Table Of Content2006 (2007). The Journal of Arachnology 34:627-633
MECHANICAL ENERGY OSCILLATIONS DURING
LOCOMOTION IN THE HARVESTMAN
LEIOBUNUM VITTATUM (OPILIONES)
Andrew T. Seesenig: Department of Entomology, University of Maryland, College
Park, Maryland 20742=4454 USA. E-mail: sensenigC®wam.umd.edu
Jeffrey W. Shultz: Department of Entomology, University of Maryland, College
Park, Maryland 20742-4454 USA
ABSTRACT, The long legs, compact body and hanging posture ofmany harvestmen are unique among
terrestrial animals, but no quantitative analyses of locomotion have been conducted to determine if this
extreme morphology is associated with novel mechanisms of locomotion. Here we have undertaken a
three-dimensional kinematic analysis ofrunning Leiobunum vittatum (Say 1821) using field-by-field anal-
ysis ofhigh-speed video. The center ofmass ofharvestmen was found to undergo vertical and transverse
displacements of unprecedented magnitude, but the pattern of displacements was consistent with those
predicted by general models of energetic efficiency and dynamic stability of pedestrian locomotion. Be-
causethese models assume substantialroles forelastic energy storagein legelements, elasticityisprobably
an important component ofthe locomotor mechanism in harvestmen, and we identify two skeletomuscular
elements as possible springs.
Keywords^ Kinematics, elastic mechanisms, running, leg springs
Many harvestmen have exceptionally long forward velocity of the center of mass occur
legs, compact bodies and an ability to move at roughly twice the frequency of fluctuations
rapidly on structurally complex horizontal and in the transverse (lateral) velocity, a pattern
vertical surfaces. Yet, the kinematics of these consistent with that predicted by the lateral
common and familiar animals has never been leg-spring model, which invokes elastic leg el-
described quantitatively let alone compared to ements as a mechanism of passive (non-re-
that of more well-studied arthropods and ver- flex) stabilization (Kubow & Full 1999;
tebrates. Here we describe locomotion of a Schmidt & Holmes 2000a, b; Schmidt et al.
common “daddy longlegs,” Leiobunum vit- 2002). These findings suggest that the legs of
tatum (Say 1821), by examining the three-di- harvestmen act as springs in both the vertical
mensional kinematics ofanimals running on a and transverse axes that provide energetic ef-
smooth, horizontal surface. We conclude that ficiency and stability, respectively.
harvestmen use the same basic locomotor
METHODS
mechanisms as other pedestrian animals, al-
though their unusual morphology significantly Kmematics,—Leiobunum vittatum {n = 6
amplifies the sinusoidal vertical andtransverse males, mass 50 ± 3 mg) (all values are mean
displacements ofthe body during locomotion. ± SE unless otherwise noted) were captured
Specifically, we find that forward kinetic en- in a wooded area in College Park, Maryland,
ergy fluctuates in phase with potential energy USA in August 2002 and were used in ex-
as predicted by the spring-loaded inverted- periments within 24 h. Voucher specimens
pendulum model, which maintains that elastic were deposited in the Denver Museum ofNa-
energy is stored at one phase ofthe step cycle ture & Science, Denver, CO. Animals were
and converted to kinetic energy in a subse- induced to run on a smooth non-slip horizon-
quent phase (Cavagna et al. 1977; Heglund et tal surface in the laboratory. They ran using
al. 1982; Alexander 1984, 1988; McMahon stride frequencies between 3.6-5.2 Hz for sev-
1985, 1990; Farley et al. 1993; Full & Farley eral seconds when disturbed butfavored lower
2000). We also observe that fluctuations in speeds at other times. Images of fast-running
627
628 THE JOURNAL OF ARACHNOLOGY
mm
animals were captured using two synchro- above the body. The center of the body
nized (gen-locked) Peak Performance video was considered a sufficiently close approxi-
cameras (120 fields/s) positioned to obtain lat- mation of the overall center of mass for use
eral and dorsal perspectives. The angle be- in calculations. Potential energy of the center
tween the cameras was about 90°. Videotapes of mass was calculated as mgh, where m was
were synchronized using a Peak Performance animal mass, g was gravitational acceleration,
manually operated event marker. A calibration and h was height ofthe centerofmass relative
frame (4 cm X 4 cm X 4 cm) was videotaped to the substratum. Forward kinetic energy of
by both cameras and filled most of the two the center of mass was calculated as Vimv'^
fields ofview. The frame consisted of 12 non- where v was velocity of the body. Total me-
coplanar points. The resolution of points of chanical energy is the sum of kinetic and po-
the calibration frame was about 0.2 mm. tential energy. Translational kinetic energies
Points in space could be located with mean- of the effective segments of leg 4 was calcu-
squared errors of0.12 mm, 0.26 mm, and 0.15 lated as where m was the mass of the
mm
for the x, y, and z positions, respectively, effective leg segment and v was the velocity
mm
yielding a 0.32 mean-squared error for of the center of mass ofthe effective segment
position. relative to the body. The rotational kinetic en-
Videotapes were analyzed using a comput- ergy of each effective leg segment was cal-
erized motion analysis system (Motus, Peak culated as where I was the inertia ofthe
Performance Technologies, Inc., version 6.0). effective segment about its center ofmass and
The field of view was such that about two (JL) was the angular velocity of that segment in
complete strides ofeach animal were captured a global coordinate system. The moment of
during a run. A sequence was analyzed only inertia for each effective segment was approx-
if it was not interrupted by pauses or obvious imated by (Vi2)mF, where / was the length of
changes in speed. The center ofthe body, dis- the segment, which assumed each segment to
tal end of the tarsus, tibia-tarsus joint, and fe- be a slender rod ofuniform density. Total limb
mur-patella joint (Fig. 1) were digitized man- kinetic energy was estimated by summing the
ually. Data from both cameras were treated translational and rotational energy fluctuations
using a low-pass, fourth-order, zero-phase- of the segments of leg 4 during a stride and
shift Butterworth digital filter with a cutoff- multiplying by eight the total number of legs.
frequency of 10 Hz (Biewener & Full 1992) This estimate was justified due to the similar
before direct linear transformation to three-di- shape and mass of the eight legs.
mensional coordinates. The overall animal
RESULTS
center of mass was calculated for each field —
and incorporated the body and the center of Kinematics. Like other phalangid har-
mass of each effective —leg segment. vestmen, Leiobunum vittatum behaved as a
Mechanical energy. Masses of the body functional hexapod, the antenniform second
and effective leg segments were obtained by legs being used primarily as tactile organs.
freezing specimens at 0° C for 30 min. Be- They used a hexapod-like alternating tripod
cause the patella was short and essentially im- gait, which provides a stable base of support
mobile relative to the tibia, the patella and tib- throughout the locomotor cycle (Delcomyn
ia were treated together as one effective leg 1985). Specifically, legs left 1, right 3 and left
segment. Each leg was severed at the tibia- 4 moved essentially together as one tripod and
tarsus, femur-patella, and coxa-trochanter moved out ofphase with the tripod formed by
joints and each effective leg segment was legs right 1, left 3 and right 4 (Eigs. 2, 3). At
weighed to the nearest jxg (ATI-CAHN C-33 the onset of a step cycle, legs of one tripod
balance). Estimates of mechanical energy contacted the substratum and members of the
were derived from kinematic and mass mea- other tripod were lifted. At this point, the cen-
surements (Kram et al. 1997). The body con- ter of mass moved to its lowest level of 10 ±
stituted 73.0 ± 0.8% of total mass. When leg 0.4 mm or 1.7 ± 0.2 body lengths above the
segments were taken into account, the overall substratum. Retraction ofleg 4 ofa supporting
center of mass was indistinguishable from the tripod began at 16 ± 1% of the stride period
center of the body, except in the vertical axis, before the lowest position of the center of
where the center of mass was located 0.5-2.0 mass was reached (Fig. 4). The center ofmass
SENSENIG & SHULTZ—LOCOMOTION IN LEIOBUNUM 629
—
Figures 1-3. 1. Semi-diagrammatic retrolateral (posterior) view ofthe first leg ofLeiobunum vittatum
showing basic anatomy and locations of possible spring-like mechanisms. 2. Body trajectory of a har-
vestman running at an approximate net speed of 17 cm/s from dorsal and lateral perspectives. Highlighted
leg tips indicate the tripod of support. Scale bars = 1 cm. 3. An example of changes in kinetic and
potential energy and in forward and transverse velocity in a harvestman running at an approximate net
speed of 17 cm/s. The upper graph shows that forward kinetic and gravitational potential energy of the
center ofmass fluctuate in phase, as predicted by the spring-loaded inverted-pendulum model. The middle
graph shows fluctuations in forward and transverse velocity of the center of mass. Note that negative
velocities indicate transverse velocities when the centerofmass is leftofthe net axis oftravel and positive
values are used when the center ofmass is on the right. The pattern is roughly consistent with predictions
ofthe lateral-leg-spring (LLS) hypothesis. The lower graph shows the stepping pattern (alternating tripod
gait), with periods of support indicated by dark bars. Vertical dotted lines indicate the approximate point
at which one tripod of support shifts to the other.
630 THE JOURNAL OF ARACHNOLOGY
15% of the mechanical energy oscillations of
the center of mass.
DISCUSSION
Significance o—fvertical fluctuations ofthe
center ofmass. Comparative studies ofleg-
ged locomotion in arthropods and vertebrates
have revealed patterns of movement that tran-
scend leg number, body size and phylogenetic
&
distance (Full Koditschek 1999; Blickhan
& &
Full 1993; Farley et al. 1993; Full Farley
2000). Cyclical changes in the vertical posi-
0.00 0.05 0.10Time(s)0.15 0.20 0.25 tion of the body’s center of mass is one such
4 pattern and is hypothesized to increase overall
—
Figure 4. Average and SD ofthe centerofmass energetic efficiency through the interchangeof
position ofrunning harvestman. Displacement over kinetic and gravitational potential energy. The
1 stride from four individuals was normalized to inverted pendulum (IP) model (Cavanga et al.
step period (Motus, Peak Performance Technolo- 1977) applies to an animal moving forward
gies, Inc., version 6.0). while vaulting over a stiffened leg, as exem-
plified by a person using a pair of crutches.
In the initial part of the step eycle, some ki-
then moved upward to 13 ± 0.4 mm (2.2 ± netic energy used in moving the animal for-
0.2 body lengths) as leg 4 of the supporting ward also raises the center of mass and in-
tripod appeared to push the body over the set creases gravitational potential energy. As the
of “crutches” formed by legs 1 and 3. Sig- center of mass falls, potential energy is con-
nihcantly, the plane of extension of leg 4 was verted into kinetic energy, some of which can
not parallel to the overall axis of travel, and be used in initiating the next step cycle. The
the center of mass was displaced transversely IP model predicts that changes in potential
toward the side opposite the extending leg by and forward kinetic energy occur 180° out of
4.7 ± 0.4 mm (0.8 ± 0.2 body lengths). This phase. Significantly, behavior consistent with
mechanism resulted in a lurching motion with the IP model has never been observed in ar-
instantaneous forward velocity of the center thropods and was not observed in L. vittatum.
of mass varying almost sinusoidally from 5- In the spring-loaded inverted-pendulum
1
25 cm/s when the animal ran at an average (SLIP) model (Cavagna et al. 1977; Heglund
speed of 20 cm/s (30.3 body lengths/s) (Figs. et al. 1982; Alexander 1984, 1988; McMahon
&
2, 3). — 1985, 1990; Farley et al. 1993; Full Farley
Mechanical energy. Forward kinetic and 2000), elastic elements in the legs serve as
potential energy ofthe centerofmass changed mechanisms of transient energy storage. Spe-
approximately in phase, with the average cifically, as the center of mass descends under
phase difference being less than the video the force ofgravity elastic elements in the legs
time resolution. Vertical excursion of the cen- (that is, tensed muscles, tendons, and skeletal
ter of mass in L. vittatum spanned slightly less structures) are deformed, and forces produced
than one body length, such that changes in by subsequent elastic recoil of these elements
potential energy (1.1 ± 0.10 p.J) were about are used to propel the center of mass upward
twice that of the corresponding changes in ki- and forward to initiate a new cycle. In contrast
netic energy (0.7 ± 0.06 p.J). Individual legs to the IP model, the SLIP model predicts that
were 2.8-4.2% of total body mass. The ki- forward kinetic and gravitational potential en-
netic energy associated with stopping and ergy fluctuate in phase. The SLIP model
starting leg 4 during a stride was 0.020-0.025 matches locomotion in many vertebrates
p.J, with about 14% of this energy due to ro- (Biewener et al. 1981; Alexander 1984; Farley
tation of the segments. Assuming that kinetic et al. 1993), crabs (Blickhan & Full 1987),
energy of all legs was similar to leg 4 at ob- and cockroaches (Full & Tu 1990). Our ob-
served running velocities, the magnitude of servations of L. vittatum were also consistent
the limb kinetic energy oscillations was 9- with the SLIP model, and this species is the
SENSENIG & SHULTZ—LOCOMOTION IN LEIOBUNUM 631
least massive animal in which the predictions velocity. Kinematic analysis of the cockroach
of the model have been met. Blaberus discoidalis largely corroborates pre-
Significance of tra—nsverse displacements dictions of the model (Schmidt et al. 2002).
in the center ofmass. The magnitude ofthe Kinematics in running Leiobunum was also
transverse displacements ofthe center ofmass roughly consistent with the LLS model (Fig.
observed in running L. vittatum (peak-to-peak 3). Specifically, the transverse-velocity sinu-
displacement of 0.78 body lengths) (Figs. 2- soid has a wavelength about twice that of the
4) are unprecedented. By comparison, the cen- forward velocity and the peaks and troughs of
ter of mass of the cockroach Blaberus discoi- the transverse velocity plot occur near the
dalis deviates laterally from the net axis of peaks in forward velocity. However, in con-
mm
travel by less than 0.4 or 0.01 body trast to the fairly simple sinusoid displayed by
lengths (Full & Tu 1990). The existence of forward velocity, transverse velocity showed
substantial transverse accelerations of the a more complex pattern and may even have
body would seem to be energetically ineffi- had a low-amplitude, short-wavelength veloc-
cient (Manton 1977) in the absence ofa mech- ity fluctuation superimposed on the predicted
anism analogous to the SLIP model. Recent waveform. In addition, peaks in the transverse
work suggests that cyclical transverse dis- waveform appeared to precede peaks in for-
placements are associated with a passive ward velocity rather than occuiTing simulta-
spring-based mechanism of directional stabi- neously as predicted. Significantly, the phase
lization that can respond to external pertur- difference between the forward and transverse
bations to forward locomotion more rapidly velocity peaks was also observed in the cock-
than reflexes (Kubow & Full 1999; Schmidt roach (Schmidt et al. 2002: fig. 6). The overall
& Holmes 2000a, b; Schmidt et al. 2002). similarity ofthe predictions ofthe LLS model
Specifically, when a running animal experi- and empirical observations indicate that lat-
ences a transverse perturbation to the center eral springs are probably important for loco-
of mass (wind, uneven substratum, another motion and specifically for stabilization. How-
animal, etc.), leg springs could potentially ab- ever, given that two arthropods deviate from
sorb the energy and thereby prevent signifi- expectations in the same manner, the LLS
cant deviation from the net axis of travel. model probably needs refinement. —
Some ofthis stored energy could also be con- Locations of possible leg springs. Com-
verted to transverse kinetic energy upon elas- patibility of locomotor kinematics with the
tic recoil and stored transiently by elastic el- SLIP and LLS models indicate that elastic en-
ements in the legs on the opposite side of the ergy storage is a significant component of lo-
animal. Theoretically, it is possible that ener- comotion in L. vittatum, but the anatomical
gy from a brief transverse perturbation could placement of appropriate elastic mechanisms
be dissipated by elastic mechanisms over sev- is not known. The existence ofhighly efficient
eral strides while the center of mass oscillates springs has already been documented at the
along the net axis of travel. tibia-tarsus joint in L. vittatum, although its
The lateral-leg-spring model (LLS) of sta- precise role in locomotion has yet to be de-
bilization makes specific predictions about the termined (Sensenig & Shultz 2003). The tibia-
timing of forward and transverse fluctuations tarsus joint of each leg is spanned by a pair
of the center of mass (Kubow & Full 1999; of deformable sclerites that store energy dur-
Schmidt & Holmes 2000a, b; Schmidt et al. ing flexion and return up to 90% of this en-
2002). Specifically, velocities of forward and ergy during extension. Gravity can potentially
transverse displacement are predicted to vary assist muscles in deforming the elastic scler-
sinusoidally during locomotion, with peak for- ites of legs 1 and 3 during locomotion, but
ward velocity occurring in phase with peak flexion of this joint in leg 4 occurs only when
rightward and leftward transverse velocities. the leg is offthe ground and it is unlikely that
When transverse velocity of the center of the sclerites could be loaded by gravity.
mass is assigned negative values wheneverthe In principle, any muscle-tendon complex
center of mass deviates to the left of the net can store externally generated mechanical en-
axis of travel and positive values when to the ergy if its contractile and/or connective ele-
right (as in Fig. 3), the wavelength of trans- ments have intrinsic tensile resilience and ex-
verse velocity should be twice that offorward perience externally generated tensile forces
.
632 THE JOURNAL OF ARACHNOLOGY
(McMahon 1990). Shultz (2000) identified 13 tilegged locomotion: bouncing like a monopode.
intrinsic leg muscles in Leiobunum, but the Journal of Comparative Physiology A 173:509-
msuesecmlse-ptaerntdiocunlacrolymplweelxl osfuittheedcltoawac(tFiga.s 1a) Cav5a1g7n.a, G.A., N.C. Heglund & C.R. Taylor. 1977.
spring. Here a long tendon attaches to the Mechanical work in terrestrial locomotion: two
basic mechanisms for minimizing energy expen-
claw distally, spans the length of the multi-
diture. American Journal of Physiology: Regu-
segmented tarsus, and attaches proximally in latory, Integrative and Comparative Physiology
the tibia and patella via muscles (Guffey et al. 233:R243-R261.
2000; Shultz 2000). The tarsus is typically Delcomyn, F. 1985. Factors regulating insect walk-
curved when supporting the animal, both ing. Annual Review ofEntomology 30:239-256.
when standing and during locomotion (Fig. 2). Farley, C.T., I. Glasheen & T.A. McMahon. 1993.
Forces from gravity, propulsive movements or Running springs: speed and animal size. Journal
transverse perturbations during locomotion of Experimental Biology 185:71-86,
imnagytebnesnidontohne tthaersmuusscfulret-htere,ndtohnerceobmyplinecxreaansd- FraVziaerrn,eyS,.F.R,.AG..S.DiLCaarpsreino, &D.SN.eNf.f,ZiLl.l.Q1u9i9m9b.y,ElaMs.-
ticity and movements of the cockroach tarsus in
storing energy within its elastic elements. walking. Journal of Comparative Physiology
Elastic energy might thee be converted to ki- 185:157-172.
netic energy toward the opposite direction Full, R.J. & C.T. Farley. 2000. Musculoskeletal dy-
once the tensile load was released causing the namics in rhythmic systems: a comparative ap-
tendon to shorten and the tarsus to “unbend.” proach to legged locomotion. Pp. 192-206. In
A comparable mechanism exists in other ar- Biomechanics andNeural Control ofPosture and
thropods, where elasticity of the tarsal tendon Movement. (J.M. Winters & P.E. Crago, eds,).
maintains postural equilibrium in the face of Springer Verlag, New York.
&
external perturbation (Frazier et al. 1999). Full, R.J. D.E. Koditschek. 1999. Templates and
However, determining the precise role of the anchors: eeuromechanical hypotheses of legged
claw tendon and other potentially elastic ele- locomotion on land. Journal ofExperimental Bi-
ology 202:3325-3332.
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ACKNOWLEDGMENTS 148:129-146.
Guffey, C, V.R. Townsend, Jr. & B.E. Felgenhauer.
Andrew Sensenig was supported by a Uni- 2000. External morphology and ultrastructure of
versity of Maryland Research Assistantship the prehensile region of the legs of Leiobunum
and Jeff Shultz was supported by the Mary- nigripes (Arachnida, Opiliones). Journal of Ar-
land Agricultural Experiment Station and NSF achnology 28:231-236.
grant IBN-9733777. Heglund, N.C., G.A. Cavagna & C.R. Taylor. 1982.
Energetics and mechanics of terrestrial locomo-
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