Journal of Applied Biomechanics, 2008, 24, 333-339
© 2008 Human Kinetics, Inc.
The purpose of this research was to determine
the functions of the gluteus maximus, biceps
femoris, semitendinosus, rectus femoris, vastus
lateralis, soleus, gastrocnemius, and tibialis
anterior muscles about their associated joints
during full (deep-knee) squats. Muscle func-
tion was determined from joint kinematics,
inverse dynamics, electromyography, and
muscle length changes. The subjects were six
experienced, male weight lifters. Analyses
revealed that the prime movers during ascent
were the monoarticular gluteus maximus and
vasti muscles (as exemplied by vastus latera-
lis) and to a lesser extent the soleus muscles.
The biarticular muscles functioned mainly as
stabilizers of the ankle, knee, and hip joints by
working eccentrically to control descent or
transferring energy among the segments during
ascent. During the ascent phase, the hip exten-
sor moments of force produced the largest
powers followed by the ankle plantar exors
and then the knee extensors. The hip and knee
extensors provided the initial bursts of power
during ascent with the ankle extensors and
especially a second burst from the hip exten-
sors adding power during the latter half of the
Keywords: electromyography, inverse dynam-
Traditionally, kinesiologists and physical educators
classify muscles in several ways: by anatomical func-
tion, by type of contraction, by level of recruitment, and
by work done by the muscle during a particular motion.
Anatomically, muscles are dened by whether they are
exors, extensors, abductors, adductors, and so on based
on their lines of action across the joints that they cross.
Muscle contractions are categorized by how a muscle’s
length changes—concentric if the muscle shortens,
The authors are with the School of Human Kinetics, Univer-
sity of Ottawa, Ottawa, ON, Canada.
Lower Extremity Muscle Functions During Full Squats
D.G.E. Robertson, Jean-Marie J. Wilson, and Taunya A. St. Pierre
University of Ottawa
eccentric if it lengthens, and isometric when it is active
but there is no change in muscle length. The recruitment
level of a muscle is usually identied by the relative
magnitude of its electromyogram (EMG) compared
with its maximal magnitude. More difcult to dene is
the work done by a specic muscle and where the energy
it produces is used within the musculoskeletal system.
To overcome this currently unsolvable problem, the
work done by the moments of force across each joint are
used to estimate the net work done by all the structures
that cross the joint. Since the main contributors to the
work done across a joint are muscles, especially when
the joint does not reach its anatomical limits, biomecha-
nists have a partial way of determining the roles of mus-
cles during motion.
One can, for example, analyze a simple exor
movement and observe an increasing moment of force
and a simultaneous increase in the EMG of the exor
muscle. To terminate the period of exion, an antago-
nistic extensor muscle may turn on to cause an extensor
moment of force. The exor muscle would be observed
to be shortening during its period of contraction while
the extensor muscle would be shown to be lengthening
or eccentrically contracting. The situation becomes
more complex when multiple joints are involved and
some of the muscles cross more than one joint. For
example, researchers have come to opposite conclusions
when analyzing the role of biarticular muscles during
the vertical jump. Bobbert and Van Ingen Schenau
(1988) stated that energy was transferred distally by
biarticular muscles, whereas Pandy and Zajac (1991)
showed a distal-to-proximal transfer of energy. To reach
their conclusion, Pandy and Zajac determined the con-
tributions of muscles based on a musculoskeletal model
of the lower extremity. They pointed out that muscles
crossing a particular joint can deliver power to segments
remote from the joint(s) that they cross. If only it were
possible to attach power meters to the muscles to watch
the ows of mechanical energy as we do to measure the
ow of electrical energy to a house.
Elftman (1939a, 1939b) suggested a partial solution
to this problem and applied it to walking. His approach
was to calculate the powers due to the net forces and
moments at each joint as well as the instantaneous
334 Robertson, Wilson, and St. Pierre
1988), vertical lifting (Molbech, 1965; Wilson & Rob-
ertson, 1988), sprinting (Simonsen et al., 1985), and
jumping (Bobbert & Van Ingen Schenau, 1988; Pandy
& Zajac, 1991; Zajac, 1993; Prilutsky & Zatsiorsky,
1994; Jacobs et al., 1996).
The purpose of this study was to determine the
functions of the major lower limb muscles, particularly
the biarticular muscles, during full squats (descent and
ascent) based on EMG activity, inverse dynamics,
moment powers and estimated muscle length changes.
Past research (Molbech, 1965; Wilson & Robertson,
1988) examining biarticular muscles during full squat-
ting has provided some evidence for the existence of
paradoxical muscle activity. A study by Andrews (1985)
attempted to dene paradoxical activity through the
examination of a rst-order differential relationship
between muscle length and joint angle that yields the
moment arm length. Unfortunately, his method did not
account for changes in muscle recruitment.
The subjects were six male experienced weight lifters.
The subjects varied in height from 1.78 to 1.90 m and in
mass from 71.8 to 95.5 kg. The body was modeled as
four rigid segments connected by frictionless pin joints
at the hip, knee, and ankle. Segmental masses, radii of
gyration, and centers of gravity were calculated from
proportions described by Dempster (1955) and Plagen-
hoef (1971). The length of the muscles of interest
(soleus, tibialis anterior, gastrocnemius, vastus lateralis,
semitendinosus, biceps femoris, rectus femoris, and
gluteus maximus) were calculated using Frigo and
Pedotti’s (1978) model with modications by Hubley
(1981) to allow scaling for different sized persons. The
bar was treated as a particle with its center of gravity
acting at its geometric center. Angular motion of the bar
about its center of gravity was considered negligible
(McLaughlin et al., 1978).
Before data collection, pairs of silver–silver chlo-
ride electrodes were placed on the muscles at locations
specied by Delagi et al. (1975). Skin impedance was
conrmed to be below 20 kΩ and the interelectrode dis-
tance set to 2.5 cm to reduce cross talk (Winter et al.,
1994). High-input-impedance (10 MΩ) differential
ampliers (>110 dB CMRR, 10–500 Hz band-pass)
were used to obtain reliable EMG signals. The full-
wave-rectied EMG signals were ltered through 2nd-
order Butterworth lters with a 6-Hz cutoff frequency
(Winter, 1990), yielding their linear envelopes.
Following a warm-up and rest period, the subjects
were required to perform 12 full squat (knees maximally
exed) trials with 3 min of rest between trials. Six of the
trials were performed unloaded as a warm-up, and the
other half were performed with a load representing 80%
of each subject’s previously recorded maximum. The
squat consisted of a 2-s descent during which the ankle,
hip, and knee became exed into a full squat followed
immediately by a 2-s ascent during which the three
powers of each segment. The segmental powers could
then be accounted for by the ows of energy to or from
the segment at each end. Winter and Robertson (1978)
used his methods to show that energy could be tracked
during gait and proved that during the push-off phase of
walking, work generated by the ankle plantar exor
moment was used to supply energy to the foot, leg,
thigh, and even the trunk by the transfer of energy
though passive joint structures. However, no effort was
made to identify which muscles were responsible for
the various bursts of positive and negative work during
the complete gait cycle.
In this study, we will apply inverse dynamics and
moment power analysis to determine the work done at
the joints coupled with information about various major
muscles of the lower extremity to determine how the
motions of the full squat are achieved. In particular, the
roles of the biarticular muscles will be elucidated based
on their levels of contraction (EMGs) and their states of
contraction (lengthening or shortening). For example, a
curious paradox can occur when two opposing biarticu-
lar muscles contract simultaneously to produce motion
at both joints instead of stiffening the joints they cross.
Such a situation, rst described by Duchenne (in 1885,
see Kuo, 2001) and Lombard (1903) and subsequently
named Lombard’s paradox, is observed when rectus
femoris and biceps femoris contract concurrently during
the motion of rising from a chair. The extension seen at
both the hip and knee is the result of the differential
moment arms of the two muscles at each joint. Since the
rectus femoris has a greater moment arm across the
knee, due to the patella, it creates an extensor moment at
the knee. Biceps femoris has the longer moment arm at
the hip so it creates an extensor moment there. Thus,
simultaneous contractions of these muscles from the
seated position causes extension of the both the knee
Experimentally determining how two-joint muscles
contribute during a full squat requires information about
muscle lengths, joint kinematics, and net moments of
force. Molbech (1965) suggested that biarticular mus-
cles of the lower extremity act in a “paradoxical” fash-
ion when the movement is constrained or controlled.
For his example, the movement consisted of having the
feet motionless on the ground and the hips following a
vertical track. He showed that a paradoxical situation
occurred because when a biarticular muscle, such as the
gastrocnemius contracted, it caused knee extension
when normally it was a knee exor. In a subsequent
paper (Carlsöö & Molbech, 1966), he and Carlsöö pro-
posed that a similar situation existed for seated cycling
where knee exors, such as the hamstrings, acted as
knee extensors. They considered cycling a controlled
motion since the pelvis was xed to the seat and the feet
must travel a circular path. Other studies have docu-
mented that paradoxical activity may occur during
movements when several joints have reduced degrees of
freedom, for example, during seated bicycling (Gregor
et al., 1985; Andrews, 1987), rowing (Robertson et al.,
Muscle Activity During Full Squats 335
joints extended concurrently. The minimum exion
angles for all three joints occurred at the end of descent.
Because there were no signicant differences in the
ranges of motion of the joints between the unloaded and
loaded conditions, based on a dependent groups t test (p
= .055), and since it was the loaded conditions that were
of most interest, only results from the loaded conditions
At all three joints the peak angular velocities
occurred simultaneously. The peak negative angular
velocity occurred at just after 10% of the cycle whereas
the peak positive angular velocity occurred at 90% of
the cycle. The peak angular velocities at the hip and
knee joint (approximately 2 rad/s), however, were sub-
stantially higher than that of the ankle joint (<1.0 rad/s).
The hip, knee, and ankle joints had very distinct
patterns of the net moments of force (Figures 2, 3, and 4).
The hip and ankle joints showed extensor moments
throughout ascent and descent, whereas the knee joint
started and ended with a exor moment, with an exten-
sor moment in between. Peak moments varied between
subjects but, on average, the highest peak moments were
produced at the hips (maxima around –300 N·m) fol-
lowed by the ankles (approx. –200 N·m) and then the
knees (between ±100 N·m).
The moment powers (Figures 2, 3, and 4) at the
knee differed notably from the patterns seen at the other
two joints. The power patterns for both the hip and the
ankle extensors were eccentric during the descent and
concentric during the ascent. In contrast, power values
at the knee started with the exors acting concentrically
and then with the extensors acting eccentrically for the
rest of the descent. The ascent began with the extensors
switching to concentric contractions and ended with the
exors working eccentrically. Again, the peak powers
were highest for the hip extensors followed by the ankle
plantar exors and then the knee extensors.
The functions of the moments of force at the hip
and ankle divide into two phases (Figures 2 and 4). In
the descending phase, extensor moments dissipated
energy in order to control the rate and amount of the
descent, whereas, in the ascending portion, work was
generated by extensor moments about these joints. In
contrast, the functions of the knee moments of force
divided into four phases (Figure 3)—two during descent
and two during ascent. Initially during descent, positive
work was performed by the knee exors to unlock the
knee and initiate downward motion (0–15% of the
cycle). During the rest of the descent, energy was dissi-
pated by the knee extensors in an effort to control knee
exion (15–53% of the cycle). Positive work performed
by the knee extensors signaled the start of the ascent
(53–85% of the cycle). Near the end of the ascent, the
knee exors started to perform negative work (acted
eccentrically) to reduce the rate of knee extension and
presumably prevent hyperextension (85–100% of the
The ensemble-averaged lengths of the muscles as
proportions of their standing lengths during the full
joints extended to return to an upright posture. The load
lifted during the full squats varied from 600 to 1226 N.
The subjects executed full squats with their right
feet on a force platform (Kistler 9261A). Cinemato-
graphic, electromyographic, and kinetic data were col-
lected simultaneously. A cine camera was positioned
perpendicular to the plane of motion, and all data were
sampled at 50 Hz. Following the 12 trials, the subjects
were required to perform three maximal isometric con-
tractions for each muscle. To elicit the MVCs, each sub-
ject adopted a partial squat position with the heels not
touching the ground and performed a maximal isomet-
ric contraction against a chain that was connected with
the ground. In pretesting, this procedure was shown to
produce MVCs in all of the major muscle groups that
were used in this study. The EMG results were averaged
and the maximum contraction values were used to detect
the relative EMG activation states of the muscles during
the full squats.
Within each of the two testing conditions (with and
without load), linear-envelope EMG signals for each
muscle were normalized over time and to maximum
EMG values. These data were then averaged for each
subject over six trials to yield an ensemble average
EMG pattern for each muscle. All within-subject ensem-
ble averages were then averaged to produce the across-
subject grand ensemble average (Yang & Winter, 1984)
for each muscle and testing condition.
The lm data were digitized to an accuracy of less
than 0.5 mm and then processed with the Biomech
Motion Analysis System (http://www.health.uottawa.
ca/biomech/csb/biomech.htm). The motion data were
smoothed with a zero-lag, 4th-order, Butterworth lter
set to a cutoff frequency of 6 Hz. Joint angular displace-
ments and velocities were derived from the motion data
and combined with the force plate data for inverse
dynamics analysis that resulted in the calculation of net
internal moments of force and their associated powers
(Robertson & Winter, 1980) at the ankle, knee, and hip.
These kinematic and kinetic data were then time nor-
malized and averaged across subjects.
Muscle-tendon-unit lengths for each subject were
calculated from relative angle changes, (Frigo & Pedotti,
1978; Hubley, 1981) normalized to their length during
standing and then ensemble averaged. These averages
were time normalized and then averaged across sub-
jects, resulting in grand ensemble, muscle length
A slightly greater portion of the squat was required for
the descent phase (0–53%) than for the ascent phase
(53–100%) based on the change from exion to exten-
sion of the three joints. The changes that occurred in the
angles of the joints are illustrated in Figure 1. During
the descent, all three joints exed, simultaneously; the
reverse was seen during the ascent, in which all three
336 Robertson, Wilson, and St. Pierre
descent and lengthening on ascent. Gastrocnemius,
semitendinosus, and biceps femoris each shortened by
8%, 20%, and 6%, respectively, during descent.
Linear-envelope electromyograms averaged across
subjects and normalized to each subject’s maximum
voluntary contractions (MVCs) are displayed in Figure
6. These curves show the onset and recruitment levels of
each muscle during the squatting motion. The descent
phase of the full squat was characterized by tibialis
anterior, vastus lateralis, and rectus femoris activity,
squats are displayed in Figure 5. Three of the monoar-
ticular muscles acted at lengths beyond their standing
lengths. Soleus, gluteus maximus (GM), and vastus lat-
eralis (VL) all lengthened beyond their standing lengths
during descent, by 7%, 29%, and 18%, respectively,
before returning to their standing lengths at the end of
ascent. Only the monoarticular tibialis anterior muscles
shortened 5% during descent before returning to their
standing lengths during ascent.
Of the biarticular muscles, the rectus femoris mus-
cles stayed close to their standing lengths with changes
of less than 2%. They were also unusual by having a
bimodal pattern—lengthening then shortening during
both descent and ascent. All other biarticular muscles
exhibited unimodal contraction patterns—shortening on
Figure 1 — Joint angles (in degrees ± 1 SD) during loaded
and unloaded full squats.
Figure 2 — Ankle angular velocity, net moment of force, and
moment power (± 1 SD) during loaded full squats.
Figure 3 — Knee angular velocity, net moment of force, and
moment power (± 1 SD) during loaded full squats.
Figure 4 — Hip angular velocity, net moment of force, and
moment power (± 1 SD) during loaded full squats.
Muscle Activity During Full Squats 337
of the antagonistic muscles was observed at the knee
and hip joints as the rectus femoris, gluteus maximus,
vastus lateralis, semitendinosus, biceps femoris, and
gastrocnemius contracted simultaneously during the
extension (ascent) phase. EMG activity of the semiten-
dinosus paralleled that of the biceps femoris since both
are part of the hamstrings group, as did vastus lateralis
and rectus femoris, both part of the quadriceps group.
Thus, the hamstrings and gastrocnemius acted antago-
nistically to the actions of the quadriceps group at the
knee while the gluteus maximus acted antagonistically
to the rectus femoris at the hip during the early portion
of the ascent.
The tibialis anterior contracted concentrically about the
ankle during descent to assist dorsiexion. Soleus, as
expected, functioned eccentrically but contributed little
based on its relatively low level of EMG activity. In con-
trast, gastrocnemius, which also had a relatively low
level of recruitment, contracted concentrically. As a
two-joint muscle, the role of the gastrocnemius may
have been to assist knee exion, whereas the soleus
acted to limit the amount of ankle dorsiexion during
descent. This observation is supported by the fact that
soleus level of recruitment increased to almost 50%
MVC as the subjects reached maximum descent.
Muscle activity about the knee during descent was
characterized by two periods—one of concentric work
and one of eccentric work. During the initial brief period
of concentric work gastrocnemius, semitendinosus, and
biceps femoris acted together to initiate exion of the
knee. These muscles concentrically contracted and were
active at around 25% of MVC. In particular, gastrocne-
mius exhibited a brief burst that combined with the two
hamstring muscles was enough to unlock the knee and
permit descent. Afterward, knee exion continued with
the knee extensors acting eccentrically to control and
eventually terminate the descent. During the eccentric
part of descent, continuous activity of the vastus latera-
lis contracting eccentrically was evident. Rectus femo-
ris (RF), another knee extensor, exhibited increasing
EMG activity as the descent reached maximum depth.
During the second half of decent, however, RF was
shortening slightly so it may have acted more as a hip
exor or as a stabilizer at both hip and knee. Since RF’s
length changed less than 2%, one could characterize its
role as being isometric and therefore was responsible
for transmitting energy across the hip and knee joints
for dissipation by the knee extensors and ankle plantar
exors. This type of mechanism has been shown for
jump landings by Prilutsky and Zatsiorsky (1994), but
the exact nature of RF’s contributions are difcult to
gauge using only inverse dynamics (Zajac, 1993).
The hip moment of force was consistently extensor
through the squat. During descent, the extensor moment
of force did negative work to control the rate and amount
whereas the ascent phase showed increasing levels of
activity from all the muscles, excepting tibialis anterior,
At the ankle joint, little evidence of coactivation of
antagonistic muscles occurred except at the deepest part
of the descent and during the early part of the ascent
phase (50–70% of cycle duration). Gastrocnemius and
soleus EMG patterns followed each other synergisti-
cally, and both these muscles were relatively inactive
(<25% MVC) during periods of signicant tibialis ante-
rior activity. In contrast, coactivation (i.e., >25% MVC)
Figure 5 — Lengths of the muscles (± 1 SD) as proportions
of their standing lengths during loaded full squats.
Figure 6 — Linear-envelope EMGs (± 1 SD) during loaded
full squats as percentages of maximum voluntary contractions
338 Robertson, Wilson, and St. Pierre
not vary much (<2%) so they may have acted to prevent
excessive hip extension, which might result in the sub-
ject falling backward.
The antagonistic hamstrings, biceps femoris, and
semitendinosus, were also recruited during this period
especially at mid-ascent, but contracted eccentrically.
Gastrocnemius, another biarticular knee exor, was also
actively recruited during ascent and like the hamstrings
contracted eccentrically. These antagonists would
appear to be working against knee extension but their
combined actions may in fact assist extension. If we
consider that their lines of action are both partly directed
rearward, their vector sum would produce a force that
pulls the knee joint backward and into extension. Such a
mechanism has been suggested for biarticular muscles
when the segments are not constrained, as in jumping
(Zajac, 1993), but may also be true for lifting activities,
in which the distal ends of the kinematic chain (i.e., the
feet) are constrained by the ground. This paradoxical
ability of the biarticular muscles was suggested by Mol-
bech (1965) but was not investigated for a situation
where two sets of biarticular muscles (gastrocnemius
and hamstrings) acted simultaneously. The difculty
with Molbech’s principle is that he assumed that the
biarticular muscles shortened whereas for full squats the
biarticular muscles lengthened. Thus, his paradoxical
muscle activity cannot be said to have occurred during
At the hip, the gluteus maximus was clearly a major
contributor to the work done. The gluteus maximus
muscles contracted concentrically throughout the ascent
and were actively recruited to near maximum levels
especially during the rst two-thirds of the ascent. Its
antagonist, RF, was also heavily recruited but only
during the earliest third of the ascent when it was eccen-
trically contracting. As mentioned previously, RF
offered resistance to hip extension but may also have
been fullling its role as a knee extensor by transmitting
energy from the torso to the leg (tibia). Rectus femoris
could have transmitted energy because of its relatively
stiff behavior as shown but its minimal length change
(Prilutsky & Zatsiorsky, 1994). At the end of ascent, RF
shortened but its recruitment level was nearly zero and
therefore did not contribute energy to the motion.
In conclusion, analysis of the EMG, inverse dynam-
ics, moment powers, and muscle length changes during
squatting revealed the complex relationships among the
contributions of the various major muscles of the lower
extremity. Not surprisingly, there was a close agreement
between the results of the six participants, which sup-
ports the notion that they all performed the squat in a
similar fashion. The results support Pandy and Zajac’s
(1991) notion that energy is provided in a proximal-to-
distal sequence with the hip extensors providing the
greatest contributions during ascent, followed by the
ankle plantar exors, and then the knee extensors. The
important role of the knee exors as the initiators of the
squatting motion by unlocking the knee and permitting
the start of descent was also identied.
of hip exion. Gluteus maximus contracted eccentrically
throughout the descent with EMG levels starting at 10%
MVC and increasing to about 25% MVC around mid-
descent. The gluteals curiously reduced their activity
level at maximum squat depth. Presumably, they were
not needed to maintain stability or perhaps they permit-
ted an extra degree of hip exion that would have created
a deeper counter-movement immediately before ascent.
Counter-movements enable stronger contraction forces
when they are done rapidly and immediately before a
powerful movement (Van Ingen Schenau, 1984).
Not surprisingly, during the ascent phase all three
moments of force were extensor and performed concen-
tric work. The hip extensors dominated earliest and
throughout the ascent, having the largest peak moments
(>300 N·m) and the largest peak powers (>200 W at
60% of cycle time with a second peak >300 N·m at 85%
of cycle time). The knee extensors produced relatively
the lowest powers of the three moments and only con-
tributed positive work for the rst two-thirds of the
ascent. The ankle plantar exors produced larger powers
than the knee extensors but did not contribute their max-
imum power until near the end of the lift (at 85% of
cycle time). This order of power production, from prox-
imal (hip) to distal (ankle), is similar to that of counter-
movement jumping (Nagano et al., 1998). Despite this
ordering of the powers, examination of the EMGs show
that all exors and extensors (excepting tibialis anterior)
were recruited almost simultaneously as compared with
vertical jumping (Bobbert & Van Ingen Schenau, 1988),
for which the order of recruitment was hip, knee, and
then ankle muscles. This may be due to the static start
and nish required for the full squat. One obvious dif-
ference with the squat was that all muscles relax at the
end of the movement whereas in vertical jumping many
muscles continue to contract until and after the end of
The soleus was the major contributor to ankle
extension since it concentrically contracted and was
recruited almost maximally. Gastrocnemius was also
heavily recruited but did no positive work during this
period because it was contracting eccentrically and so
could have been involved with transferring energy prox-
imally due to its biarticular nature (Van Soest et al.,
1983, Zajac, 1993; Prilutsky & Zatsiorsky, 1994). As
expected, the antagonistic tibialis anterior reduced its
activity level during ascent but was partly activated, pre-
sumably to stabilize the ankle against unexpected
During the rst two-thirds of ascent, the knee exten-
sor moment did positive work. The vastus lateralis, and
presumably the other vasti, contracted concentrically
and were recruited near maximally. The RF, another
member of the quadriceps group, was also recruited
based on its high levels of EMG but did not contribute
positive work to the body as it acted eccentrically
through the rst half of the ascent, during which the
majority of the external work by the knee extensors was
done. In fact, as mentioned previously, RF’s lengths did
Muscle Activity During Full Squats 339
McLaughlin, T.M., Lardner, T.J., & Dillman, C.J. (1978).
Kinetics of the parallel squat. Research Quarterly, 49,
Molbech, S. (1965). On the paradoxical effect of some two-
joint muscles. Acta Morphologica Neerlando-Scandi-
navica, 6, 171–176.
Nagano, A., Ishige, Y., & Fukashiro, S. (1998). Comparison
of new approaches to estimate mechanical output of indi-
vidual joints in vertical jumps. Journal of Biomechanics,
Pandy, M.G., & Zajac, F.E. (1991). Optimal muscular coordi-
nation strategies for jumping. Journal of Biomechanics,
Prilutsky, B.U., & Zatsiorsky, V.M. (1994). Tendon action
of two-joint muscles: Transfer of mechanical energy
between joints during jumping, landing and running.
Journal of Biomechanics, 27, 25–34.
Plagenhoef, S. (1971). Patterns of human motion—A cinemat-
ographic analysis. Englewood Cliffs, NJ: Prentice-Hall.
Robertson, D.G.E., Stothart, J.P., & Wilson, J-M. (1988).
Electromyographic and impulse analysis of ergometer
rowing. Biomechanics XI-B (pp. 869–873). Amsterdam:
Free University Press.
Robertson, D.G.E., & Winter, D.A. (1980). Mechanical energy
generation, absorption and transfer amongst segments
during walking. Journal of Biomechanics, 13, 845–854.
Simonsen, E.B., Thomsen, L., & Klausen, K. (1985). Activ-
ity of mono- and biarticular leg muscles during sprint
running. European Journal of Applied Physiology, 54,
Van Ingen Schenau, G.J. (1984). An alternative view of the
concept of utilization of elastic energy in human move-
ment. Human Movement Science, 3, 301–336.
Van Soest, A.J., Schwab, A.L., Bobbert, M.F., & Van Ingen
Schenau, G.J. (1993). The inuence of the biarticularity
of the gastrocnemius on vertical-jumping achievement.
Journal of Biomechanics, 26, 1–8.
Winter, D.A. (1990). Biomechanics and motor control of
human movement (2nd ed.). Toronto: John Wiley &
Winter, D.A., Fuglevand, A.J., & Archer, S.E. (1994). Cross-
talk in surface electromyography: Theoretical and practi-
cal estimates. Journal of Electromyography and Kinesi-
ology, 4, 15–26.
Winter, D.A., & Robertson, D.G.E. (1978). Joint torque and
energy patterns in normal gait. Biological Cybernetics,
Wilson, J.M., & Robertson, D.G.E. (1988). Analysis of bio-
mechanical principles in weighted deep-knee bends. Pro-
ceedings: Fifth Biennial Conference and Symposium of
Canadian Society for Biomechanics. London: Spodym
Yang, J.F., & Winter, D.A. (1984). Electromyographic ampli-
tude normalization methods: Improving their sensitivity
as diagnostic tools in gait analysis. Archives of Physical
Medicine and Rehabilitation, 65, 517–521.
Zajac, F.E. (1993). Muscle coordination of movement: A per-
spective. Journal of Biomechanics, 26(Suppl. 1), 109–
Thanks to the National Sciences and Engineering Research
Council for nancial support of this project and to Graham
Caldwell, University of Massachusetts at Amherst, for a
Andrews, J.G. (1985). A general method for determining the
functional role of a muscle. Journal of Biomechanical
Engineering, 107, 348–353.
Andrews, J.G. (1987). The functional roles of the hamstrings
and quadriceps during cycling: Lombard’s paradox revis-
ited. Journal of Biomechanics, 20, 565–575.
Bobbert, M.F., & van Ingen Schenau, G.J. (1988). Coordina-
tion in vertical jumping. Journal of Biomechanics, 21,
Carlsöö, S., & Molbech, S. (1966). The functions of two-joint
muscles in a closed muscular chain. Acta Morphologica
Neerlando-Scandinavica, 7, 377–386.
Delagi, E.F., Perotto, A., Iazzatti, I., & Morrison, D. (1975).
Anatomic guide for the electromyographer—The limbs.
Springeld, IL: C. Thomas.
Dempster, W.T. (1955). Space Requirements of the Seated
Operator. Geometrical, Kinematic and Mechanical
Aspects of the Body with Special Reference to the Limbs.
WADC Technical Report (pp. 55–159). Ohio: Wright Air
Development Centre, Air Research and Development
Command, United States Air Force, Wright-Patterson
Air Force Base.
Elftman, H. (1939a). Forces and energy changes in the leg
during walking. The American Journal of Physiology,
Elftman, H. (1939b). The function of muscles in locomotion.
The American Journal of Physiology, 125, 357–366.
Frigo, C., & Pedotti, A. (1978). Determination of muscle
length during locomotion. In R.C. Nelson & C.A. More-
house (Eds.), Biomechanics VI-A (pp. 355–360). Balti-
more, MD: University Park Press.
Gregor, R.J., Cavanagh, P.R., & Lafortune, M. (1985). Knee
exor moments during propulsion in cycling–A creative
solution to Lombard’s Paradox. Journal of Biomechan-
ics, 18, 307–316.
Hubley, C.L. (1981). An analysis of assumptions underlying
vertical jump studies used to examine work augmenta-
tion due to pre-stretch. Unpublished Master’s Thesis.
University of Waterloo, Waterloo.
Jacobs, R., Bobbert, M.F., & van Ingen Schenau, G.J. (1996).
Mechanical output from individual muscles during
explosive leg extensions: The role of biarticular muscles.
Journal of Biomechanics, 29, 513–523.
Kuo, A.D. (2001). The action of two-joint muscles: The legacy
of W. P. Lombard, M. Latash, & V. Zatsiorsky. Classics in
Movement Sciences, Chapter 10 (pp. 289–315). Cham-
paign, IL: Human Kinetics Publ.
Lombard, W.P. (1903). The action of two-joint muscles. Amer-
ican Physical Education Review, 8, 141–145.