Michael Colarossi
Honors Thesis Proposal
Advisor: Professor John Moosbrugger
March 8, 2007
Developing a Multi-Link Model to Describe the Motion of a Person Standing on an
Oscillating Base
Abstract:
The objective of this project is to develop a multi-link model to describe the
motion of a person standing on a platform base with small amplitude and oscillating
motion. An understanding of how this motion is propagated through the linkage will help
with future testing of how a person balances himself/herself. Previous work has
primarily focused on modeling forces on the ankle, where the body is treated as an
inverted pendulum with a lumped mass. Forces between the ankle and platform and the
location of these forces have been measured, and ankle torque and sway angle of the
ankle can be estimated. In this project, it is proposed to include additional joints such as
the knee, hip, and the lumbro-sacral (lower spine), and model how they affect the motion.
Stiffness and damping elements will be included in the joint couplings. Stabilization
through feedback forces/moments may also be explored. Joint stiffness and damping
coefficients and centers of mass will be required. These can be estimated experimentally,
and most of this will be done in the SLIP-FALLS-STEP (Sliding Linear Investigative
Platform for Assessing Lower Limb Stability with Synced Tracking, EMG and Pressure
measurements) laboratory. This lab has equipment where a subject can stand on a
platform undergoing specified motion. The subject can be stabilized in a harness (to limit
error in results). Control and data acquisition systems are coupled to this platform, to
control the platform motion and displays and records important data, ranging from center
of pressure on the ankle to torque at the head.
Background and Previous Work:
There have been several studies aimed at understanding how a small perturbation
can affect a person’s balance. Some of these focus on the effect on the ankle, and others
look at how the whole body can be affected. For this thesis, it is important to understand
the methodology, results, and the equipment used in these experiments.
Pilkar et al. measured and modeled ankle angle changes while standing on a
platform subjected to a small motion perturbation. The equation of motion is derived
from a free-body-diagram of the ankle, and treating the body as an inverted pendulum.
With the inverted pendulum idea, there is a lumped mass with a gravity force, inertial
mass force and an ankle torque1. This is shown below in Figure 1. After the subject is
given a small perturbation, multiple measurements were made on the ankle angle
position, ankle torque, center of pressure, and center of mass. This demonstrates the type
of measurements that can be made, though this project aims to explore more than just the
ankle; it will involve how motion of a platform affects other areas of the body and how
the subject reacts to balance himself/herself. Also, since this work was performed at
Clarkson, the equipment is the same equipment that will be used for ongoing
experimental work parallel to this thesis.
Figure 1 – Body Treated as an Inverted Pendulum
Ji et al. utilized the same idea of an inverted pendulum and also measured similar
categories, but used a different method to better evaluate sway and directly calculated
ankle moment and ankle stiffness from the reaction forces from the ground2. A free-body
diagram of the ankle is made, and equations for sway angle and torque are determined.
Instead of using the center of mass (COM) results from the measuring device (they
believed that the device’s accuracy was not perfectly reliable), the equation used for
COM in this experiment was:
COM = height of the person*angle(θ).
Using this formula, the COM results are about 1% higher than the device’s results. For
this thesis, it may be useful to use simplifying equations like this if it can be as accurate
as or more accurate than finding experimental data.
Corbeil et al. used the same methodology, but they determined how someone’s
mass can affect balance. The main result was that greater mass leads to greater risk of
falling3. This is because the center of mass is further away from the ankle for a heavier
person, which leads to a greater moment on the ankle and a greater ankle torque is
required to counter-balance it3. This work is useful for here because of the method used
to find the center of mass. Percentage of mass was found for certain areas of the body,
and this will be helpful since this thesis project may require finding centers of mass
between segments of the body.
Gruneberg et al. tested the idea that multiple joints help in balancing a person.
They concluded that balancing from pitch perturbations is controlled by ankle and knee
joints, while hip and lumbro-sacral joints balance a person from roll perturbations4. They
also concluded that these balancing corrections are independent of one another4. Subjects
were standing on a platform that was given a perturbation in the pitch direction and then
in the roll direction after a small delay. It was observed that during this delay there were
small changes in the pitch motion of the legs and trunk but after the movement in the roll
direction there was a balancing motion in the legs and trunk4. This is shown below in
Figure 2. This is important because even though a multi-link model is to be developed in
this thesis, some body motion couplings may be more important than others.
Figure 2 – How Trunk Roll and Pitch Angle are Affected by a Delay in the Roll
Direction
Storey et al. developed a kinematic methodology to describe the motion of a
multilink model. In this approach there is a translation and rotation of a set of joints to
certain coordinates and then a continuation to translate and rotate them back to the
original position, while modeling the motion throughout the process. A computational
model computes position and orientation of individual limb segments and joints5. Matlab
is used to develop a matrix that has each of the limb vertices and the x, y, and z position
coordinates. This matrix is used to describe the coordinates after a joint is rotated or
translated. It is seen that the yaw, pitch, and roll angles change from rotation about a
joint5. This paper used animal joints to help describe the modeling, but this idea can be
used for human joints and limbs.
Description of Proposed Work:
The objective of this project is to develop a linkage system model that describes
the motion of a person standing on a platform with oscillating motion. Such a model will
help in understanding what joints in the human body have a role in balancing someone
and how they help with balancing. It will also aid in the interpretations and design of
experiments. The literature will be surveyed to ascertain the current understanding of
how the body reacts to an oscillating base. Free-body diagrams will be developed to
derive the equations of motion for the multi-link model. In the free-body diagrams, each
joint will have a stiffness and damping coefficient that opposes the direction of motion,
and there will be an inertial mass force. There may be additional external forces or
torques on the person or the joints and this will be needed to be determined. Concurrent
with modeling, testing of subjects will be performed in the SLIP-FALLS-STEP lab.
Control and data acquisition systems will be used to control the amplitude of the
sinusoidal wave that affects the platform motion, and will collect and store data of how
the person reacts to the motion of the platform. The data collected from the testing will
be compared to model results to improve and validate the model. Ultimately the aim is to
use the model to help describe how the motion of the platform is propagated through the
subject’s body.
Members of Professor Robinson’s group in the SLIP-FALLS-STEP laboratory
will be collaborating on this project. They will assist in training, equipment operation,
and in performing experiments. They will also provide advice and consultation in the
development of the model.
Thesis Timeline:
February/March 2007:
-Research previous works relating to thesis topic
-Develop hand-written sketch of possible model of multi-linkage system
-Finish thesis proposal
April 2007:
-Become familiar with lab equipment
-Revise and edit model
August/September 2007:
-Develop model using computer program (such as Matlab)
-Finish research on previous works
October/November 2007:
-Test model in laboratory
-Revise and re-test model as necessary
-Analyze data and model to develop conclusions
January/February 2008:
-Write rough draft of thesis
-Revise thesis
March 2008:
-Finish final copy of thesis/presentation
References:
1) R. Pilkar, J. Moosbrugger, V. Bhatkar, R. Schilling, C. Storey, C. Robinson, “A
Biomechanical Model That Confirms Human Ankle Angle Changes Seen During
Short Anterior Perturbations of a Standing Platform,” Center of Rehabilitation,
Engineering, Science and Technology, Clarkson University.
2) Z. Ji, F. Thomas, H. Chaudry, B. Bukiet, “Computational method to evaluate ankle
postural stiffness with ground reaction forces,” Journal of Rehabilitation
Research & Development, vol. 41, no. 2, pp. 207-214, April 2004.
3) P. Corbeil, M. Simoneau, D. Rancourt, A. Tremblay, N. Teasdale, “Increased Risk
for Falling Associated with Obesity: Mathematical Modeling of Postural
Control,” IEEE Transactions, vol. 9, no. 2, June 2001.
4) C. Gruneberg, J. Duysens, F. Honegger, J.H.J. Allum, “Spatio-Temporal Separation
of Roll and Pitch Balance-Correcting Commands in Humans,” Journal of
Neurophysiology, July 2005.
5) C. Storey, A. Hollister, C. Robinson, N. Witriol, D. Anderson, “A representation for
multilinked systems with arbitrary revolute joints in human and arthropod
limbs,”