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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