizes the calculations for I3 and I4 .

Table E.7.2 Values for determination of I3 and I4 .

pelvic width femoral neck length h

mm mm mm

instep length heel to malleolus length

mm mm mm

australopithecine 115 47 105

modern human 124

120

170 60

40 80

68

130

110


184

Patricia Ann Kramer 464 Crockett St. Seattle, WA 98109-2133 Home Number: (206) 286-6698 email: [email protected]

Current Position:

Department o f Anthropology Box 353100 Seattle, WA 98195-3100

Sept. 1997-present: Instructor, Intra-American Studies and Social Sciences, Shoreline Community College, Seattle, WA Anthropology 201: Introduction to Physical Anthropology. March 1998-present: Instructor, Department of Anthropology, University of Washington, Seattle, W A Biological Anthropology 201: Introduction to Biological Anthropology.

Work Experience:

June 1997-Sept 1997: Instructor, Department of Anthropology, University ofWashington, Seattle, W A Biological Anthropology 487: Human and Comparative Osteology. Mar. 1997-Dec. 1997: Instructor, Department of Anthropology, University ofWashington, Seattle, W A Biological Anthropology 499: Independent Research—Forensic Anthropology. Oct. 1993-June 1997: Research/Teaching Assistant, Department of Anthropology, University ofWashington, Seattle, WA. Courses taught include the laboratories for Introduction to Biological Anthropology and Human Fossils and Evolution. Oct. 1990-Oct. 1993: Lead Structures Engineer, The Boeing Company, Seattle, WA: responsible for the stress analysis of primary floor structure on 777 new aircraft. Oct. 1988-Oct. 1990: Stress Engineer, LTV Corporation, Dallas, TX: detailed stress and durability analysis of wing skins and spars on B-2 bomber. Oct. 1987-Oct. 1988: Senior Structures Engineer, The Colley Associates, Architects and Engineers, Corpus Christi, Texas: industrial plant design and analysis and extensive drawing review. June 1984-Oct. 1987: Structures Engineer, E-Systems, Greenville Division, Greenville, Texas, stress analysis and drawing review of major structural modifications of existing aircraft including MC-130H, C-141, and F-4


185 Education:

BSCE with honors University of Texas at Austin May 1984 Ph.D. University of Washington June 1998 Title: LocomotorEnergetics and Leg Length in Hominid Bipedality Licensed Professional Engineer in the State of Texas

Teaching Experience:

Human and Comparative Osteology (1 quarter)—instructor Introduction to Physical (Biological) Anthropology (3 qtrs)—instructor Introduction to the Primates (1 quarter)—instructor Independent Research in Forensic Anthropology (3 qtrs)—instructor Hominid Fossils and Evolution ( 6 quarters)—teaching assistant Introduction to Biological Anthropology (1 qtr)—teaching assistant Introductory Engineering Statistics (1 semester)—teaching assistant

Submitted Manuscripts:

American Journal of Physical Anthropology (in review). The Costs o f Human Locomotion: M aternal Investment in C hild Transport. submitted for review December 1996; reviews received July 1997; resubmitted December 1997.

Manuscripts In Work:

M odeling the Locomotor Energetics o f E xtinct Hominids. to be submitted to the Journal of Experimental Biology. Locomotor Energetics and Leg Length in H om inid Bipedality. to be submitted to the Journal of Human Evolution.

Presentations:

American Association of Physical Anthropologists. The locomotion o f Australopithecus afarensis: a dynamic analysis and comparison with modem humans, poster presentation April 1998. American Association for the Advancement o f Science. Was Lucy's Gait Inefficient? A M ethodfo r Evaluating the Locomotor Efficiency o f E xtinct Hominids. poster presentation February 1997; honorable mention. American Association of Physical Anthropologists. The Costs o f Human Locomotion: M aternal Investment in Infant Carrying. oral presentation April 1996.


186 Honors and Awards:

National Merit Scholar Alpha Lambda Delta (freshman honor society) Tau Beta Pi (national engineering honor society) Chi Epsilon (national civil engineering honor society) 5 Outstanding Achievement Awards in Engineering from Boeing Co. Honorable Mention in the 1997 Student Poster Competition of the national meeting of the American Association for the Advancement of Science (AAAS)

Departmental Service:

Graduate student representative to the Graduate and Professional Student Senate Graduate representative on the departmental Human Subjects Review Committee Graduate representative on the Faculty Search Committee Chair, Graduate Student Submissions Committee, Chimaera Research Forum

Professional Affiliations:

American Association of Physical Anthropologists American Association for the Advancement of Science Professional Engineer in the State of Texas


IMAGE EVALUATION TEST TARGET ( Q A - 3 )

1.0

|

L_

* l.l

2£

^0

H

25

UlM 1 2.2

1 2

I

L. ^

■— 141

KUu

1.8

1.25

1.4

1.6

150m m

I M /4 G E . I n c 1653 E ast Main Street Rochester. NY 14609 USA Phone: 716/482-0300 Fax: 716/288-5989 0 1993. Applied Image. Inc.. All Rights R eserved
