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Incorporating joint compliance within a rigid body simulation model of drop jumping

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Abstract

Impact forces of up to 13 times bodyweight have been observed in dynamic jumping activities such as the triple jump [1]. It has long been accepted that the human skeletal system is capable of damping such impact shock waves and avoiding direct transmission of impact forces to internal structures. The force attenuating mechanisms responsible, including foot arch and heel pad compliance; lower extremity joint compression; and spinal compliance, have previously been overlooked in forward-dynamics whole-body simulation models in aid of simplistic representations. Indeed, a general assumption of the existing models has been the simplistic modelling of frictionless pin joints and fixed segment lengths. Pin joint representations have therefore resulted in unrealistic dissipation of force and acceleration throughout the body following impact and hence difficulty in accurately reproducing experimentally measured ground reaction forces [1]. Previous studies have attempted to overcome this limitation by modelling excessive wobbling mass movement or compression at the foot-ground interface to compensate for the lack of compression and thus force dissipation within the joint structures [1, 2, 3]. Allen et al.[1] stated that whilst unrestricted ground compression was appropriate for simulating performance, accurate internal force replication would require compliance elsewhere within the rigid link system. The purpose of this study was therefore to investigate the effect of incorporating joint compliance on the ability of a computer simulation model to accurately predict ground reaction forces during dynamic jumping activities.
XVI International Symposium on Computer Simulation in Biomechanics
July 20th 22nd 2017, Gold Coast, Australia
INCORPORATING JOINT COMPLIANCE WITHIN A RIGID BODY SIMULATION MODEL OF DROP
JUMPING
1 S.A. McErlain-Naylor, 1 S.J. Allen and 1 M.A. King
1 School of Sport, Exercise and Health Sciences, Loughborough University, United Kingdom
Corresponding author email: S.A.McErlain-Naylor@lboro.ac.uk
INTRODUCTION
Impact forces of up to 13 times bodyweight have
been observed in dynamic jumping activities such
as the triple jump [1]. It has long been accepted
that the human skeletal system is capable of
damping such impact shock waves and avoiding
direct transmission of impact forces to internal
structures. The force attenuating mechanisms
responsible, including foot arch and heel pad
compliance; lower extremity joint compression;
and spinal compliance, have previously been
overlooked in forward-dynamics whole-body
simulation models in aid of simplistic
representations. Indeed, a general assumption of
the existing models has been the simplistic
modelling of frictionless pin joints and fixed
segment lengths. Pin joint representations have
therefore resulted in unrealistic dissipation of
force and acceleration throughout the body
following impact and hence difficulty in accurately
reproducing experimentally measured ground
reaction forces [1].
Previous studies have attempted to overcome this
limitation by modelling excessive wobbling mass
movement or compression at the foot-ground
interface to compensate for the lack of
compression and thus force dissipation within the
joint structures [1,2,3]. Allen et al. [1] stated that
whilst unrestricted ground compression was
appropriate for simulating performance, accurate
internal force replication would require
compliance elsewhere within the rigid link system.
The purpose of this study was therefore to
investigate the effect of incorporating joint
compliance on the ability of a computer simulation
model to accurately predict ground reaction
forces during dynamic jumping activities.
METHODS
A planar computer simulation model was
constructed within AUTOLEVTM. The model
consisted of nine rigid segments representing the
forefoot, triangular rearfoot, shank, thigh, lower
trunk, upper trunk, head and neck, upper arm,
and lower arm. The model incorporated wobbling
mass elements in the shank, thigh and trunk
(spanning upper and lower trunk segments). The
foot-ground interface was modelled using non-
linear spring-damper functions vertically and
horizontally at the toe, MTP joint, and heel. The
MTP, ankle, knee, hip, shoulder, and elbow joints
were each driven by extensor and flexor torque
generators, whilst the neck angle did not vary.
Ankle plantarflexion and knee and hip flexion and
extension were driven by biarticular joint torque
generators [4,5] with the joint torque determined
by activation level as well as the angle and
angular velocity at both the primary and a
secondary joint (e.g. knee extension torque
determined from knee and hip kinematics).
In addition, viscoelastic elements were
incorporated at the ankle, knee, hip, mid-trunk,
and shoulder joints connecting the distal end of
one rigid segment with the proximal end of the
adjacent rigid segment. These represent the
internal compliance within the human medio-
longitudinal foot arch as well as within the
articulating joints and the curvature of the spine.
The compliant joint spring-damper force, Fj, was
given by
=3− ̇
where kj and βj are the stiffness and damping
coefficients, respectively, and s and are the
stretch and stretch rate of the spring-damper,
respectively.
The position of the upper arm insertion along the
rigid upper trunk segment was determined by a
cubic fit against shoulder joint angle, replicating
depression and elevation of the shoulder girdle as
the upper arm is lowered or raised respectively.
The simulation model was made specific to a
national level male 100 m sprinter (23 years, 1.86
m, 88.6 kg, personal best 10.50 s) using
experimentally collected data obtained during
drop landings and maximal drop jumps, including
arm swing, from drop heights of 0.30, 0.445,
0.595, and 0.74 m. Lightweight Dytran triaxial
accelerometers (1000 Hz) were positioned over
the first metatarsophalangeal (MTP) joint, the
distal and proximal anteromedial aspects of the
tibia, the anterolateral distal femur (all on the
17
dominant leg), the L5 vertebra, and the C6
vertebra. The positioning of these
accelerometers was measured and accelerations
at the same positions on the simulation model
were output for the purpose of acceleration
attenuation comparison and evaluation.
Rigid and wobbling segmental inertia parameters
were determined from anthropometric
measurements taken according to the protocol of
Yeadon [6]. Subject-specific monoarticular and
biarticular joint torque parameters were calculated
from maximum voluntary torque measurements at
the ankle, knee, hip, and shoulder joints taken
using an eccentric-concentric protocol on a Con-
Trex isovelocity dynamometer. MTP torque
parameters were scaled from those at the ankle.
The stiffness and damping coefficients of the
wobbling masses, compliant joint springs, and
foot-ground contact springs were determined
alongside model evaluation during a matching
optimisation process. A parallelised genetic
algorithm varied these parameters as well as the
torque generator activation parameters to
minimise an RMS of cost functions between the
model and corresponding experimentally
collected whole body kinematic and ground
reaction force data for a 0.595 m drop jump, given
the same conditions at touchdown.
Penalties were applied to the cost function in any
simulation where displacement at a viscoelastic
element exceeded predefined anatomical limits.
The compliant ankle joint spring was assumed to
represent ankle joint compression as well as
medio-longitudinal arch depression and navicular
drop inferior to this position. Penalty thresholds
were determined with reference to the relevant
literature. Similarly, displacement limits at the
knee and hip were determined with reference to
relevant joint space and distraction gap literature.
Both the mid-trunk and shoulder spring limits
were determined from the collected experimental
data of drop jumps and drop landings. The mid-
trunk represented the observed resultant length
change between the C7 and L5 vertebra, with the
shoulder spring replicating the experimental acute
change in hip to shoulder distance following
impact with the ground.
The novel introduction of compliance within joint
structures enabled a reduced magnitude of
compliance elsewhere in the system, and thus
more realistic displacement limits at the wobbling
masses and foot-ground interface. At the foot-
ground interface new limits were determined with
reference to scientific literature investigating foot-
shoe-ground horizontal displacement, and shoe
compression with the addition of heel pad
compression at the heel. Wobbling mass
displacement limits were determined from a
spectral analysis of marker movement in relation
to the underlying rigid segment during the
experimental drop jump and drop landing data
collection.
In addition to the above matching and model
evaluation process (compliant model), the same
process was repeated for comparative purposes
with a similar model featuring pin joints in place of
the viscoelastic joint springs (rigid model) and the
same penalty limits.
RESULTS AND DISCUSSION
The overall difference in kinetic and kinematic
time-histories between the compliant model and
experimental performance during the evaluation
and parameter determination process was less
than 5%. This included an RMS of vertical and
horizontal ground reaction forces that was also
less than 5% of peak vertical ground reaction
force. All viscoelastic displacements were within
the bounds imposed and so no penalties were
incurred. In comparison, RMS differences were
greater for the rigid model with traditional pin
joints. The difference between model and
experimental performance data was less than
10%. Ground reaction forces differed from
experimental data by greater than 10%. Again,
no penalties were incurred.
Thus, the incorporation of viscoelastic elements
at key joints enables replication of experimentally
recorded ground reaction forces within realistic
whole body kinematics and removes the previous
need for excessive compliance at wobbling
masses and/or the foot-ground interface. Future
research should continue to evaluate the force
and acceleration transmission within a compliant
model and assess the ability to generate realistic
joint reaction forces within a relatively simplistic
whole body simulation model.
REFERENCES
1. Allen, S.J. et al. J Biomech 45: 1430-1436,
2012.
2. King, M.A. et al. J Appl Biomech 22: 264-274,
2006.
3. Yeadon, M.R. et al. J Biomech 43: 364-369,
2010.
4. King, M.A. et al. Int J Multiscale Com 10: 117-
130, 2012.
5. Lewis, G.C. et al. J Appl Biomech 28: 520-
529, 2012.
6. Yeadon, M.R. J Biomech 23: 67-74, 1990.
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  • S J Allen
Allen, S.J. et al. J Biomech 45: 1430-1436, 2012.
  • M R Yeadon
Yeadon, M.R. et al. J Biomech 43: 364-369, 2010.
  • G C Lewis
Lewis, G.C. et al. J Appl Biomech 28: 520-529, 2012.