Olivero, Pavlik, Sierra, Tessier
HW #2
September 17, 2009
ME6105
Task 1
–
Identify the Decision Situation
With veterans returning from abroad and a relatively large
defense
budget to
accommodate their needs, now is the time to introduce new prosthetics to the market.
This project explores the decisions leading to the production of a transtibial prosthesis.
Most transtibial prosthetics do not mimic the propulsive forces sup
plied from the ball of
the foot. The amputee must provide the assistive force to pull the foot up to the top of
the
gait
path using femoral or core muscles to maintain a normal gait. This can result in
fatigue, decreased gait speed, and back injuries.
A
n example of
an
existing
powered transtibial prosthesis is shown below in
Figure 1. It is composed of two springs and a hinge. When the amputee puts their
body weight on their heel, the heel spring compresses to store this energy. This energy
is then transferred to
a
torsional spring and released to power the step.
Figure 1
–
Powered Transtibial Prosthesis System
The fundamental objective of this project is to maximize amputee mobility. This
requires the prosthetic to maximize energy efficiency so that the amputee uses as little
assistive force as possible. The specific design decisions to reach this objective ar
e
material, weight, spring constants, type of springs, and dampers. Assuming this
prosthesis is being built from scratch, the team has full control over
these
parameters
.
Task 2
–
Determine an Objectives Hierarchy
Figure 2
–
Fundame
ntal Objectives Hierarchy
Error!
Reference source not found.
Figure 3
–
Means Objectives Network
Objective
Attribute
(1) Maximize robustness for ground
conditions
When
going from
rest to maximum
speed
on an incline, a flat surface, and
a decline, subject has constant
acceleration within a standard deviation
of normal gait.
(2) Maximize speed
When walking at x mph for y meters on
an incline, a flat surface, and a decline,
subject r
eaches a maximum speed
within a standard deviation of normal
gait.
(3) Maximize prosthetic efficiency
Engage prosthesis for x steps and
measure the efficiency (F
out
/F
in
). F
in
is
measured by multiplying the mass of
the subject and the distance the sp
ring
is deformed. F
out
is measured by
attaching a force meter to the ball of
the prosthesis.
Table 1
–
Attributes
The design study will focus on the above objectives and attributes
since they
are
both comprehensive and measurable. In order for objective one and two to be
measurable, data from gait studies will be used to verify normal gait behavior for the
age and weight range within the design horizon. Attribute three
will be
measured us
ing
a scale, a ruler, and a force meter.
Task 3: Identify the Design Alternatives
The design
of the system
will be abstracted
to a 2

dimensional kinematics
problem. We will assume that the person walks without slipping
and that the bottom of
the
foot and the ground are both flat surfaces.
Each
segment
of the prosthetic
will be
treated as
a
rigid bod
y
.
Frictionless
joints with 1

rotational degree of freedom will
connect the rigid bodies.
.
Friction in these joints is disregarded
since the energy loss
due to friction is negligible compared to the energy loss
in the dampers.
Springs and
damp
ers
will be treated as
having no
mass
.
D
ifferent design alternatives can be derived
from
various
leg geometries and configurations. This involves the shape, dimensions
and masses of the different rigid bodies, the number and location of joints, the number
a
nd
type
of
springs and dampers (linear or rotational), and the spring and damp
ing
constants associated with each spring and dampe
r
respectively
. Sketches of different
types of prosthetic leg designs are displayed below.
Error!
Reference source not found.
Figure 4
–
Design Alternatives
Depending on the design chosen, there are a variety of design variables.
The
design variables will be limited
to the spring and dampe
r constants, and materials of the
rigid body, which will be used for mass analysis. Dimensions of the different parts of the
prosthetic can also be considered
design variables,
since
each
user
would require
different sizes, but for the scope
of this project, it will be best to choose dimensions that
represent
the
average person
’
s foot and
a
n
k
le.
Legend:
Rotational Joint
Rotational Spring
and Dampener
Linear Spring
and Dampe
r
Task 4: Identify the Structure of the Design Problem
Chance events are elements in the design problem for which the designer
has
no
control over and are usually hard to predict
; the outcome of which must be decided
before the decision can be made
.
Chance
elements in the design of the prosthetic leg
include
t
he weight of the user, the ground conditions, and the conditions of use. The
dimension
s
of the components of the system will be determined in part by the user
s
’
weight
,
and
by the conditions of use of the
system, either walking, jogging, or running.
The type of terrain, the condition of use, as well as the user weight will determine the
spring constants and damper coefficients needed for optimum performance. A heavier
person will produce different spring
compressions and different damper behavior
.
The
ground condition
s
will
also
affect
the way the system operates. Walking uphill will
require
a greater force output than
walking downhill or on a flat terrain. We will assume
there is no slipping between the system and the ground and therefore will not accou
nt
for types of terrain condition such as a slippery floor or a rough surface
because we are
assuming that
the friction force
will
be
large
enough
to prevent any slipping. The type of
use the system is given may also imp
act
its physical behavior. For example, if the user
is walking, the system configuration for optimum performance may be different than if
the user
is
jogging or running.
S
everal cases
will be modeled to
try to design
the
sys
tem
so
it can be used for a range of
scenarios.
Computational outcomes are factors which must be determined before a decision
is made.
The following computational outcomes will be considered
:
t
he energy stored
and released by the device,
adaptability
to ground conditions
, force input requirements,
average speed, market price
to appeal to an average customer
, expected lifetime
,
and
the
appeal to potential customers. Some of those outcomes depend on other
s
as
depicted in the
i
nfluence diagram in Figure
5
below.
All
of the outcomes
are
ultimately
affecting
the fundamental objective, which is to
maximize
the user
’
s mobility
.
Figure 5
–
Influence Diagram
Task 5: Identify the Simulation Scenario for an
Energy

Based System
Model
The design team identified the following
objectives:
m
aximize average speed of
user, maximize adaptability of the system to different terrain conditions
,
minimize the
force input requirement
and
minimize
cost. The first
three
objectives
allow for an
energy

based model in order to relate them to our decision alternatives. This will not
only make the decision
of
which alternative to c
hoose easier, but also a better informed
one, since
simulations will
predict
the response of all design alternatives to different
operating
conditions. On the other hand, the fifth objective, minimizing cost, is one that
cannot have an energy

based model since it is not directly related to physical properties
and does not involve energy transfers.
However, the cost of the product will be
com
pared to similar products currently in the market.
The cost of the product ultimately
effects the user
’
s mobility because if the user cannot afford the device, the user cannot
benefit from the enhanced mobility provided by the system.
The system
is purely mechanical
, so the energy is
kinetic and potential.
The
potential ene
rgy
comes from the
user
’
s
weight
and spring displacement
stored in
the
heel spring
.
This potential energy is
then
released
in the form of
kinetic
energy
when
the
user pushes off the ground
and the torsional spring releases the energy stored in the
heel spring
.
The energy loss due to friction between components and between the
system and the ground is
negligible
compared to the energy loss in the damper
.
Similarly, it is assumed that there is no slip between
the
ground and
the
bottom of the
prosthetic
foot
. Another assumption
is that walking
can
be approximated by a
sinusoidal signal. This signal will be the input of the system when modeling walking on
di
fferent terrain conditions.
Task 6: Asses
s
your plan
There exists some uncertainty in the plan of undertaking the modeling of a
prosthetic leg. As a group we
lack knowledge regarding
human gait analysis
. This is
i
mportant information
necessary for the modeling of the prosthetic
and assess
the
accura
cy
of the model
represent
ing
an actual leg. This
data
can be obtained by
searching papers that have previously studied the motion and forces that are involved
with walking.
The model will be altered as needed
if
the
model
is not
producing
results
that emulate
a normal
gait. A
djustments can be made to the geometry, the spring and
damper coefficients
,
and other design factors.
Another issue where we lack knowledge in is the modeling of the ground. It will
be difficult to model the different types of ground such as grounds with a slope, slippery
surfaces, sandy surfaces, and the other types of
surfaces that
will
alter the gait
.
Currently we are unsure
how to model these uncertainties
,
but we
are confident
that
with
more lessons on Dymola and
the
advice
from Dr. Paredis and the TA we will be
able to model
surface
conditions
. It may be too difficult to accurat
ely model
more
complicated
situations, such as soft sand and slipping so we may need to make
assumptions and
restrict our scope
to modeling
simpler situations.
Task 7
–
Articul
a
te your Learning Objectives
Daniel Olivero:
I hope
to gain a sound understanding of Dymola so that once this class
is over I will be comfortable to model different systems with confidence. I hope to learn
to apply Dymola to design problems so to facilitate the analysis and evaluation of the
design problem.
Hopefully this will allow me to create better designs in less time. I hope
that by using Dymola I will not have to put in as many resources into testing and I will be
able to produce a prototype that is closer to the finished product. I hope to be able to
apply problem solving methods to the engineering problems which are presented to me.
This will hopefully allow me to make a better decision and create better solutions. I also
hope to apply the methods which I am learning in this course to a systematic de
sign
method.
Beth Pavlik:
Coming from two years in the aerospace industry, I
have first hand
experience about the value of modeling outside of the classroom.
Modeling allows you
to simulate the final product before manufacture so that you have the ability to test the
limits of the system in a situation that may not be testable in real life. For instance,
when designing algorithms for discrimination for Patriot
radar, it is necessary to
model
missiles
threatening an asset because performing this test in real life would cost many
millions of dollars.
I hope to eventually go into the biomedical device industry; and
similar to the defense industry, testing devices
in real life is highly
impractical
. It is more
cost effective
for the company
and safer for the patient if the device is modeled before
implantation
so that the limitations of the device are thoroughly understood
.
From this
class I hope to gain a better understanding of how to incorporate modeling into the
design process.
Working
for
a small biomedical device company will require me to go
through the design process
on a frequent basis since devices tend to have a s
hort
product cycle.
This class will enable me to have a better understanding of how to
structure my design decisions so that my decisions will have a coherent and solid
foundation.
Having a
sound
design process and experience modeling in Dymola will
give
me an edge when applying for jobs in the biomedical device industry.
Carlos Sierra:
Before taking this class, I was unaware of the amount of analysis the
development of a product demanded at its earliest stages.
As an undergraduate, we
are taught to design, according to certain criteria, specific aspects of a system in order
to meet some specific needs.
When solving problems as an undergraduate, all data
need to solve the problem is given and therefore uncertain
ty about different aspects of
your design and the amount of critical decisions that need to be made are reduced
drastically.
This class and an intern experience I had last summer showed me another
side of engineering I was not very exposed to.
Real world
design involves a lot of trade

off between different parts of your product.
Most of these tradeoffs are not independent
but instead they affect one another.
Decision analysis then becomes an indispensable
tool in order systematically divide the problem
into smaller sub problems that can be
easily model and solved.
Model simulation return information useful at the moment of
solving all sub problems and their combined solution will suggest a solution for the
overall design problem.
From this class I woul
d like to take the following:

Learn how to systematically tackle a design problem and use decision analysis to help
simplify the process.

Gain enough modeling understanding to be able to model any systems I might face in
the future.

Learn how to divide
a problem into sections that can be easily model and use results
from the simulations to improve my overall design.

Improve my teamwork and communication skills.
Sean Tessier:
I would like to learn about the methods to follow when modeling a
complex
system. I want to learn more about how problems should be framed and
abstracted so that they represent the system in a reasonable way, but are still solvable.
I
’
d also like to learn how systems models could be used to help make decisions in
design problems
. For that reason, I think this project will be a good learning experience,
because the system is reasonably complex and will require us to learn more about
system modeling to represent the system properly. I also want to learn about optimizing
of design v
ariables, which this project will also illustrate.
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