Russell 2012

RESEARCH ARTICLE

Computer models offer new insights into the mechanics of rockclimbing

SHAWN D. RUSSELL1, CHRISTOPHER A. ZIRKER1, & SILVIA S. BLEMKER1,2,3,4

1Department of Mechanical & Aerospace Engineering, University of Virginia, Charlottesville, VA, USA,2Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA, 3Department of Radiology,

University of Virginia, Charlottesville, VA, USA and 4Department of Orthopaedic Surgery, University of Virginia,

Charlottesville, VA, USA

(Received 7 April 2012; accepted 3 October 2012)

AbstractThree computer models of varying complexity were developed in order to investigate the kinematics, kinetics, muscleoperating ranges, and energetics of rock climbing. First, inverse dynamic models were used to investigate the joint angles andtorques used in climbing and to quantify the total mechanical work required for typical rock climbing. Climbing experiencewas found to have a significant effect on the kinematics used in climbing; however, there were no significant differences inmechanical work. Second, a musculoskeletal model of the whole body was developed, this model combined with thekinematic data was used to analyze the operating ranges of the upper and lower limb muscles during climbing. In general, theexperienced climbers employed kinematic motions that corresponded to muscle fibers used for climbing operating muchcloser to their optimum length than the kinematics of inexperienced climbers. Third, a forward dynamic model wasdeveloped to predict the metabolic goal of climbing. The results of this model suggest that an experienced climbing styleminimizes the fatigue of muscles while an inexperienced climbing style minimizes the total joint torques generated.

Keywords: climbing, biomechanical modeling, work, efficiency, optimum climbing strategies, inverse dynamics

Introduction

Rock climbing poses unique demands on the human

musculoskeletal system. In standard walking, the

lower body is primarily responsible for locomotion

and support; however, in climbing, both the upper

body and lower body provide both locomotion and

support. Climbing entails significant motion in the

vertical plane and is not primarily limited to the

horizontal motion typically associated with walking

(McIntyre, 1983). Climbing results in motion

mechanics that are drastically different from those

the body typically performs in everyday activities.

These unique mechanics and energetics are currently

poorly understood. An advanced understanding of

climbing mechanics will elucidate new methods for

training which will help decrease the loads during

climbing, reducing the chance of injury; increase the

efficiency of climbing, reducing the energy needed to

climb; and offer a deeper understanding of human

motor learning strategies and physical adaptation

development for atypical motions.

To date, research regarding the kinematics and

dynamics of rock climbing has focused on analysis of

the strategies the climbers use to maintain stability

while holding a static posture during climbing.

Marino and Kelly (1988) reported that as climbing

slopes increased from 608 to 1208 (908 being vertical),

the percentage of body weight supported by the

upper body increased from approximately 20% to

40%. Others have investigated the dynamic changes

in the support forces, applied through the hands and

feet, when transitioning from a static quadrupedal

state (four-limb support) to a static tripedal state

(three-limb support) by removing a support foot

(Quaine, Martin, & Blanchi, 1997a; Quaine &

ISSN 1934-6182 print/ISSN 1934-6190 online q 2012 Taylor & Francis

http://dx.doi.org/10.1080/19346182.2012.749831

Correspondence: S.D. Russell, Department of Mechanical & Aerospace Engineering, University of Virginia, 122 Engineers Way, P.O. Box 400746,

Charlottesville, VA 22904-4746, USA. E-mail: [email protected]

Sports Technology, AugustNovember 2012; 5(34): 120131

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Martin, 1999). Although these studies attempted to

limit the center of mass (CoM) motion resulting in

static trials, they found that to maintain balance,

climbers began the transfer of reaction forces away

from the limb to be removed prior to initiating the

transfer from a quadruped to a triped state. Others

have found similar balance strategies employed when

varying wall slope (Noe, Quaine, & Martin, 2001)

and for various optimal and suboptimal climbing

postures (Quaine, Martin, & Blanchi, 1997b; Testa,

Martin, & Debu, 1999). However, each of these

methods limited the climber to static positions, and

none have calculated the joint loads associated with

the climbing moves.

Previous work regarding the efficiency of rock

climbing has been focused on comparing the

anthropometry and physiology of climbers and non-

climbers. This work has demonstrated that climbers

are typically small in stature with elevated strength to

body mass ratios (Grant, Hynes, Whittaker, &

Aitchison, 1996; Watts, 2004). Aerobic power

analysis has shown that climbers tend to have lower

oxygen consumption compared with the mean

endurance athlete (Booth, Marino, Hill, & Gwinn,

1999; Mermier, Janot, Parker, & Swan, 2000),

suggesting that their aerobic fitness level is consistent

with one required for quick recovery from high

intensity effort. Mermier, Robergs, McMinn, and

Heyward (1997) found that oxygen consumption of

elite rock climbers on moderate terrain is equivalent to

running at 2.6 ms21. However, climbing is a

stochastic activity with spurts of action interspersed

with periods of resting/static support. It is, therefore,

difficult to measure a steady-state VO2 consumption

rate, and the reports of mean VO2 range widely from

18.6 to 43.8 ml(kgmin)21, for similar climbing

conditions (Billat, 1995; Mermier et al., 1997;

Watts, Daggett, Gallagher, & Wilkins, 2000).

Although these measurements offer insight into

individual climbers and their climbing strategies, it

is difficult to apply those strategies to the general

population due to the effects of individual condition-

ing, rest to climb ratio, and averaging.

Computer models have the potential to offer

insights into complex human motions. Previously,

simple forward dynamics models with limited degrees

of freedom have been used to demonstrate multiple

complex properties of walking, including stability and

control of joint angles (Garcia, Chatterjee, Ruina, &

Coleman, 1998; Goswami, Espiau, & Thuilot, 1996;

Morgan, Mochon, & Julian, 1982), and also the

efficiency of motion due to the distribution of joint

torque (Kuo, 2002). In addition, more complex

models are often used in both forward and inverse

dynamic simulations of human movement. These

inverse models have been used to quantify joint

torques and forces, muscle mechanics and motor

control of human walking (Arnold, Ward, Lieber, &

Delp, 2010), running (Edwards, Taylor, Rudolphi,

Gillette, & Derrick, 2010), and jumping (Anderson &

Pandy, 1999). However, these models have primarily

focused on motions supported entirely by the lower

extremity and were not developed to include the

upper extremity as a part of the support and control of

locomotion.

In this paper, we describe our recent work using

three computer models of climbing with varying

complexity to answer a range of questions regarding

the mechanics and energetics of climbing. The first

inverse dynamics model was developed to quantify

the kinematic, kinetic, and energetic differences

between experienced and inexperienced climbing

motions. The second musculoskeletal model was

used to evaluate how differences in these kinematic

strategies affect muscle force-generating capacity.

Finally, the third forward dynamic model was

developed to investigate the energetic goals of

differing strategies for rock climbing. Each of these

models was created based on a set of human climbing

motion capture experiments that made use of a

custom climbing wall instrumented with six force

plates.

Methods

Human climbing experiments

Twelve healthy participants participated in this study,

including seven inexperienced climbers and five

experienced climbers, where experienced was defined

as comfortable climbing 5.10 on the YosemiteDecimal System (5.10 YDS, VII-UIAA, or 20Australia). The inexperienced climber group con-

sisted of five males and two females averaging

26.7 ^ 5.0 years of age, 177.1 ^ 5.7 cm in height,

and 75.3 ^ 9.1 kg in mass. The experienced climber

group included two males and three females averaging

29.8 ^ 8.6 years of age, 169.8 ^ 9.4 cm in height,

and 62.0 ^ 9.4 kg in mass. All tests were conducted in

the Motion Analysis and Motor Performance Lab-

oratory at the University of Virginia. Participant

consent was approved by the University of Virginias

Human Investigation Committee and was obtained

for all participants.

Participants were given up to 20 min of free

climbing time prior to data collection to acclimate

themselves to the climbing wall. They were then

instructed to climb the wall (approximately 35 cm

steps) using their self-selected climbing strategy.

Participants were instructed to ascend then descend

the climbing wall three times per trial, pausing briefly

in a four-point stance when changing directions.

Kinetic data were collected using a climbing wall

instrumented with six custom force plates (Bertec,

Mechanics of rock climbing 121

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Figure 1. Experimental set-up used in data collection, including the instrumented climbing wall with typical grip placement.

S. D. Russell et al.122

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Columbus, OH, USA), each with seven possible

grip-mounting locations (Figure 1). 3D kinematic

data were collected using a six-camera Vicon Motion

Analysis System (Oxford Metrics, Oxford, UK) at

120 Hz, and a modified full-body Plug in Gait marker

set, 35 markers. At least three ascents were

performed and measurements were averaged for

each trial, with the participants moving from one

four-point posture to another four-point posture.

Analyzed data began at the initiation of movement

from the lower grip set and ended when the climber

reached a neutral posture on the upper grip set.

Inverse dynamic model

To quantify the kinematics and joint kinetics of

climbing, a 3D, 17 segment, 16 joint, participant-

specific model (Figure 2) was created for each

participant in MSC.Adams, using the LifeMod plug-

in (Biomechanics Research Group, San Clemente,

CA, USA), from individual anthropometric data

(age, weight, height, and gender). The 17 model

segments included the following: head, neck, upper

torso, central torso, lower torso, upper arms (2),

lower arms (2), hands (2), upper legs (2), lower legs

(2), and feet (2) (Figure 2). The segments physical

properties were defined using the Generator of Body

Data (GeBOD) database (Cheng, Obergefell, &

Rizer, 1994). The 16 joints were each specified as a

ball joint with three degrees of freedom; however, the

elbow and wrist joints are reduced to two axis and the

knee joints are reduced to only one axis.

Development of this model in the MSC.Adams

environment facilitated the application of external

forces (wall contacts) from two sources: (1) direct

application of experimentally measured forces (Ber-

tec force plates) and (2) the predictive modeling of

wall contact forces. Wall contact, from grasping and

releasing climbing grips, was also modeled in the

MSC.Adams environment. For simulations

described in this study, model inputs were the

measured marker positions exported from VICON to

the LifeMod model and measured contact for data

and position, and outputs based on inverse kinematic

and dynamic models were joint angles, forces, and

torques. From these parameters, we can calculate

energetic parameters as described below. An advan-

tage of this model over others (Willems, Cavagna,

& Heglund, 1995) is that it facilitates the quantifi-

cation of energetics down to the level of each joint

degree of freedom.

Total work, Wtot, is the sum of the external work

Wext, work done to move the system CoM, and the

internal work Wint, work done to move the body

segments about the CoM:

W tot W int W ext X

i

jtiDuij; 1

W ext X

i

jFjDSj j; 2

where ti is the torque at joint i, ui is the angle of joint i,Fj is the composite force applied to the wall in the jth

cardinal direction, and Sj is the composite body CoM

displacement in the jth cardinal direction. All

mechanical work data presented in this study have

been normalized by climber mass and the vertical

distance traveled, J(kgm)21.

Musculoskeletal model

The second musculoskeletal model was similar to the

first in degrees of freedom and was developed in the

Opensim environment. This full-body model

(Figure 3) combines previously developed models

of the upper extremity (Holzbaur, Murray, & Delp,

Mono

Colo

Figure 2. Three-dimensional inverse dynamics model utilized for

inverse dynamic simulations and work calculations.


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2005) and lower extremity (Arnold et al., 2010). The

combined model includes 112 independent muscles

(54 in the lower extremity and 58 in the upper

extremity). Muscles that cross only the wrist and

finger joints were excluded from the upper extremity

model to reduce computation time and simplify data

analysis. Measured motion data were used as input

for the inverse kinematic simulations, which resulted

in muscle parameters for each movement pattern as

the output.

Of particular interest are the fiber lengths of each

muscle as the participants perform their climbing

task. Muscle fiber length is directly related to skeletal

kinematics, and the maximum force generated by a

muscle is a function of fiber length (Zahalak &

Motabarzadeh, 1997). This analysis allows one to

determine how chosen climbing kinematics may

affect the amount of available muscle force being

used in climbing and the amount of strength in

reserve. This has obvious implications for injury

prevention, training, and also may have implications

on the efficiency of force generation.

Forward dynamic model

A third, 2D sagittal plane, model with five degrees of

freedom was created using Adams/View (MSC.Soft-

ware Corporation, Santa Ana, CA, USA) to mimic the

Figure 3. A full-body musculoskeletal model was used to

determine muscle behavior during climbing.

Figure 4. Forward dynamic climbing model created in

Adams/View. Actuators (red arrows) and joints at contact points

(blue arrows) are shown (Colour online).


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sagittal plane motion which occurs during the

standing/pulling phase of climbing (Figure 4). This

model capable of both inverse and forward dynamic

simulations was developed to predict the joint torques

required for optimum efficiency of a desired climbing

trajectory, given a specified cost function. The model

consists of seven rigid bodies linked together by

revolute joints. The seven bodies represent the foot,

shank, thigh, torso/head, humerus, forearm, and hand

while the joints between segments represent the ankle,

knee, hip, shoulder, elbow, and wrist. The torso

segment includes a rigidly attached circular body to

represent the head and to maintain accurate

distribution of mass between the segments. Each

segment of the model is scaled based on the

participant-specific anthropometry while the masses

and (CoM) locations of each of the segments were

chosen based on normalized values in the literature

(Winter, 1990).

For this model, two simplified (sagittal plane only)

kinematic and CoM positioning strategies for the

ascension phase (standing/pulling up) of climbing

were analyzed (Figure 5).

(1) Experienced style: Elbows extended, CoM further

away from the wall.

(2) Inexperienced style: Elbow bent, CoM close to the

wall.

Matlab-MSC.Adams co-simulation routines (Zirker,

2011) were used with this model to calculate the joint

torques required to perform these movements. This

was done using two solution methods: first using

measured wall reaction forces and inverse dynamics

to calculate the actual joint moments used by the

climber, and second using optimization routines for

forward dynamic predictive simulations. The second

solution method employed Matlab-based SQP

optimization algorithms to calculate the optimum

joint torques required to reproduce the reference

kinematics.

For optimization, three cost functions that

characterized the efficiency of the climbing model

in unique ways were implemented. The first cost

function was the sum of total mechanical work done

by each joint, as described in the inverse dynamics

model. The second cost function was the sum of the

square of the joint torques (Tsqr). The third cost

function was the sum of the square of the normalized

joint torque (Tmax), where the torque developed by

each muscle group is normalized by the maximum

isometric joint torque. These values have been shown

to be representative of the efficiency of individual

muscle groups to do work. The maximum isometric

torques were found in the literature for the

lower extremities (Arnold et al., 2010), shoulder

(Holzbaur et al., 2005), elbow, and wrist (Holzbaur,

Delp, Gold, & Murray, 2007). The trunk and wrist

muscles were not included in the Tmax calculations.

This was due to the limited data regarding

maximum isometric torques related to our trunk

joints, and the small values of wrist torque and

associated noise.

For comparison purposes, all results were normal-

ized by the inverse dynamic solutions of an average

climb. Total work is not dependent on the number of

simulated time steps. However, Tsqr and Tmax values

were dependent on the climbing duration, so these

values were also normalized by the number of

discretely simulated steps for each simulation.

Statistics

Repeated measures ANOVA were performed to

determine any differences between the climbing

styles. To quantify differences between performed

Figure 5. Schematic detailing the kinematics of each climbing style over the course of a single climbing stride.


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tasks, Students paired t-tests (two-tailed) were used.

Data were considered significant for p , 0.05.

Results

Motion capture measurements of climbing demon-

strated that the joint kinematic trajectories varied

greatly both between climbers and between trials for

individual climbers. However, the general climbing

patterns used were similar to those reported for

ladder climbing (Armstrong, Young, Woolley, Ash-

ton-Miller, & Kim, 2009; Hammer & Schmalz,

1992; McIntyre & Bates, 1982; McIntyre, 1983).

These climbing patterns included diagonal and

lateral gait, coordinated movement of the contral-

ateral arm and leg, and the collateral arm and leg,

respectively. Each climbing style had a temporal

pattern of two beats, concurrent motion of limbs, or

four beats, with slight delay between coordinated

limb motions. In addition, we found some climbers

employed a strategy not reported in ladder climbing.

These strategies, leading limb climbing, employed

four distinct movements (four beat motion) where

the climbing gait was initiated with either, the

reaching up with both hands followed by stepping

up with both feet, or stepping up with both feet then

reaching up with both hands.

Generally the experienced group of climbers used

a different kinematic strategy than the inexperienced

climbers. Experienced climbers maintained a posture

with a more extended elbow and flexed knee

compared to inexperienced climbers (Figure 6).

These differences in climbing kinematics can be seen

in the differing joint force trajectories of a typical

climb from each group (Figure 7). The result of these

kinematics is that, contrary to the common assump-

tion that experienced climbers tend to keep their

bodies close to the climbing surface to reduce loads,

the experienced climbers climbed with their CoM

farther from the wall compared to the inexperienced

climbers (Figure 8).

Climbing requires substantially more mechanical

work than walking: climbing in our study typically

required over 10 times more work than walking;

total mechanical work for climbing was 18.0^

2.2 J(kgm)21 compared to the total mechanical

work for healthy walking which has been previously

reported to be 1.02.0 J(kgm)21 (Mian, Thom,

Ardigo, Narici, & Minetti, 2006; Russell, Bennett,

Sheth, & Abel, 2011; Willems et al., 1995). Despite

the different kinematic strategies employed by the

experienced and inexperienced climbers, there were

no significant differences in the work done between

the groups. Of the work done in climbing, Wextrepresented 62.2 ^ 6.3% of the total work, which is

similar to normal walking where the mean contri-

bution of Wext to Wtot is 55% (Willems et al., 1995).

Further analysis showed the distribution of Wtot done

by sections of the body was upper body

36.7 J(kgm)21, trunk 12.4 J(kgm)21, and lower

Figure 6. Comparison of a representative climbing stride, experienced (dark blue) and inexperienced (orange) climbers. As shown above,

each climber stepped up with the left foot followed by the right, then stood/pulled up followed by reaching up with the left then the right hand.

Joint angles (left) and torques (right) are shown for the ankle and knee joints (Colour online).


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body 50.9 J(kgm)21, and experience had no

significant effect.

Analysis of the musculoskeletal model demon-

strated that the kinematic movement patterns resulted

in differences in operating ranges of muscles during

climbing, between the experienced and inexperienced

climbers. The force generating capacity of a muscle

fiber is a function of the fiber length (background of

Figure 9) where optimum fiber length corresponds to

the length of maximum force generation (Zajac,

1989). Normalized fiber lengths were found to vary

between groups (Figure 9). Experienced climbers

used climbing strategies that kept the operating fiber

lengths of the biceps brachii closer to their optimal

fiber lengths than the inexperienced climbers. Con-

versely, the inexperienced climbers used strategies in

which the triceps brachii operated closer to its

optimum fiber length.

Using the third model to explore which parameters

climber might be trying to minimize, the efficiency

Figure 7. Kinematic differences between the experienced (dark blue) and inexperienced (orange) were more pronounced in the upper

extremities. Differences between the elbow and knee, minimum, mean, and maximum, joint angles are shown. 08 represents joint neutral

(normal posture in extension) (Colour online). *p , 0.05, **p , 0.01, and ***p , 0.001.

Figure 8. Distance of climbers CoM from the wall in normal

climbing, experienced (dark blue) and inexperienced (orange)

climbers. Minimum, mean, and maximum distances reported over

onestride (Colouronline). *p , 0.05,**p , 0.01, and***p , 0.001.


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measures, work, Tsqr, or Tmax. We found the relative

efficiency of each climbing style (Figure 5) varied

depending on the cost function. Calculations from

actual joint torques used in each of the two desired

climbing trajectories showed that experienced climb-

ing strategy (straight arms) was the most efficient

for all efficiency quantities (Figure 10). More

interestingly, optimization of the joint torques

resulted in kinetics with increased efficiency

(decreased values of efficiency quantities) for all

simulations conducted except for the Tmax value for

the experienced climbing strategy which remained

nearly the same as the inverse dynamic calculation.

This may indicate that Tmax is a quantity that

experienced climbers are minimizing through

training.

Figure 9. Minimum,mean, and maximum fiber lengths of experienced (dark blue) and inexperienced (orange) climbers are identified by asterisks

or circles depending on significance of the differences between the two groups (Colour online). *p , 0.05, **p , 0.01, and ***p , 0.001.

Figure 10. Total costs for inverse dynamic (measured) and optimized (simulated) joint torques for the experienced (dark blue) and

inexperienced (orange) climbing styles. Note that the inverse dynamic Tmax for the experienced climbing style does not reduce with

optimization (Colour online).


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Discussion

The three models presented here provide a new

paradigm for the analysis of the kinematics, kinetics,

efficiency, and control of dynamic rock climbing.

Here, these models have been used to quantify differ-

ences between experienced and inexperienced clim-

bers. The first model showed that the experienced

and inexperienced climbers used different joint

kinematics at the elbow and knee when climbing.

This resulted in differing CoM trajectories, but no

difference in the total mechanical work done by each

group. The second model depicts how the elbow

kinematics employed by the experienced and

inexperienced groups facilitate greater maximum

force generation in the biceps brachii (elbow flexion)

and triceps brachii (elbow extension), respectively.

Simulations from the third model show that climbers

may use different physiologic goals when climbing,

inexperienced climbers minimize the magnitude of

force they develop in climbing, Tsqr, whereas

experienced climbers minimize magnitude of force

generated relative to their maximum force generating

capacity, Tmax. Each model has been developed and

implemented to further our knowledge about a

unique aspect of climbing.

Kinematic differences between groups lead to

experienced climbers maintaining their CoM farther

from the climbing surface than the inexperienced

climbers (Figure 8). Zampagni, Brigodoi, Schena,

Tosi, and Ivanenko (2011) reported similar differences

between the CoM position of experienced and

inexperienced climbers. This was unexpected as the

generally accepted method for efficient climbing is to

minimize the distance of the CoM to the wall, thus

reducing the increased load due to the increased CoM

induced moment. This may be due to the size of the

grips used in these studies, both used large easy to hold

grips allowing for the distribution of force across the

entire hand; expert climbing routs often incorporate

small grips where few and occasionally only one finger

is used to support the climbers load. In these cases, the

added load caused by an increased CoM couple may be

the difference in a successful climb or a fall. In cases of

climbing with reduced grip size, studies may find that

experienced climbers begin to move their CoM closer

to the climbing surface. In addition, the kinematics

used in climbing result in an energy-intensive method

of locomotion. This is evident when the energy cost of

climbing are compared to the energy required for

typical bipedal walking on level ground (Mian et al.,

2006; Russell et al., 2011; Willems et al., 1995).

However, it is interesting that the total mechanical

work done for experienced and inexperienced climbers

was not different despite the varying kinematic

approaches used by the two groups, and the qualitative

differences observation in their energy levels at the end

of data collection.

In climbing, the elbow contributes to the vertical

motion in the upward direction by developing a

flexion moment. When overlaying the operating

ranges of the normalized fiber lengths of the biceps

brachii (primary elbow flexor), developed using the

second model, on the normalized forcelength curve

of muscle, it is apparent that the different kinematics

used shifting the operating length of the muscle fibers

closer to optimal fiber length for the experienced

climbing group (Figure 9). The forcelength curve

represents the maximum available force generation of

the muscle at full activation. Muscles operating at or

near the peak are able to generate much more force

per activated fiber than one operating below the peak

(Murray, Buchanan, & Delp, 2000), which would

theoretically result in a more metabolically efficient

development of joint torque. Thus, although doing

the same amount of work as the inexperienced

climber, the experienced climber may employ

climbing kinematics that put the muscles used in

climbing closer to their optimum fiber lengths,

allowing them to do that work with more efficiency

and with more force available in reserve.

It is generally accepted that when humans move we

do so with an objective of reaching a destination or a

goal while minimizing some quantity. Although many

parameters are likely included in this minimized

quantity, i.e., distance, metabolism, pain, boredom,

and weather, we often simplify it to only include

some measure of energetics, such as work, force

generation Tsqr, or fatigue Tmax. Our simulations

using the third model indicate that the experienced

climbers employed a climbing strategy that mini-

mized the energetic quantity of Tmax. Tmax represents

the percentage of the total available muscle force used

in climbing and has been related to muscle fatigue

(Ackermann & van den Bogert, 2010). This would

indicate that experienced climbers have learned that

fatigue is the limiting factor when climbing. However,

the inexperienced climbing strategy was most efficient

when the Tsqr value was used as the cost function,

indicating that the inexperienced climbers are not

worried about fatigue as much as they are about the

metabolic cost of generating muscle force (Umberger

& Rubenson, 2011).

When the results are combined, the three models

presented here are capable of offering a broad picture

of how successful climbing is achieved, and the role

of experience in developing climbing style. However,

the models in their current forms have limitations.

The first two models do not incorporate muscle co-

contraction, the simultaneous contraction of agonist

muscle pairs about a joint often employed to increase

the stability of a joint often when learning new

movements. The inclusion of co-contraction would


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likely result in higher work numbers for all climbers,

the current model reports the net work done at a joint

while the actual work would include both the positive

and negative work done by antagonist muscle. We

hypothesize that inexperienced climbers would have

a higher level of co-contraction, thus increasing the

differences in work between groups. In the second

model co-contraction may also result in changes in

muscle length, co-contracting muscles would

increase the net force on a muscle that may result

in increased stretch of the muscle tendons and

shortening of the muscle belly. Finally, the kin-

ematics of the third model were fixed while the joint

torques were optimized based on a given cost

function. Relaxing the joint kinematics constraints

may allow the model to be useful for the prediction of

better, reduced work, peak loads, reaction forces,

etc., climbing modalities. The accuracy of Tmaxresults was limited by the use of published average

muscle volumes. Previous work has shown that

experienced climbers tend to have a smaller and

more compact physique compared to inexperienced

climbers that may manifest in the difference between

muscle volumes in the two groups.

This work provides a basis for comparison for any

future climbing studies that analyze joint kinematics

or make quantitative comparisons between experi-

enced and inexperienced climbers. Future studies

should investigate whether climbing kinematics in

general have an effect on work done. In addition, the

models and techniques developed here should be

used to elucidate the differences between how and

where (joint specific) the experienced and inexperi-

enced climbers generate the work done in climbing.

This would allow us to better tailor training

regiments to increase the efficiency of the climber,

and more importantly it would allow us to under-

stand the increased loads due to various climbing

strategies, increasing our understanding of where

and when injuries may occur. This may help to

understand the overrepresentation of injuries to the

upper body reported in sport climbers (Peters,

2001). We are currently incorporating MR imaging

and climber-specific muscle volumes into the models

to increase the fidelity of the effects of musculature

on climbing movements. This forward dynamic

model demonstrates that simple models can offer

unique insights into human movement. This paper

described the use of three simple cost functions;

however, the model is developed to allow the

addition of other more complex cost functions for

optimization. In addition, the kinematics of this

model were constrained as an input; however, these

constraints can be removed to allow the model to

optimize both joint torques and kinematics. Such

simulations could offer even more information on

how climbers choose their climbing strategies and

how those choices change with experience.

Conclusion

Rock climbing is increasing in popularity both as a

competitive sport and as an outdoor adventure

activity. With this increase in popularity, little has

been done to investigate the biomechanics of

climbing. The energetics and mechanics of climbing

are complicated. This paper demonstrates how

models can provide new insights into the complex-

ities of climbing mechanics and energetics, which

would not be achievable through experiments/obser-

vation alone. These new insights can help us to better

understand why we choose specific climbing kin-

ematics. In addition, they may lead to new more

efficient climbing and training strategies that mini-

mize injury risk while maximizing climbing ability.

Acknowledgements

The authors would like to thank the staff at the

Motion Analysis and Motor Performance Lab,

KCRC, at the University of Virginia. This work was

funded by the DARPA-DOD Z-Man Program.

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