Passive tools for enhancing muscle-driven motion and locomotion
Institute for Biophysical and Clinical Research into Human Movement, Manchester Metropolitan University Cheshire, UK
* e-mail: a.e.minetti{at}mmu.ac.uk
Accepted 19 January 2004
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Summary |
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Key words: locomotion performance, passive tool, muscle-driven motion, energy cascade, swimming, human
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Introduction |
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Versatility is a crucial feature in the biological world, and species can expand their habitats as long as they are comfortable with a variety of gaits and environments. Animals simultaneously capable of climbing trees, diving, running and flying probably do not exist, although some (e.g. flying squirrels, seagulls, flying fishes) display a challenging combination of those locomotion modes. Other animals, such as cheetahs and horses, favour a specialized motion and have difficulties performing well in other diverse situations.
While representing an intermediate condition between those two extremes, with a particular propensity for moving on land, humans continuously strive to improve their speed of progression in terrestrial, aquatic and aerial modes. Furthermore, humans have always been ethologically interested in increasing their offensive power. These research processes started a few millennia ago (use of skis in Scandinavia, halteres in ancient Greece) and involved ingenuous and empirical ergonomics (e.g. African bow and arrows), culminating in the last few decades with the success of human-powered flight, made possible by the combination of high-tech aeronautical engineering, exercise physiology and biomechanics.
The wide variety of invented tools, having the common feature that they do not supply any additional mechanical energy to the body, provided effective compensation for limitations in anatomical design, inadequacy of muscle performance and for the insufficient power-amplification of biological elastic structures. In the following, before discussing the different `augmented' motor activities, I try to describe the path from force generation to the achieved motion, with reference to the strategies used to make such a transformation the most effective.
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From muscle contraction to mechanical work via metabolic consumption |
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The ability to generate force depends on muscle length (maximum at
intermediate lengths) and on the speed at which it shortens. In particular,
high contraction speeds are associated with low force produced
(Hill, 1938). By multiplying
the two axes of the force vs. speed relationship, we obtain the
muscle mechanical power, which is maximum at about 1/3 of the maximum
contraction speed. The first characteristic (force/length) does not remarkably
penalize our daily activities because muscles are assembled in the body to
operate near their optimal length. The second characteristic (force/speed) is
more crucial, particularly when the increase in movement or locomotion speed
would require muscle to contract faster. To cope with this problem, biology
provides elastic structures, as tendons, working as power amplifiers or as a
mechanical energy reservoir. The higher force produced by a slow contraction
can be elastically stored, then the deformation energy can be released at a
faster rate. The total mechanical work input is not very different from the
output, whereas the output power is much higher. Examples of this mechanical
power-amplification strategy are the catapult-like jumping in locusts, frogs
and galagos. By contrast, tendons are used as a mechanical energy reservoir
during bouncing gaits (hopping, running, trotting, galloping), where limb
extensor muscles tend to operate quasi-isometrically while tendons store the
energy of landing (which otherwise should be lost) and subsequently release it
to assist take-off (Roberts et al.,
1997
; Biewener et al.,
1998
). This avoids fast muscle contraction and minimizes the
amount of fresh energy to be provided to the system.
The next step is how muscles act across joints. Here, for the same final torque, muscles need to contract more forcefully the smaller the moment arm. Also, the simultaneous action of agonist and antagonist muscles, while stabilizing the joint and helping modulate the intended motion, implies the use of extra metabolic energy beyond the minimum that is strictly necessary to generate the same net moment.
Finally, the interaction of the body with the environment is crucial in
generating motion. So-called external mechanical work can be mainly
partitioned as the work necessary to accelerate and raise the body centre of
mass and that needed to overcome friction and other media (terrain, air,
water) forces that oppose motion. For friction to operate we need to slide
with respect to the medium under consideration (it does not act, for example,
between the foot and the terrain when running). Another component of the total
mechanical work is the internal work, which is needed to reciprocally
accelerate body segments with respect to the body centre of mass and to
overcome internal friction in body tissues
(Fenn, 1930). This depends on
the segment inertia and on their motion pattern.
Considering locomotion, both the metabolic and mechanical demand are
expressed as costs, i.e. as energy per unit distance (e.g. ml O2
m1 or J m1). The metabolic cost is the key
index of the `economy' of locomotion, and corresponds to the amount of fuel
(litres of petrol) needed by our cars to travel a given distance (say 100 km).
The proportion of the metabolic cost (or power) resulting in mechanical cost
(or power) is termed `efficiency' and, when the whole mechanical energy flux
is known and the metabolism is aerobic, cannot exceed the value of
2530% (Woledge et al.,
1985). This upper limit is set by the product of the efficiency
related to phosphorylation (60%) of metabolic substrates to ATP molecules and
that of muscle contraction itself (from ATP molecules to force/displacement
generation, equal to 50%). Although often mistakenly thought to be
interchangeable concepts, efficiency and economy (the inverse of metabolic
cost) are not. Schematically, economy needs efficiency, but efficiency does
not imply economy. An efficient locomotion is one where most of the metabolic
energy input is transformed into mechanical work, but it is possible that some
of this mechanical work is not necessary for propulsion, resulting in a worse
economy. If most of the mechanical work done contributes to progression, and
if the mechanical work to propel ourselves is close to the minimum necessary,
we also have an economical locomotion. If, for the same mechanical cost,
efficiency and economy are directly related, their relationship is more
deceptive when the work and metabolic energy both vary. An example is the
comparison between walking and cycling at the same speed, where the same
efficiency is seen together with a much lower economy of walking. This is due
to the much lower mechanical work necessary in cycling.
The general term `efficiency', as mentioned, can be envisaged as the ratio
between the energy out and the energy in. While the latter is straightforward,
the energy out can be chosen from the minimum amount of work necessary to move
(in ideal conditions), the measured mechanical work, the external mechanical
work (included the ones against air/water drag, rolling resistance and so on),
etc. The first of this variety of numerators defines the so-called `overall or
performance efficiency', while the others can be used to break down this
efficiency into a cascade of sub-efficiencies. Such an approach permits
detection of any energy wastage occurring at the levels of muscle, appendages
and associated passive tools. Depending on the type of locomotion being
investigated, the efficiency cascade can be complicated by the different
components of external work, internal work (including the deformation of all
the body/tool parts) and the extent to which muscles are optimized for that
task. Schematically, however, the overall efficiency can be considered as the
product of two main components: muscle efficiency and the so-called
`transmission efficiency' (Cavagna,
1988), referring to the ability to transform net muscle force into
the minimum external work necessary to move (see discussion on fin swimming,
below).
In summary, to improve locomotion (and motion), mechanical work should be limited to just the indispensable type and the muscle efficiency be kept close to its maximum. Thus it is important to avoid: (1) operating muscles at too short or too long length, (2) contracting them at too high speed, (3) using joint angles with disadvantageous moment arm, (4) using co-contraction (or useless isometric force), (5) raising or lowering the overall body centre of mass too much, and (6) accelerating limbs too much with respect to the body centre of mass. Other factors to take into account include: (7) external friction should be reduced to the minimum level, (8) most of the external force should be effectively transformed into forward propulsion, and (9) mechanical energy should be stored into elastic structures for successive power-amplification purposes.
In this perspective, every passive tool collaborating to fulfil one or more of the above requirements is welcome. In the rest of this paper, numbers in bold typeface refer to the above strategies.
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Where to gain more range/power |
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Long jump (in its `standing' variation) is less easily investigated as an
`augmentable' motor act. Recent research
(Minetti and Ardigó,
2002) indicated how added hand-held masses, such as the halteres
used in ancient Olympic games by pentathlon athletes, can increase the jump
distance by 5%. The halteres (Fig.
1), whose optimal mass for two was in the range of 78 kg,
allow the body's centre of mass not only to take off in an anterior and upper
position, but also to land posterior to the contact point of the feet,
compared to an unloaded jump. This causes the parabolic flight trajectory to
be prolonged and translated forward, for the same take-off speed. Also,
computer simulations and experiments have shown that the whole body, by better
exploiting the shoulder rotator muscles (2) and the elastic structures
along the kinematic chain (9), produces a higher mechanical power when
loaded. Further enhancement of the standing long jump, which was introduced in
the early modern Olympics (the record by R. C. Ewry was 3.46 m), was obtained
by innovative British jumpers in the late 19th century. Joseph Darby and John
Higgins, in the attempt to successfully jump over canals, developed the
technique of backward-throwing the loads (dumbells of about 3.5 kg each)
during the flight phase, obtaining additional propulsion (Darby's reported
record was 4.49 m).
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As far as running is concerned, there is little that can be done to improve
performance substantially, although quite different from the concept of a
portable passive tool, a compliant `tuned' (9) track for athletics
proved to be successful in (slightly) enhancing running speed
(McMahon and Greene, 1978). The
main limitations of running reside in: (i) the inverse relationship between
contact time and speed, which makes the ability to store/release mechanical
energy into/from the elastic structures a limiting factor, (ii) the constraint
of stopping the foot with respect to the ground, which implies that (iia) the
limbs need to move with respect to the body centre of mass at the same speed
that the centre of mass moves with respect to the ground, largely increasing
the mechanical internal work (6), and (iib) muscle contraction
generates less force for propulsion (2), being directly related to the
progression speed. Certain gaits can inherently circumvent these limitations.
All the `skating' techniques, using tools (in chronological sequence) such as
ice-skates, cross country skis or roller-skates, demonstrate how a gait that
is still bipedal can be fast. This occurs not only because of decreased
friction with the medium (7), but also because at high progression
speeds the appendages push while continuing to slide on the medium, thus the
contraction speed is much lower than in running (2). If in addition the
vertical excursion of the body centre of mass is reduced (5) and the
pendulum-like mechanism is still operating (measured in cross country skiing;
Minetti et al., 2000
), it is
not surprising that the `skating' gaits perform much better than running (1 h
endurance record: running=20 km, roller skating=40 km; see
Fig. 2). The residual
limitation of skating gaits is that the upper limbs are not used, or, if they
are, the poles need to stop with respect to the ground, with all the drawbacks
discussed above for the lower limbs (2, 6). Further enhancement
of cross-country skiing, therefore, needs be sought in a new design of poles
that would allow the pushing portion to slide. In the last few years
ice-skaters have adopted an ingenious variation tool, the clapskate (Ingen
Schenau, 1996), which increases speed performance by allowing the blade to be
in contact with the ice for a longer time at the end of the push.
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Leaving bipedal locomotion, we come to the most important invention that
has revolutionised personal transportation. The bicycle (1 h endurance
record=50 km) combines three very good ideas that make it the vehicle of
choice for long human-powered journeys on (regular) land: (i) the body weight
is sustained by the saddle, avoiding the need for muscles to generate force
for postural purposes and minimizing the vertical excursion (5) of the
body centre of mass, (ii) it always allow muscles, regardless of the increased
progression speed, to operate in the optimal region of the force/velocity
relationship (2) by using gears, and (iii) the increased base of
support associated with the two wheels avoids the need for balancing work in
the sagittal plane (see how metabolically expensive is to ride a unicycle;
Fig. 2) and, assisted by the
speed generated, in the frontal plane. The early evolution of cycling, dating
back from 1820 to 1890 (Minetti et al.,
2001), was mainly addressing point (ii) by making the structure
less `shaking', while modern bicycle technology is mostly devoted to reduce
the rolling resistance (7) and the main force opposing high speed
progression, i.e. the aerodynamic drag (di
Prampero, 2000
). However, the advantages of an extraordinary tool
like the bicycle can be overtaken again by walking and running when the path
slope is steeper than 25% (Ardigó et
al., 2003
).
The world records of most of the locomotion modes described so far are plotted in Fig. 2, where the estimated metabolic cost at the different progression speeds can be appreciated (see legend to Fig. 2).
Assisted aquatic locomotion
Turning to water locomotion, it does not require any biomechanical
knowledge to realize that the human body is not perfectly suited to that
medium. We need to move at the airwater interface, and this generates
mechanically expensive bow waves, we cannot efficiently undulate our body
because of lack of musculoskeletal design and, even if we could do so,
the undulating parts would not efficiently contribute to propulsion. In
contrast to aquatic animals, we had to inaugurate paddling with our upper
limbs to cope with the body inadequacy. While an advantage is certainly there
(compared to just kick swimming), the hands and forearms did not evolve for
that task, thus the overall efficiency remains low. It is apparent, therefore,
that this is a field where there is great scope for speed to be generated by
passive tools. A recent study (Zamparo et
al., 2002) analysed the mechanical and energetic advantage of
using fins in kick swimming. The gain in speed, resulting from the application
of several strategies (2, 6, 8), is particularly
remarkable only if upper limbs do not contribute to propulsion, and this is
the reason why fins are so effective in scuba diving. However, the efficiency
cascade is not dramatically improved by fins and remains well below the
standard for terrestrial locomotion (see
Fig. 3 for a comprehensive
analysis). A further improvement has been achieved by using the monofin, a
device mimicking the tail fluke of dolphins and simultaneously operated by the
two lower limbs. Fig. 4
compares world records of monofin swimming with those of front crawl. It is
apparent that, despite the use of a smaller mass of muscle (only lower limbs
are active), the monofin is associated with a much better economy of energy
and, thus, a higher cruising speed. Also, the analysis shows that, similarly
to running (Fig. 2) and
different from front crawl, the metabolic cost of swimming with this tool is
almost speed-independent.
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Assisted launching
It is beyond the aims of this Commentary to propose a fully comprehensive
list of passive tools, but it is necessary to briefly mention launching
devices. In contrast to the dumbbell-assisted long-jump where masses were
thrown (backward) to enhance the human body performance, we are here referring
to activities whose goal focuses on the forward thrown object, as in racket
sports and archery. Both categories try to remedy the inherent limitation of
the musculoskeletal system by introducing limb-lengthening (e.g. the
tool named `cesta' in the `pelota vasca', the golf club and the
cricket/baseball bat) and elastic tools (badmington and tennis rackets, for
example) capable of storing and releasing elastic energy (2, 9)
with power-amplifying effects. Archery is probably the most ancient passively
augmented human activity (African arrows date back to 25 000 BCE, Chinese
crossbow to 1500 BCE). From hunting to war making, the technical evolution of
spear/stone/arrow throwing has allowed man to continuously increase the
distance thrown and the degree of precision. Modern commercial crossbows,
manually loaded tools where the elastic energy of their limb deformation is
held by a catch mechanism, are capable of releasing the arrow at about 360 km
h1, for a distance range (=v2
g1) of about 1 km. The actual record distance for
the foot bow (a crossbow where both upper and lower limbs are involved in
loading) is 1.8 km (corresponding to a release speed of at least 480 km
h1 and an estimated distance on the Moon of 10.8 km). The
traditional bow and its modern evolution, the compound bow (H. W. Allen,
1969), deserve a special mention for their technological simplicity and
ingenuity. In both tools the mechanical work needed to bend their elastic
limbs (9) is slowly done (2) by muscles (back/shoulder) stronger
than the ones involved in forward hand throwing. One of the drawbacks of
traditional bows, i.e. that the isometric force needed to sustain the tension
increases with the distance drawn backward, making the aiming phase with
strong bows quite stressful, has been very recently (1969) attenuated by the
compound bow. Such an invention consists of a normal bow with limbs, having
asymmetrical cams located at the ends, which act as pulleys for the string.
The variable moment arm generated at the limb ends results in a higher
tension, and thus a greater storage of elastic energy at mid-draw, but enables
the aiming phase (end-draw) to start by sustaining a fraction (the so-called
`let-off' of, say, 40%) of the `normal' isometric tension. Since the total
energy stored in the bow is represented by the area below the force
vs. length curve, a higher power amplification and a better precision
(due to a more relaxed aiming) are expected. The distance record for a
compound bow is today about 1.4 km. All of the quoted records can be regarded
as feats if we consider that hand-throwing an arrow, as some colleagues and I
recently experienced in the field, results in a maximal distance of about 21
m.
Other augmented activities
For sake of brevity, we conclude by mentioning those activities where
multiple tools (thus multiple power enhancing and energy saving strategies)
have been simultaneously adopted, as for instance, in roller/ice skate racket
sports (hockey), aerofoil-bicycle-propeller for human powered flight (Gossamer
Condor,
web.mit.edu/invent/www/ima/maccready_intro.html),
hydrofoil-bicycle-propeller for speed record of human powered boat
(Decavitator,
lancet.mit.edu/decavitator/),
bicycle and propeller inhuman powered submarines
(www.isrsubrace.org),
armchair+bicycle in recumbent bikes, etc.
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Conclusions and perspectives |
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Appendix |
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![]() | (Ai) |
![]() | (Aii) |
![]() | (Aiii) |
The lower iso-cost curve [C=270 J m1 or 3.6 J (kg m)1 for mass=75 kg] is very well matched to the world records of running. This comes at no surprise since we know that running cost is speed independent and very close to that value. The curve is much higher than the experimental points for short performance duration, where the acceleration in the starting phase requires extra energy and penalizes the average speed (this is supposed to happen in all activities where a standing start is imposed). To draw other iso-cost curves for higher C values can help to estimate the average metabolic cost in short distance sprint race [e.g. for 400 m sprint running, the cost is approximately 400 J m1 or 5.3 J (kg m)1, corresponding to +48% if compared to normal steady state speed].
In Fig 2, running represents the most expensive form of terrestrial locomotion (except for unicycle), while a progression towards more economical modes is apparent. Hybrid forms (legged + wheels or + skates) imply a 4050% energy saving, while the bicycle (point mass + wheels) gives a 60% advantage. This increases the average speed and the range (in 1 h humans can run 20 km, rollerskate 40 km and cycle 50 km).
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Acknowledgments |
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References |
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