First published online September 5, 2008
Journal of Experimental Biology 211, 2989-3000 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.014357
Running on uneven ground: leg adjustment to vertical steps and self-stability
Sten Grimmer1,*,
Michael Ernst1,
Michael Günther1,2 and
Reinhard Blickhan1
1 Friedrich-Schiller-Universität, Institut für Sportwissenschaft,
Lehrstuhl für Bewegungswissenschaft, Seidelstraße 20, D-07749 Jena,
Germany
2 Eberhard-Karls-Universität, Institut für Sportwissenschaft,
Arbeitsbereich III, Wilhelmstraße 124, D-72074 Tübingen,
Germany
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Fig. 1. The running track setup near the force plates. (A) View from above. The
track is instrumented with two force plate sections. The first one (first
contact) consists of two small Kistler force plates (Kistler 9282BA, size 600
mmx400 mm) and the second (second contact) of one large Kistler force
plate (Kistler 9285C, size 900 mmx600 mm). (B) View from the side.
Before, between and after the force plates the track is uneven (vertical
perturbation between 1 and 2.5 cm). These small perturbations are made with
wooden bars (width 120 mm). Note that in this sketch the ratio between the
width of the bars and the length of the force plates is exaggerated for
clarity. The first force plate represents ground level of vertical height
zero. The second force plate acts as a single perturbation (step), which is
variable in vertical height. Four track conditions were measured: level track
(no perturbation at all) and an uneven track, i.e. varying height of bars
before and after the force plates plus vertical steps of 5, 10 and 15 cm onto
the second force plate.
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Fig. 3. Leg force and leg length during stance phase of the two subsequent
contacts. The solid black lines represent level to level running (track type
0, N=99) and the grey shaded area is ±1 s.d. of this reference
run on the undisturbed track, the dotted line from level to 5 cm up (track
type 1, N=106), the dashed line from level to 10 cm up (track type 2,
N=108) and the dashed-dotted line from level to 15 cm up (track type
3, N=110). (A,B) A quasi-elastic leg operation is observed in both
contacts. However, the net energy balances are not zero (see
Table 4). (C) The peak leg
force is slightly increased in preparation for the consecutive step. (D)
However, in the case of a perturbation the maximum leg force decreases in
proportion to vertical step height. (E) The leg compression in the first
contact is not affected in preparation for the vertical step. (F) Here, the
leg length at initial contact (touch-down, TD) is shortened as well as the
minimum leg length during contact in proportion to the vertical step height.
Thus, leg compression remains almost constant.
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Fig. 7. Simulation results of peak spring force (Fspring) and
maximum spring compression ( l) for a 15 cm step in the second
contact dependent on a variation of spring stiffness
( ) and angle of attack
( TD). All simulations started before the first contact on
ground level with identical initial conditions
( x,0=4.5 m s-1,
y0=0.95 m) and system parameters
( =35.7, TD=68 deg.,
m=80 kg, l0=1 m). (A,C) By using a fixed angle of
attack and decreasing spring stiffness we found that spring force decreased
while spring compression increased. Dash-dotted line,
=25.5, TD=61 deg.;
dotted line =19.1,
TD=61 deg.; dashed line,
=12.7, TD=61 deg.
(B,D) In the case of varying (steepening) the angle of attack and using a
fixed spring stiffness, spring force and spring compression decreased.
Dash-dotted line, TD=59 deg.,
=19.1; dotted line,
TD=61 deg., =19.1;
dashed line, TD=63 deg.,
=19.1.
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Fig. 8. Estimation of peak spring force and maximum spring compression in the case
of a disturbed contact (15 cm step up) with a varied angle of attack and
spring stiffness for a spring–mass simulation. The dotted lines indicate
spring forces between 1.5 and 3 times gravitational force and the black lines
indicate spring compressions between 0.1 and 0.15 times initial leg length.
The arrows highlight the small areas of experimentally measured values. (A) In
the simulation, decreasing spring stiffness and steepening angle of attack led
to a decreasing peak spring force. (B) However, an increasing maximum spring
compression with increasing spring stiffness can only be realized by
substantially flattening the angle of attack. Initial conditions on ground
level were x,0=4.5 m s–1,
y0=0.95 m, m=80 kg, l0=1 m,
and were altered in the consecutive contact due to the step.
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© The Company of Biologists Ltd 2008
knee) and ankle
(
). The
black J-shaped area guarantees at least 30 following contacts (end of
simulation) and is referred to as the self-stable area. The circles (first
contact) and squares (second contact) represent the data from the track types
i=1–3 of a typical subject running at 4.8±0.16 m
s–1. Two distinct regions of stiffness and angle of attack
combinations were found. From the first to the second contact both stiffness
and angle of attack decrease in accordance with the results of the simulation.
However, in most cases the experimental results do not fit into the area of
self-stability but, rather, into an area that guarantees at least five
subsequent contacts. Initial parameter of simulation: horizontal component of
the initial velocity