# Task 1 Identify the Decision Situation

Mechanics

Nov 14, 2013 (4 years and 7 months ago)

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Olivero, Pavlik, Sierra, Tessier

HW #2

September 17, 2009

ME6105

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
.

Determine an Objectives Hierarchy

Figure 2

Fundame
ntal Objectives Hierarchy

Error!

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!

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

The following computational outcomes will be considered
:
t
he energy stored
and released by the device,

to ground conditions
, force input requirements,
average speed, market price

to appeal to an average customer
,

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.

s

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

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.

Articul
a

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

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.

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
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

-
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