Hi-Octane fitness Playground
Submitted as a partial requirement
for the course INME4058: Section 040
Design Course for B.S. in Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Students:
Bracero Arévalo, Pablo L.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Ruiz Tubéns, Pablo.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, P
Santana Torres, Damaris.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Vázquez Colón , Ana M.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Faculty Advisor:
Vijay K. Goyal, PhD
Professor at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
December 2009
Project Report
To:
Dr. Vijay K. Goyal
From: Bracero Arévalo, Pablo; Ruiz Tubéns, Pablo; Santana Torres, Damaris;
Vázquez Colón, Ana M.
Date: December 5, 2009
Re:
Engineering Design Project (INME4058: Section 040)
Dear Prof. Goyal:
Greetings! Our intention is to present to you three unique designs of playgrounds for children
with ages from three to seven. The idea is to improve what is already in the market and satisfy all the
desire qualities (Cost effective, Eco-friendly, specific dimensions, develop your child motor skills and
safety). Enclosed is a report containing the description of the project.
At the moment of purchasing a playground, a list of requirements should be taken in
consideration. The safety as well as how it will help your child to develop himself is very
important. Countless of playgrounds in the market suffer from lack of richness and variety
causing the absence of interest in the children. These are some considerations that we have taken
at the moment of creating a new design. The purpose of developing these new designs is to
respond for the need of a unique and durable playground in which your child could be able to
develop different motor skills in a safety way and at the same time maintaining it affordable. If
we can be of further help, please do not hesitate to contact us.
Regards,
Bracero Arévalo, Pablo
Ruiz Tubéns, Pablo
Santana Torres, Damaris
Vázquez Colón, Ana M.
i
Hi-Octane fitness Playground
Bracero Arévalo, Pablo; Ruiz Tubéns, Pablo;
Santana Torres, Damaris and Vázquez Colón, Ana M.
The requirements of the modern life style have made that a parent or parents invest the majority of
their time working to sustain their families. Because of this, the quality time spent with their children has
been considerably reduced, thus indoor activities such as watching TV or video games have become a norm
while outside activities are left behind.
These bad habits are correlated with risk factors for health such as obesity and poor academic
performance. Also it creates violent behavior and desensitization to violence. This is why it is important that
our kids learn to spend more of their time playing outdoors with elements that creates an
environment to inspire children in their intellectual, social, emotional and physical development.
It is very important in the development of a child to conduct activities that helps them to
improve and grow different motor skills. Activities such as running, throwing, catching,
balancing, etc. gives them strength and a better performance. A playground is the best resource
to combine all these activities, interact with other kids and spend time with their parents. There
are thousands of playgrounds in the market but all them suffer from lack of variety, colors and do
not allow children to take challenges which are what calls the kids attention.
As possible solutions we have created three different designs. The first design consists in
a unique playground with a breakfast theme. It has different stations like swings, trampolines and
slides creating the important elements as part of a complete breakfast. The second design allows
your kid to play with the most important monuments from around the world all at once. It brings
all the basic elements for your kid to explore and play. Monuments include the Eiffel Tower, the
Taj Mahal, the Great Wall of China and the Golden Bridge. The third and last design is a
combination of different stations like swings, monkey bars, climbers, a hop scotch and a
basketball ring all of them intended to develop a different motor skill.
Our main goal is to create a unique, safe, affordable and eco-friendly playground to fit more than three
children between the ages of three to seven years old. The three designs have a space limitation of 20ft by
20ft area and are made of recycled materials. Knowing and comparing the price range of other designs in
the market we acknowledge that our product needs to be between $300 and $600 making it affordable. We
compromise ourselves to deliver and provide unique designs that satisfy and exceed our customer
expectations. The timeframe available for the completion of the project is a total of 113 days with
0 days remaining.
ii
Acknowledgements
As a team we would like, first of all, thank God for giving us the opportunity and
guidance to work as a group and illuminating our minds during this project. To Professor Dr.
Vijay K. Goyal for giving us his advice and encouraged us to use our imagination and abilities.
Last, but not least, our thanks to our families; without their support we would not be here.
iii
Table of Contents
List of Figures ................................................................................................................................ vi
List of Tables ................................................................................................................................ vii
Chapter 1 Preliminary Remarks ...................................................................................................... 1
1.1
Background ...................................................................................................................... 1
1.2
Literature Survey .............................................................................................................. 2
1.3
Problem Description ......................................................................................................... 4
1.4
Expected Outcomes .......................................................................................................... 6
Chapter 2 Project Description ......................................................................................................... 7
2.1
Description of the Project................................................................................................. 7
2.2
Criteria.............................................................................................................................. 7
2.2.1
First Idea ................................................................................................................... 9
2.2.2
Second Idea ............................................................................................................. 10
2.2.3
Decision Matrix ...................................................................................................... 12
2.2.4
Selected Design ....................................................................................................... 14
2.3
Methodology .................................................................................................................. 16
Chapter 3 Optimization ................................................................................................................. 17
3.1
Design Problem .............................................................................................................. 17
3.2
Design Variables ............................................................................................................ 18
3.3
Objective Function ......................................................................................................... 19
3.4
Constraints...................................................................................................................... 19
3.5
Discussion ...................................................................................................................... 22
Chapter 4 Finite Element Analysis ............................................................................................... 23
4.1
Introduction .................................................................................................................... 23
4.2
Geometry ........................................................................................................................ 23
4.3
Mesh ............................................................................................................................... 24
4.4
Loads and Boundary Conditions .................................................................................... 25
4.5
Analysis .......................................................................................................................... 26
4.6
Shape Optimization ........................................................................................................ 28
Chapter 5 Results and Discussion ................................................................................................. 31
iv
5.1
Present Design ................................................................................................................ 31
5.2
Discussion ...................................................................................................................... 33
5.3
Cost Analysis.................................................................................................................. 34
5.3.1
Multi-Theme Aluminum ......................................................................................... 35
5.3.2
Multi-Theme Stainless Steel ................................................................................... 36
5.3.3
Multi-Theme Titanium............................................................................................ 37
Chapter 6 Final Remarks .............................................................................................................. 39
6.1
Conclusion...................................................................................................................... 39
6.2
Recommendations .......................................................................................................... 39
References ..................................................................................................................................... 40
Appendix A Submitted Proposal .................................................................................................. 41
Appendix B Method of Lagrange Multipliers .............................................................................. 42
Appendix C ANSYS Tutorial ....................................................................................................... 47
Student Vitae................................................................................................................................. 61
Evaluation Sheet ........................................................................................................................... 62
v
List of Figures
Figure 1.1 Playground – Swing ….……………………….……………………………………………….. 1
Figure 1.2 Playground – Slide ..….……………………….……………………………………………….. 1
Figure 1.3 Playground – Tubes …..……………………….………………………………………………. 2
Figure 1.4 Playground – Climb ...…………………………………………………………………………. 2
Figure 1.5 Playground – Traditional Playground ...……………………………………………………….. 2
Figure 1.6 Playground – Slide & Swing Set ..…………………………………………………………….. 2
Figure 1.7 Playground – Double Swing Set ………………………………………………………………. 2
Figure 1.8 Playground – Playground – Slide …...……………………………………………...…………. 3
Figure 1.9 Playground – Playground - Slide …………………………………………………..…………. 3
Figure 1.10 Playground – Contemporary Playground …..……………………………………..…………. 3
Figure 1.11 Playground – Wooden Sandbox …………………………………………………..…………. 3
Figure 1.12 Playground – Plastic Sandbox ...…………………………………………………..…………. 3
Figure 1.13 Playground – Adventure Playground ……………………………………………..…………. 4
Figure 1.14 Playground – Expensive Playground ……………………………………………..…………. 8
Figure 1.15 Playground – Dual Playground .…………………………………………………..…………. 8
Figure 2.1 Breakfast Playground ………………………………………………………………………... 11
Figure 2.2 Around the World Playground ……………………………………………………................ 12
Figure 2.3 Multi-Theme Playground …………………………….……………………………................ 13
Figure 2.4 Datum…………………………….……………………………............................................... 14
Figure 3.1 Curved Beam ……….………………………………………………………………………... 16
Figure 3.1 Cross-Section ……….………………………………………………………………………... 17
Figure 4.1 Swing Beam ……….…………..……………………………………………………………... 22
Figure 4.2 ANSYS Curved Beam …..…………………………………………………………………… 23
Figure 4.3 ANSYS Mesh Beam..………………………………………………………………………… 24
Figure 4.4 ANSYS – Load & Boundaries …..…………………………………………………………… 25
Figure 4.5 ANSYS – von Mises .………………………………………………………………………… 26
Figure 4.6 ANSYS – Deformation.….…………………………………………………………………… 26
Figure 4.7 ANSYS – Shape Optimization 1……………………………………………………………... 28
Figure 4.8 ANSYS – Shape Optimization 2..…………………………………………………................. 29
Figure 4.9 ANSYS – Shape Optimization 3 ...…………………………………………………………... 30
Figure 5.1 Shaped Storing Wall …………………………………………………………………………. 31
Figure 5.2 The Bubble Climber …………………………………………………………………………. 32
Figure 5.3 Nop Scotch …………………………………………………………………………………... 32
Figure 5.4 Slides ………………………………………………………………………………………… 33
Figure 5.5 Selected Design layout ………………………………………………………………………. 34
Figure 5.6 Pipe Chart Budget Allocation for Aluminum ……………………………………………….. 35
Figure 5.7 Pipe Chart Budget Allocation for Stainless Steel …………………………………………… 36
Figure 5.8 Pipe Chart Budget Allocation for Titanium ……………………………………………….… 37
vi
List of Tables
Table 2.1 Pugh’s Matrix ………………………………………………………………………8
Table 3.1 Aluminum 6061 Properties ………………………………………………………..17
Table 5.1 Cost Analysis – Aluminum ………………………………………………………..35
Table 5.2 Cost Analysis – Stainless Steel ……………………………………………………36
Table 5.3 Cost Analysis – Titanium ………………………………………………………….37
vii
Chapter 1
Preliminary Remarks
1.1
Background
A playground is an outside play area for children consisting in a combination of structures for
climbing, crawling, jumping, etc. It is very common to find them in parks or even in our own backyard. For
many people a playground is considered just a toy with no importance or meaning. For others, it is a
dangerous place where their kids can get injured easily. The real meaning and purpose of a playground is to
offer the child a place where they can explore, be creative, enhance and develop the important motor skills
at their age and interact with other kids as well with their parents. To achieve all this purposes, the child
must be attracted to it. In the market over the years designs suffer from lack of variety, imagination or
structures that are not challenges for kids anymore. This drives us to change what is on the market and
design something innovative, unique and new.
In our case, as Mechanical Engineer students, we are trying to achieve and meet all our client
requirements and standards. The main idea is to provide something different and unique that can help the
child to develop his motor skills in a unique way. Figures 1.1 and 1.2 display examples of playgrounds that
are common these days. Also this figures show that not more than 2 kids are able to play. They do not call
the child’s attention because they are typical and does not involve challenges for kids. Moreover, in Figures
1.3 and 1.4 we can observe designs that suffer from lack of variety and limits the imagination of the child.
Therefore we will provide ideas that involve all this important requirements in a playground.
Figure 1.1 Playground-Swing
Figure 1.2 Playground-Slide
1
Figure 1.4 Playground-Climb
Figure 1.3 Playground-Tubes
1.2
Literature Survey
After an extended research, from the vast variety of playgrounds three categories were
determined. We have denominated these categories as “Traditional Playgrounds”,
“Contemporary Playgrounds” and “Adventure Playgrounds”.
The Traditional Playground; these are mainly composed by slides and swings. (See
Figure 1.5). Examples of different styles are: 1) Double Swing Set approximately priced between
$200 to $300. Figure 1.6, shows this type of playgrounds. 2) Single Slides are approximately
priced between $90 to $120. Figures from 8 to 9 demonstrate this type of style.
This category has its advantages and disadvantages. Advantages we can mention the
following: 1) They are economic. 2) They do not occupy much space. 3) An average of 3 to 4
kids can play at the same time. 4) Help kids interact and socialize with others. Some
disadvantages are: 1) They suffer from lack of variety. 2) Do not present challenges for the kids.
3) Do not present the necessary exercises to help develop the child motor skills. 4) Supervision
required.
Figure 1.5 Traditional
Playground
Figure 1.6 Slide & Swing Set
Figure 1.7 Double Swing Set
2
Figure 1.8 Playground-Slide
Figure 1.9 Playground-Slide
The Contemporary Playgrounds; these are mainly composed by sand boxes and mounds.
(See Figure 1.10). Examples of different styles are: 1) Sandbox approximately priced between
$60 to $200). Figures 1.10 to 1.12 shows different types of this style.
This category has its advantages and disadvantages. Some advantages are: 1) Multiple
kids from different ages can play at the same time. 2) Easy to install. 3) They are economic. 4)
Help kids interact and socialize with others. Disadvantages are: 1) Dangerous objects can be
hidden under the sand 2) Supervision at all times must be required. 3) Not recommended to use
indoors. 4) Not recommended for kids under the age of two.
Figure 1.10 Contemporary
Playground
Figure 1.11 Wooden Sandbox
Figure 1.12 Plastic Sandbox
The Adventure Playgrounds; this type of playgrounds are distinguished by the variety of
stages prepared to develop the children motor skills. It is proven that kids play the longest in this
type of playgrounds because of the challenges and diverse activities like climbing, jumping and
many more. (See Figure 1.13). Examples of this type of playgrounds are: 1) Out-Door
Playgrounds approximately priced between $600 to $1000.
3
Figure 1.13 Adventure Playground
This category has its advantages and disadvantages. Some of the advantages are: 1)
encourages the kids to play while they develop different parts of their body. 2) Helps improve
the basic motor skills. 3) Help kids interact and socialize with others. 4) Multiple kids from ages
from 3 to 7 can play at the same time.
1.3
Problem Description
Playgrounds come in a variety of forms, colors, size, materials and types of
entertainment. At a glance, maybe all of them satisfy all the requirements, for a kid to have a
nice place to play, but does it mean it is the right playground? In the early stages of their life,
playing becomes an intrinsic part of the children development. It is through play that children at
a very early age engage and interact in the world around them. Play allows children to use their
creativity while developing their imagination, dexterity, and physical, cognitive, and emotional
strength. It has been proven that today’s playground no longer aloud children to have challenges.
A wide variety of them suffers from lack of richness and variety which is what captures the
attention of a child. With the typical design, children are not able to manipulate their
environment and adapt to what they really need. Over the years what we have been seeing are
more complex designs but they remain just as fixed in form limiting the creativity of the
children.
With the increasing tendency of children to videogames and computers, obesity has
become a more serious illness during childhood. It not only impacts directly the children health,
but also isolates them from the real word reducing the opportunity to socialize among themselves
and limiting their imagination to grow. To counteract this tendency, parents must encourage kids
to be more active and promote physical recreation. For this, a playground is a perfect solution.
Playgrounds contribute to the development of the gross motor skills. Gross motor skills
are the movements of the large muscles of the body. In the first years of their life, children
acquire a great number of them. Their brain's development and the environment in which they
mature affect the acquisition of these skills. Movement allows children to discover their body, to
learn that they are independent beings who are able to go off and explore the world. Children
4
with poor gross motor development may have difficulty with activities such as writing, sitting up
in an alert position, sitting erect to watch classroom activity, and writing on a blackboard. The
development of gross motor skills allows them to perform better in other, more academic and
physical ways. Activities such as running, throwing and catching, jumping, kicking, crawling,
balancing, etc. help children to develop and improve gross motor skills. These types of activities
will also help your child to build strength and be healthy.
Although playgrounds can fit more than two kids at the same time, bigger isn't always
better. Most of the playgrounds manufactures build these days, are too big to be placed in a
typically backyard and the bigger the playground the higher the cost. When yard space and cost
is at a premium, the size of play equipment is an important consideration. It has been found in
the market that a playground as simple as two slides and a stair can cost more than $7,000 and
have a minimum of used zone closed to 572 square feet as show in Figure 1.14. It can also be
found smaller playgrounds costing less than $600 that can be fit in a typically backyard. This
example is shown in Figures1.14. The problem with these two examples of playgrounds is that
they are not in harmony with what they have to offer in comparison with cost and space. What
they have in common is the lack of creativity that both can encourage to children. This lack is
also visible in Figures 1.14 through1.15. We are aiming for a playground with a minimum used
zone of 20 ft by 20 ft that can encourage creativity and imagination so children can be able to
build their own world. Smaller play equipment that encourages imaginative play will likely hold
your child's interest as well, if not better, than elaborate, expensive sets with a huge array of
accessories. Before buying a deluxe play system, one should ask how much equipment your kids
will really use. Chances are a simple play set will delight your child.
The safety of each individual piece of playground equipment as well as the layout of the
entire play area should be considered when designing or evaluating a playground for safety.
Since falls are a very common playground hazard pattern, the installation and maintenance of
protective surfacing under and around all equipment is crucial to protect children from severe
head injuries.
Because all playgrounds present some challenges and because children can be expected
to use equipment in unintended and unanticipated ways, adult supervision is highly
recommended. Appropriate equipment design, layout, and maintenance, are also essential for
increasing playground safety. Research has been made and it was found that playgrounds are
typically made of plastic, metal or wood. When deciding which type of materials will be used
for a playground, is important to know where the playground would be installed. Understanding
the type of surroundings will help choose wisely the perfect materials.
Therefore, after knowing what is the problem about and finding out what the market offers, the
goal of this design is to create a playground for a three year old kid that will last until he/she is
seven years old. This new playground design should satisfy the customer requirements. It should
be easy assembly. It needs to be resistant to humidity to prevent rust, so it will last longer. This
factor has been considered based on the costumer location in which the indices of humidity are
5
normally high. It also needs to be a strong material but not heavy so it will be easy to move
around. The design must encourage kids to move around, helping them to develop and improve
their motor skills. This will also help maintain the kid healthy and strong. It should be safety at
all times and be able to fit in a 20 ft by 20 ft area. The design must eliminate the lack of
motivation of the existing playgrounds and must empower children to be endlessly creative. All
of these needs must be achieved within a budget of $300 to $600.
Figure 1.14 Expensive Playground
1.4
Figure 1.15 Dull Playground
Expected Outcomes
What we expect from our design is to have a fun, safe, economic and eco friendly playground
that will revolutionize the market using our creativity. It will have capacity for three kids from
ages 3-7 having fun developing their motor skills instead of playing video games or indoor
activities. A playground is a childhood dream and we will make it real with an affordable price a
family can pay.
6
Chapter 2
Project Description
2.1
Description of the Project
Based on the customer requirements and needs, a unique playground design that can
contribute to the development of the gross motor skills with activities such as running, jumping,
balancing, etc. must be created. This helps prevent obesity, maintaining he/she healthier and
strong and also gives the child the opportunity to socialize and interact with other kids. We are
aiming to create a playground with a minimum used zone of 20 ft by 20 ft specifically for a three
year old kid that will last until he/she is seven years old. It should be easy assemble, safe, also
resistant to humidity. This last factor has been considered based on the costumer’s location.
When safety is needed, the installation and maintenance are very essential on the playground.
The design must eliminate the lack of motivation of the existing playgrounds and must empower
children to be endlessly creative. All of these needs must be achieved within a budget of $300 to
$600.
2.2
Criteria
A series of criteria must be defined in order to compare ideas; they will help us to choose the
best option. The designs will be compared in terms of Safety, Cost, Capacity, Maintenance,
Material and Originality using the Pugh’s Method. Following, you will find a brief description of
each one of them and an explanation about why it was assign a particular score to the designs.
Safety
When referring to safety, it signifies how safe will the kids be while playing. For these
parameters we considered altitudes, sharp edges, and the material for the floor (if it is shock
absorbent) among others. For this criterion the first two options have different elements such as
sand and cereal pools, climbing objects and trampolines. It was assigned a higher score for
Design #3 for the fact that it has more ground activities compared with the others, minimizing
this way the risk of fallings.
Cost
7
This involves manufacturing, materials and installation costs. Also, this criterion
considers what price will be fair for the customer to pay. In this particular case, it was assigned
the same score for all three designs. Some components of the three ideas are made from the same
material and basically their maintenance, manufacturing and installation costs are the same.
Capacity
This refers to the number of child that can be fit in the playground area and can play
safely. The three designs were made having in mind that more than three kids could play
comfortable and with different activities. For this criterion, the same amount of score was assign
to the three ideas. In all of the three designs, more than three kids can play at the same time.
Maintenance
This refers to how often the customer needs to provide the appropriate maintenance to the
equipment. This is a very important criterion since the safety of the kids depends on how regular
the playground is being checked for maintenance issues. For this criterion, it was assigned the
highest point for the Multi-Theme design. This score was based on the fact that the other two
options have sand and cereal pools incorporated, increasing the risk of buried danger objects.
This does not mean that our selected option cannot be checked with the same regularity than the
rest.
Material
When talking about the material, we take into consideration the following criteria:
durability, resistant to humidity, shock absorbent and Eco-Friendly. Design #1 and Design #2,
have the highest scores since the entire playgrounds are made out of the same material which is a
recyclable one. For design #3, this changes since it has different stages that require different
materials, depending on the usage and the purpose of it. The advantage of having Eco-Friendly
materials is that it will be considered the environmental impact the playground can have.
Originality
This parameter refers to the uniqueness of the design, comparing it with what is already
in the market. It will also take into consideration how much fun and enjoyment the children will
have with a playground that nobody else have seen before. For this particular criterion the
Design #2 took the highest score. It is an original design that does not only give the child the
opportunity to climb and play with famous monuments but they can learn while playing.
After evaluating the six different criteria by the Pugh’s Method, the best design was obtained by
evaluating the design with the highest weighted total score. From the three designs, Design #3: MultiTheme playground utmost the other designs.
8
2.2.1 First Idea
The breakfast playground, as shown in Figure 2.1, consists of a group of elements with
shapes of different foods that make the experience of playing interesting. It covers a 20 ft by 20
ft area ideal for kids with ages from 3 to 7.
This playground elevates the entire conception of breakfast to a whole new level. The
kids will be able to climb a buttered toast, jump over two sunny sides up egg yolks, climb two
boiled eggs and at the top slide through two slices of bacon. It also contains a colorful cereal
pool and a swing in the form of a banana. The floor has the shape of an egg container which
gives the sensation as if walking through small hills.
This unique playground contains trampolines in the form of two sunny side up eggs. The
yolks will be the trampolines that will give your kid the sensation of flying. The egg whites will
serve as the couch to absorb safely a fall. Also it has in the middle a cereal pool. The special
feature of it is that it will not be full of balls; instead it will contain colorful stars, moons and
horseshoes to give the impression of a famous cereal. To the side you will find a banana that will
serve as a swing and a buttered toast that your kids can climb. In the other side of the playground
your kid can be able to climb two boil eggs that serve as the base for two slides in the shape of
bacon. Do not forget that it can motivate your kids to eat.
It is required that your kids play under the supervision of an adult. The cereal will have
round edges to avoid accidents. The swing should not be used for infants; kids should be over the
age of three and under an adult supervision to play safely. The floor will be made of a Rubber
Mulch to avoid injuries if the kid falls.
All the equipment will be made of recyclable material. The Rubber Mulch is a unique
rubber made of 100% recycled tires. It is mostly used for playgrounds safety surfacing because it
is the safest and most economical choice. The rest of the equipment will be made out of recycled
plastics (high-density polyethylene). It is very important to mention that when purchasing this
product, besides the direct benefit to communities, you will be helping our planet.
This playground has a series of advantages over the playgrounds in the market. This playground
consists of learning the important elements of a complete breakfast. Breakfast is an essential meal of a
daily basis because after 6 to 8 hours of sleep, the body needs vitamins, proteins, fibers and
carbohydrate. As a parent, you should teach your child the importance of a well balanced food
and the big importance of breakfast. The playground also consists in a variety of equipments that
helps develop the child’s motor-skill such as climbing, a trampoline and a ball pool. In addition,
the design of the playground would allow parents to have from 3 to 6 kids playing in the
playground simultaneously. The assembly may require at least two adults.
9
Figure 2.1 Breakfast Playground
2.2.2 Second Idea
Around the World is the theme for an awesome playground that will fill your kids with
history and amazement while having fun with some of the most famous monuments in the world.
You will encounter smaller replicas of monuments such as the Golden Gate Bridge, the Taj
Mahal, the Eiffel Tower and the Great Wall of China. This unique playground will cover a 20ft
by 20 ft area and it is ideal for children’s with ages from three to seven.
Around the World will contain a replica of the famous Taj Mahal in which the front
fountain has been converted into two sand boxes. It also serves as a play house letting your kids
to play inside of this replica. It will be surrounded by the Great Wall of China to separate it from
the other parts. It will also include a non-stable version of the Golden Gate Bridge from San
Francisco that will help develop your balance when walking through it. To finalize they will be
able to climb a replica of the Eiffel Tower. Each one of these stations has its purpose when it
comes to your child’s development. It helps build their body, gain agility and the ability to
control their basic motor skills. The sand box will be a great activity that your kids will love
giving them the opportunity to build, create, bury and dig their toys up.
This exciting playground will give your children the opportunity to learn about some of
the most important monuments in history while socializing with friends and spending time with
their family. The kids should have the supervision of their parents at all times. If your child is
10
playing in the area of the sand box, you have to be aware that it does not get into your child’s
eyes and remind them that it is not eatable. The floor will be made of Rubber Mulch to help
absorb the fall if this is the case and the Bridge will have support to the sides so your child can
hold on to them while walking.
The entire playground is made out of recycled materials. The ground is made of Rubber
Mulch which is rubber made with 100% recycled tires. Also the material used in the monuments
is a recycled plastic which in this case high-density polyethylene. When purchasing this product
you are not only contributing to your child’s development and well being but helping conserve
our only planet. Figure 2.2 show the Around the Word Playground.
One of the advantages of the playground is to teach kids the importance of history. At the
same time we are showing the kids the variety of cultures in the World. The playground consists
also with a variety of equipments to develop the child’s motor-skill such as climb, balanced, and
free movement. In addition the design of the playground would allow parents to have a variety of
kids playing in the playground simultaneously.
The assembly of the playground may require at least two adults. Parents have to be careful when
kids are in the sand box to prevent them from eaten the sand (hazarded materials).
Figure 2.2 Around the World Playground
11
2.2.3 Decision Matrix
In order to decide which idea to use, the Pugh’s Method was applied. For this Figure 2.4 was
established as the Datum. The chosen evaluation criteria is:
+2- Meets criterion much better than Datum.
+1- Meets criterion better than Datum.
0- Meets criterion as well as Datum.
-1- Meets criterion not as well as Datum.
-2- Meets criterion much worse than the Datum.
Figure 2.4 Datum
12
Table 2.1 Pugh’s Matrix
Pugh's Method
Design #1 Design #2
Criteria
1. Safety
2. Cost
3. Capacity
4. Maintenance
5. Material
6. Originality
Total
Total Positive
Total Negative
Weighted Total
Design #3
Datum
Traditional
Playground
among price
range
Score
(%)
Breakfast
Around
the Word
Multi-Theme
27
18
10
14
14
17
-1
-2
+2
-2
+2
+1
-1
-2
+2
-2
+2
+2
0
-2
+2
0
+1
+1
0
0
0
0
0
0
100
…
0
+5
-5
-26
1
+7
-5
-9
2
+4
-2
15
0
0
0
0
…
…
Rating Scale
Table 2.1 shows how each design playground was evaluated in order to decide which one
meets our criteria better. When compared to the datum, the Breakfast playground and the Around
the World playground presented a less safe environment. For the safety criterion the Breakfast
playground and the Around the World playground have different elements such as sand and
cereal pools, climbing objects and trampolines. For this reason a score of -1 was assigned for
those playgrounds. The Multi-theme playground has more ground activities compared with the
others, minimizing the risk of fallings which is why it was considered more safe than the two
others design but equally to the datum.
In the cost criteria manufacturing, materials and installation costs are involved. All three
designs, after a cost analysis was performed, exceeded the price of the datum for more than 50%
making it worse than the datum. That is why all of them have a score of -2.
The capacity criteria refer to the number of children that can be fit in the playground area and
can play safely. Each design received a score of +2 because when compare to Figure 2.4 (Datum)
it can be seen that more than three children can play with the features of the playground and do
not have to wait for others to finish using it.
13
When comparing the Breakfast playground and the Around the World playground with the
datum, it was notice that maintenance represented a complex task due to the elaborated design of both
playgrounds. These complexities make both designs much worse than the datum receiving a score of 2. In the contrary, the Multi-theme playground receives a neutral score since maintenance has the
same level of complexity as the datum.
When talking about the material, we take into consideration the following criteria: durability,
resistant to humidity, shock absorbent and Eco-Friendly. The Breakfast playground and the Around
the World playground have the highest scores since the entire playgrounds are made out of the
same recyclable material. This makes both designs much better than the datum receiving a +2
score. The Multi-theme playground has different stages that require different materials depending
on the usage and the purpose of it. Because of this it was decided that it will only better than the
datum and it will receive a +1 score.
The originality parameter refers to the uniqueness of the design, how much fun and
enjoyment the children will have and how it impacts the future life of children. For this particular
criterion the Around the World playground took the highest score (+2). It is an original design
that does not only give the child the opportunity to climb and play with famous monuments but
they can learn while playing. For the two other designs, a score of +1 was assigned meeting the
criterion better than the datum.
2.2.4 Selected Design
The multi-theme playground was made with the purpose to develop basic skills such as
balance, agility and learn to have control of their own body. To start with the features, an
ingenious mushroom was created that contains comfortable swing. This swing will be safe and
fun for toddlers. The multi-playground comes with an integrated ladder for kids to climb
motivating them to reach the top and develop strength and coordination. Once on top, they will
have the option to slide down through two fun slides, slip down a pole or finally pass through a
bridge-hanger that will exercise your child by making him lift his own weight.
This unique playground has a swing integrated with the shape of a Space-ship. This
colorful swing is able not only to move back and forward but spin around at the same time. It
contains two steer wheels so the kids can drive while flying. Also includes a basketball court and
a hop scotch fixed on the floor to motivate the kids to jump and run around. Five bouncers that
can be used as seats or a fun way to make balance are incorporated to the floor. Finally to teach
children correlate shapes and different forms like stars, squares or circles, a Shape Sorting wall
was integrated.
Supervision of parents is required at all times. The playground is made in the safest way
but precaution should all ways be taken. The floor is covered with Rubber Mulch to absorb the
14
children fall if this is the case and every bolt and sharp edges are protected and covered to
prevent injuries and cuts. All this descriptions are reference to Figure 2.3.
This playground has a series of advantages over any design. The playground is an easy
assemble system and multi pattern playground. It consists also in a variety of equipments to
develop the child’s motor-skill such as climb, balanced, memory, free movement, coordination
and agility. In addition the design of the playground would allow parents to have a variety of
kids playing in the playground simultaneously with the proper supervision. The assembly of the
playground may require at least two adults.
Figure 2.3 Multi-Theme Playground
15
2.3
Methodology
The first step in the design process was to understand what was the problem about and interview the
customer in order to find the needs for what is desire. Once the problem and needs where identified, a
survey was performed to clearly know what the market was offering and what was missing that need
improve. It was observed that, a wide variety of playgrounds suffers from lack of richness and
variety which is what captures the attention of a child. With the typical design, children are not
able to manipulate their environment and adapt to what they really need. The majority of them
also presented a limitation in the types of movement kids will developed while playing, limiting
their motor skills. It was also notice that safety was not always a priority, putting in danger the
kid’s life. To solve these problems and to fulfill the client’s needs three designs were developed.
The first one consists of a group of elements with shapes of different food for breakfast that
make the experience of playing interesting. With this idea we wanted to emphasize the
importance of breakfast in order to become a healthy human being. The second idea was
developed having in mind worldwide history. Although it’s a good idea, its limitation in cost and
available space to play, doesn’t make it feasible for our expectations. The last idea was an
improve of what already existed but with a touch of qualities that satisfies closely the main goal.
This design is much simpler but involves a series of different stages of complexity for playing.
After comparing all three, utilizing the Pugh’s Method, the third one became the winner. This
idea was subjected to optimization, FEM and cost analysis until the final desired product was
reached.
16
Chapter 3
Optimization
3.1
Design Problem
The design involves a series of steps and processes, including a series of analysis. The
analysis depends on what properties or parameters need to be verified such as static or dynamic
analysis. The design must tolerate loads, impacts, pressure or concentration of stresses. One very
critical specification of our product is the child’s safety. For this we have selected a specific
component to perform an optimization analysis, to minimize the risk of failure.
Among the several components that comprise our full design, the following component will be
analyzed and optimize in order to obtain the best solution for our design. Figure 3.1 shows the
arms that support the swing, which will be analyzed. This component has been selected since it is
the most critical part subjected to bending stresses.
Figure 3.1 Curved Beam
The design has a complex geometry; a simplification was done in order to make the
process feasible. As seen in Figure 3.1. The square arm will be modeled as a hollow aluminum
6061. This 113in length tube will be attached to the base at one end. The other end is attached to
a bracket to join the tubes and swing which is being modeled for a maximum force of 55lb. The
optimization process consists of minimizing the arm’s mass while constraining the Von Misses
stresses to be less than the allowable value for safety.
17
Parameters are to be considered in order to optimize this design
Table 3.1 Aluminum 6061 Properties
σy
6.9 ksi
σUTS
16.7 ksi
E
1088 ksi
ρ
0.0975 lb/in3
ν
0.33
3.2
Design Variables
The design variables for our problem would consist in the height, width, and thickness of
the cross-sectional face of the tubing. The design variables and its nomenclature are:
t
𝑥1 = ℎ
𝑥2 = 𝑏
𝑥3 = 𝑡
h
b
Figure 3.2 Cross-Section
The geometrical properties are:
𝐹 = 55 𝑙𝑏𝑓
3≤ℎ≤5
ℎ=𝑏
1
𝑡=
4
Expressed mathematically in a column vector form:
𝑋 = {𝑥1 𝑥2 𝑥3 }𝑇
The dimensions held constant are:
18
𝑏𝑎𝑠𝑒𝑥 = 4.8 𝑓𝑡
𝑏𝑎𝑠𝑒𝑦 = 6.5 𝑓𝑡
3.3
Objective Function
The purpose of this analysis is to minimize the weight of the component given the stress
constraints. This criteria can be modeled using the following objective function expressed below
which is a function of our design variables.
𝑊=
𝜌𝑉𝑔 𝜌𝑔𝐿 ∗ 2𝑡(ℎ + 𝑏)
=
𝑔𝑐
𝑔𝑐
Using the nomenclature for our design variables
𝑓(𝑥) =
𝜌𝑔𝐿 ∗ 2𝑥3 (𝑥1 + 𝑥2 )
𝑔𝑐
𝑓(𝑥) = 𝑥3 (𝑥1 + 𝑥2 )
3.4
Constraints
The totals of constraints imposed on our design were 2 equalities in which our major concern
will be the force due to weight. Aluminum was the material chosen for the element to be analyzed
because of its properties, which include its resistance to corrosion, economic price, its low density
which permits the easy movement because of its light weight and high specific strength. Geometrical
constraints are summarized next.
𝑔1 (𝑥) = 3 − 𝑥1 ≤ 0
𝑔2 (𝑥) = 𝑥1 − 5 ≤ 0
ℎ1 (𝑥) = 𝑥1 − 𝑥2 = 0
1
ℎ2 (𝑥) = 𝑥3 − = 0
4
Using the Von Misses Criterion
2
𝜎𝑣𝑚 = √𝜎𝑥2 + 𝜎𝑦2 + 𝜎𝑥2 𝜎𝑦2 + 𝜏𝑥𝑦
19
For the loading of 55 𝑙𝑏 applied on the tip of the swing support cause only bending stress
is applies, therefore Von Misses equation is reduce;
𝜎𝑣𝑚 = √𝜎𝑥2
Constraint for the bending stress:
𝑀𝑦
𝐼
𝐹 ℎ
2 𝑙 ( 2)
𝜎𝑣𝑚 =
𝜎𝑣𝑚 =
1 3
𝑏
6 ℎ 𝑡 (1 + 3 ∗ ℎ)
𝜎𝑣𝑚 =
𝐹𝑙
2.6668ℎ3 𝑡
Performing a substitution:
𝜎𝑣𝑚 =
𝜎𝑒𝑞 =
770.67
𝑥12 𝑥3
770.67
≤ 𝜎𝑎𝑙𝑙
𝑥12 𝑥3
𝜎𝑎𝑙𝑙 =
𝜎𝑦
𝑛
𝑛=2
𝜎𝑎𝑙𝑙 =
6900𝑝𝑠𝑖
= 3450 𝑝𝑠𝑖
2
𝑔3 (𝑥) =
770.67
− 𝑥12 𝑥3 ≤ 0
3450
𝑔3 (𝑥) = .2233 − 𝑥12 𝑥3 ≤ 0
20
Method of Lagrange Multiplier
From the constraint Multivariate Methods we will apply the Lagrange Multiplier. The
Lagrange multiplier will determine the maximum or minimum subject to the constraints
(𝑥1 , 𝑥2 𝑎𝑛𝑑 𝑥3 ).
The problem in standard form:
𝑓(𝑥) = 𝑥3 (𝑥1 + 𝑥2 )
Subject to
𝑔1 (𝑥) = 3 − 𝑥1 ≤ 0
𝑔2 (𝑥) = 𝑥1 − 5 ≤ 0
𝑔3 (𝑥) = .2233 − 𝑥21 𝑥3 ≤ 0
ℎ1 (𝑥) = 𝑥1 − 𝑥2 = 0
1
ℎ2 (𝑥) = 𝑥3 − = 0
4
𝑥 = {𝑥1 𝑥2 𝑥3 }𝑇 Єℝ
Determine the lagrangian:
ℒ(𝑥, µ, 𝜆)= ƒ(𝑥) + µ1 ℎ1 (𝑥) + µ2 ℎ2 (𝑥) + 𝜆1 𝑔1 (𝑥) + 𝜆2 𝑔2 (𝑥) + 𝜆3 𝑔3 (𝑥)
1
= 𝑥3 (𝑥1 + 𝑥2 ) + µ1 (𝑥1 − 𝑥2 ) + µ2 (𝑥3 − ) + 𝜆1 (3 − 𝑥1 ) + 𝜆2 (𝑥1 − 5) + 𝜆3 (.2233 − 𝑥21 𝑥3 )
4
1) Ensure that the Lagrangian will be stationary:
𝜕ℒ
= 𝑥3 − 𝜆1 + 𝜆2 − 2𝜆3 𝑥1 𝑥3 + µ1 = 0
𝜕𝒙1
𝜕ℒ
= 𝑥3 − µ1 = 0
𝜕𝒙2
𝜕ℒ
= 𝑥1 + 𝑥2 + µ1 − 𝜆3 𝑥12 = 0
𝜕𝒙3
In order to satisfy the second K-T Condition
𝜆1 (3 − 𝑥1 ) = 0
𝜆2 (𝑥1 − 5) = 0
𝜆3 (.2233 − 𝑥21 𝑥3 ) = 0
µ1 (𝑥1 − 𝑥2 ) = 0
1
µ2 (𝑥3 − ) = 0
4
For more information please refer to Appendix C
21
3.5
Discussion
After performing the Lagrangian Multiplier method we find feasible point that will represent
our design variables for base, height and thickness on the swing poles. The weight of the poles
will be our main objective to optimize without affecting the safety of them while being in use. In
the analysis we use the thickness as equality constrain of ¼ in that will be fixed and two
inequalities constrains that will represent a width of 5in and a height of 5in. With this dimension
we obtain minimum weight of 2.5 lb.
22
Chapter 4
Finite Element Analysis
4.1
Introduction
An important aspect of this project is to perform a structural analysis in the critical part of
our playground. ANSYS would be used to perform a Finite Element Analysis (FEA) of our most
relevant component, the curved beam for the swing. The FEA includes three main general stages:
Pre-processing; Processing and Post-processing. Following, the main parts of FEA of the curved
beam component will be described, and explained.
4.2
Geometry
Once the component to be analyzed has been selected, it needs to be discretize in terms
that the program can recognize and interpret. This requires the definition of the material
properties, and the geometry of the component evaluated. In order to create the geometry
SolidWorks was used. Once the cad part was created the part was save as IGES with surface
representation/system preference: ANSYS.
The purpose of our FEA analysis was focused in acquiring structural analysis of the
component, when subjected to specified loads, and restrictions. Specifically, we were looking for
the deflection and stresses results due to a point load on the top extremity (weight load), and this
way would verify that the design variables obtained in the Lagrange Optimization Method
comply with the conditions the component will be subjected to. Figure 4.1 illustrates the curved
beam section that will be analyzed in ANSYS.
Figure 4.1 Swing Beam
23
The following pictures demonstrate the beam as geometry at ANSYS. As we can observe
ANSYS import the beam from SolidWorks without any problem.
Figure 4.2 ANSYS – Curved Beam
4.3
Mesh
This section actually proved to be the most complicated one for the pre-processor section
of the FEM. Understanding the correct way to properly mesh required a few trials by error. For
this particular FEA, we choose to divide our geometry, using an average size mesh, to attain a
reasonable level of results. A higher accuracy mesh size could have been selected, but it would
become too costly in time and resources, and the analysis would take large amounts of disk
space, which is also a main reason to diminish the element division just to the needed level of
study. For our analysis we used “mapped face meshing” and “refinement”, meaning, it would
give us with an average acceptable divisions that approximate our solution to a relatively high
degree. From a customer’s point of view, this represents a “good quality” degree of the
product. See Figure 4.3 for meshed geometry.
For the element divisions, we chose a solid element, to represent our component
behavior. From the solids available we choose, SOLID 187. This element is a higher order 3-D,
10-node element. It has a quadratic displacement behavior and is well suited to modeling
irregular meshes. The element is defined by 10 nodes having three degrees of freedom at each
node: translations in the nodal x, y, and z directions. The element has plasticity, hyperelasticity,
creep, stress stiffening, large deflection, and large strain capabilities. It also has mixed
formulation capability for simulating deformations of nearly incompressible elastoplastic
materials, and fully incompressible hyperelastic materials.
24
Figure 4.3 ANSYS – Mesh Beam
4.4
Loads and Boundary Conditions
Once the geometry has been defined subdivided into sub-elements, using the meshing
mentioned in the previous section, the loads and boundary conditions are specified. This includes
defining the restrictions of the beam (to simulate the real conditions of that specific component
in the real life). This permits the evaluation of resulting stresses and deflections due to a
condition applied with the specified restricted ends.
We are designing our curved beam to withhold weight from 25 to 55lbs. For our analysis,
we wanted to simulate the effect of worst case scenario. The swing is been design to hold a total
weight of 55lbs. The bottom end of the curved beam would be fixed to the ground at ANSYS
will be represented as all its DOF will equal 0. In the following figure the load and fixed support
are shown. The next figure demonstrate the load and boundaries
25
Figure 4.4 ANSYS – Load & Boundaries
4.5
Analysis
From the ANSYS analysis, the design can handle the choosen weight magnitude it was
subjected to. Our material, aluminum 6061 proved to be a good material choice since it allows
the frame to be relatively light when compared with other material densities. It is a light metal,
while provides the needed strength and acceptable deflection for the purpose of our design.
While working with ANSYS is very important to know that results will always vary
depending on how the problem is approached and the different analysis choices that are made.
For our analysis we take in consideration the equivalent stresses and total deformation. From the
type of element that is selected, to how the geometry is drawn or the constraints that are
established. In the end, all these parameters were selected to suit our specific model. Figure 4.5
illustrates the von-Mises Stress plot. From this plot we can appreciate that the stress increases as
we close-up to middle of the curved beam, which agrees with the expected behavior. The
maximum stresses experienced by the beam are below the material’s allowable stress. Figure 4.6
illustrates the deflection distribution across the beam. The free end results in the worst deflection
at .121”. This value is acceptable.
26
UTS = 16.7 ksi
Figure 4.5 ANSYS – von Mises
27
Figure 4.6 ANSYS - Deformation
4.6
Shape Optimization
After the analysis we want to see if we can remove extra material from the curve beam.
Using ANSYS Workbench we made the analysis. The next figures demonstrate possible
location to remove material. This analysis does not mean that removing the material is the
best approach to use less material. Removing this material in our case will be more expensive
than leaving the material.
As seen in Figure 4.7, the analysis suggests removing small amount of material. We can
compare this analysis from ANSYS and our optimization analysis from chapter 3 (Lagrange
method) and determine that we acquire an optimum point in the Lagrange method. In the
pictures the red means the material that can be remove and the gray the material you would
keep. Also you have a transactional area seen as beige.
SHOULD BE BETTER EXPLAINED!
28
Figure 4.7 ANSYS – Shape Optimization 1
29
Figure 4.8 ANSYS – Shape Optimization 2
Figure 4.9 ANSYS – Shape Optimization 3
30
Chapter 5
Results and Discussion
5.1
Present Design
Figures 5.1 through 5.4 present the main components of the playground to be design.
These components hold the main idea of what a playground should include to amused children
but at the same time it contains features that encourage children to discovered, learn, exercise be
creative while they play.
The shape storing wall helps children to learn and familiarize with basic geometric figures such as
circles, squares, triangles. This will also help improve children’s fine motors kill.
40 in
48 in
90 in
Figure 5.1 Shape Storing Wall
The bubble climber helps children to work with coordination and balance. This feature also helps to
works strengths in their entire body.
31
93 in
48 in
Figure 5.2 The Bubble Climber
The hop scotch it’s a fun way for children to start learning numbers, count from 1 to 10 and colors.
12 in
12 in
84 in
Figure 5.3 Hop scotch
32
The slides are an essential part of a playground where kids can always interact.
70 in
Figure 5.4 Slides
5.2
Discussion
The inspiration to create this design was to improve the life of a child. We implemented old
ideas of playgrounds design with modern ideas. This was achieved by doing a survey with children in
the ages from 3 to 7. The survey helps us to come with three ideas. These ideas were shown to the
kids that participate in the survey and they preferred two of them. To select the best idea we made a
rough cost analysis to determine the playground that would be suitable for the price range.
This idea is based on developing important skills for children’s such as: balancing,
memory, walking and jumping, and motor skills. Adding all this features to the playground was
an important task for us. At the same time we want to minimize the space required for the
playground. This playground has a free layout setup and it could be arrange in a square area of
20 by 20 or less as shown in the figure below.
33
FREE SPACE
Figure 5.5 Selected Design layout
5.3
Cost Analysis
A cost analysis was executed to establish the costs involved in the productions of one
unit. One of our main goals is to maximize the safety of the playground and at the same time
keep the weight low and costs down. Our budget incorporates two main areas. These areas are
money for parts and manufacture. For parts, we are referring to every component that is needed
to create the playground. When referring to manufacture, it is the money due to the assembly of
the parts in order to accomplish the final product.
The cost analysis includes part name, material that will be used, quantity, total material
cost, manufacture processing time, manufacture processing cost per time, and total manufacture
processing cost. Table 5.3.1 through 5.3.3 presents the tabulated data of the details for the criteria
mentioned before. Furthermore, Figure 5.6 (also see Figure 5.7 and 5.8) represents the budget
required for each part by percentage and cost of each part. In general, the design will consist on
the following materials: steel, plastic, rubber and miscellaneous parts. The cost analysis will be
only focused on the important parts of the design.
34
5.3.1
Multi-Theme Aluminum
Table 5.3.1 Cost Analysis - Aluminum
Parts
Material
Qty
Pounds
Material
Cost ($)
Basket
Mushroom
Swing
Hopscotch
Multi-activity
Slide
Monkey Bars
Climber
Rubber Mulch
AL / HDPE
HDPE
HDPE
EVA foam
HDPE
HDPE
AL
AL / HDPE
Rubber
1
1
1
10
1
2
10
1
1
200
50
75
30
-
75.00
100.00
100.00
15.00
75.00
50.00
80.00
75.00
150.00
720.00
Total Material Cost per unit
Manufacture
Processing time (min)
Cost/time
($/min)
10
1.21
20
2.42
20
2.42
5
0.60
15
1.81
10
1.21
15
1.81
15
1.81
Total Manufacture processing cost
per unit
Manufacture
Processing Cost ($) *
Qty
1.21
2.42
2.42
6.04
1.81
2.42
18.13
1.81
36.25
756.65
Total Cost per unit
Total Cost Analysis
Basket
11%
Mushroom
25%
Swing
16%
7%
7%
23%
4%
5%
Hopscotch
Multi-activity
Slide
Monkey Bars
2%
Climber
Rubber Mulch
Figure 5.6 Pipe Chart-Budget Allocations for Aluminum
35
5.3.2
Multi-Theme Stainless Steel
Table 5.3.2 Cost Analysis - Steel
Parts
Material
Qty
Pounds
Material
Cost ($)
Basket
Mushroom
Swing
Hopscotch
Multi-activity
Slide
Monkey Bars
Climber
Rubber Mulch
SS / HDPE
HDPE
HDPE
EVA foam
HDPE
HDPE
SS
SS / HDPE
Rubber
1
1
1
10
1
2
10
1
1
200
50
75
30
-
125.00
100.00
100.00
15.00
75.00
50.00
150.00
125.00
150.00
890.00
Total Material Cost per unit
Manufacture
Processing time (min)
Cost/time
($/min)
10
1.21
20
2.42
20
2.42
5
0.60
15
1.81
10
1.21
15
1.81
15
1.81
Total Manufacture processing cost
per unit
Manufacture
Processing Cost ($) *
Qty
1.21
2.42
2.42
6.04
1.81
2.42
18.13
1.81
36.25
926.25
Total Cost per unit
Total Cost Analysis
Basket
11%
Mushroom
25%
Swing
16%
7%
7%
23%
4%
5%
Hopscotch
Multi-activity
Slide
Monkey Bars
2%
Climber
Rubber Mulch
Figure 5.7 Pipe Chart-Budget Allocations for Stainless Steel
36
5.3.3
Multi-Theme Titanium
Table 5.3.1 Cost Analysis - Titanium
Parts
Material
Qty
Pounds
Material
Cost ($)
Basket
Mushroom
Swing
Hopscotch
Multi-activity
Slide
Monkey Bars
Climber
Rubber Mulch
TI / HDPE
HDPE
HDPE
EVA foam
HDPE
HDPE
SS
SS / HDPE
Rubber
1
1
1
10
1
2
10
1
1
200
50
75
30
-
350.00
100.00
100.00
15.00
75.00
50.00
300.00
225.00
150.00
1365.00
Total Material Cost per unit
Manufacture
Processing time (min)
Cost/time
($/min)
10
1.21
20
2.42
20
2.42
5
0.60
15
1.81
10
1.21
15
1.81
15
1.81
Total Manufacture processing cost
per unit
Manufacture
Processing Cost ($) *
Qty
1.21
2.42
2.42
6.04
1.81
2.42
18.13
1.81
36.25
1401.25
Total Cost per unit
Total Cost Analysis
Basket
11%
Mushroom
25%
Swing
16%
7%
7%
23%
4%
5%
Hopscotch
Multi-activity
Slide
Monkey Bars
2%
Climber
Rubber Mulch
Figure 5.7 Pipe Chart-Budget Allocations for Titanium
37
Since we are looking for the best choice to fulfill all our customer needs, we can say that
the best material for our playground is the aluminum. It is one of the lightest materials and also
the most affordable. Is important to mention that the mechanical properties of metals are
excellent choices when considering a material to create a playground. We can say the other two
materials may also satisfy our needs, but their prices are too high in comparison with the
aluminum.
Most of the prices and costs were approximate values of the expected required costs and
should be further analyzed before any actual production of the unit. Because this table shows the
cost of just one playground produced by hand, the cost would be higher than the actual massproduced cost of the playground.
It is expected to produce a total of 22 playgrounds per week by working eight hours a day;
meaning that nine workers will be needed to achieve the desired goal. It will be a total of
$261,000/wk. These prices are subject to changes if we produce the playground in mass production
(In this case, the material would be cheaper). Other parameters to take in consideration are: Create a
system in which the product could be managed robotically or using self generation energy (Green
Energy).
38
Chapter 6
Final Remarks
6.1
Conclusion
As with every parent, when it refers to their kids they always consider what is safer, good
for their childhood and also what is better for their pockets. With the creation of “Multi-Theme
Playground”, a whole new concept was raised since it inspires children to recreate themselves,
develop their creativity and imagination and enhance their motor skills in a safe and exciting
way. This design covers important aspects that every responsible parent should consider at the
moment when buying a playground like safety, uniqueness, capacity and economic.
What brought major challenges when searching for the perfect design, was trying to
reunite all our customer requirements within a price range. All our ideas were limited by the fact
that our designs needed to stay within a range between $300 and $600. This restriction helped us
think out of the box; How can I improve what is already in the market? What will make it
unique? And if I were to be the customer, Will I buy it?. At the end the result was a potentially
unique design.
We as a team, consider that our design is the best option and solution to comply with our customer
requirements. It is the most convenient solution with great marketability potential.
6.2
Recommendations
Our design is the best option for every modern parent that always aims the best for their kids. It is not
only limited for kids with ages from 3 to 7 but some of the features contained in the design can be used by
older ones. It is important to mention that supervision should be always present. Due to the size of the
playground, it is recommended to place it outdoors or in large spaces. Remember that the main purpose of a
playground is not merely the fact that your child will be working out while playing, but they will learn the
importance of socializing, playing safe and bound with their family in a safe environment.
39
References
1) The Plastic Web. (n.d.) Plastic Resin Price. Retrieve: Seprember19, 2009, from
http://www.ides.com
2) Playsites + Surfaces, Inc. (n.d.) Specializing in Safe Playgrounds Installations. Retrieve:
September 15, 2009, from http://www.playsitesplus.com/default.htm
3) Diamont Safety Concept (n.d.) Resilient and Anti-Slip Flooring Solutions. Retrieve:
September 15, 2009, from http://www.diamond-safety.com/index.html
4) U.S. Consumer Product Safety Commission (n.d) CPSC Home Page. Retrieve:
September 20, 2009, from http://www.cpsc.gov/cpscpub/pubs/325.pdf
5) American Academic of Pediatrics (n.d) American Academy Of Pediatrics Web Site.
Retrieve: September 20,2009, from http://www.aap.org/pressroom/playFINAL.pdf
40
Appendix A
Submitted Proposal
41
Hi-Octane fitness Playground
Submitted as a partial requirement
for the course INME4058: Section 040
Design Course for B.S. in Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Students:
Bracero Arévalo, Pablo L.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Ruiz Tubéns, Pablo.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, P
Santana Torres, Damaris.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Vázquez Colón , Ana M.
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Faculty Advisor:
Vijay K. Goyal, PhD
Professor at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
September 2009
Proposal
To:
Dr. Vijay K. Goyal
From: Bracero Arévalo, Pablo L.; Ruíz Tubéns, Pablo; Santana Torres, Damaris; and Vázquez
Colón, Ana M.
Date: September 23, 2009
Re:
Engineering Design Project Proposal (INME4058: Section 040)
Dear Dr. Goyal:
Greetings! Our intention is to present to you three unique designs of playgrounds for children
with ages from three to seven. The idea is to improve what is already in the market and satisfy all the
desire qualities (Cost effective, Eco-friendly, specific dimensions, develop your child motor skills and
safety). Enclosed is a brief description of the project.
At the moment of purchasing a playground, a list of requirements should be taken in
consideration. The safety as well as how it will help your child to develop himself is very
important. Countless of playgrounds in the market suffer from lack of richness and variety
causing the absence of interest in the children. These are some considerations that we have taken
at the moment of creating a new design. The purpose of developing these new designs is to
respond for the need of a unique and durable playground in which your child could be able to
develop different motor skills in a safety way and at the same time maintaining it affordable.
We are honored that you have taken our proposal into consideration and we expect to
fulfill and achieve all your requirements and standards .If we can be of further help, please do
not hesitate to contact us.
Regards,
Pablo L. Bracero Arévalo
Damaris Santana Torres
Pablo Ruíz Tubéns
Ana M. Vázquez Colón
2
Hi-Octane fitness Playground
Pablo L. Bracero Arévalo, Pablo Ruíz Tubéns
Damaris Santana Torres and Ana M. Vázquez Colón
Project summary
The requirements of the modern life style have made that a parent or parents invest the majority of
their time working to sustain their families. Because of this, the quality time spent with their children has
been considerably reduced, thus indoor activities such as watching TV or video games have become a norm
while outside activities are left behind. These bad habits are correlated with risk factors for health such as
obesity and poor academic performance. Also it creates violent behavior and desensitization to violence.
This is why it is important that our kids learn to spend more of their time playing outdoors with
elements that creates an environment to inspire children in their intellectual, social, emotional
and physical development.
It is very important in the development of a child to conduct activities that helps them to
improve and grow different motor skills. Activities such as running, throwing, catching,
balancing, etc. gives them strength and a better performance. A playground is the best resource
to combine all these activities, interact with other kids and spend time with their parents. There
are thousands of playgrounds in the market but all them suffer from lack of variety, colors and do
not allow children to take challenges which are what calls the kids attention.
As possible solutions we have created three different designs. The first design consists in
a unique playground with a breakfast theme. It has different stations like swings, trampolines and
slides creating the important elements as part of a complete breakfast. The second design allows
your kid to play with the most important monuments from around the world all at once. It brings
all the basic elements for your kid to explore and play. Monuments include the Eiffel Tower, the
Taj Mahal, the Great Wall of China and the Golden Bridge. The third and last design is a
combination of different stations like swings, monkey bars, climbers, a hop scotch and a
basketball ring all of them intended to develop a different motor skill.
Our main goal is to create a unique, safe, affordable and eco-friendly playground to fit
more than three children between the ages of three to seven years old. The three designs have a
space limitation of 20ft by 20ft area and are made of recycled materials. Knowing and comparing
the price range of other designs in the market we acknowledge that our product needs to be
between $300 and $600 making it affordable. We compromise ourselves to deliver and provide
unique designs that satisfy and exceed our customer expectations. The timeframe available for the
completion of the project is a total of 113 days with 73 days remaining.
1
1.0 Introduction
A playground is an outside play area for children consisting in a combination of
structures for climbing, crawling, jumping, etc. It is very common to find them in parks or even
in our own backyard. For many people a playground is considered just a toy with no importance
or meaning. For others, it is a dangerous place where their kids can get injured easily. The real
meaning and purpose of a playground is to offer the child a place where they can explore, be
creative, enhance and develop the important motor skills at their age and interact with other kids
as well with their parents. To achieve all this purposes, the child must be attracted to it. In the
market over the years designs suffer from lack of variety, imagination or structures that are not
challenges for kids anymore. This drives us to change what is on the market and design
something innovative, unique and new.
In our case, as Mechanical Engineer students, we are trying to achieve and meet all our
client requirements and standards. The main idea is to provide something different and unique
that can help the child to develop his motor skills in a unique way. Figures 1 and 2 display
examples of playgrounds that are common these days. Also this figures show that not more than
2 kids are able to play. They do not call the child’s attention because they are typical and does
not involve challenges for kids. Moreover, in Figures 3 and 4 we can observe designs that suffer
from lack of variety and limits the imagination of the child. Therefore we will provide ideas that
involve all this important requirements in a playground.
Figure 4.1. Playground - swing
Figure 4.2. Playground - slide
Figure 4.3. Playground - tubes
Figure 4.4. Playground - climb 2
2.0 Problem Description
Playgrounds come in a variety of forms, colors, size, materials and types of
entertainment. At a glance, maybe all of them satisfy all the requirements, for a kid to have a
nice place to play, but does it mean it is the right playground? In the early stages of their life,
playing becomes an intrinsic part of the children development. It is through play that children at
a very early age engage and interact in the world around them. Play allows children to use their
creativity while developing their imagination, dexterity, and physical, cognitive, and emotional
strength. It has been proven that today’s playground no longer aloud children to have challenges.
A wide variety of them suffers from lack of richness and variety which is what captures the
attention of a child. With the typical design, children are not able to manipulate their
environment and adapt to what they really need. Over the years what we have been seeing are
more complex designs but they remain just as fixed in form limiting the creativity of the
children.
With the increasing tendency of children to videogames and computers, obesity has
become a more serious illness during childhood. It not only impact directly the children health,
but also isolates them from the real word reducing the opportunity to socialize among themselves
and limiting their imagination to grow. To counteract this tendency, parents must encourage kids
to be more active and promote physical recreation. For this, a playground is a perfect solution.
Playgrounds contribute to the development of the gross motor skills. Gross motor skills
are the movements of the large muscles of the body. In the first years of their life, children
acquire a great number of them. Their brain's development and the environment in which they
mature affect the acquisition of these skills. Movement allows children to discover their body, to
learn that they are independent beings who are able to go off and explore the world. Children
with poor gross motor development may have difficulty with activities such as writing, sitting up
in an alert position, sitting erect to watch classroom activity, and writing on a blackboard. The
development of gross motor skills allows them to perform better in other, more academic and
physical ways. Activities such as running, throwing and catching, jumping, kicking, crawling,
balancing, etc. help children to develop and improve gross motor skills. These types of activities
will also help your child to build strength and be healthy.
Although playgrounds can fit more than two kids at the same time, bigger isn't always
better. Most of the playgrounds manufactures build these days, are too big to be placed in a
typically backyard and the bigger the playground the higher the cost. When yard space and cost
is at a premium, the size of play equipment is an important consideration. It has been found in
the market that a playground as simple as two slides and a stair can cost more than $7,000 and
have a minimum of used zone closed to 572 square feet as show in Figure 5. It can also be found
3
smaller playgrounds costing less than $600 that can be fit in a typically backyard. This example
is shown in Figures 6. The problem with these two examples of playgrounds is that they are not
in harmony with what they have to offer in comparison with cost and space. What they have in
common is the lack of creativity that both can encourage to children. This lack is also visible in
Figures 1 through 4. We are aiming for a playground with a minimum used zone of 20 ft by 20 ft
that can encourage creativity and imagination so children can be able to build their own world.
Smaller play equipment that encourages imaginative play will likely hold your child's interest as
well, if not better, than elaborate, expensive sets with a huge array of accessories. Before buying
a deluxe play system, one should ask how much equipment your kids will really use. Chances are
a simple play set will delight your child.
The safety of each individual piece of playground equipment as well as the layout of the
entire play area should be considered when designing or evaluating a playground for safety.
Since falls are a very common playground hazard pattern, the installation and maintenance of
protective surfacing under and around all equipment is crucial to protect children from severe
head injuries.
Because all playgrounds present some challenges and because children can be expected
to use equipment in unintended and unanticipated ways, adult supervision is highly
recommended. Appropriate equipment design, layout, and maintenance, are also essential for
increasing playground safety. Research has been made and it was found that playgrounds are
typically made of plastic, metal or wood. When deciding which type of materials will be used
for a playground, is important to know where the playground would be installed. Understanding
the type of surroundings will help choose wisely the perfect materials.
Therefore, after knowing what is the problem about and finding out what the market
offers, the goal of this design is to create a playground for a three year old kid that will last until
he/she is seven years old. This new playground design should satisfy the customer requirements.
It should be easy assembly. It needs to be resistant to humidity to prevent rust, so it will last
longer. This factor has been considered based on the costumer location in which the indices of
humidity are normally high. It also needs to be a strong material but not heavy so it will be easy
to move around. The design must encourage kids to move around, helping them to develop and
improve their motor skills. This will also help maintain the kid healthy and strong. It should be
safety at all times and be able to fit in a 20 ft by 20 ft area. The design must eliminate the lack of
motivation of the existing playgrounds and must empower children to be endlessly creative. All
of these needs must be achieved within a budget of $300 to $600.
4
Figure 4.1. Example of simple but expensive
playground
Figure 4.2. Example of a dull playground
3.0 Major Assumptions
The playground is designed to support kids of a weight up to 52 pounds and for a height of 4
ft tall, this is with the fact that the playground will be for kids from ages of 3-7 years. This is the
most important assumption since based on this we will determine the level of difficulty and skills
the kids need to develop. We assume that the children will play safely and that fights are
completely prohibited on a space of 20 ft by 20 ft area properly prepared (flat). This playground
will be located away from the streets and far from cars or objects on movement that can cause
kids to get injured or hurt. Also, this space will be conformed to all the safety features necessary
for the kids to have a good time without accidents while playing. This does not imply that
parents’ supervision is unnecessary since it is the key for safety and well behavior for kids. We
need to mention that the playground is not designed for kids with disabilities considering the
limitations of space and budget.
4.0 Expected Outcomes
What we expect from our design is to have a fun, safe, economic and eco friendly playground
that will revolutionize the market using our creativity. It will have capacity for three kids from
ages 3-7 having fun developing their motor skills instead of playing video games or indoor
activities. A playground is a childhood dream and we will make it real with an affordable price a
family can pay.
5.0 Project Description
After interviewing the costumer and learning what the needs for the playgrounds were, we
have developed three different ideas. The preliminary ideas discuss below focus on developing
motor skills on children as well as to encourage them to explore their creativity to the maximum.
These ideas will also allow that more than three kids play at the same time making it even more
exciting and attractive to them.
5
5.1.
Breakfast
Figure 1.1. “Breakfast” design
How perfect would it be if your kids could learn the importance of a well balanced and
healthy breakfast at the same time they are playing? The breakfast playground, as shown in
Figure 1.1Error! Reference source not found., consists of a group of elements with shapes of
different foods that make the experience of playing interesting. It covers a 20 ft by 20 ft area
ideal for kids with ages from 3 to 7.
This playground elevates the entire conception of breakfast to a whole new level. The kids
will be able to climb a buttered toast, jump over two sunny sides up egg yolks, climb two boiled
eggs and at the top slide through two slices of bacon as shown in Figure 1.1. It also contains a
colorful cereal pool and a swing in the form of a banana. The floor has the shape of an egg
container which gives the sensation as if walking through small hills.
This unique playground contains trampolines in the form of two sunny side up eggs. The
yolks will be the trampolines that will give your kid the sensation of flying. The egg whites will
serve as the couch to absorb safely a fall. Also it has in the middle a cereal pool. The special
feature of it is that it will not be full of balls; instead it will contain colorful stars, moons and
horseshoes to give the impression of a famous cereal. To the side you will find a banana that will
serve as a swing and a buttered toast that your kids can climb. In the other side of the playground
your kid can be able to climb two boil eggs that serve as the base for two slides in the shape of
bacon. Do not forget that it can motivate your kids to eat.
6
It is required that your kids play under the supervision of an adult. The cereal will have round
edges to avoid accidents. The swing should not be used for infants; kids should be over the age
of three and under an adult supervision to play safely. The floor will be made of a Rubber Mulch
to avoid injuries if the kid falls.
All the equipment will be made of recyclable material. The Rubber Mulch is a unique rubber
made of 100% recycled tires. It is mostly used for playgrounds safety surfacing because it is the
safest and most economical choice. The rest of the equipment will be made out of recycled
plastics (high-density polyethylene). It is very important to mention that when purchasing this
product, besides the direct benefit to communities, you will be helping our planet.
This playground has a series of advantages over the playgrounds in the market. This
playground consist of learning the important elements of a complete breakfast. Breakfast is an essential
meal of a daily basis because after 6 to 8 hours of sleep, the body needs vitamins, proteins, fibers
and carbohydrate. As a parent, you should teach your child the importance of a well balanced
food and the big importance of breakfast. The playground also consists in a variety of
equipments that helps develop the child’s motor-skill such as climbing, a trampoline and a ball
pool. In addition, the design of the playground would allow parents to have from 3 to 6 kids
playing in the playground simultaneously. The assembly may require at least two adults.
7
5.2.
Around the World
Figure 2.1. “Around the World” design
Around the World is the theme for an awesome playground that will fill your kids with
history and amazement while having fun with some of the most famous monuments in the world.
You will encounter smaller replicas of monuments such as the Golden Gate Bridge, the Taj
Mahal, the Eiffel Tower and the Great Wall of China. This unique playground will cover a 20ft
by 20 ft area and it is ideal for children’s with ages from three to seven.
Around the World will contain a replica of the famous Taj Mahal in which the front fountain
has been converted into two sand boxes. It also serves as a play house letting your kids to play
inside of this replica. It will be surrounded by the Great Wall of China to separate it from the
other parts. It will also include a non-stable version of the Golden Gate Bridge from San
Francisco that will help develop your balance when walking through it. To finalize they will be
able to climb a replica of the Eiffel Tower. Each one of these stations has its purpose when it
comes to your child’s development. It helps build their body, gain agility and the ability to
control their basic motor skills. The sand box will be a great activity that your kids will love
giving them the opportunity to build, create, bury and dig their toys up.
This exciting playground will give your children the opportunity to learn about some of the
most important monuments in history while socializing with friends and spending time with their
family. The kids should have the supervision of their parents at all times. If your child is playing
8
in the area of the sand box, you have to be aware that it does not get into your child’s eyes and
remind them that it is not eatable. The floor will be made of Rubber Mulch to help absorb the fall
if this is the case and the Bridge will have support to the sides so your child can hold on to them
while walking.
The entire playground is made out of recycled materials. The ground is made of Rubber
Mulch which is rubber made with 100% recycled tires. Also the material used in the monuments
is a recycled plastic which in this case high-density polyethylene. When purchasing this product
you are not only contributing to your child’s development and well being but helping conserve
our only planet. Figure 2.1 show the Around the Word Playground.
One of the advantages of the playground is to teach kids the importance of history. At the
same time we are showing the kids the variety of cultures in the World. The playground consists
also with a variety of equipments to develop the child’s motor-skill such as climb, balanced, and
free movement. In addition the design of the playground would allow parents to have a variety of
kids playing in the playground simultaneously.
The assembly of the playground may require at least two adults. Parents have to be careful
when kids are in the sand box to prevent them from eaten the sand (hazarded materials).
5.3.
Multi-theme Playground
Figure 3.1. “Multi-Theme” design
9
The multi-theme playground was made with the purpose to develop basic skills such as
balance, agility and learn to have control of their own body. To start with the features, an
ingenious mushroom was created that contains comfortable swing. This swing will be safe and
fun for toddlers. The multi-playground comes with an integrated ladder for kids to climb
motivating them to reach the top and develop strength and coordination. Once on top, they will
have the option to slide down through two fun slides, slip down a pole or finally pass through a
bridge-hanger that will exercise your child by making him lift his own weight.
This unique playground has a swing integrated with the shape of a Space-ship. This
colorful swing is able not only to move back and forward but spin around at the same time. It
contains two steer wheels so the kids can drive while flying. Also includes a basketball court and
a hop scotch fixed on the floor to motivate the kids to jump and run around. Five bouncers that
can be used as seats or a fun way to make balance are incorporated to the floor. Finally to teach
children correlate shapes and different forms like stars, squares or circles, a Shape Sorting wall
was integrated.
Supervision of parents is required at all times. The playground is made in the safest way
but precaution should all ways be taken. The floor is covered with Rubber Mulch to absorb the
children fall if this is the case and every bolt and sharp edges are protected and covered to
prevent injuries and cuts. All this descriptions are reference to Figure 3.1.
This playground has a series of advantages over any design. The playground is an easy
assemble system and multi pattern playground. It consists also in a variety of equipments to
develop the child’s motor-skill such as climb, balanced, memory, free movement, coordination
and agility. In addition the design of the playground would allow parents to have a variety of
kids playing in the playground simultaneously with the proper supervision. The assembly of the
playground may require at least two adults.
6.0 Budget Summary
For the playground, we made a detailed cost analysis to obtain a preliminary budget. The cost
analysis include part name, material that will be used, quantity, total material cost, manufacture
processing time, manufacture processing cost per time, and total manufacture processing cost,
Table 1 through Table 3 presents tabulated data of the details mentioned before. Furthermore,
from Figure 1.1 to Figure 3.1 shows the graphical representations of the cost analysis. In general
the design will consist on the following materials: steel, plastic, rubber and miscellaneous parts.
The cost analysis will be focused on the important parts of the design and briefly on
miscellaneous. A research on prices of similar playgrounds shows that the prices are around
$450-$800 dollars and it is expected that the design will be around $600.
10
6.1.
Breakfast Playground
Table 1. Breakfast Playground Cost
Parts
Structure
Bacon
Bread
Boil Egg
Fried Egg
Cereal
Banana
Rubber Mulch
Material
Qty
Pounds
Material
Cost ($)
LLDPE
LLDPE
LLDPE
LLDPE
LLDPE
LLDPE
LLDPE
Rubber
1
2
1
2
1
50
1
1
200
30
25
20
15
1
50
-
280.00
84.00
35.00
56.00
21.00
70.00
70.00
379.44
Manufacture
Processing time (min)
10
1.21
7
0.85
5
0.60
15
1.81
10
1.21
3
0.36
15
1.81
Total Manufacture processing cost
per unit
995.44
Total Material Cost per unit
Cost/time
($/min)
Manufacture
Processing Cost
($) * Qty
1.21
1.69
0.60
3.63
1.21
18.13
1.81
28.28
1023.72
Total Cost per unit
Cost Analysis
Structure
27%
37%
Slide
Stairs
8%
Mini Stairs
Trampoline
7%
6%
9%
Ball Pool
4%
2%
Up and Down
Rubber Mulch
Figure 1.1. Breakfast Cost Analysis Graph
11
6.2.
Around the World
Table 2. Around The World Playground Cost
Material
Qty
Pounds
Material
Cost ($)
Manufacture
Processing time (min)
Eiffel Tower
LLDPE
1
100
140.00
10.0
Manufacture
Process Cost
($)
1.21
Taj Mahal
LLDPE
1
200
280.00
20.0
2.42
2.42
Golden Bridge
LLDPE
1
75
105.00
10.0
1.21
1.21
Great Wall
Great Wall
(T)
LLDPE
1
100
140.00
5.0
0.60
0.60
LLDPE
1
80
112.00
5.0
0.60
0.60
Rubber Mulch
Rubber
1
-
612.00
Parts
Total Material Cost per unit
1389.00
Manufacture Processing
Cost ($) * Qty
1.21
Total Manufacture processing cost per
unit
6.04
1395.04
Total Cost per unit
Cost Analysis
10%
Effiel Tower
44%
20%
Taj Mahal
Golden Bridge
8%
8%
10%
Great Wall
Great Wall (T)
Rubber Mulch
Figure 2.1. Around The World Cost Analysis Graph
12
6.3.
Multi-Theme
Table 3. Multi-Theme Playground Cost
Parts
Basket
Mushroom
Swing
Hopscotch
Multi-activity
Slide
Monkey Bars
Climber
Rubber Mulch
Material
STEEL /
HDPE
HDPE
HDPE
EVA foam
HDPE
HDPE
STEEL
STEEL /
HDPE
Rubber
Qty
Pounds
Material
Cost ($)
Manufacture
Processing time (min)
Cost/time
($/min)
Manufacture
Processing Cost ($) *
Qty
1
-
140.00
10
1.21
1.21
1
1
10
1
2
10
200
50
75
30
-
280.00
70.00
15.00
105.00
84.00
284.40
20
20
5
15
10
15
2.42
2.42
0.60
1.81
1.21
1.81
2.42
2.42
6.04
1.81
2.42
18.13
1
-
150.00
15
1.81
1.81
1
-
612.00
1128.40
Total Material Cost per unit
Total Manufacture processing cost
per unit
36.25
1164.65
Total Cost per unit
Cost Analysis
Basket
Mushroom
8%
34%
16%
Swing
4%
Hop Scotch
Multi-activity
1%
9%
17%
6%
5%
Slide
Monkey Bars
Climber
Rubber Mulch
Figure 3.1. Multi-Theme Cost Analysis Graph
13
7.0 Conclusions
After performing an extensive research, it has been found that nowadays playgrounds tend to
be boring and less exciting. These augment the tendency of children to spend more time playing
video games or watching television which increases chances of obesity and poor academic
performance. This is why we have proposed three playground designs that will enhance and
improve the creativity, health and basic motor skills in a safe way. It will provide an environment
to inspire children in their intellectual, social, emotional and physical development. Our unique
Around the World, Breakfast and Multi-Theme playground design, will revolutionize the market
capable to give fun for more than 3 kids in a safe place. Each one of these design will provide
rubber mulch floor, protective caplugs for screws or other metal elements and a nice comfortable
location for parents. It is our believed that these three unique ideas are the greatest out in the
market and we hope you consider us as your best option.
14
8.0 References
1) The Plastic Web. (n.d.) Plastic Resin Price. Retrieve: Seprember19, 2009, from
http://www.ides.com
2) Playsites + Surfaces, Inc. (n.d.) Specializing in Safe Playgrounds Installations. Retrieve:
September 15, 2009, from http://www.playsitesplus.com/default.htm
3) Diamont Safety Concept (n.d.) Resilient and Anti-Slip Flooring Solutions. Retrieve:
September 15, 2009, from http://www.diamond-safety.com/index.html
4) U.S. Consumer Product Safety Commission (n.d) CPSC Home Page. Retrieve:
September 20, 2009, from http://www.cpsc.gov/cpscpub/pubs/325.pdf
5) American Academic of Pediatrics (n.d) American Academy Of Pediatrics Web Site.
Retrieve: September 20,2009, from http://www.aap.org/pressroom/playFINAL.pdf
15
Appendix A. Qualifications
Our team is composed by four competitive and talented Mechanical Engineer students at
the University of Puerto Rico at Mayaguez. Their past experiences in the industry have brought
them the knowledge necessary to achieve the main goals of this project. All of the members have
contributed in different parts of this proposal making this a successful project design. Following
are the team member’s qualifications:
1. Bracero Arévalo, Pablo Luis
He has done several investigations and a COOP in Boeing Co. at Everett, WA. The
investigations were in nanoparticles & nanofluids and turbine blades. In Boeing, Pablo
helped to developed engineering test plan for Boeing 787 payloads and flight engineer
test for Boeing 777. Simultaneously was mentor for new employees. As well, he has been
involved in the design and simulations of turbine blades.
2. Ruiz Tubens, Pablo
He has two internship at Pratt & Whitney at Hartford, CT as a Facilities and Service
Engineer his assignments include design new parking lots layouts, contractor’s
supervision and HVAC design and recommendations. He also did a COOP at GE Energy
in Patillas, P.R as a manufacturing and Quality engineer during this experience he design
new tools to improve efficiency on assembly lines and ergonomics problems also lead
quality audits and layouts.
3. Santana Torres, Damaris
In 2005, she completed a BS Degree in Surveying at the University of Puerto Rico at
Mayaguez. Her experiences include a 10 month work as a Surveyor in Ponce, Puerto
Rico and a COOP experience at the Naval Undersea Warfare Center (NUWC) Division
Newport, RI. At NUWC, Damaris was able to improve her skills working with
SolidWorks® modeling and stress calculations. She also experience working with
HyperWorks® for future FEA studies.
4. Vázquez Colón, Ana M.
She is a senior mechanical engineer student at the University of Puerto Rico at Mayaguez
Campus. She has done two internships with Hamilton Sundstrand at Hartford, CT as a
project engineer with the Engine and Control Systems group. A COOP in GE-Aviation at
Cincinnati, OH in the Aviation Component Service Center and an internship with Pepsi
Co. at Cidra, PR. This work experiences has granted Ana the opportunity to work closely
with clients as well as implementing new ideas to design projects and also know the
necessary information and data to achieve our goal.
16
Appendix B. Task Breakdown (Gantt Chart)
Following is the task breakdown presented in Table 4. This includes all details of the project coursework. The duration of each task is
based on the dates specified by the customer. The current status of the project is represented by a star bullet.
Table 4. Gantt Chart
17
Appendix B
Method of Lagrange Multipliers
42
From the constraint Multivariate Methods we will apply the Lagrange Multiplier. The
Lagrange multiplier will determine the maximum or minimum subject to the constraints
(𝑥1 , 𝑥2 𝑎𝑛𝑑 𝑥3 ).
The problem in standard form:
𝑓(𝑥) = 𝑥3 (𝑥1 + 𝑥2 )
Subject to
𝑔1 (𝑥) = 3 − 𝑥1 ≤ 0
𝑔2 (𝑥) = 𝑥1 − 5 ≤ 0
ℎ1 (𝑥) = 𝑥1 − 𝑥2 = 0
1
ℎ2 (𝑥) = 𝑥3 − = 0
4
𝑥 = {𝑥1 𝑥2 𝑥3 }𝑇 Єℝ
Determine the lagrangian:
ℒ(𝑥, µ, 𝜆)= ƒ(𝑥) + 𝜆1 𝑔1 (𝑥) + 𝜆2 𝑔2 (𝑥) + µ1 ℎ1 (𝑥) + µ2 ℎ2 (𝑥)
1
= 𝑥3 (𝑥1 + 𝑥2 ) + 𝜆1 (3 − 𝑥1 ) + 𝜆2 (𝑥1 − 5) + µ1 (𝑥1 − 𝑥2 ) + µ2 (𝑥3 − )
4
Find the Lagrange point (𝑥 ∗ , 𝜆∗ , µ∗ )
1) Ensure that the Lagrangian will be stationary:
𝜕𝓛
𝜕𝒙1
0
𝜕𝓛
𝛻𝐿 =
= {0}
𝜕𝒙 2
0
𝜕𝓛
{ 𝜕𝒙 3 }
43
𝜕ℒ
= 𝑥3 − 𝜆1 + 𝜆2 + µ1 = 0
𝜕𝒙1
𝜕ℒ
= 𝑥3 − µ1 = 0
𝜕𝒙2
𝜕ℒ
= 𝑥1 + 𝑥2 + µ1 = 0
𝜕𝒙3
In order to satisfy the second K-T Condition
𝜆1 (3 − 𝑥1 ) = 0
𝜆2 (𝑥1 − 5) = 0
µ1 (𝑥1 − 𝑥2 ) = 0
1
µ2 (𝑥3 − ) = 0
4
To find the Lagrange points, let us start the trivial solution (unconstrained optimization
problem):
𝜆1 = 0, 𝜆2 ≠ 0, µ1 ≠ 0, µ2 ≠ 0
Solve the system of equation:
𝑥3 − 𝜆3 + 𝜆4 = 0 ⇨ 𝑥3 + 𝜆2 + µ1 = 0
𝑥3 − 𝜆1 + 𝜆2 = 0 = 0 ⇨ 𝑥3 − µ1 = 0
𝑥1 + 𝑥2 + µ1 = 0
𝜆1 (3 − 𝑥1 ) = 0 ⇨ 𝑎𝑢𝑡𝑜𝑚𝑎𝑡𝑖𝑐𝑎𝑙𝑦 𝑠𝑎𝑡𝑖𝑠𝑓𝑖𝑒𝑑 0 = 0
𝜆2 (𝑥1 − 5) = 0 ⇨ 𝑥1 − 5 = 0
µ1 (𝑥1 − 𝑥2 ) = 0 ⇨ 𝑥1 − 𝑥2 = 0
1
1
µ2 (𝑥3 − ) = 0 ⇨ (𝑥3 − ) = 0
4
4
Hence
44
𝑥1 = 5,
𝑥2 = 5,
𝑥3 =
1
4
Unconstrained problem:
5
𝑥1
5
𝑥2
1
⁄4
𝑥3
∗
ℒ𝑎 = 𝜆1 = 0
1⁄
𝜆2
2
µ1
1⁄
4
{µ2 }
{−10}
Condition 1 state that the point must be feasible:
5
5
𝑥𝑎∗ = {1}
4
𝑓|𝑥 = 𝑥 ∗ =
5
𝐷𝑒𝑓𝑖𝑛𝑒𝑑 𝑔𝑜𝑜𝑑!
2
𝑔1 |𝑥 = 𝑥 ∗ = −2 ≤ 0 𝐺𝑜𝑜𝑑!
𝑔2 |𝑥 = 𝑥 ∗ = 0 ≤ 0 𝐺𝑜𝑜𝑑!
ℎ1 |𝑥 = 𝑥 ∗ = 0 ≤ 0 𝐺𝑜𝑜𝑑!
ℎ2 |𝑥 = 𝑥 ∗ = 0 ≤ 0 𝐺𝑜𝑜𝑑!
It’s a good candidate and the solution suggests that the inequality constrain 𝑔1 is inactive while
𝑔2 is active and it suggest that the equality constrains ℎ1 𝑎𝑛𝑑 ℎ2 are active.
Verify the second condition:
𝜆1 𝑔1 |𝑥 = 𝑥 ∗ = (0)(−2) = 0 𝐷𝑒𝑓𝑖𝑛𝑒𝑑 𝑔𝑜𝑜𝑑!
𝜆2 𝑔2 |𝑥 = 𝑥 ∗ = (1⁄2)(0) = 0 𝐷𝑒𝑓𝑖𝑛𝑒𝑑 𝑔𝑜𝑜𝑑!
45
𝜇1 ℎ1 |𝑥 = 𝑥 ∗ = (1⁄4)(0) = 0 𝐷𝑒𝑓𝑖𝑛𝑒𝑑 𝑔𝑜𝑜𝑑!
𝜇2 ℎ2 |𝑥 = 𝑥 ∗ = (1⁄2)(0) = 0 𝐷𝑒𝑓𝑖𝑛𝑒𝑑 𝑔𝑜𝑜𝑑!
Verify the sufficient condition:
𝑯(ℒ𝑎∗ ) =
𝜕2 ℒ
𝜕2 ℒ
𝜕2 ℒ
𝜕𝑥12
𝜕𝑥1 𝑥2
𝜕𝑥1 𝑥3
𝜕2ℒ
𝜕2 ℒ
𝜕2 ℒ
𝜕𝑥2 𝑥1
𝜕𝑥2 𝑥3
𝜕2ℒ
𝜕𝑥22
𝜕2 ℒ
[𝜕𝑥3 𝑥1
𝜕𝑥3 𝑥2
𝜕𝑥32
0
= [0
1
𝜕2 ℒ
]
(𝑥 = 𝑥𝑏∗ , 𝜇 = 𝜇𝑏∗ , 𝜆 = 𝜆∗𝑏 )
0 1
0 1]
1 0
The eigenvalues obtain were: -1.4142, 0 and 1.4142
46
Appendix C
ANSYS Tutorial
47
The following tutorial is a step by step procedure using ANSYS Workbench.
After having the part drawn in SolidWorks go to File/ANSYS 11.0/Workbench
48
After clicking the Workbench you would see the following screen
Select New Simulation from the CAD Geometry Tasks
49
You would see your CAD design in ANSYS Workbench
50
First we must create the mesh. Right click “Mesh” at the left tree

Insert/Mapped Face Meshing. Left Click
51

Selescte the two front lower legs face
52
We must create a refined mesh. Right click “Mesh” at the left tree
 Insert/Refiniment



Righr click the CAD part and select “select all” (the part would turn green)
Hit apply at the bottom left
Change refinement to 3
53
After creating the Mapped/Face Meshing and Refiniment we must tell ANSYS to create the mesh
 Right click “Mesh” in the left tree and select “Generate Mesh”
Now we must select what type of studies we want to achieved
 From the menu select New Analysis/Static Structural and Shape Optimization
Let applied the load and boundary conditions
 Right click “Static Structural” go to Insert/Force
o Select the face you want to apply the load (our case the face would be were the swing would be hanging) and applied
the load of 55lbs in the –y direction.
54
For the boundary conditions we are goint to set the bottom face of the legs as fixed point
 Right click “Static Structural” go to Insert/Fixed Support
55
We must select now what type of solution we want to evaluate.
 Right click “Solution” and select Insert/Stress/Equivalent (von Mises)
 Right click “Solution” and select Insert/Deformation/Total
Now you are ready to began the simulation. The simulation would take several minutes.
 Right click “Solution” and select Solve
If you select a complex mesh the solution make take longer.
56
For the Shape optimization make the following steps:
 Right click “Shape Optimization” go to Insert/Force
o Select the face you want to apply the load (our case the face would be were the swing would be hanging) and applied
the load of 55lbs in the –y direction.
For the boundary conditions we are goint to set the bottom face of the legs as fixed point
 Right click “Shape Optimization” go to Insert/Fixed Support
Next step is to solve for the shape optimization
 Right click “Shape Optimization” and select SOLVE
Output Data:
57
58
59
60
Student Vitae
The group was composed of four students, these are:
Name: Bracero Arévalo, Pablo L.
Discipline: Mechanical Engineer
Parent Institution: University of Puerto Rico, Mayagüez Campus
Expected date of graduation: December 2009
E-mail address: pablo.bracero@upr.edu
Name: Vázquez Colón, Ana M.
Discipline: Mechanical Engineer
Parent Institution: University of Puerto Rico, Mayagüez Campus
Expected date of graduation: May 2010
E-mail address: ana.vazquez.colon@gmail.com
Name: Ruiz Tubéns, Pablo
Discipline: Mechanical Engineer
Parent Institution: University of Puerto Rico, Mayagüez Campus
Expected date of graduation: May 2010
E-mail address: pablo.pabloru@gmail.com
Name: Santana Torres, Damaris
Discipline: Mechanical Engineer
Parent Institution: University of Puerto Rico, Mayagüez Campus
Expected date of graduation: December 2009
E-mail address: santana.damaris@gmail.com
61
Evaluation Sheet
Points
Evaluation Criteria
Obtained
Draft
Max
Obtained
Final
Max
Title
Is the title descriptive?
12 words or less
Encloses the main idea of the project
Relevant and attractive
4
4
4
4
8
7
9
5
15
8
15
10
---
15
10
10
5
8
4
2
1
5
---
1
3
10
5
4
5
4
10
100
5
100
Convert to 30
Convert to 70
Cover Letter
Is it signed?
Good job introducing the work being submitted
Is not too short neither too long
The letter head information is correct (names, dates, subject)
Project Summary
Includes the correct the title
Has each team member’s names
The summary is descriptive enough to have a good idea of the proposal
Introduction is clear
What is being proposal and how it will be done
The time-frame and approximate cost
Chapter 1. Preliminary Remarks
Offers a good background to the project
Motivation of the problem need
Why is there a need for what is being designed
Clearly and precisely explains the problem in hand
How it will be attacked with all the details.
A detailed description of a possible solution
Uses figures to describe the text
Chapter 2. Project Description
Offers a clear description of the project
Clearly explains each idea with disadvantages and advantages
Uses the Pugh’s method to choose the best design and justifies each criteria
used.
Includes Figures to reinforce the descriptions
Chapter 3. Design Optimization
Explains the design problem
Explains the objective function, design variables, and constraints
Successfully uses the method of Lagrange multipliers
Talks about the final optimized design parameters
Chapter 4. Finite Element Analysis
Clearly explained step-by-step assumptions and approximations in performing
CAD
Chapter 5. Results and Discussion
Talks about the final design
Explains and criticizes the design
Provides an extensive cost analysis
Chapter 6. Final Remarks
All ideas are brought to an end.
Not a summary
Kept the reader wonder about the proposal
References
Includes at least 5 references.
All are numbered
Appendix A. Submitted Proposal
Includes the submitted proposal
Appendix B. Lagrange Multipliers
Details of the Optimization Method
Appendix C. ANSYS’s Project Tutorial
Details of the CAD
Figures and Tables
Includes figures and tables to support the proposal.
They all have captions
They are all referenced in text
Technical Writing
Spell check
Grammatically correct and sound
Overall presentation
TOTAL