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Team C.R.A.M. [TWO PENDULUM HARMONOGRAPH]
i
1. Table of Contents1. Problem Formulation .............................................................................................................. 1
1.1 Introduction...................................................................................................................... 1
1.2 Objective .......................................................................................................................... 1
2. Problem Analysis and Literature Review ................................................................................ 1
2.1 Problem Analysis .............................................................................................................. 1
2.1.1 Introduction .............................................................................................................. 1
2.1.2 Specifications ............................................................................................................ 1
2.1.3 Considerations .......................................................................................................... 2
2.1.4 Criteria....................................................................................................................... 2
2.1.5 Usage ......................................................................................................................... 2
2.1.6 Production ................................................................................................................. 2
2.2 Literature Review ............................................................................................................. 3
2.2.1 Introduction .............................................................................................................. 3
2.2.2 Client Information ..................................................................................................... 3
2.2.3 Waste in Humboldt County ...................................................................................... 3
2.2.4 Up-cycled Projects .................................................................................................... 3
2.2.5 Machine Mechanisms ............................................................................................... 6
2.2.6 Types of Art Making Machines ............................................................................... 11
2.2.7 Art Materials ........................................................................................................... 15
2.2.8 Safety Precautions .................................................................................................. 19
2.2.9 Getting Kids Engaged .............................................................................................. 19
3. Alternative Solutions ............................................................................................................. 20
3.1 Introduction.................................................................................................................... 20
3.2 Brainstorming ................................................................................................................. 20
3.3 Alternative Solutions ...................................................................................................... 20
3.3.1 Two Pendulum Harmonograph .............................................................................. 203.3.2 The Whirlpool ......................................................................................................... 21
3.3.3 The Jackson Pollock Machine.................................................................................. 22
3.3.4 The Gravitron .......................................................................................................... 23
3.3.5 Topsy Turvy ............................................................................................................. 23
3.3.6 Shake and Paint ....................................................................................................... 24
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3.3.7 Artistic Explosion ..................................................................................................... 25
3.3.8 Rotary Harmonograph ............................................................................................ 25
3.3.9 Hangmans Last Harmony....................................................................................... 26
3.3.10 The Tumblr .............................................................................................................. 26
3.3.11 The Spirograph Spinner .......................................................................................... 27
4. Decision Process ................................................................................................................... 28
4.1 Introduction.................................................................................................................... 28
4.2 Criteria Definitions ......................................................................................................... 28
4.3 Decision Choices ............................................................................................................. 28
4.4 Decision Process ............................................................................................................. 29
4.5 Final Decision Justification ............................................................................................. 32
5. Solution Specification ........................................................................................................... 32
5.1 Introduction.................................................................................................................... 32
5.2 Solution Description ....................................................................................................... 32
5.2.1 The Table ................................................................................................................. 33
5.2.2 The Gimbals ............................................................................................................ 34
5.2.3 The Brick Weights ................................................................................................... 35
5.2.4 The Pen Arm Pendulum .......................................................................................... 36
5.2.5 The Writing Platform Pendulum ............................................................................. 37
5.3 Cost Analysis ................................................................................................................... 385.3.1 Cost of Materials ..................................................................................................... 38
5.3.2 Design Cost .............................................................................................................. 39
5.3.3 Maintenance Cost ................................................................................................... 40
5.4 Maintenance .................................................................................................................. 40
5.5 Implementation Instructions ......................................................................................... 40
5.5.1 Assembly ...................................................................................................................... 40
5.5.2 Use ............................................................................................................................... 43
5.6 Prototype Performance .................................................................................................. 46
6. Appendices: ........................................................................................................................... 47
6.1 Appendix A: Bibliography ............................................................................................... 47
6.2 Appendix B: Brainstorming Notes .................................................................................. 49
6.3 Appendix C: AutoCad Drawings ..................................................................................... 52
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Figure 1-1 Black Box Model describes the goal of the project ...................................................... 1
Figure 2-1 Macintosh G4 towers up-cycled into a desk. ................................................................ 4
Figure 2-2 Engine block reused for a Coffee table
(http://www.neatorama.com/2006/03/02/engine-block-coffee-table/) ...................................... 4
Figure 2-3 EPS packaging sheets(http://boxbrosla.com/boxtest/product/catalog/moving/shipping-supplies/styrofoam-sheets-
48-x-24-x-2) ..................................................................................................................................... 5
Figure 2-4 Example of a Gear Train................................................................................................. 6
Figure 2-5 Compound Gear Train (http://www.rlt.com/14010) .................................................... 7
Figure 2-6 Two wheel Pulley System
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml) .. 8
Figure 2-7 Cam Diagram
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml) .. 8
Figure 2-8 Different Cam Shapes
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml) .. 9Figure 2-9 Figure 2 9 A Class 1 Lever
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml) 10
Figure 2-10 A Class 2 Lever
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml) 10
Figure 2-11 A Parallel Motion Linkage
http://lizarum.com/assignments/physical_computing/2008/mechanisms/linkages.html ......... 11
Figure 2-12 An image created by a harmonograph. ..................................................................... 12
Figure 2-13 Two Disc Harmonograph (http://mrhonner.com/2012/05/11/turntable-
harmonograph/) ........................................................................................................................... 13
Figure 2-14 These are some intricate images produced by a spirograph. (Images by Google
Images) .......................................................................................................................................... 14Figure 2-15 SCRAP Humboldt's existing paint spinner machines (Images by SCRAP Humboldt). 15
Figure 2-16 Watercolors (Image from Google Images) ................................................................ 16
Figure 2-17 Acrylic Paint with a high viscosity (http://www.painting-with-a-palette-
knife.com/acrylic-paint/) .............................................................................................................. 17
Figure 2-18 Thick oil paint (http://www.artistoilpaint.tdparts.com/) .......................................... 17
Figure 2-19 Home made Paints
(http://www.cd3wd.com/cd3wd_40/ap/Natural_paint_basics.html) ........................................ 18
Figure 3-1 Two Pendulum Harmonograph ................................................................................... 21
Figure 3-2 The Whirlpool Inspiration
(http://terpconnect.umd.edu/~cpalumbo/MarylandScienceCenter.html) ................................. 21Figure 3-3 The Whirlpool Drawing by Alejandro Infanzon-Marin ................................................ 22
Figure 3-4 Drawing of the Jackson Pollock Machine by Aaron Hu ............................................... 22
Figure 3-5 Drawing of The Gravitron by Aaron Hu ....................................................................... 23
Figure 3-6 Drawing of the Topsy Turvy by Aaron Hu .................................................................... 24
Figure 3-7 Drawing of Shake and Bake by Aaron Hu .................................................................... 24
Figure 3-8 Drawing of the Artistic Explosion by Mark Attarian .................................................... 25
Figure 3-9 Drawing of a Rotary Harmonograph by Mark Attarian ............................................... 25
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Figure 3-10 Drawing of Hangman's Last Harmony by Mark Attarian ........................................... 26
Figure 4-1 Visual Matrix of the decision process of Team C.R.A.M .............................................. 32
Figure 5-1 A Lissajous Figure, which is a visual of harmonic motion between the two pendulum
frequencies ................................................................................................................................... 33
Figure 5-2 Two Pendulum Harmonograph Diagram (Group Photo)............................................. 33
Figure 5-3 AutoCad design of the card table used ....................................................................... 34Figure 5-4 AutoCad Drawing of the Gimbals Created by Mark Attarian ...................................... 34
Figure 5-5 The Harmonograph at rest with brick weights attached (Group Photo) .................... 35
Figure 5-6 Two Bolt Clamping Method (Group Photo) ................................................................. 35
Figure 5-7 One Bolt Clamping Method (Group Photo) ................................................................. 36
Figure 5-8 Pen Arm Pendulum ...................................................................................................... 37
Figure 5-9 Writing Platform Pendulum ......................................................................................... 38
Figure 5-10 Design cost pie chart in Hours for Team C.R.A.M for a total of 114 hours ............... 39
Figure 5-11 Unfold the Card Table Legs (Group Photo) ............................................................... 41
Figure 5-12 Insert Pendulums through the table slots (Group Photo) ......................................... 41
Figure 5-13 Pendulum Slot Placement (Group Photo) ................................................................. 42Figure 5-14 Insure the Gimbal goes into the Gimbal dimple (Group Photo) ............................... 42
Figure 5-15 Paper Platform weight clamping (Group Photo) ....................................................... 43
Figure 5-16 Pen Arm weight single bolt mechanism (Group Photo) ............................................ 43
Figure 5-17 Adjusting weight ........................................................................................................ 44
Figure 5-18 Place paper and writing utensil. ................................................................................ 44
Figure 5-19 Put pendulums into motion. ...................................................................................... 45
Figure 5-20 Drop pen arm and watch. .......................................................................................... 45
Figure 5-21 Possible Parameter Changes ..................................................................................... 46
Figure 5-22 First Graders at Morris Elementary School in Mckinleyville testing the
Harmonograph (Group Photo) ...................................................................................................... 46
Figure 5-23 Drawings made by our Two Pendulum Harmonograph (Group Photo) .................... 47Figure 6-1 Brainstorm Notes Page 1 ............................................................................................. 50
Figure 6-2 Brainstorm Notes Page 2 ............................................................................................. 51
Figure 6-3 Brainstorm Notes Page 3 ............................................................................................. 51
Figure 6-4 Brainstorm Notes Page 4 ............................................................................................. 52
Figure 6-5 Table with dimensions ................................................................................................. 52
Table 2-1 Criteria and Constraints .................................................................................................. 2
Table 4-1 Weighted Criteria .......................................................................................................... 29
Table 4-2 Delphi Matrix for Alternative Solutions ........................................................................ 30
Table 5-1 Itemized Materials Cost ................................................................................................ 39Table 5-2 Maintenance Cost in Dollars ......................................................................................... 40
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1.Problem Formulation1.1IntroductionThe problem formulation describes the objective of the project using a Black Box model. The
solution is discussed in the objective section and the goal of the project is shown in Figure 1-1.
1.2ObjectiveThe objective of the project is to construct a machine that is both entertaining and safe for
adults and children. The art machine should be an example of how to use waste products in a
fun and easy way. Figure 1-1 is our Black Box model which describes the change the art
machine brings to the world before and after creation.
2. Problem Analysis and Literature Review2.1Problem Analysis2.1.1 IntroductionThe problem analysis section analyzes the intended purpose and function of the Art Machine.
Taken into account are specifications the art machine must follow, considerations for its
function and intended purpose, and criteria on which to grade various proposed designs.
2.1.2SpecificationsThe specifications for this product are specific characteristics that must be included when
designing the machine. The specifications for this project are:
The machine must be able to be carried by one or two people The machine must be able to fit in the back of the clients 1998 Volkswagen Beetle
Black Box
InputAdults and children
have a lack of
knowledge and
experience with art
machines made out
of reused materials
in Humboldt County
OutputAdults and childrenhave knowledge
and experience with
art machines made
from reused
materials after
using the machine
Figure 1-1 Black Box Model describes
the goal of the project
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The materials used to build this machine must consist of at least 75% reused material.
2.1.3ConsiderationsConsiderations are the conditions the project will be under, and must be able to endure in
order to function properly. The considerations are: Both children and adults will be using this machine. The machine must be easy to setup and transport The people transporting the machine will most likely be older Our client already has an art spinner, and is looking for an art machine that differs from
that.
2.1.4CriteriaCriteria are design characteristics that are carefully defined in order to weigh different design
options against one and another in order to come to a decision.
Table 2-1 Criteria and Constraints
Criteria Constraints
Durability Must endure use by children
Reparability Moving parts must be easily replaceable
Cost Must spend under $300
Engaging More fun than Tic Tac Toe
Unique and Cool Art Must be able to create at least 5 unique designs
Portability Machine must be less than 60 lbs, and fit in the trunk of a 1998
Volkswagen Beetle
Safety Must be no blatant safety hazards for people of all age
Ease of Use Children must be able to operate the machine after being
demonstrated on how to use it
2.1.5UsageThe art machine will be used to entertain and teach both children and adults at both SCRAP
Humboldts events as well as at schoolsand art festivals. The art machine will teach how
materials can be diverted from the waste stream to make useful products while also making a
cool art product.
2.1.6ProductionA single Art Machine will be produced and used, with various prototypes produced as needed.
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2.2Literature Review2.2.1 IntroductionThe literature review covers the research done pertinent to the development an art machine
for our client, SCRAP Humboldt. References for all research are found in Appendix A. Topics
covered are: SCRAP Humboldt, Client Criteria, Waste in Humboldt County, Up-cycled Projects,Machine Mechanisms, Types of Art Machines, Art Materials, Safety Precautions, and Getting
Kids Engaged.
2.2.2Client InformationSCRAP Humboldt is a local chapter of the national nonprofit, SCRAP, and operates out of Arcata,
CA. SCRAP is an acronym which stands for (School Community Reuse Action Project). The
mission of SCRAP Humboldt is to inspire creative reuse and environmentally sustainable
behavior by taking materials out of the waste stream, then providing educational programs and
affordable materials to the community. (SCRAP, 2013)
2.2.3Waste in Humboldt CountySince the Industrial Revolution, more products and waste have been made than ever before.
Every year more and more materials are recycled, however recycling is energy intensive
(Pichtel, 2010) and it is often more beneficial to collect products out of the waste stream and
reuse or repurpose them. Reusing clothing alone can result in a 14%-45% reduction in
greenhouse gases produced and overall human toxicity. Reusing products that are more heavily
manufactured will provide greater environmental benefits. (Farrant, 2010)
In 2010, Humboldt County successfully diverted over 170,000 tons of waste from being
landfilled, and in addition landfilled 19,000 tons less garbage than 2004. (Planning Commission,
2010) However, of the 91,000 tons of waste sent to landfills, over 1/3 was sent to a facility 175
miles away in Medford, Oregon, and the remaining 2/3 was sent over 140 miles to a landfill in
Redding, California. (Planning Commission, 2010)
2.2.4Up-cycled ProjectsIn this section we discuss different materials that have been commonly repurposed from their
original intent into something new, and art projects that have used these materials. Upcyclingisthe process of converting waste materials into new materials or products that give the waste
object a use beyond its original design. Take for example the desk in Figure 2-1 made out old
computers and a spring from the suspension of a car.
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2.2.4.1
MaterialsMany materials can be easily upcycled. Plastic is a material that is recycled but can be used inother ways. There are many different types of plastics, and they can all be upcycled rather than
being thrown away or melted down.
Wood can be taken out of the waste stream and will provide a variety of good building
materials. Old broken furniture that is thrown out can be reused. Construction sites often have
a lot of unused wood as well as other materials.
Another source of materials is the automotive industry. Cars that are sent to a landfill to be
crushed can be salvaged (Cool Gizmo Toys, 2012). For example, an engine block can be used as
the base of a coffee table as in Figure 2-2. A more classic example is a car tire that is turned intoa rope swing.
Figure 2-2 Engine block reused for a Coffee table (http://www.neatorama.com/2006/03/02/engine-block-coffee-
table/)
Figure 2-1 Macintosh G4 towers up-cycled into a desk.
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Glass can be reused in a variety of ways, for example crushed glass held together by cement to
make a table surface. Electronics have many parts and can be dismantled to create something
completely new such as the computer towers used to make a desk in Figure 2-1. Another
example is a hard drive becoming a paperweight.
Industrial materials such as combustion products, iron, steel slags, and paper mill residuals
could also be used. Most of these materials have chemical, physical, and engineering attributes
that make them valuable resources but end up in the waste stream (U.S. EPA, 2008).
All these materials have the potential to become something more valuable than if they were
thrown away or recycled.
2.2.4.2 Up-cycled Art ProjectsWaste materials are an inexpensive way to gather art supplies. Some examples of waste
materials used in art projects are magazine collages, old cloths, old jewelry, buttons, electronic
parts, scrap metal and much more. The reuse of old containers such as baby wipes can be made
into paintbrush holders; they may not be art themselves, but they give the container a new life.
Objects such as oatmeal containers, drink-mix cartons, plastic milk containers are great for
shaping sculptures of abstractions or animals (Brooks, 2013). Using cardboard packaging, pizza
boxes, and used string or twine work well for printing projects. (Brooks, 2013). EPS (Expanded
Polystyrene) packaging sheets such as the ones in Figure 2-3, can be used for flat-plane
sculptures or paint trays.
Figure 2-3 EPS packaging sheets (http://boxbrosla.com/boxtest/product/catalog/moving/shipping-
supplies/styrofoam-sheets-48-x-24-x-2)
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2.2.5 Machine MechanismsA machine is an apparatus using or applying mechanical power to perform a particular task.
One of the most important aspects of the machine is the mechanical mechanisms used to
perform the task. A mechanism is a part that has an input of motion and force, and an output of
a different motion and force. The point of a mechanism is to make a particular job easier to do.
(BBC, 2013) There are five common machine mechanisms: gears, pulleys, cams, linkages, andlevers.
2.2.5.1 GearsGears are toothed wheels fixed to shafts. The teeth of multiple wheels interlock to transfer
motion from the first gear (the driver) to another (the follower). A series of gears is called a
gear train as shown in Figure 2-4. The motion of the driver gear in the clockwise direction turns
the follower gear in the counterclockwise direction.
Figure 2-4 Example of a Gear Train.
One important aspect of gears is the gear ratio, or velocity ratio. When there are gears of two
different sizes, the smaller will rotate faster than the larger. The number of teeth is used to
calculate the gear ratio:
Gear ratio = number or teeth on follower gear number of teeth on the driver gear (BBC, 2013)
Using the gear ratio, we can then figure out the Output speed using:
Output speed = input speed gear ratio (BBC,2013)
Another type of gear train is the compound gear train as show in Figure 2-5. This type allows for
further slowing down the gear speeds in the successive transfers from small gears to large
gears.
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Figure 2-5 Compound Gear Train (http://www.rlt.com/14010)
2.2.5.2 Pulley SystemsPulley Systems can be used to change the torque, speed, or direction of rotation of a system.Pulleys consist of at least two wheels and a belt, which rotary motion and force from the driver
to the follower shaft shown in Figure 2-6.
Like the gears, the smaller wheel in a pulley system will spin faster than the larger wheel, and
this difference can be calculated as a velocity ratio:
Velocity ratio = diameter of the driven pulley diameter of the driver pulley (BBC, 2013)
Using both the velocity ratio and input speed results in the output speed:
Output speed = input speed velocity ratio (BBC 2013)
The velocity ratio is also important in determining the amount of force, or torque, from the
driver pulley to the follower pulley:
Output torque = input torque velocity ratio (BBC, 2013)
The advantages of a pulley system are that you can twist the belt so the direction of the wheel
can be reversed. In addition, pulleys require no lubrication like chains do, though unlike chains,
they can slip.
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Figure 2-6 Two wheel Pulley System
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml)
2.2.5.3 CamsCams are shaped pieces usually made of metal or plastic which are fixed to a rotating shaft.
(BBC 2013) There are three parts, the cam, the slide, and the follower shown in Figure 2-7.
Figure 2-7Cam Diagram
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml)
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The cam itself it irregularly shaped, and has the drive shaft off center, so that as the crank turns,
the cam rotates to push the follower up. This drives the mechanism, and the follower is held in
place by the slide, ensuring it does not move. When the follower is not moving it is said to be
dwelling.
The shape of the cam determines how frequent the mechanism is driven, as well as if the
mechanism falls, rises, or is dwelling examples are shown in Figure 2-8. (BBC 2013)
Figure 2-8 Different Cam Shapes
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml)
Ultimately, the cam turns the rotary motion of a crank into a reciprocating motion of a shaft
moving up and down.
2.2.5.4 LeversA lever is one of the simplest types of mechanisms, which are divided into three types, or
classes of levers. All levers have a load, which is an object being moved, an effort, which is the
work done on the object, and the fulcrum, which is where the object is pivoted.
2.2.5.4.1 Class 1 LeversA class 1 lever has a load and effort on opposite sides of the fulcrum shown in Figure 2-9. It
works by using less work to move a weight, which is done by extending the total distance
travelled, thereby reducing the amount of work done. This is expressed in the equation for
Force, which is Force equals work times distance. By making the distance a smaller amount, the
work portion subsequently becomes much smaller as a result.
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Figure 2-9 Figure 2 9 A Class 1 Lever
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml)
2.2.5.4.2 Class 2 LeversA class 2 lever has an effort and a load on the same side. The load is between the effort and the
fulcrum. The best example of this is a wheelbarrow. Again by extending the distance travelled,
the overall work done is lowered.
Figure 2-10 A Class 2 Lever
(http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev3.shtml)
2.2.5.4.3 Mechanical Advantage and Velocity Ratio of Class 1 & 2 LeversBoth class 1 and class 2 levers allow a larger output of load for a smaller effort. This is called
mechanical advantage.
To calculate mechanical advantage, we use the equation:
Mechanical advantage = load effort (BBC, 2013)
Because you move a large load with smaller effort, it may seem like youre getting something
for nothing. However, in order for the lever to work, you must move the load over a longer
distance.
This is called the velocity ratio, and can be calculated using:
Velocity ratio = distance moved by effort distance moved by load (BBC, 2013)
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2.2.5.4.4 Class 3 LeversClass 3 levers do not have mechanical advantage. They operated with the effort closer to the
fulcrum and the effort farther away. They are often used to pick up small things, or things thatmay be fragile. A good example of a Class 3 Lever is a pair of tweezers.
2.2.5.5 LinkagesA mechanical linkage is a way to manage forces and movement through an assembly of
connected bodies shown in Figure 2-12. The body, or link, is considered to be rigid because the
links movement is studied using geometry. The link connections are modeled as providing
movement, such as rotation or sliding, and are called joints. Linkages can change the direction
of motion, the type of motion, and/or the magnitude of a force.
Figure 2-11 A Parallel Motion Linkage
http://lizarum.com/assignments/physical_computing/2008/mechanisms/linkages.html
A linkage consists of a system of rigid materials, usually rods, connected by joints or pivots. The
moving and fixed pivots limit the ability of the rods to move. The input at one end of the
mechanical linkages will be different from the output, in both speed and direction (BBC, 2013).
2.2.6Types of Art Making Machines2.2.6.1 HarmonographA harmonograph is a machine that uses pendulums to create a geometric image. Most
commonly they are used to create curves that show harmonic motion, also known as Lissajous
figures, as demonstrated in Figure 2-12. The simplest types of harmonograph uses twopendulums that swing across perpendicular axes, with one pendulum attached to a pen and
the other attached to a piece of paper (Ashton 2001). The result is that the pattern the pen
draws is a combination of the frequencies of the pendulums. The resulting image not only looks
interesting but is a visual representation of harmony between the pendulum frequencies. This
visual modeling of frequencies can also be applied to harmonies between musical notes,
because if the pendulums are set to the same frequency as the notes, their resulting harmonies
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make visually appealing drawings. In fact, harmonographs were first used to model the
frequencies between musical notes before computers. Varying the frequency of the pendulum
swings can produce different patterns.
In a simple two pendulum harmonograph, there are a few elements that affect the motion and
consequently, the image that the machine produces. It is very important to understand the
physics of the motion of a pendulum swing. The first property to consider is that a pendulum of
a fixed length will always have the same frequency. So as a pendulum falls, the amount of
energy of the swing (amplitude) will decay but the frequency will stay the same. This physical
property allows the pendulum swing frequency to model musical notes. By adjusting the ratio
of the pendulum lengths you can simulate basic harmonics in music (Ashton 2001).
Another way to make a harmonograph is to take two discs that are spinning and connect to
them two arms within a bell crank linkage. Connect both arms to a pen, which draws on paper.
This kind of harmonograph takes advantage of two gears spinning at relative frequencies as
opposed to pendulums. Figure 2-13 provides a better visual representation of this type of
harmonograph.
Figure 2-12 An image created by a harmonograph.
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Figure 2-13 Two Disc Harmonograph (http://mrhonner.com/2012/05/11/turntable-harmonograph/)
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2.2.6.2 SpirographA spirograph is a type of drawing machine that makes geometric patterns, technically referred
to as epitrochoids and ashypotrochoids. Spirographs have been produced as popular toys for
young children, as they produce some very interesting patterns with minimal knowledge of
mechanics. Spirographs work by drawing from a point inside a circle that rotates within another
fixed circle. The patterns produced can be varied by moving the pen closer or
farther from the center of the smaller gear on the inside. This alters the amount of rotation at a
certain point. Figure 2-14 shows some of the images that can be made with a spirograph. Other
interesting figures can be produced by superimposing multiple drawings on top of each other.Most of the time these machines are made out of little plastic gears, one big one with teeth on
the inside and a smaller one with teeth on the outside. (Kller 2000)
2.2.6.3 Paint spinnerA paint spinner is a very simple type of art machine in operation. It is a rotor with paper and
paint on it, and the rotor spins at a high velocity, which sends the paint outwards making
splatter-like patterns. Paint spinners can utilize a variety of different spinning sources, including
electric motors from fans, or human powered with machines like bicycles. Paint spinners often
are used to produce colorful mixes of vibrant colors, but dont work as well with darker colors.
SCRAP Humboldt already has two of these machines in use as seen in Figure 2-15.
Figure 2-14 These are some intricate images
produced by a spirograph. (Images by Google
Images)
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Figure 2-15 SCRAP Humboldt's existing paint spinner machines (Images by SCRAP Humboldt)
2.2.7Art MaterialsThis section will focus on art materials and their traits. Something to look for in art materials is
their permanence or the ability to withstand exposure to light and humidity without darkening,
shifting color, or fading. Many things play a role in the permanence of an art project forexample, if the paper doesnt absorb the paint the paint will fade off. Paint also has a role in
this though; certain paints have a tendency to fade faster than others. The next three sections
explore three materials used in art that are relevant to the criteria given by our client. These
materials are paint, paper, and pens.
2.2.7.1 PaintThere are many types of paint such as; industrial paint, spray paint, face paint, and the different
art paints from acrylic paint to watercolor. Discussed here are paints, what type of painting
they are primarily used for, what they are composed of, and their traits.
Watercolors are a very easy way to get pastel and vivid colors as shown in Figure 2-16. Painting
with watercolors you can essentially paint anything from sharp photorealist paintings and
vibrant abstracts to landscapes and cityscapes (McArdle, 2011).
Watercolors are made with two main ingredients, Arabic gum which acts as a binder, and finely
ground pigment for color. A moisturizer is added to keep the Arabic gum from becoming brittle.
For the paint to flow and be absorbed easier a wetting agent is added (McArdle, 2011). A
valued trait of watercolors is their ability to let light pass through the paint and reflect the
white surface of the paper.
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Figure 2-16 Watercolors (Image from Google Images)
Acrylic paints can be used in many different ways to create a variety of painting styles (McArdle,
2004). They are made with synthetic acrylic resins and pigments and can either be water based
or solvent based (Rossol, 1995). Acrylic paints are known because they have higher permanence
ratings than oil and watercolor paints (McArdle, 2004). The viscosity or consistency of acrylic
paints varies, providing the variety of painting styles that can be achieved with this paint. Heavy
body acrylic paints have a buttery consistency that facilitate color mixing and blending and
preserves brushstrokes this is shown by the acrylic paint in Figure 2-17. Fluid acrylics have a
lower viscosity good for detailed work, watercolor techniques, dry-brush work and staining
(McArdle, 2004). For more elevated work acrylic mediums can be added to the paint to obtain
the desired consistency. Acrylic paints are also known for their fast drying time (McArdle,
2004). Fast drying time might render the ability of an artist to perform some of the blending
and mixing techniques these paints are good for because the paint dries before it is mixed. To
prolong the drying time retarding mediums can be added or using open acrylic paints which
already have the retarding medium in them (McArdle, 2004).
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Figure 2-17 Acrylic Paint with a high viscosity (http://www.painting-with-a-palette-knife.com/acrylic-paint/)
The last type of paint we will discuss are oil paints. Oil paints are popular because of their long
durability, and flexibility in application and working methods (Pellegrini, 2011). They are made
up of pigments suspended in an oil medium. Linseed oil, poppy seed, walnut, sunflower, andsynthetic oils are generally used (Rossol, 1995). Because they are oil based, water cannot mix
with oil paint as shown by the thick oil paint in Figure 2-18 and 2-19. Thus when the paint is dry
which can take up to a month due to the fact that oil paints dry from oxidation, they create a
tough water resistant layer (Pellegrini, 2011). The long drying period allows oil paints to be
workable for a long time. There are various ways of altering the properties of oil paints. For
example adding an impasto medium will add body, and adding linseed oil will add gloss and
translucency (Pellegrini, 2011). Water mixable oil paints have been made to avoid dealing with
oils and solvents, and allow the thinning of the paint with just water.
Figure 2-18Thick oil paint (http://www.artistoilpaint.tdparts.com/)
2.2.7.1.1 Homemade Natural PaintsThe project is designed to be interesting, educational and engaging for children. Having
materials and directions on how to make paints before using them will educate them on how
they can use common materials to make their own paints and keep them engaged while using
the art machine. By giving the option to children to make their own paint, gives children more a
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more interesting, educational and engaging experience with the Art Machine. Simple paints can
be made by mixing flour, water and a dye. Some dyes that can be used are powdered tempera
paint and food coloring, which makes safe paint. Figure 2-20 shows some homemade paints
being blended. The primary advantages of natural homemade paints are a lower VOC content
in the product, more variability in texture, color, and viscosity, and they are much more
sustainable than petroleum based paints (Abdalla, 2005).
Figure 2-19 Home made Paints (http://www.cd3wd.com/cd3wd_40/ap/Natural_paint_basics.html)
2.2.7.2 PaperThis section will discuss the types of paper available and what type of art they are good for.
Bark paper, which is made from the bark of fig and mulberry trees this paper, can be used for
bookbinding, drawing, and painting (Blick, 2010). Papyrus is another type of paper, which was
used by ancient Egyptians in their tombs and can be traced back to pastel paintings as late as
the 17th
and 18th
centuries (Southwest Art, 2006). Papyrus paper is good for drawing, writing, or
painting (Blick, 2011). Next are various types of cotton paper I will discuss the two most
common. Watercolor paper, which come in three types: hot-pressed, cold-pressed, or rough
(McArdle, 2012). Hot-pressed cotton paper has a smooth texture good for detailed work, rough
cotton paper has a rough texture which features pronounced tooth, is washable, and cold-
pressed is somewhere in the middle, making it good for detailed work as well as washes
(McArdle, 2012). Another type of cotton paper is printmaking paper. This paper is strong and
sturdy making it good for watercolor, drawing pen, ink artworks, and acrylic paint. Regular art
paper, which is heavier than regular paper but isnt as durable and sturdy as other papers. Thispaper is not typically used for painting because it will buckle or crinkle, however it is good for is
pen, pencil or ink drawings (McArdle, 2012).
2.2.7.3 PensThere are many types of pens from the old quill to the newer ballpoint; in this section we will
discuss pens commonly used for art. These include fountain pens, graphic pens, and drafting
pens. We will start with fountain pens; these pens were a big advancement because before
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them you had to dip your pen in ink. Fountain pens have a reservoir that contains the ink; the
ink then flows down into the nib where it is dispensed by a thin slit (David, 2008). These pens
are used for art because you can achieve certain artistic effects that cant be achieved by other
pens (David, 2008). The next type of pen we will discuss is a graphic pen, which is made for
precise drawing. They produce consistent, graceful and fluid lines, and they contain archival ink
or waterproof and fade resistant ink (JetPens, 2013). Graphic pens satisfy the painstakingdemands of artist, while requiring no special care or maintenance. Finally drafting pens, these
pens are for drawing lines at a consistent width (Cult Pens, 2001). The nibs for these pens come
in different sizes to allow drawing lines of varying widths making them good for sketching.
2.2.8Safety PrecautionsThis section will discuss the dangers of possible materials that could be used to make Art
Machines. Safety is large concern and the section will examine the materials and point out ones
that could be potentially harmful and how to prevent harmful substances from being
incorporated into the finished product.
2.2.8.1 MetalMany metals are dangerous and can cause illness or cancer if consumed or inhaled. However
for the Art Machine project, metal does not pose much of a threat, most metal products such
as Arsenic and Hexavalent Chromium are considered dangerous only when processing such
metals (OSHA 2008). Other metals such as lead are dangerous in their product; however their
products will not be used in the Art Maker project. The most dangerous aspect in reusing metal
is the danger of sharp edges, and diseases on metals such as Tetanus. Tetanus is a serious
disease that can attack the human body nervous system. Tetanus can be contacted through dirt
and feces, but one of the most well-known ways is contacted through rusty metals and nails.
This should be kept in-mind when constructing the Art Machine out of reused metal materials.
2.2.8.2 PaintPaints can be equally as dangerous as metals in the sense that it can cause serious bodily harm.
However, paints are only harmful when being digested or breathed in. The toxicity of paints
usually comes from the pigments. Another danger of paints is cleaning them. One of the more
well-known solvents for cleaning paints is turpentine which is toxic to humans (Rossol, 2001;
Princeton, 2007; Muse 2011). However, other solvents for the Art Machine can be used to clean
paint that isnt toxic.
2.2.8.3 PlasticPlastic is dangerous and can cause serious bodily harm; however this can only be caused by
ingesting it. Plastic can be ingested in different ways, such as through their use of containers foritems people would consume such as water bottles and plastic food containers. They can also
be ingested by breathing in burning plastics.
2.2.9Getting Kids EngagedGetting Kids engaged and thinking about art is beneficial to cognitive skills. Skills such as
reasoning and problem solving are not things that students suddenly just get out of nowhere,
you have to refine and constantly engage those skills. However the interesting part is that there
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seems to be a correlation between an increase in problem solving skills and engagement in art
at an early age (Melnick, 2011). This all comes down to learning the processes such as creative
thinking or analyzing problems and coming to conclusions. For these types of skills it is not the
end result that is important but process. For a kid making art it is not important that they make
a good finished result, it is important that they look and the problem they have, that is making
something interesting, and thinking of creative ways of solving this problem. These skills areessential in being successful in any field. Art is a very good way in engaging kids early and
teaching them some of these skills because it is fun and interactive.
3.Alternative Solutions3.1IntroductionThe Alternative Solutions section includes information both on both our brainstorming process
and the alternative solutions that were generated in those brainstorming sessions.
3.2BrainstormingTeam C.R.A.M. had one 45 minute brainstorming session. The meeting was structured in the
way that we had Aaron Hu as our diligent notetaker, but for the majority of the meeting we
kept the session unstructured in the way we approached our ideas. Our notes are detailed in
Appendix B. Overall we generated about 15 ideas, and in the post brainstorming session we
threw out four immediately as they were too ludicrous to work, but they served to inspire our
other ideas.
Our post brainstorming portion also involved merging ideas and concepts, force fitting, andfinally fleshing ideas more fully in order to get a better sense of what we would present to our
client. In addition, we made a list of pros and cons of each idea according to our criteria and
constraints in order to get an idea of what each idea best dealt with.
3.3Alternative Solutions3.3.1Two Pendulum HarmonographThis art machine is comprised with two pendulums. The first pendulum supports a flat surface
that you put a piece of paper on. The second pendulum holds a pen, pencil, or marker. As both
pendulums swing the pen is dragged across the paper creating a unique design. To make thismachine engaging the direction that the pendulums swing can be altered as well as the weights,
which will be interchangeable to show how it affects the movement of the pendulum and
therefore the drawing. By having these little changes you can create a huge amount of unique
designs. In addition, another idea to consider would be to use one pendulum as a metronome,
which would make the machine more engaging. This machine easily fits the criteria as being
portable, easy to use and safe. It can be made durable and repairable, though it will require
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more planning to do so. The machine also creates a lot of unique art designs. Though it does fit
the criteria of being engaging, the biggest drawback of this design is that is takes a bit of time,
which could lower how engaging it is for little kids. A detailed drawing of the Two Pendulum
Harmonograph is presented in Figure 3-1.
3.3.2The WhirlpoolThis design was inspired from the big funnels where coins are rolled down at museums as
shown in Figure 3-2. In this machine the coins will be replaced by marbles that are covered inpaint. It consists of two parts, one part, the funnel, which is suspended by a square shaped
table that can be made with reused wood. The other part would be the marble launching
mechanism, where the angle of descent is determined. The funnel would have paper inside so
whoever is using it has something to take home. A drawing of the proposed design can be seen
in Figure 3-3.
Figure 3-2 The Whirlpool Inspiration (http://terpconnect.umd.edu/~cpalumbo/MarylandScienceCenter.html)
Figure 3-1 Two Pendulum Harmonograph
Drawing by Mark Attarian
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Figure 3-3 The Whirlpool Drawing by Alejandro Infanzon-Marin
3.3.3The Jackson Pollock MachineThe Jackson Pollock Machine shown in Figure 3-4 is a table comprised of a disk surrounded by
circular walls with paper on them. A crank will spin the disk that will have paint reservoirs that
allow paint to come out splattering onto the sides of the walls. The disk will be connected to
the crank with either a chain or a belt. If a chain were to be used tensioners would be used to
keep the chain tight. The chain system will have a cover for protection. It is easily removed and
provides easy access for maintenance. The sides of the cylindrical walls have slits at the top to
slide paper in, and keep it from falling over while the disk is spinning.
Figure 3-4 Drawing of the Jackson Pollock Machine by Aaron Hu
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3.3.4The GravitronThe Gravitron is a machine that uses centrifugal force to make art, a sketch is shown in Figure
3-5. This works because inks are made up of various dyes, and when spun at a high velocity the
dyes separate at different rates, leaving streaks of distinct colors across a paper surface. The
machine consists of 4 parts; a crank, bike chain, platform and paper. The crank is attached to
the chain, which spins the platform for the paper. The crank needs to have a larger radius thanthe platform to take advantage of mechanical advantage and gear ratios. This means that the
bigger gear will spin the smaller gear much faster, resulting in a much greater velocity. Paper
rests on the platform and to use this machine, an ink dot must be drawn on the paper. Then,
drops of water are added to the paper. When the machine starts spinning, the crank should be
turned which make the platform spin faster and the centrifugal force should separate the
individual inks out from the ink drop on the paper, leaving a multicolored ink pattern on the
paper.
Figure 3-5 Drawing of The Gravitron by Aaron Hu
3.3.5Topsy TurvyThe Topsy Turvy is shown in Figure 3-6 a device that is similar to the childrens toy top, which
spins at a decent speed to keep itself steady. The Topsy Turvy uses a similar design where it
uses a spinning force to keep itself from falling over, however it makes art while its spinningbyplacing crayons on the outside of the top. The top itself can be made out of a circular wheel,
weights and crayons. Crayons can also be substituted for pens and fine point markers. The top
will use the pen as its spinning point and will make a unique line on paper while spun. The
weight helps the top keep it center of balance lower, to improve spin performance. A device
can also be made to spin the top at faster speeds.
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Figure 3-6Drawing of the Topsy Turvy by Aaron Hu
3.3.6Shake and PaintThe Shake and Paint shown in Figure 3-7 is a tilted marble box, an activity that requires paint,
marbles, paper and a box or drawer. Paint is places into the box and marbles dipped in paint
are put on top of the paper. Then the box can be tilted to make the marbles move around to
get a unique marble pattern on the paper. This box can be made into a machine by adding
elements in which people can operate the box without shaking the box.
Figure 3-7 Drawing of Shake and Bake by Aaron Hu
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3.3.7Artistic ExplosionThe purpose of the Artistic Explosion shown in figure 3-8 is to splatter paint onto a medium
with compressed air. The parts utilize bike and paintball marker parts. The paint ball marker
would be to supply the mechanism to propel the paint with compressed air. Paint would be putin the barrel part of the marker that normally sends paint balls flying. The compressed air would
be supplied with bicycle power. A bike crank that moves a piston that compresses air into a
tank would be used, thereby priming the mechanism with manual power.
Figure 3-8 Drawing of the Artistic Explosion by Mark Attarian
3.3.8Rotary HarmonographMuch like the other harmonographs this machine will record the harmony between two
frequencies; however the two frequencies of this machine are two discs moving at different
speeds. This machine will be bike powered and the drive will be started with a bike crank. This
will have a chain which will transfer the energy to two bike cassettes that are attached to our
two disks. By changing the position of the rods the speed and direction of the overall
mechanism changes, which results in a variety of different designs. In order to change the
relative speed of rotation we can attach a derailleur to the mechanism. Figure 3-9 shows a
drawing of the design, but Figure 2-13 also shows a rotary harmonograph.
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Figure 3-9 Rotary Harmonograph Drawing by Mark Attarian
3.3.9Hangmans Last HarmonyThis design is another variation of the harmonograph. The stand resembles a scaffold used for ahanging and off of that will hang the harmonograph pendulum mechanism. Figure 3-10 shows
that there is a single piece of wood coming from the top of the scaffold, after that single
support there is a universal joint that allows the parts lower to move in any axis. From that
universal joint there will be two pieces of wood supporting the flat area for a piece of paper.
Under that is another pendulum supported by some line that adds more variation, making a
more complex image.
Figure 3-10 Drawing of Hangman's Last Harmony by Mark Attarian
3.3.10The TumblrThis design utilizes an old washing machine drum. When combined with a hand crank, the
machine spins around, and is lined with paper so that marbles and other objects covered in
paint spin with it, thereby creating unique designs. The paddles within the machine drum would
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serve to catch the marbles in a way to prevent them from grouping together as shown in Figure
3-11. The base and stand are sturdy and collapsible to make the machine more portable. In
addition, the base would spin in some variation so that there wasnt friction between the
washing machine and the base.
Figure 3-11 Drawing of The Tumblr by Alex Saldivar
3.3.11The Spirograph SpinnerThis machine is very simple in form, with only a gear and frame mechanism. A pen is inserted in
one of the various gear holes and spun around. This creates varied and unique designs because
of how the holes are positioned. The gear and track system serve to allow the mechanism to
spin very fast while also being very precise. Figure 3-12 shows an example of a spirograph and
Section 2.2.6.2 goes into more detail over the concepts.
Figure 3-12 Picture of a Spirograph (http://www.stephenhobley.com/blog/2010/09/16/upgrading-the-doodle-
desk-now-with-added-spirograph/)
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4. Decision Process4.1IntroductionThe Decision Process is a discussion of how the alternate solutions were narrowed down and the
final design was chosen. The design process utilized a Delphi Matrix with weighted criteria, and
values assigned to each Alternative Solution on how well they met the criteria. The matrix,
considerations, and criteria were the deciding factors in our ultimate decision of which design
would be the ideal solution.
4.2Criteria DefinitionsDurability: The amount of time the art machine should be functional over a period of time
through use by both adults and children.
Reparability: Materials and effort required to make repairs.
Cost: The money and time required to collect materials and build.
Engaging: The time and energy willingly put in by participants.
Aesthetically pleasing Art:The amount of variation in the overall art products, as well as how
aesthetically pleasing it is.
Portability: The ease of which it can be moved. Considerations include overall bulkiness,
weight, and ease of assembly/disassembly.
Safety: The likelihood of injury while machine is in use and during transportation.
Ease of Use:The amount of time a participant is expected to need in order learn how to use the
machine. The main consideration is machine complexity.
4.3Decision ChoicesAll the alternative solutions are explained in detail and diagramed in Section 3. There are eleven
overall alternative solutions:
Two Pendulum Harmonograph Rotary Harmonograph
Deadmans Last Harmony The Spirograph Spinner The Tumblr Artistic Explosion Shake and Paint Topsy Turvy The Gravitron
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The Jackson Pollock Machine The Whirlpool
4.4Decision ProcessThe decision method was based on the Delphi method. The Delphi method began with deciding
the weight of the criterion based off of the impact of that criterion in the specifications and
considerations; the higher the weight the more important the criterion. The weight of the
criteria was decided by a group consensus. Finally, we consulted SCRAP Humboldt to determine
that our weighting was in line with their goals. A list of the criteria weights is shown in Table
4-1.Table 4-1 Weighted Criteria
Project Criteria Importance out of 10
Safety 10
Engaging 9
Repairability 8
Durability 7
Unique Art 7
Ease of Use 6
Portability 5
Cost 4
Each alternative solution was given a value between one and fifty, according to how well it
fulfilled each criterion. A low score meant a solution did not fulfill the defined criterion well. A
group consensus was also used to assign scores for the solutions.
The score was then multiplied by the weight of the criterion. This final Delphi matrix is
presented in Table 4-2. The solutions that scored the best were the Two Pendulum
Harmonograph, Hangmans Last Harmony, and the Hurricane Splatter. They were all within 100
points of each other.
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Table 4-2 Delphi Matrix for Alternative Solutions
List Weight
1-10 Value x Weight Value x Weight Value x Weight
Durability 7 35 245 40 280 40 280
Repairability 8 45 360 25 200 30 240
Cost 4 30 120 20 80 35 140
Engaging 9 40 360 45 405 35 315
Unique Art 7 40 280 35 245 35 245
Portability 5 45 225 20 100 40 200
Safety 10 40 400 30 300 48 480
Ease of Use 6 35 210 40 240 43 258
Criteria
Total
Two Pendulum Harmonograph Rotatary Harmonograph Hangmans Last Harmony
2200 1850 2158
Solutions
List Weight1-10 Value x Weight Value x Weight Value x Weight
Durability 7 45 315 45 315 20 140
Repairability 8 43 344 35 280 15 120
Cost 4 44 176 40 160 15 60
Engaging 9 30 270 15 135 45 405
Unique Art 7 25 175 5 35 35 245
Portability 5 47 235 5 25 20 100
Safety 10 25 250 20 200 30 300
Ease of Use 6 49 294 40 240 25 150
Criteria
Total
Solutions
The Spirograph Spinner The Tumblr Artistic Explosion
2059 1390 1520
List Weight
1-10 Value x Weight Value x Weight Value x Weight
Durability 7 45 315 20 140 40 280
Repairability 8 45 360 20 160 40 320
Cost 4 45 180 20 80 40 160
Engaging 9 10 90 35 315 35 315
Unique Art 7 5 35 20 140 25 175
Portability 5 45 225 40 200 35 175
Safety 10 40 400 30 300 35 350
Ease of Use 6 40 240 30 180 40 240
Criteria
Total
Shake and Paint Topsy Turvy The Gravitron
1845 1515 2015
Solutions
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List Weight
1-10 Value x Weight Value x Weight
Durability 7 35 245 48 336
Repairability 8 40 320 10 80
Cost 4 35 140 10 40
Engaging 9 35 315 20 180
Unique Art 7 30 210 30 210
Portability 5 37 185 15 75
Safety 10 42 420 40 400
Ease of Use 6 40 240 35 210
Criteria
Total
The Hurricane Splatter The Whirlpool
2075 1531
Solutions
Now that we narrowed the solution to three designs we looked over our criteria and
considerations again. Upon doing so, we discovered that one of our considerations had been to
make an Art Machine that was unlike the paint spinner that SCRAP Humboldt currently has(refer to Section 2.1.3). With this, we were able to eliminate the Hurricane Splatter because it
very closely relates to the paint spinner in form, function, and artistic expression.
With two designs left we decided to prototype the two harmonographs. After testing the
Hangmans Last Harmony prototype (picture in Appendix C) we decided that this design would
work well on a larger scale in a more permanent setting and this did not fit our criteria and
considerations.
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The Two Pendulum Harmonograph was chosen as the final solution. Figure 4-1 is a visual
matrix of the decision process.
Figure 4-1 Visual Matrix of the decision process of Team C.R.A.M
4.5Final Decision JustificationThe Two Pendulum Harmonograph had the highest score using the Delphi Matrix method. It
was close in score to two other proposed designs, but after further exploring the considerationsand specifications, we felt the Two Pendulum Harmonograph was the best choice. It is
important to the Frosted Flakes and SCRAP Humboldt that the Art Machine be both portable
and unlike the Art Machine SCRAP Humboldt already has, which were the deciding factors in
our decision.
5. Solution Specification5.1IntroductionThe Solution Specification describes the solution chosen in Section 4.4, the Two PendulumHarmonograph. This section details the structure of the Two Pendulum Harmonograph, provides a cost
analysis of construction and maintenance, and includes instructions for assembly and maintenance.
5.2Solution DescriptionThe Two Pendulum Harmonograph is an art machine that Team C.R.A.M constructed for SCRAP
Humboldt. The Harmonograph uses the frequency of two pendulums moving on separate
planes of motion to create drawings that are Lissajous figures, or parabolic curves that show
Beggining with
Alternative Solutions
Initial Weighting
Consult SCRAPHumboldt
Delphi Matrix
Weighing AlternativeSoltuions by Criteria
Eliminate all designs
not in the top three
Review Considerationsand Specifications:
Eliminate HurricaneSplatter
Consult SCRAPHumboldt: Eliminate
Hangman's LastHarmony
Final Decision: TwoPendulum
Harmonograph
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harmonic motion in Figure 5-1. The Two Pendulum Harmonograph can be broken up into five
distinct parts: the table, the gimbals, the brick weights, the pen arm pendulum, and the writing
platform pendulum as shown in Figure 5-2.
Figure 5-1 A Lissajous Figure, which is a visual of harmonic motion between the two pendulum frequencies
Created by Team C.R.A.M. Two Pendulum Harmonograph
Figure 5-2 Two Pendulum Harmonograph Diagram (Group Photo)
5.2.1The TableThe pendulums must rest on a platform that was tall enough and stable enough to support the
pendulumsmotion. In addition SCRAP Humboldt required the Harmonograph to be portable so
they could take it to schools and art events. An old card table with collapsible legs in Figure 5-2
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provides portability while remaining sturdy. The exact dimensions of the table are in a diagram
in Appendix C.
Figure 5-3 AutoCad design of the card table used
Created by Alejandro Saldivar
5.2.2The GimbalsIn order for the pendulums to swing freely, there must be a mechanism which allows them to
swing wth minimum interference and friction. The mechanisms used to accomplish this are
called gimbals as shown in Figure 5-3. The gimbals are lag bolts drilled through a wood
platform, and the platform is in turn attached to the pendulum itself. The gimbals rest on the
gimbal blocks on the table, and there is a metal plate with dimples for the lag bolts there tokeep the pendulums in place. Since the gimbals are bolts with pointed tips, they are afforded a
full range of motion while simultaneously providing very little friction to interfere with the
pendulum motion. The wood platform is made out of scrap wood from a housing remodel, and
the gimbal bolts were bought from Ace Hardware.
Figure 5-4 AutoCad Drawing of the Gimbals Created by Mark Attarian
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5.2.3The Brick WeightsThe brick weights perform two functions. First, they lend the pendulums more inertia so they
can swing for a much longer time. This is because the pen on the paper causes friction, thereby
slowing the pendulum swing down. Second, the weights hold the gimbals in the gimbal dimple
and keep the pendulum upright. If the weights were not present, the paper platform pendulum
would fall over to one side because it is too top heavy. Figure 5-5 shows the machine at restwith the weights attached.
Figure 5-5 The Harmonograph at rest with brick weights attached (Group Photo)
The paper platform weight uses a two bolt clamping mechanism to attach itself to the
pendulum as shown in Figure 5-6. This allows this weight to move up and down and change the
drawing by altering the frequency of the pendulums.
Figure 5-6 Two Bolt Clamping Method (Group Photo)
The pen-arm weight uses a one bolt clamping mechanism to attach itself to the pendulum as
shown in Figure 5-7. This keeps the weight in one place so at least one pendulum has a fixed
frequency. While variability is good, too much and the drawings look too chaotic so by fixing
one pendulum we allow a baseline frequency to work with.
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Figure 5-7 One Bolt Clamping Method (Group Photo)
5.2.4The Pen Arm PendulumThe pen arm moves in a front and back motion with the pendulum. This allows the attached
pen to press down on the paper and draw at the same frequency the pendulum is swinging at.
In order to minimize the amount of friction from the weight of the pen and arm, a weight is
attached to the pen arm with a bolt and wing nut as shown in Figure 5-8. This weight can be slid
back and forth according to how heavy the pen attached is, allowing for all manner of pens to
be attached to this arm. Below the pen arm itself are the two gimbals attached to the wood
platform. The wood platform was drilled out in the exact center so as to be perfectly centeredwith the pendulum, and the gimbals themselves are drilled in the center of that, to ensure the
balance of the pendulum. Finally, at the bottom of the pendulum there are weights which are
used to keep the pendulum are steady and upright, and allow the pendulum enough inertia to
continue swinging.
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Figure 5-8 Pen Arm Pendulum
Created by Aaron Hu
Both the pendulum and the pen arm are made of upcycled wood trim and the pen arm weight
is a marble trophy base. The weight at the bottom of the pendulum consists of two bricks that
sandwich the pendulum with a single bolt. This bolt goes into one hole and the brick weights on
this pendulum do not move.
5.2.5The Writing Platform PendulumThe writing platform moves in a side to side motion with the pendulum. This allows the writing
platform to swing in a perpendicular motion to the pen, which produces a drawing that is the
same frequency the pendulum is swinging at. At the top of the pendulum there is a writing
platform which holds a piece of paper that gets drawn on. Below the writing platform are the
two gimbals attached to the wood platform. The wood platform was drilled out in the exact
center so as to be perfectly centered with the pendulum, and the gimbals themselves are
drilled in the center of that, to ensure the balance of the pendulum. Finally, at the bottom
there are weights which are used to keep the pendulum steady and upright, and allow the
pendulum enough inertia to continue swinging. Shown in Figure 5-5 is a labeled diagram of all
the pendulum parts.
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Figure 5-9 Writing Platform Pendulum
Created by Alejandro Infanzon-Marin
The pendulum is made of upcycled wood trim and the writing platform is made out of scrap
wood from a remodeling project. The weight at the bottom of the paper platform pendulum
consists of two bricks that sandwich the pendulum with two bolts so the weight can be lifted up
and down.
5.3Cost AnalysisThe cost analysis consists of the cost of materials, cost of design, and cost of maintenance.
5.3.1Cost of MaterialsThere was a budget of $300 dollars towards the building of this project. All of the major
materials were upcycled, the only costs that occurred were with the hardware and the bricks.
The total project monetary cost was $17.11. Table 5-1 details the items and their projected and
actual costs. Our cost was quite a bit under our limit of 300 dollars. This was because most of
our materials were upcycled.
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Table 5-1 Itemized Materials Cost
5.3.2Design CostThe design cost is the amount of hours that Team C.R.A.M put into this design project. Building
the Harmonograph took the most time at 49 hours, and problem formulation took the least
amount of time at 5 hours. A total of 114 hours were spent on this design project as shown inFigure 5-10.
Figure 5-10 Design cost pie chart in Hours for Team C.R.A.M for a total of 114 hours
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5.3.3Maintenance CostThe maintenance costs for the harmonograph are negligible as shown in Table 5-2. The art
machine uses gravity as the driving force for motion, so no electricity is used. The only costs
then will come from replacing the pen and paper, which are upcycled at SCRAP Humboldt for a
cost of $0, and the lubricant used for the joints.
Table 5-2 Maintenance Cost in Dollars
5.4MaintenanceIn order to ensure proper use of the machine, minor maintenance will need to be performed.
First, the pen must be replaced when the ink runs out. Next, every time the machine is set up,
lubricate the joints where the pen arm connects to the pendulum. To mitigate mold and wood
warping within the wooden parts the Harmonograph should be stored in a dry area. Finally, the
surface underneath the paper may become rough from use, so it may need replacement if this
occurs, though this is unlikely.
5.5Implementation Instructions5.5.1 AssemblyThere are five steps to assemble the Two Pendulum Harmonograph:
Step 1: Unfold the card table as in Figure 5-11 and put it on a flat stable surface. (A level surface
is essential for the pendulums to work effectively!)
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Figure 5-11 Unfold the Card Table Legs (Group Photo)
Step 2: The next step is to take the pendulums and insert them through the slots in the table as
shown in Figure 5-12. The pen arm pendulum goes in the slot that orients the pen right above
the other slot. This other slot is for the paper platform. If you put the pendulums in the wrong
slots the pen arm will be pointed the wrong direction. Figure 5-13 tells which slot the respective
pendulums are inserted.
Figure 5-12 Insert Pendulums through the table slots (Group Photo)
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Figure 5-13 Pendulum Slot Placement (Group Photo)
Step 3: To insure the pendulums are properly aligned, the gimbals (the pointed bolts that are
coming out of the block of wood) must go into the dimple on the gimbal stand. This keeps the
pendulums from shifting around as shown in Figure 5-14.
Figure 5-14 Insure the Gimbal goes into the Gimbal dimple (Group Photo)
Step 4: The paper platform weight clamps down on the pendulum with two bolts cinched
together by wing nuts. This clamping mechanism allows for quick weight height adjustments
and is demonstrated in Figure 5-15.
Bolt into the gimbal dimple.
Paper-Platform Pendulum
goes here.
Pen-Arm Pendulum go
here.
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Figure 5-15 Paper Platform weight clamping (Group Photo)
Step 5: The pen arm weight has a long bolt that must be fed through a hole in the pendulum as
shown in Figure 5-16. This weight is not meant to be adjusted.
Figure 5-16 Pen Arm weight single bolt mechanism (Group Photo)
5.5.2 UseNormal operation of the harmonograph is quite simple:
Step 1: Make sure that the weight on the pen arm pendulum is the height that you want. You
do this by clamping the weights together with the two bolts with wing nuts.
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Step 2: Place a writing utensil in the pen arm and a piece of paper on the paper platform. The
paper is attached with a clothes pin and the writing utensil is clamped down between the two
pieces of wood that constitute the pen arm. Tighten the bolt with a wing nut.
Figure 5-18 Place paper and writing utensil.
Step 3: Put the pendulums into motion by rocking them back and forth to the desired
amplitude. It is easiest to stand over the paper platform and hold the pen arm and paper at the
same time.
Figure 5-17 Adjusting weight
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Figure 5-19 Put pendulums into motion.
Step 4: Drop the pen arm and watch.
Figure 5-20 Drop pen arm and watch.
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Figure 5-21 Possible Parameter Changes
5.6Prototype PerformanceWe have determined through our testing that our Two Pendulum Harmonograph fit the criteria
quite well. We did extensive testing in our workshop and also let some elementary school
students test it as shown in Figure 5-18. Our final product turned out to be very safe, we did not
have any problems with the elementary school students and that age group was the biggest
concern. The kids were able to use the machine once being shown, making the machine easy touse. It was very engaging, it is a lot of fun to use this machine and the art that comes out is very
interesting and unique.
Figure 5-22 First Graders at Morris Elementary School in Mckinleyville testing the Harmonograph (Group Photo)
Parametersto changein order toobtain
differentdrawings:
1) The position of the pen arm weightson the bottom of the pendulum.
2) Starting the pendulums at differentpositions in their swing.
3) Put more or less energy into apendulum before letting them go.
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We were able to make a product that is very portable, though we have not been able to see if it
fits in a 1998 Volkswagen Beetle, we expect it to fit fine, as it fit quite easily into the trunk of a
Honda Civic with plenty of room to spare. As far as durability we expect it to meet our goals but
we have not been able to observe how it lasts over an appreciable amount of time.
The machine also produced drawings that were both highly variable and very skilled as shownin Figure 5-19. Both the children and Engineering students we demonstrated for were highly
engaged with the machine and impressed with the drawings.
Figure 5-23 Drawings made by our Two Pendulum Harmonograph (Group Photo)
6.Appendices:6.1Appendix A: BibliographyAlejandro Infanzon-Marin:
"Barkpaper." Blick. Blick Art Supplies, 15 Apr. 2010. Web. 23 Feb. 2013..
"Paper Works!." Southwest Art 36.1 (2006): 116-135. OmniFile Full Text Mega (H.W.
Wilson). Web. 23 Feb. 2013. "Black Ink Egyptian Papyrus Paper." Blick. Blick Art Supplies, 28 Dec. 2011. Web. 23 Feb.
2013. . McArdle, Thaneeya. "Drawing Papers for Pen and Ink Artwork."Art Is Fun. N.p., 5 Mar.
2012. Web. 24 Feb. 2013. .
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Rossol, Monona. "Using Artist Paints." Paints. N.p., 10 Oct. 1995. Web. 24 Feb. 2013..
McArdle, Thaneeya. "Acrylic Paint."Art Is Fun. N.p., 12 Jan. 2004. Web. 24 Feb. 2013..
Pellegrini, Nicole. "Information on Different Types of Oil Painting." EHow. DemandMedia, 16 Apr. 2011. Web. 24 Feb. 2013..
Shirley, Rachel. "What Defines Oil Paint." Science of Colour. N.p., 30 July 2001. Web. 24Feb. 2013. .
David, Isaiah. "How Does a Fountain Pen Work?" EHow. Demand Media, 12 Dec. 2008.Web. 24 Feb. 2013. . JetPens. "Graphic Drawing Pens."JetPens. N.p., 21 Jan. 2013. Web. 24 Feb. 2013.
. McArdle, Thaneeya. "Pen and Ink Drawings."Art Is Fun. N.p., 1 Feb. 2009. Web. 24 Feb.
2013. .
Cult Pens. "The Cult Pens Guide to Technical Drawing Pens." Pencyclopedia. N.p., 7 Apr.2001. Web. 24 Feb. 2013. .
Elgan, Mike. "Recycle Your Electronics ... Into Furniture!" Houzz. N.p., 9 Apr. 2007. Web.25 Feb. 2013. . Construction Initiative: Supporting Green Design in Construction Through Industrial
Materials Recycling. [Washington, DC]: U.S. Environmental Protection Agency, Office of
Solid Waste and Emergency Response, 2008.
Cool Gizmo Toys. "10 Awesome Eco Gadgets Made From Recycled Car Parts." CoolGizmo Toys. N.p., 6 Aug. 2012. Web. 25 Feb. 2013.
. Brooks, Nancy E. J. "Recycling Kandinsky." Arts & Activities 141.5 (2007): 19-58.
Academic Search Elite. Web. 25 Feb. 2013.
Alejandro Saldivar:
BBC GSCE Bitesize (2013). Systems and Control: Mechanisms Design and Technology,
(Feb. 24, 2013).
Pichtel, John (2010). Waste Management Practices: Municipal, Hazardous, and Industrial,Chapter 6, CRC Press, Kentucky.
Humboldt County Planning Commission (2010). Humboldt County General Plan, Section 10.5.
Waste Management, 2nd Draft, Eureka, CA.
Farrant, L. Olsen, S. I. Wangel, A. (2010) Environmental benefits from reusing clothes The Int.
J. of Life Cycle Assess. August 2010, 15(7), 726-736
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Mark Attari