Final Report Heel-Actuated Bass Drum Pedal

APD2011-Team 3

David Carr Chris Chan

Travis Dehne Yundi Lin

12th December 2011

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ABSTRACT Current bass drum pedals are actuated by pivoting the foot about the heel while pressing on the pedal with the front part of the foot (the toe pedal). However, such a motion is unnatural and tiring for many people. This is a major challenge faced by those who have recently started playing the drum set. Also, many experienced drummers with joint aliments such as keen/angle injuries are unable to use the current pedals. Therefore, our goal is to design a new bass drum pedal that is actuated by a more intuitive human motion, and improves the learning experience for novices. We completed our design and have constructed a working model that has being tested. There needs to be further improvements done on the pedal, but the test of the concept of our design has proved to be a success.

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TABLE OF CONTENTS

ABSTRACT .............................................................................................................................................................. 1

1 INTRODUCTION ..................................................................................................................................................... 4

1.1 User Scenario ................................................................................................................................................. 4

1.2 Purpose of Design ......................................................................................................................................... 4

1.3 Market Analysis ............................................................................................................................................. 4

2 PREVIOUS DESIGNS ............................................................................................................................................. 6

2.1 Conventional Drum Pedal ......................................................................................................................... 6

2.2 Existing Patents ............................................................................................................................................. 7

2.3 Conclusion ....................................................................................................................................................... 8

3 DESIGN OBJECTIVES AND REQUIREMENTS ............................................................................................. 8

3.1 Problem Statement ...................................................................................................................................... 8

3.2 Design Objectives ......................................................................................................................................... 9

3.3 Design Requirements .................................................................................................................................. 9

3.4 Product Positioning Chart ...................................................................................................................... 11

4. CONCEPT GENERATION AND SELECTION ............................................................................................. 11

4.1 Analyzing Alternative Options ............................................................................................................. 11

4.2 Evaluation of Conceptual Solutions ................................................................................................... 12

4.3 Preliminary Survey ................................................................................................................................... 12

4.4 Early Prototypes ........................................................................................................................................ 13

4.5 Anticipated Design Process ................................................................................................................... 17

5. ENGINEERING FUNCTIONALITY ANALYSIS .......................................................................................... 17

5.1 Engineering Design ................................................................................................................................... 17

5.2 Beta prototype ............................................................................................................................................ 18

5.3 Other Changes to Prototype .................................................................................................................. 20

5.4 Life-cycle Analysis ..................................................................................................................................... 24

6 EMOTIONAL AND AESTHETIC ANALYSIS ............................................................................................... 24

7 ECONOMIC ANALYSIS ...................................................................................................................................... 25

7.1 Market Size ................................................................................................................................................... 25

7.2 Competitor Analysis ................................................................................................................................. 25

7.3 Demand Function ...................................................................................................................................... 25

7.4 Revenue Function ...................................................................................................................................... 29

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7.5 Cost Function .............................................................................................................................................. 29

7.6 Profit Function ............................................................................................................................................ 30

7.7 Break Even Analysis ................................................................................................................................. 31

7.8 Internal Rate of Return (IRR) ............................................................................................................... 31

8 PRODUCT DEVELOPMENT PROCESS ........................................................................................................ 32

9 BROADER IMPACT ............................................................................................................................................ 33

10 REFERENCES ..................................................................................................................................................... 34

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1 INTRODUCTION For the introduction of our design proposal, we will first provide a user scenario to explain why a new concept is necessary. Next we define the purpose of our design and give a brief market analysis. 1.1 User Scenario John, age five, has always wanted to play drums. All his idols are famous drummers, and the faster they can play, the better John started taking drum lessons, and was very enthusiastic. He thought that he would play like his idols in no time. However, John’s legs started to ache badly from bass drum pedaling within minutes. The pain became worse as he continued to play, eventually forcing John to stop. His instructor told him that this was normal and that it takes years or even decades to become as proficient as his idols. As he left his first class, John felt discouraged by his inability to master the beats well. John doesn’t want to wait for years for playing to feel natural. Why isn’t there a product that feels like you’ve been using it for years even though you’ve just started? 1.2 Purpose of Design When drummers play a bass drum, they must use a foot pedal attached to the rim of the drum in order. The toe actuated pedal is ubiquitous, and has not changed since the 1940’s. This style of pedal can become very strenuous and difficult to play over long periods of time. I may take years of diligent practice to overcome these difficulties and become a proficient with this model. We are trying to design a new bass drum pedal to reduce the strain placed on a drummer when playing the bass drum, as well as to create a pedal that takes less time to become familiar to the user. 1.3 Market Analysis Here, we define our target market and the portions of the market that could be negatively affected. 1.3.1 Target Market Before finalizing our design, we must consider future user of our bass drum pedal and the users of current bass drum pedals. We realize our future users have a large range of ages (5-70 years) and experience levels (beginners to veteran professionals). From these considerations, we believe that the demographic who will benefit the most from our design are those between the ages of 5-15 and 60+, and those of beginner experience. We predict that a more intuitive pedal will attract new drummers because they will be able to improve at a faster rate, and older players will enjoy it because it will not put as much strain on their joints. 1.3.2 Negatively Affected Experienced players may be negatively affected by our pedal design. As stated above, it may take years of practice to become proficient at using a bass drum pedal. Veteran

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players will have adapted themselves to suit the current pedal design. Even though our pedal will feel more intuitive for a novice player, it will most likely feel alien to experienced players. There are no laws or regulations that restrict the design of a new pedal; however, the physical space that the pedal can occupy is somewhat limited. Ultimately, our future designed pedal cannot become so large that is interferes with other drums or motions that are involved in playing a full drum set. In all, we have taken all of these things into our concept. 1.4 Our Proposed Design We have taken all of these things into our consideration and have synthesized the heel actuated drum pedal shown below in Figure 1. In the next few sections, we will take you through our research and design process and explain why we chose this design. Figure 1: Heel actuated bass drum pedal

Mallet

Sprocket Wheel

Base

Pedal

Chain

Adjustment Bar

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1.5 Nomenclature The following table lists the dimensions we used in the report. Table 1: List of dimensions used

Dimension Units Symbol angle of wheel Degrees theta w

total height Inches Ht total length Inches Lt

radius of rotation Inches Lp angle of mallet Degrees theta s radius of wheel Inches R length of chain Inches Lc angle of chain Degrees theta c angle of pedal Degrees theta p length of cam Inches Lk angle of cam Degrees theta k

length of mallet Inches Ls Force Location Symbol

Weight of hammer head Center of gravity of hammer head Wh Weight of handle attached to hammer Center of gravity of handle Ws

Tension in chain Along chain T Force experienced by user At edge of pedal F

Weight of pedal Center of gravity of pedal Wp Normal reaction at pin, horizontal direction At pin Rx

Normal reaction at pin, vertical direction At pin Ry Normal reaction at hinge, horizontal direction At hinge Nx

Normal reaction at hinge, vertical direction At hinge Ny 2 PREVIOUS DESIGNS In this section, we present information on the current drum pedal design as well as current patents. We then conclude this section by analyzing why a new concept is necessary. 2.1 Conventional Drum Pedal The drum set, as it is now recognized, was first invented in the 1940’s with the advent of Bebop Jazz. Though there were many different concepts for bass drum pedals, Gretsch had the most successful design utilizing the toe down motion. It was played by many big name drummers such as Elvin Jones, Tony Williams, and Art Blakey. The design became ubiquitous, and all current bass drum pedals are based on its movement principles. The conventional drum pedals are shown in Figure 2. The difficulty of playing with a toe actuated drum pedal is rarely documented as a deterrent to beginners, because it is the only option. However, we believe that a using a different foot motion of playing a bass drum pedal would expedite the learning process of new drummers. There are no

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specially designed drum pedals on the market to reduce the difficulty experienced by beginners. Most players just focus adapting to get the technique right [1]. The price of current drum pedals ranges from $70 to over $500. 2.1.1 Advantages There is a lot of history and tradition behind this design. For decades, all of the idolized drummers have adapted their technique for this style bass pedal. This leads their followers to want to mimic them and continue to use the conventional pedal. As with most design concepts, the simplest design is usually the most efficient and durable. The conventional drum pedal has a simple design concept. The Gretsch pedal design was popular for good reason. It’s motion is simple and robust, the player’s energy is conserved for the most part, and it could be used accurately and precisely with enough practice. 2.1.2 Disadvantages As mentioned in the Introduction, the toe actuated design is very strenuous on the drummer, especially on a beginner. We aim to come up with a new concept that makes drumming easier without undermining the simplicity that the conventional drum pedal has.

2.2 Existing Patents Further research into the available patents for drum pedals also shows that little was done to make learning the drums easier. Most current patents serve to improve the stability of drum pedals [2]. There is also in existence a patent that makes drum pedals more versatile by allowing the height of the drum pedal to be adjusted relative to the bottom board based on the user’s needs [3]. Another patent is supposed to allow the drummer to present fast sequences of drum excitement and setting accents using a switchable foot pedal system [4]. There are some patents that could potentially reduce the difficulty of learning the drums, but they primarily focus on providing quicker beats. Electronic drum pedaling allows the triggering of 2 beats instead of 1 thus creating beats twice as fast [5]. A patented device increases the return speed of the pedal thus potentially providing quicker beats [6]. We discovered one previous design that utilizes heel motion to use the pedal shown in Figure 3. However this product has not made it into the market. We believe that this is

Figure 2: Conventional drum pedal

Figure 3: Pedal that uses heel motion

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due to the complicated system of belts and rollers it uses to move the beater. All of these moving parts most likely increased the price of the pedal and made it difficult to use.

2.3 Conclusion The use of bass drum pedals is one of the most difficult skills in drumming. Many musicians would greatly benefit from the development of a new bass drum pedal design that is more intuitive and less strenuous. Our research shows that no significant effort has been invested to make it easier for users to learn bass drum pedaling. The existing drum pedals make it difficult for young beginners to pick up drumming due to the physical barrier (takes a lot of practice to master the technique). Current patents also do not provide an easier way of hitting the drum pedal. There is a space in the bass drum pedal market for our design. 3 DESIGN OBJECTIVES AND REQUIREMENTS Here, we present our problem statement, define our requirements, and elaborate on our design objectives. Note that our objectives and requirements may change as we progress further on in this project. 3.1 Problem Statement Current base drum pedals are actuated by pivoting the foot about the heel and pressing on the pedal in a downward motion. This design was based on a patent in the 1950’s for jazz drumming. However, the motion for pressing the pedal is not a natural motion for the foot, and results in two main challenges. First, the speed at which the pedal can be pressed is relatively slow. This was sufficient for jazz drumming in the 1950’s, but contemporary drumming requires a much faster speed and much more power. It takes much more practice to achieve the required speed and power for today music. Also, the foot tires quickly when repeating the above motion, which means that sustained drumming practices for novices is unpleasant. Hence, we decided to explore alternative designs that will allow the novice drummers to become comfortable with the pedal quickly and with little discomfort.

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3.2 Design Objectives In order to design a new drum pedal, we have identified the following objectives (if applicable) that are to be taken into consideration during the design process. Below is an itemized summary of our objectives. 3.2.1 Weight The weight of the pedal should be between three and ten lbs. (excluding additional weights attached as a means of providing more stability). This is intended to provide both a degree of stability (which requires the pedal to be heavier) and a degree of portability (which requires the pedal to be lighter).

3.2.2 Durability The pedal is a sizable investment and should per perceived as durable by the user. This can be achieved by ensuring that the parts are made of durable materials, and that all moving contact points (e.g. the contact point between the chain and the pedal) should be oiled or protected with a soft cushioning material. The pedal should at least not fail within the first five years of usage.

3.2.3 Price The pedal should not cost more than $100, because that is the price of currently available novice-level drum pedals.

3.3 Design Requirements We have also laid down the following design requirements that should be met (if applicable) in addition to our design objectives. 3.3.1 Size The size of the pedal should not exceed 22” in length, 6” in width and 10” in height (excluding the re-attachable mallet) because of the limited space drummers have due to the way the drums are arranged. The height of the mallet is adjustable to suit the different sizes of drums available.

3.3.2 Adjustability The heel pedal is a very novel design, and hence it should be made possible to convert the pedal back to a traditional toe pedal without too much hassle. This can be measured by a user survey on their opinions after using the pedal.

3.3.3 Does not conflict with other needs of the drummer The pedal should not compete with the other needs of the drummer during drumming, especially the drummer’s needs to play the other drums in front of him. This can be measured by a survey of drummers after they have tried using the pedal.

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3.3.4 Intuitive The pedal must be intuitive to use. The user should be able to play the pedal immediately without feeling as though they must adapt to it. This can be measured by a user survey after they have used the pedal during drumming. 3.3.5 Precision Our pedal must have a repeatable motion, such that if the drummer presses on the pedal at the same spot using the strength, then the sound produced should be the same. We can quantify precision by documenting the strength and the spot at which the mallet hit the drum surface when actuated with a constant force. The precision of the pedal should be directly related to the stability of the pedal. We can use that data to establish the variance in our pedal and compare that result to pedals currently in the market. 3.3.6 Stability Our pedal must be stable during play, such that the user only feels the movement of the pedal itself and not the other parts (e.g. the chain or the belt) while drumming. This can be measured by a user survey after use. 3.3.7 Responsiveness Our pedal must respond to the actuation motion of the user well and not feel sluggish while in use, as sluggish motion can result in uneven beats and decreased precision. We can quantify responsiveness by measuring the resistive force felt by the user during use. The theoretical force output for a given force input into the pedal can be calculated, and we can use a force gauge to measure the actual output, and find the percentage of energy lost in the pedal. The measurement can be repeated on currently available pedals. Hence, we can know whether there are excessive resistance forces present, which will result our pedal becoming less responsive. 3.3.8 Health risks Also, it must not cause health problems for the user over the course of a lifetime (many drummers start as teenagers and play well into their 60s or even 70’s). Drumming is nothing more than a few simple movements repeated billions of time over the life span of the user. Arthritis and tendinitis are very real concerns for drummers. A concept that makes drumming easier but applies a lot of shock to the knees of the drummer might not be very favorable. This can be measured by a user survey after they have used the pedal. 3.3.9 Complexity The pedal should be designed with few moving parts, both to reduce cost and to ensure that the pedal does not suffer from failures during use. We intend to measure this against currently available drum pedals and aim to not have more than eight total moving parts (about double the number of moving parts on the current simplest drum pedals).

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3.4 Product Positioning Chart We compared our product with the main types of bass drum pedals available on the market, namely, a linkage-driven pedal, a belt-driven pedal, and a chain-driven pedal, using intuition and adjustability as our two main criteria. We chose these two criteria because we believe that they are not adequately satisfied in the pedals available on the market today. Our proposed new pedal should be able to fill in the market niche. As we can see from Figure 2 , the other pedals are not very well positioned in both of these criteria, and our new design should be able to meet both these criteria while at the same time not compromising on the other requirements. Figure 2: Comparing Different Types of Drum Pedal

4. CONCEPT GENERATION AND SELECTION In this section, we present how we derived our concept. First, we laid down a few criteria that the alternative solutions should satisfy. Then we analyze how well each option meets the criteria. Finally, we present our preliminary survey before deciding on our concept. 4.1 Analyzing Alternative Options Up until now, almost all bass drum pedals are actuated by user pressing their toe down. Since this action in strenuous, it is the main aspect of the design that we will change. Our team considered many possible ways of actuating a pedal including using: electronics, other limbs, knee motion, swiveling the toe side to side, swiveling the heel side to side, pushing the toe up, rocking the foot side to side, and pushing the heel down. We based our analysis on several criteria as shown in Table 1. We based the first round of analysis on our 4 most important criteria: intuition, precision, responsiveness, and health risks. Table 2: Analysis on alternative methods

Method Intuition Precision Responsiveness Health Risks

Electronic Great Great Great Great

Other Limbs Great Great Great Great

Linkage-driven pedal

Belt-driven pedal

Chain-driven pedal

Proposed new pedal

Adju

stab

ility

Intuition

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Knee Motion Mediocre Poor Great Poor

Swivel Toe Side to Side Poor Poor Poor Poor

Swivel Heel Side to Side Poor Mediocre Poor Mediocre

Push Toe Up Poor Poor Mediocre Poor

Rock Foot Side to Side Poor Poor Poor Poor

Push Heel Down Great Great Great Great

The three highest ranking options for pedal action are the use of electronics, the use other limbs, and the motion of pushing the heel down. 4.2 Evaluation of Conceptual Solutions We further evaluated the three best concepts based on the next three most important criteria: estimated complexity of the design, estimated price of pedal, and whether the design will conflict with the other needs of the drummer while drumming. Table 3: Further Evaluation of Conceptual Solutions

Method Complexity Price Conflict with Other Needs

Electronic Probably very complex (with many electronic-mechanical interface)

Expensive (control software and

electronic motor)

None or slight

Other Limbs Probably complex Normal High chance of conflict

Push Heel Down Probably not so complex Normal Low chance of conflict From Table 2 above, we can see clearly that the push heel down conceptual design will be the best concept to meet our design objectives and design requirements. Hence, we will focus our efforts on testing the push heel down concept using prototypes. 4.3 Preliminary Survey We first conducted preliminary surveys and a local music store to discover what drummers thought of using electronics for a drum pedal. On average, they were concerned that while electronics would offer a speed advantage, they wouldn’t transfer the small differences in various foot strokes that result in dynamic control. They also feared that the use of electronics to enhance performance would be perceived as “cheating” by the rest of the drumming community. The use of other limbs also has problems. Drummers play complex rhythms using all of their limbs and once. A pedal that requires the user’s hand would limit the complexity of their rhythms. Finally we concluded that the best option for actuating a bass drum pedal is for the user to push their heel down.

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4.4 Early Prototypes We constructed a few prototypes using the Solidworks software to test out our concepts and analyze the pros and cons of each design concept. We then chose the best concept and built our alpha prototype according to that concept. 4.4.1 Prototype 1 Our first prototype is a very simple heel pedal with a protruding part at the front of the pedal. A chain is attached to that portion and used to drive the mallet through a sprocket wheel. This is shown in Figure 3 below Figure 3: Prototype 1

This design, however, cannot be converted easily to a toe-driven pedal if necessary, so we came up with a more complex design for a toe pedal. Also, the protrusion at the front might get in the way if we convert the pedal to a toe actuated one. 4.4.2 Prototype 2 We designed the following prototype to overcome the problem of ease of conversion to a toe pedal.

Base

Pedal

Chain

Sprocket Wheel

Mallet

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Figure 4: Prototype 2

This design features a more complex pedal, with a more complicated set of sprockets forming the mechanical connection between the pedal and the mallet. The pedal functions like the first prototype in the configuration shown in Figure 4, but the additional hinges allows the rear part of the main pedal to be folded to expose the rear pedal, which allows the pedal to function like a toe pedal, as shown in Figure 5 below. Figure 5: Prototype 2 with Main Pedal Folded

However, this design is very complex and the folded up main pedal may cause an obstruction when using this design in the toe pedal configuration. Also, the pin-in-slot

Sprocket Wheels

Mallet

Chain

Main Pedal

Rear Pedal

Hinges

Folded Main Pedal

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design can be both difficult and expensive to manufacture and may be a large source of friction. 4.4.3 Prototype 3 We decided to revert back to prototype 1 to reduce complexity, but instead of using a protrusion at the end of the pedal, the protrusion is now at the side. This gives us additional flexibility that will allow us to make our pedal better, as shown below. Figure 6: Prototype 3

Figure 7: Another View of Prototype 3

Sprocket Wheel

Mallet

Chain

Pedal

Base

Adjustment Bar

Sprocket Wheel

Mallet Chain

Pedal

Base

Adjustment Bar

Extra Screw Holes

Stand

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The new design features a side adjustment bar. There is a slot milled into the adjustment bar that allows the chain to sit inside it. In order to allow the length of the chain to be adjustable, we will attach a set screw to the end of the chain, and the set screw can then be placed into one of the many holes drilled into the adjustment bar. Also, we included 2 extra screw holes at the end of the base. They serve as the mounting points when the stand in the front of the pedal is shifted to the back to convert the set-up to a toe pedal. The new set-up is shown below in Figure 8. Figure 8: Toe Pedal Set-up using Prototype 3

In order to decide which design to use, we compared all 3 prototypes in the table below according to our design objectives and requirements. Table 4: Comparison between the 3 Prototypes Prototype 1 Prototype 2 Prototype 3 Comfort to User Good Good Good

Weight (lbs) < 10 > 11 < 10

Durability Good Good Good Price Cheap Expensive Moderate Size Within limits Within limits Within limits

Adjustable Spring Present (not shown) Present (not shown) Present (not shown)

Ease of Conversion Not possible Easy Moderate

Complexity Simple Complex Moderate As we can see from Table 3 above, Prototype 3 may not be the best pedal design in every aspect, but it is able meet all the objectives and requirements. We therefore decide that prototype 3 is the most promising design.

Sprocket Wheel

Mallet

Chain

Pedal Base

Adjustment Bar Removed

Original Screw Holes for Stand

Stand

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4.5 Anticipated Design Process We will build the beta prototype based on the alpha prototype using the actual materials provided. We will weigh and measure the beta prototype to ensure that the weight and size are within the limits set. Then, we will give the beta prototype to several drumming instructors so that they and their students can test out the new pedal. We will then conduct a survey to find out if they find the pedal is comfortable, durable, and easy to convert to a toe pedal. We can then calculate the cost of manufacturing and decide if the cost meets our objective. A further table outlining the anticipated design process based on our team design procedure can be found in Appendix C. 5. ENGINEERING FUNCTIONALITY ANALYSIS Here we present our analysis on the engineering design, our beta prototype and possible changes 5.1 Engineering Design In order to meet the requirements of our design, we decided that we should optimize our design by reducing the length of the cam to a minimum. This is because, in order to minimize the length of the cam, the chain and the cam will have to form a straight line. This design enables us to not only to reduce weight by not using unnecessary extra materials, it also enables us to maintain precision and responsiveness of the pedal by having the shortest physical connection from the pedal to the mallet. Having a straight-line connection also helps to increase stability by eliminating any unnecessary motion when pressing the pedal.

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Figure 8: Names of parts

We also learned that the neutral position of the human ankle is 21° with respect to the horizontal[7], with a standard deviation of ±6°. Hence, we decided to let the un-depressed angle of the pedal be 21° from the horizontal, with additional allocations to change the un-depressed angle of the pedal to suit personal preferences. 5.2 Beta prototype In order to develop a model that enables us to calculate the ideal length of the cam and the position of the set screws that are drilled into the cam, we came up with a list of constants and variables that will enable us to make this calculation. Table 5: List of constants

Dimension Value Units Symbol radius of wheel 1 Inches R angle of wheel 70 Degrees theta w length of chain 9 Inches Lc

total height 6.0625 Inches Ht total length 6.03125 Inches Lt

radius of rotation 1.884352 Inches Lp length of mallet 6 Inches Ls angle of mallet 45 degrees theta s

Whee

Chain (modeled

Cam Pedal

Axle

Stock

Mallet

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Table 6: List of variables

Dimension Unit Symbol angle of chain Degrees theta c angle of pedal Degrees theta p length of cam Inches Lk angle of cam Degrees theta k

Figure 9: Dimensions

We used the following equations and applied the restrictions as listed in table 3: Ht = R x COS(theta w) + Lc x SIN(theta c) + Lk x SIN(theta k) + Lp x SIN(theta p) Lt = - R x SIN(theta w) + Lc x COS(theta c) + Lk x COS(theta k) - Lp x COS(theta p) Table 7: List of restrictions

Dimension Condition Value

Ht = 6.0625 inches

Lt = 6.03125 inches

theta c = theta k

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Using the Excel Solver, we determined the list of optimal cam length given a certain angle of the pedal (theta p). The results of our computation are listed below in Table 7. From our results, we determine the optimal design length for our cam and hence achieve many of our design objectives. Table 8: Results of solver

theta p 9 15 21 27 33 Lc 1.366 1.231 1.083 0.924 0.755

theta c 31.563 30.763 30.024 29.355 28.764 There are 3 variables (theta p is pre-determined) and 1 constrain in our model, giving a total of 2 degrees of freedom. Additionally, we also calculated the maximum angle that the wheel can rotate through, (if the pedal is fully depressed), and the results are shown below in Table 8. From our results, it can be seen the minimum angle the axle can rotate through is about 53 degrees, while we determine that the mallet only need to rotate through a maximum of 45 degrees to hit the drum. Table 9: Maximum angle axle can rotate

theta p 9 15 21 27 33 max angle of rotation of the

axle 53.28 88.80 124.32 159.84 195.36

For our design, we also considered keeping the size of the cam fixed and changing the point at which the chain is hooked onto the wheel (effectively changing the length of the chain, Lc). The corresponding length of the chain is given in Table 9 below. Table 10: Respective chain length for wheel radius of 1 inch

theta p 9 15 21 27 33 Lc 9.12 8.98 8.83 8.67 8.50

theta c 31.56 30.76 30.02 29.35 28.76 5.3 Other Changes to Prototype Here, we present other changes to our prototype. They include shortening the cam and wheel, changing the double strain chain to a single strain chain and the possibility of shortening or removing the stock from our design, and changing the radius of the wheel. 5.3.1 Shorten cam and wheel: In the final product, we will be more concerned with minimizing the weight of the wheel + chain + cam assembly. This is because this assembly is the major moving assembly apart from the mallet, and minimizing the weight of this assembly will minimize the inertia of the moving components of the pedal, thus making the pedal feeling less sluggish to the drummer. In order to achieve that, we

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allowed more of our parameters to become variable. Table 10 below showed the new list of constants, while Table 11 shows the new list of variables. Table 11: List of constants for final product

Dimension Value Units Symbol angle of wheel 70 Degrees theta w

total height 6.0625 Inches Ht total length 6.03125 Inches Lt

radius of rotation 1.884352 Inches Lp angle of mallet 45 Degrees theta s

Table 12: List of variables for final product

Dimension Unit Symbol radius of wheel Inches R length of chain Inches Lc angle of chain Degrees theta c angle of pedal Degrees theta p length of cam Inches Lk angle of cam Degrees theta k

length of mallet Inches Ls We also set the following restrictions for the weight minimization calculations, as presented in Table 12. Table 13: List of restrictions for final product

Dimension Condition Value

Ht = 6.0625 inches

Lt = 6.03125 inches

theta c = theta k

R >= 0.5

Lk >= 1.25

We imposed minimal length requirements on R and Lk due to the fact that we believe a length shorter than that stated above will result in difficulties in manufacturing and likely drive up the production cost of our final product. We estimated the weight of a unit length of each component and scaled the weight of the components according to the total length of the components. The unit weight of each component is presented in Table 13 below. The unit length of the wheel is R = 1, the unit length for the chain and the cam are both 1”

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Table 14: Unit mass of each component Component Unit weight (lbs)

Wheel 0.3

Chain[8] 0.015

Cam 0.07385 + (Lc-1) x 0.02369

We used the solver to minimize the sum of the total weight of the assembly, and the solver returned a result where both R and Lk are at their minimum allowed dimension. This is because the unit weight of the chain is lighter than the unit weight of either the cam or the wheel. Hence, the assembly is the lightest when we maximize the length of the chain. In the future, we can remove the cam from our design if we are able to make further changes to our beta prototype to ensure that the chain alone will be able to handle the stability requirements. As we have seen in the analysis above, the weight of the assembly can be further reduced if we replace the cam with a chain of the same length. This can reduce the complexity of manufacturing, cutting both the cost of material acquisition and the cost of construction. 5.3.2: Change the double strand chain to a single strand chain: A force analysis was performed using MATLAB as the solver, and the detailed analysis can be found in Appendix F. We will just present the most important results here. In order to facilitate our discussion, the locations and the list of symbols for the forces involved in the motion of the pedal is listed below. All the forces are measured in pounds. Table 15: List of forces Force Location Symbol

Weight of hammer head Center of gravity of hammer head Wh

Weight of handle attached to hammer Center of gravity of handle Ws Tension in chain Along chain T Force experienced by user At edge of pedal F Weight of pedal Center of gravity of pedal Wp Normal reaction at pin, horizontal direction At pin Rx

Normal reaction at pin, vertical direction At pin Ry Normal reaction at hinge, horizontal direction At hinge Nx

Normal reaction at hinge, vertical direction At hinge Ny

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Figure 10: Force notations

From our force analysis, we can see that no matter the how the length of the mallet changes (it cannot be longer than 12 inches because the smallest bass drums have a radius of 12 inches), or how the radius of the wheel changes, the forces on the chain is not going to exceed 38.12 lbs. The maximum working load on the chain is 114 lbs, which means that we have a safety factor of at least 3. Table 16: Force experienced by chain (in lbs) for various dimensions

R = 0.5 R = 1 Ls = 3 8.24 3.76 Ls = 6 13.97 6.27 Ls = 9 23.93 10.90 Ls = 12 38.12 17.64

5.3.3 Other possible changes: We explored other changes that can be made to our pedal. For example, we explored the possibility of shortening or removing the stock from our design, and changing the radius of the wheel. From our force analysis (done with theta p of 21°, the mean neutral position of the human ankle), we realized that if we removed the stock, the pin will experience a very high load compared to the rest of the system, as we can see clearly from table 16 below. Over time, this may wear out the pin, and go against our design objective of durability. We therefore decide not to apply this change.

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Table 17: Comparison of presence and absence of stock Force F Nx Ny Rx Ry

With 6” stock -0.27 -0.09 0.09 5.52 -2.45 Without stock -0.77 -1.3 1.35 16.63 -9.88 We also explored the possibility of reducing the radius of the wheel. Our force analysis results (analysis done with theta p of 21°, the mean neutral position of the human ankle), shown below, showed that if we reduce the radius of the wheel, the force experienced by the user will as a result increase, and the force experienced by the pin will also increase. This goes again our design objective of durability, and will result in the user feeling more discomfort. Hence, we decide not to apply this design change as well. Table 18: Comparison of different wheel radius Wheel radius F Nx Ny Rx Ry

1” -0.27 -0.09 0.09 5.52 -2.45 0.5” -0.61 -0.94 0.94 13.04 -7.48

5.4 Life-cycle Analysis Since the pin is the most difficult part of the pedal to replace, we focused the life-cycle analysis on the pin. We found that most of the cheaper pedals for beginners tend to fail within the first few years due to using poor quality parts to reduce cost. We therefore used corrosion-resistant aluminum and steel for our pedal. We also used hardened steel as the material for the pin in our pedal to ensure the longevity of the pedal. Using our force analysis done in section 5.3, we can further calculate the maximum stress on the pin, which works out to be 17,700 pounds per square inch, with a safety factor of 3. Hardened steel has a carbon content of about 0.8%, which translates into a life-cycle of 108 repetitions if stress does not exceed 42,000 pounds per square inch. This gives us a further factor of safety of 3, resulting in a total factor of safety of 9. Assuming that the drummer presses the pedal 2,000 times a day, 365 days a year, the life-time of the pedal is expected to be 13 years. 6 EMOTIONAL AND AESTHETIC ANALYSIS The design is intended to present itself as a well-engineering product on first sight. In order to achieve a good visceral design, we painted the pedal black to give the impression that this is a professionally designed and manufactured product. We also focused on achieving a good surface of the pedal during the manufacturing process to reflect good craftsmanship. In terms of behavioral design, our product is designed to enable the user to enjoy physical pleasure by allowing him to play the bass drum with a very natural motion of the foot, increasing user comfort and stamina, and allowing the user to feel more inclined to use our product compared to other drum pedals. In terms of reflection design, we intended for the user to portray himself as a “liberal” and “adventurous” drummer, as someone who is different from other traditional drummer, because of the new equipment

25

that he is using. This helps the user to feel special and stand out amongst all his fellow drummers, and gives the user a good feeling about using this special pedal. The user also enjoys physiological pleasure by being set apart from the rest of the drummers with his use of a special pedal, which helps him to stand out amongst his fellow drummers. 7 ECONOMIC ANALYSIS We first present our market sizing and competitor analysis. Then we show our derivation of our demand, revenue, cost and profit function. After which we end of with our break even and internal rate of return analysis. 7.1 Market Size Here we first determine the market size for our drum pedal design. Based on this source(1), 5% of people in the professional service in 1930 are musicians or teachers of music, and this 5% would be our base figure. To take into consideration the increase in popularity of music since 1930, as well as including amateur musicians, we will assume that 23% of all Americans play music. That would make 72 million musicians in the States. Various industry reports claim that 1% of musicians actually focus on drums, leading us to estimate that there are 0.72 million drummers in the States right now. 7.2 Competitor Analysis Although there isn’t a design like ours in the market currently, we still anticipate stiff competition. Our main competitors would be the companies that are specialized in manufacturing and selling the toe actuated pedals for decades. Another factor to note is that these competitors would have acquired loyal customers over time and it would be difficult to convert these customers into consumers of our product. From our research, the most popular manufacturers of drum pedals are DW, Sonor, Pearl, Yamaha, Tama and Mapex. Even, with six competitors, we would not assume that we can command one seventh of the market. We conservatively estimate that we can get 5% of the market. 7.3 Demand Function Here we present two methods to determine our demand function. The first method involves coming up with assumptions through online sales figures. The second method uses data that we have accumulated through our surveys. 7.3.1 Demand Function 1st Method: The demand curve is determined by this formula,

PQ λθ −= where θ signifies the total demand for drum pedals, P is price and deriving λ would require more analysis. The most expensive drum pedal found on EBay is $750, so we’ll assume that any drum pedal at $900 would get no demand. With that, we get λ=80. Our demand curve is shown below. Based on the analysis of both the demand curve and the revenue function, the optimum price would be $450.

26

7.3.2 Survey Data and Logit Model In order to obtain a simple and reasonable model for our market analysis and estimate the effects of our design factors, we evaluated our design objectives and requirements and decided to use durability and price as our two factors quantifiable in the market analysis model. Additionally, we made the following assumptions in order to simplify our marketing model. 1. There are no other factors influencing customer choice except durability and price 2. The other attributes of our pedal and existing pedals in the market are the same 3. The competitors’ pedals are identical to each other These three assumptions enable us to obtain a reasonable estimate for the potential share of the market that our drum pedal is able to obtain. From our survey data, we were able to obtain the following beta values for our two variables, durability of the pedal and the price of the pedal. Table 19: Survey result for effects of durability Durability (years) 5 10 15

estimated beta -1.79 0.4 1.39

Figure 11: Graphical representation of effects of change in durability

0

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80

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-2-1.5

-1-0.5

00.5

11.5

2

0 5 10 15 20

Esti

mat

ed B

eta

Estimated Durability (years)

Figure 10: Demand function of first method

27

Table 20: Survey results for effects of price Price ($) 50 150 250 350 450 550 estimated beta 3.63 3.96 3.34 2.26 -0.27 -12.92

Figure 12: Graphical representation of effects of change in price

These beta values are used in the Logit model to predict the demand for our pedal compared to existing pedals. We estimated that the total number of drummers in the US to be around .72 million people. The number of drum pedals sold will hence be the total number of drummers divided by the number of years the pedal can last. Hence, making our pedals more durable will decrease its demand per year. Using the beta values and a spline function, we predicted the part worth value for our product for a given set of price and durability values. From our survey data, we also obtained the estimated part worth value for a no choice condition. That beta value turns out to be 3.14. Using these two values, we predicted the percentage of market share our product is predicted to obtain. We then use the predicted market share to obtain an estimate of our total sales and total profit. The results are presented below. While attempting to maximize market share, we obtained the following data: Durability (years) 8.87 Price $143.86 Market Size 81138 Market Share 70% Quantity Sold 56562 Revenue $8,137,093.67 Cost $5,730,374.94 Profit $2,406,718.73

-14

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28

While attempting to maximize profit, we obtained the following data: Durability (years) 13.24 price 378.95 Market Size 54400 Market Share 54% Quantity Sold 29139 Revenue $11,042,320.22 Cost $3,284,209.32 Profit $7,758,110.90 These data indicate a very optimistic future for our product. However, we must remember the uncertainties in our estimates and the inadequacies of the Logit model. These include the omission of effects of other independent factors on the demand, and the lack of consumer knowledge on our project. Hence, we only project our project to capture 5% of the market share initially. This yields the following: Quantity Sold 2720 Revenue $1,030,756.72 Cost $927,625.86 Profit $103,130.86 We hope that eventually our market share will rise steadily as we gain more penetration, eventually reaching the 54% predicted in the long run. 7.3.3 Demand Function 2nd Method: For this method, we analyzed data that we got from our survey to six drummers. We analyzed the price they are each willing to pay for our drum concept, and the graph is shown below. The reformulated demand model looks at how product attribute elasticies affect the demand curve. Our additional attribute is to have our drum pedal adjustable to be toe and heel actuated. We also added a table with some of their particulars. The formula is

αλλθ ∆+−= Tdp PQ

Table 21: Data from our survey of 6 people Person Age Age Started Price willing to Pay for Non

Adjustable Pedal Price willing to Pay 2 for

Adjustable Pedal A 30 12 150 150 B 17 6 200 400 C 26 10 550 625 D 32 13 100 100 E 22 9 300 350 F 33 10 200 400

29

The will use the Demand Model from our Marketing Analysis in our Profit Maximization Analysis. The equation is Q=-7.66P+4900. The derivation of this equation will be explained in greater detail at 6.3.2. 7.4 Revenue Function To determine the revenue we can get, we use the formula,

TR =P * Q In terms of price, both our methods give us $450 and $373.75. We have decided to go with our second method since it is the most conservative price estimate. Through our Market Size and Competitive Analysis, we determined that we would get a 5% market share of the drum pedal industry, so that makes it 3600 drum pedals a year. We multiplied the y axis of the demand function of our second method and the revenue model is shown below.

We can see the maximum revenue we can get a year is $787,744 through the sale of 2,450 pedals. 7.5 Cost Function Here, we separate our costs into variable costs, fixed costs and operating costs.

0

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Figure 13: Demand Functions. One is derived from survey data, the other taken from marketing analysis by adding durability

Figure 14: Revenue function. Maximum revenue of $783,744 is achieved at a price of $320

Demand curve of non-adjustable pedal

Demand curve from adding durability

Maximum Revenue = $783,744

30

7.5.1 Fixed Costs: Our main sources of fixed costs are shown below. These items are long term assets that we purchase at the very beginning once. Table 22: List of fixed costs

Capital item Per unit ($) # of units Total ($) CNC machine 15,000 5 75,000

Other tools 10,000 1 10,000 Furnishing 150,000 1 150,000

TOTAL 235,000 7.5.2 Variable Costs: Regarding the variable cost function, we can first consider the price of every component and part used to manufacture the drum pedal that we bought and modified. Most of the prices stated in the table below come of McMaster. From the table, we can see that the variable cost of each manufactured pedal is $89.20 Table 23: List of variable costs

Item Per unit ($) Pedal 4.99 Stock 19.65 Hinge 3.99 Chains 19

Steel Shaft 3.79 Base 26.78 Cam 6.00

Miscellaneous 5.00 TOTAL 89.20

7.5.3 Operating Costs: The costs below represent our operating costs. These costs are constant regardless of the number of pedals we sell and occur annually. Table 24: List of operating costs

Annual expense Per unit ($) # of units Total per year ($) Building lease 50,000 1 50,000

Wages per worker 40,000 5 200,000 Utilities 50,000 1 50,000

Advertising 100,000 1 100,000 Maintenance 25,000 1 25,000

Miscellaneous 25,000 1 25,000 TOTAL 450,000

7.6 Profit Function By incorporating variable costs into Figure 13, our profit maximization curve is shown below. Note that this profit maximization curve does not include fixed cost.

31

As we can see from the Figure above, our yearly maximum profit is $580,420. 7.7 Break Even Analysis Here we determine that it would take us over one year to break even. Our chart is shown below where we present our net cash flows and the present value of the cash flows. For the interest rate used to calculate the present value of cash flows, we used 6% which we determined from the interest rates used for Treasury Notes over the past decade.

7.8 Internal Rate of Return (IRR) Here, we show how we determined the IRR of our business plan over the span of three years. Table 25: Future values of yearly cash flows

Year Present Cash Flow

Future Value (3 years)

1 $130,421 $146,541 2 $130421 $138,246 3 $130,421 $130,421

0

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1 2 3Cash

($)

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Cash Flows

Present Value of Cash Flows

Figure 15: Profit Maximization. Maximum profit of $580,420 is achieved at a price of $365

The cash flow in the table is determined from subtracting the yearly profits from sales with annual operating costs, both of which we assume remain constant. We then calculate the future value of those cash flows three years into the future.

Figure 16: Break Even Analysis. Our breakeven point is after year one.

Maximum Profit = $580,420

Price = $365

Quantity = 2141 Pedals

32

Using the formula, PV (1 + 𝑖)𝑡=FV Where PV is the present value of investment costs (fixed costs and 20% of yearly operational costs in this case), FV is the future value of our cash flows and t is the number of years, we determined IRR to be 8.51%. 8 PRODUCT DEVELOPMENT PROCESS Figure 17: Actual process diagram and design structure matrix for the pedal Motivation Design Objectives

User

Designer

CAD Design

Design Evaluation

Objectives achieved/Acceptable trade-offs

Objectives not achieved/Unacceptable trade-offs

Construct Alpha Prototype

Testing and Evaluation

Fail

Estimated Production

Estimated Cost Producer

User input/ survey

Construct Beta prototype

Pass

Testing and Evaluation/FMEA

Fail

Construct Beta Plus prototype Business Plan

33

The actual design process is not very different from our initial process diagram. Most of the analysis and testing evaluation steps remain unchanged. However, there was one more round of testing than we thought due to the increase in available time for test between the alpha, beta and beta-plus prototypes. We learned that a very good design on paper does not translate to a good physical design, and that testing of a prototype often reflects many flaws that would have gone unnoticed in the paper design. A functioning prototype also helps to communicate our designing ideas much clearer compared to a CAD model of our design. 9 BROADER IMPACT Our team members were generally concerned with the impact that our design has on the way people communicate with each other, or with the environment. Chris mentioned in his essay that a successful product such as cellphone can drastically change the ways in which people communicate. He also mentioned that a well thought out marketing campaign can help communicate certain traits about the owner of the product. He believes that our current product can help to communicate a positive image for the drummer who uses it, especially in helping to identify himself as someone who is forward-thinking and willing to try out new innovations in the hope that they will be accepted by the drumming community. Travis mentioned in his essay that a well-designed product can help users interact better with the environment around them, while a badly-designed product does the opposite. He hopes that our pedal will provide a positive interaction between the user and the pedal, allowing the learning curve for a beginner drummer to be less steep and allowing them to drum more comfortably. David mentioned that with improvements in design for digital musical aids, digitization in music have allowed it to be communicated better to a larger audience. He hopes that the pedal will allow more people to appreciate music that are not digitally altered, while also hoping that the pedal allow music of good quality to be produced and recorded so that they can be digitized and appeal to those who prefer digitized music. Yundi’s essay focused how designs with no regard for the society at large was bringing harm to everyone in the society, exemplified by the improvements in weapons design. He stressed the need for designers to keep in mind the potential impacts of their designs in mind as they come up with new designs, and try to maximize positive impacts while limiting negative impacts. He hopes that the pedal will not have any negative social impact, and is glad that there is no immediately visible negative social impact associated with the product. We all agreed that as designers, it is very important to take into consideration the impact of our product on the users and the society in general. Most importantly, our product needs to benefit the user, for a product that does not serve its purpose will

34

only cause disappointment and frustration to the user. Next, if possible, our product should benefit the whole society. It does not mean that the products we design must have a visible benefit to society, but that our designs should at least not cause visible harm to society. We believe our product will benefit many aspiring drummers overcome their fear of learn the base drum pedal. It can also help many older drummers with joint ailments to pick up drumming again. Ultimately, we hope that the drum pedal will prove to be easier to play and less strenuous on the user than current pedals, reducing chances of injury and improving overall comfort when drumming. We foresee that our design is very radical, considering the basic design for a drum pedal has remained unchanged for over fifty years. There may be reluctance in accepting the product, and a lack of “experts” using this pedal may also hurt its image. A potential problem is that a new user will be branded as an “outcast” in the drumming community for using the new pedal and will give up before even trying. We hope to overcome this through obtaining early endorsements from drum instructors and professionals and include them in our marketing campaign to promote a positive image for our product. In conclusion, the final design was chosen because it reflects the team’s belief that a good design should benefit the user and help them overcome the difficulties they face. It should also aid in the user’s interaction with other people, with the environment, and project a positive image of him to others. Our design also reflects flexibility. We abandoned a few initial designs that were less flexible, and left room for further improvements and adaptations. Most importantly, there are no negative social impacts associated with its use, and it should not in any way, result in damage to the society as a whole. 10 REFERENCES

1. http://www.ehow.com/way_5179074_drum-pedal-technique.html 2. http://www.patentstorm.us/applications/20050103185/description.html 3. http://patents.com/us-7579539.html 4. http://patents.com/us-7268284.html 5. http://patents.com/us-7435888.html 6. http://patents.com/us-7408104.html 7. http://msis.jsc.nasa.gov/sections/section03.htm 8. http://www.ocm.co.jp/en/pro/roller/03_01_02.pdf 9. http://dohistory.org/archive/doc099/099_p20_txt.html

Appendix A

!

!

! !

Motivation! Design!Objectives!User!input!

Designer!input!

Preliminary!Design!

Design!Evaluation!

Objectives!

achieved/Acceptable!

trade>offs!

Objectives!not!

achieved/Unacceptable!

trade>offs!

Construct!Working!

Model!

CAD/Numerical!

Analysis!

Testing!and!

Evaluation/FMEA!

Fail!

Initial!Production!Analysis!

Initial!Cost!Estimation!Producer!input! User!input!

Construct!Final!

Prototype!

Pass!

Final!Testing!

Fail!

Pass!Enter!Production!

Final!Production!Analysis!

Final!Cost!Estimation!Producer!input!

User!input!

Designer!input!

Product(Development(Process(

Output!

Feasibility!of!Product!(Market!Demand)!

Market!Needs!

Designing(a(New(Base(Drum(Pedal(Process( Input( Output(

Motivation! Not!easy!to!learn!to!use!foot!to!press!base!drum!pedal!(from!user)! Redesign!base!drum!pedal!Market!Needs! Survey!the!users!of!drum!pedals! Determine!the!advantages!and!disadvantages!of!

current!pedals!Feasibility!of!Product! Determine!potential!in!market! A!new!concept!to!satisfy!client!needs!Design!objectives! Press!the!pedal!that!requires!a!more!natural!motion!of!the!foot!(from!

designer)!Design!a!base!drum!pedal!that!uses!the!heel!

Preliminary!Design! Pedal!needs!to!be!actuated!by!heel! Use!system!of!gears!and!pulleys!to!achieve!the!motion!of!hitting!the!drum!using!a!heel!action!

Design!Evaluation! Gears!and!pulleys!are!used! Gears!and!pulleys!are!suitable!CAD/Numerical!Analysis! Design!pedal!that!uses!gears!and!pulleys!and!conduct!motion!

simulation!and!testing!Engineering!drawings!from!CAD!model!are!

obtained!and!the!working!model!is!expected!to!pass!testing!

Construct!Working!Model! Design!a!pedal!using!gears!and!pulleys,!engineering!drawings!from!CAD!(if!applicable)!

Working!model!of!pedal!to!demonstrate!preliminary!design!ideas!

Initial!Production!Analysis! Analyse!whether!the!product!is!easy!to!mass!produce!(from!producer)! Product!is!easy!to!mass!produce!Initial!Cost!Estimation! Analyse!whether!the!product!requires!many!expensive!or!custom!

made!parts!(from!producer)!Product!does!not!require!many!expensive!or!

custom!made!parts!Testing!and!Evaluation/FMEA! Working!model!of!pedal! Pedal!design!generally!met!requirements,!need!

small!changes!(from!user).!All!possible!failure!issues!have!being!addressed!

Construct!Final!Prototype! Testing!revels!that!minor!adjustments!are!needed! Final!prototype!constructed!Final!Production!Analysis! Analyse!whether!the!product!is!easy!to!mass!produce!(from!producer)! Product!is!easy!to!mass!produce!Final!Cost!Estimation! Analyse!whether!the!product!requires!many!expensive!or!custom!

made!parts!(from!producer)!Product!does!not!require!many!expensive!or!

custom!made!parts!Final!Testing! Test!production!model!to!ensure!that!all!requirements!are!met!and!all!

problems!are!addressed!Production!model!meets!all!requirements!

Enter!Production! Production!model! Marketed!product!

!

Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Motivation! 1 1

Market!Needs! 2 1 2 Feasibility!of!Product! 3 1 3 Design!objectives! 4 1 4 1 Preliminary!Design! 5 1 5 Design!Evaluation! 6 1 6

CAD/Numerical!Analysis! 7 1 7 Construct!Working!Model! 8 1 1 8 1 Initial!Production!Analysis! 9 9 Initial!Cost!Estimation! 10 10

Testing!and!Evaluation/FMEA! 11 1 1 1 11 Construct!Final!Prototype! 12 1 12 1 Final!Production!Analysis! 13 13 Final!Cost!Estimation! 14 14

Final!Testing! 15 1 1 1 15 Enter!Production! 16 1 16

1I Team Roles Worksheet

There exist a variety of ways to describe and present team roles. One approach is to distinguish importantroles according -to titles and brief distinguishing features. The categorized roles are not meant to pigeonholeor otherwise limit a team. They are simply meant to provide guidance and assist us in understanding how adesign team functions.

Role Primary Team Member(s)Administrator I Reviewer Monitors project andjudges outcomes accurately. Sees the bigpicture. Compares results with goals.Troubleshooter I Inspector Repairs problemsand solves difficult impediments to progress. UProducer I Test Pilot Brings tasks to fruitionand reality. Treats tasks realistically. Pushes r Aperformance envelope. Makes things happen.Manager! Coordinator Supervises and leadstasks. Encompasses a practical perspective.Focuses effort and saves time.Conserver! Critic Preserves the team’s andproject’s goals and concerns. Addresses Caesthetic and moral issues.Expediter I Investigator Experiences the teamgoals, gets facts and know-how.Conciliator! Performer Detects and fixesinterpersonal issues.Prototyper! Model Maker Builds and testsrough prototypes.Visionary Imagines various product forms anduses.Strategist Speculates on and plans project and i_— .product future. (2’Needfinder Evaluates human factors andconsumer issues.Entrepreneur! Facilitator Explores newproducts and methods, inspirers and motivates.Diplomat I Orator Harmonizes team, client, andcustomer.Simulator I Theoretician Attempts tounderstand phenomena; analyzes performanceand efficiency.Innovator Synthesizes new products; ( Aimprovises solutions.Director I Programmer Supervises and leadstasks. Encompasses a practical perspective.Focuses effort and saves time.

4.

1 of 1

Appendix B

II

Design Criteria and User Scenario Worksheet

List your design criteria (design specs) and quantify as many of them as possible (don’tignore qualitative criteria). The goal of this exercise is to help you understand the designrequirements, to make your design goals explicit, and to give you a detailed list of criteriathat you can use to analyze and compare your design alternatives.

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Write a short story of a user in the environment that your product will be used in. Give itsome thought, and use details about the environment and the user. (Are theredistractions around? Might the user have something else on his mind? Are her kidsnagging her? Is the user a worker performing a repetitive or monotonous task?) Ifappropriate, describe the problem, difficulty, or aggravation that the user is facing (thisshould be the problem that you are trying to solve). The goal of this exercise is to helpyou to see the situation from the user’s point of view. Keep this scenario around andrefer to it as you explore design alternatives. The scenario will also illustrate the need foryour product, and it will highlight important issues that your product should address.These exercises can help you to avoid large oversights that can lead to a poor, difficultto use, or useless product.

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—2 of 2

Information Gathering

Identify Stakeholders: These are the people that will interact with or be affected by theproduct that you design. Your design will affect all of these people’s lives, and you needto consider them all in your design. Take the time out to make sure you know who thesepeople are. This list can get you started:

- Who will use the product?/(oeO PV &ovv\ E4-

- Who will buy the product?Th’e .vvec I ev avvet Y’

- Who will sell the product?

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- Who will manufacture the product?

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- Who will transport the product?A i’e F-e

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- Who will store the product?The se eS’es

- Who will maintain the product?v41 j.1t4vc -oCe.

- Who will recycle or dispose of the product?--

- Whom else the product will affect?

e ‘Je

User: The person who uses your product probably has the most to lose or gain from yourdesign. Remember that the user is often not like you, and s/he probably does not seethe product from your point of view. You need to understand your users wants andneeds as well as possible. Be systematic about it. Write down everything you knowabout your users. This list can get you started:

- What is the user’s lifestyle and background?Av\t iv” d4 covtiu t1t

O kcc ‘

- What are the user’s expectations?

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When will the product be used?Dic eYttQ,cocI yik

e€ce,How often will the product be used?Oc’ oc- t’1OV.

What is the user thinking, about while using the product?

pecJ I eci-

Is it possible to use the product in a way that was not intended?

YQe eç wWhat are the user’s limitations (cognitive, physical, etc)

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2 of6

Environment: The environment that your product is used in can have a huge impact ondesign requirements. Often it is difficult to know a priori which aspects of theenvironment might affect your design. Temperature? Noise level? User distractions? Youwant to understand the environment as much as you can. Get some personalexperience in the environment if possible. You want to be able to think like the user inthe user’s environment so that you can identify potential issues early in the designprocess. Talk to people involved, and get a sense for what the environment is like. Visitthe place where the product might be used.

- Make an outline of the activities surrounding the environment where the productmight be used. An example is shown below for a product that was designed tohelp with managing clean laundry:

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3 of 6

Out’ine of activities surrounding the use of your product:

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The following template can help you to get started analyzing your product and benchmarking it against competitors. The goalsof this exercise are to help you to systematically explore relationships between design criteria and engineering quantities, tohelp you quantify as many aspects of your design as possible, and to help you compare your design to other products that areavailable. Use any system of weights and notation that works for you, but be sure to include a legend of notation.

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CUSTOMERREQUIREMENTS 1

IMPORTANCE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20— -

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OBJECTIVETARGETVALUES

2 of 2

Appendix C

APD Worksheet and Information Based Upon Canadian NRC - IRAP Design for Environment Guide Page 4

MET Matrix Worksheet Material Cycle | Energy Use | Toxic Emissions (input/output) (input/output) (output) ____________________________________________________________________________________ Production and supply of all materials and components Mining for metal/ water acidification Forging, casting, milling, Finishing, painting, packaging/ solvents, Sawing/ air pollutants, heavy metal discard, plastic waste Metal waste, petroleum depletion ____________________________________________________________________________________ In-house production ____________________________________________________________________________________ Distribution ____________________________________________________________________________________ Use:

• operation

• servicing ____________________________________________________________________________________ End-of-Life system:

• recovery

• disposal

Taking apart the pedal Removing nuts, blots and screws.

No toxic emissions

Salvaging the workable parts of the pedal

Removing nuts, blots and screws.

No toxic emissions

Making sure moving parts are well oiled and still functional No toxic emissions. Clean

up spilled oil Tightening nuts and bolts.

No supply of materials needed. Pedaling the drum pedal No toxic emissions

No supply of materials needed. Petrol needed for transportation

Carbon emissions

A well functional pedal to work on

Forging, casting, milling No toxic emissions

APD Worksheet and Information Based Upon Canadian NRC - IRAP Design for Environment Guide Page 5

DfE Improvement Options Worksheet DfE Strategies Improvement Options 1. New Concept Development 1. Smaller Base 2. Direct Pedal Connection 3. Thinner Pedal 2. Physical Optimization 1. Narrower Pedal 2. Thinner Pedal 3. Direct Connection 4. Noise Damper on Pedal 3. Optimize Material Use 1. Thin Pedal 2. Plastic or Fiberglass instead of metal 3. Collapsible for smaller package 4. Comes in pieces for smaller package 4. Optimize Production 1. Less steps in pedal production 2. Multiple parts from same raw metal 3. Stamping of parts

4. Lower production E consumption Heating metal before processes

5. Optimize Distribution 1. Smaller packages from home assembly 2. Cardboard packaging for recycling 3. Larger shipments for efficiency 4. Clean diesel transportation 6. Reduce Impact During Use 1. Durable drives so less replaced parts 2. Durable springs for less replacement 3. Padded hammer tip for less drum canvas damage 4. Padded pedal for less floor damage 7. Optimize End-ofLife Systems 1. Reusable metals 2. No corrosive materials 3. Reusable packaging 4. Recyclable rubber components

Appendix D

Assignment 5

Team 3

From the Pugh matrix that can be found attached to the end of this worksheet, we decide to use the heel pedal design for this assignment. This is because that design shows the most promise and is able to meet most of the design criteria that we listed.

Design Requirements 1. Weight

The weight of the pedal should be between 3 lbs and 10 lbs (excluding additional weights attached as a means of providing more stability). This is intended to provide both a degree of stability (which requires the pedal to be heavier) and a degree of portability (which requires the pedal to be lighter).

2. Durability the pedal should last as long as possible, which can be achieved by ensuring that the parts are made of durable materials, and that all moving contact points (e.g. the contact point between the chain and the pedal) should be oiled or protected with a soft cushioning material.

3. Price The pedal should not cost more than $100, as that is the price of currently available novice-level drum pedals.

4. Size The size of the pedal should not exceed 18” in length, 5” in width and 10” in height (excluding the re-attachable mallet) because of the limited space drummers have due to the way the drums are set up. The height of the mallet is adjustable to suit the different sizes of drums available.

5. Adjustability The heel pedal is a very novel design and hence it should be made possible to convert the pedal back to a traditional toe pedal without too much hassle.

6. Does not conflict with other needs of the drummer The pedal should not compete with the other needs of the drummer during drumming, especially the drummer’s needs to play the other drums in front of him.

7. Intuitive The pedal must be intuitive to use, allowing the user to play quickly and with control.

8. Precision Our pedal needs to have a repeatable motion, such that if the drummer presses on the pedal at the same spot using the strength, then the sound produced should be the same every time.

9. Stability Our pedal needs to be stable during play, such that the user only feels the movement of the pedal itself and not the other parts (e.g. the chain or the belt) while drumming.

10. Responsiveness Our pedal need to respond to the actuation motion of the user well and not feel sluggish while in use, as sluggish motion can result in uneven beats and decreased precision.

11. Health risks Also, it must not cause health problems for the user over the course of a lifetime (many drummers start as teenagers and play well into their 60s or even 70’s). For example, a concept that makes drumming easier but applies a lot of shock to the knees of the drummer might not be very favorable.

12. Complexity The pedal should be designed with few moving parts, both to reduce cost and to ensure that the pedal does not suffer from failures during use.

Product Developmental Process Model Process Input Output

Motivation Not easy to learn to use foot to press base drum pedal (from user)

Redesign base drum pedal

Market Needs Survey the users of drum pedals Determine the advantages and disadvantages of current pedals

Feasibility of Product Determine potential in market A new concept to satisfy client needs

Design objectives Press the pedal that requires a more natural motion of the foot (from designer)

Design a base drum pedal that uses the heel

Preliminary Design Pedal needs to be actuated by heel Use system of gears and pulleys to achieve the motion of hitting

the drum using a heel action Design Evaluation Gears and pulleys are used Gears and pulleys are suitable CAD/Numerical

Analysis Design pedal that uses gears and pulleys

and conduct motion simulation and testing Engineering drawings from CAD

model are obtained and the working model is expected to

pass testing Construct Working

Model Design a pedal using gears and pulleys,

engineering drawings from CAD (if applicable)

Working model of pedal to demonstrate preliminary design

ideas Initial Production

Analysis Analyse whether the product is easy to

mass produce (from producer) Product is easy to mass produce

Initial Cost Estimation Analyse whether the product requires many expensive or custom made parts (from

producer)

Product does not require many expensive or custom made parts

Testing and Evaluation/FMEA

Working model of pedal Pedal design generally met requirements, need small

changes (from user). All possible failure issues have being

addressed Construct Final

Prototype Testing revels that minor adjustments are

needed Final prototype constructed

Final Production Analysis

Analyse whether the product is easy to mass produce (from producer)

Product is easy to mass produce

Final Cost Estimation Analyse whether the product requires many expensive or custom made parts (from

producer)

Product does not require many expensive or custom made parts

Final Testing Test production model to ensure that all requirements are met and all problems are

addressed

Production model meets all requirements

Enter Production Production model Marketed product

Product Decisions

We can make decisions on all the requirements listed earlier except price, complexity and adjustability. As we modify our design, we may need it to become more complex to trade off for other advantages. However, the other 9 requirements are very basic design features seen on most of the bass drum pedals available in the market right now, and those requirements are also demanded by drummers in the market for a bass drum pedal. Hence, we need to ensure that our drum pedal fits their needs.

Quantifiable Variables

We can quantify precision by documenting the strength and the spot at which the mallet hit the drum surface when actuated with a constant force. The precision of the pedal should be directly related to the stability of the pedal. We can use that data to establish the variance in our pedal and compare that result to pedals currently in the market.

We can quantify responsiveness by measuring the resistive force felt by the user during use. The theoretical force output for a given force input into the pedal can be calculated, and we can use a force gauge to measure the actual output, and find the percentage of energy lost in the pedal. The measurement can be repeated on currently available pedals. Hence, we can know whether there are excessive resistance forces present, which will result our pedal becoming less responsive. The responsiveness of the pedal should be inversely related to the complexity of the pedal, i.e. the less complex the pedal, the better the responsiveness.

The size of the pedal should also be inversely related to the complexity. Usually, the less complex is the pedal, the smaller is the size of the pedal, due to the need for extra space to accommodate the extra parts. However, there may be cases when a slightly larger pedal will turn

Appendix E

Survey'Results'

The$following$is$a$table$summarizing$our$survey$results.$

From$the$results,$we$can$see$that$about$44.4%$of$the$respondents$faced$at$least$some$difficulty$in$using$the$toe$pedal.$Also,$66.7%$of$the$respondents$found$that$a$heel$pedal$will$be$easier$to$use$than$a$toe$pedal,$even$amongst$experienced$drummers$with$more$than$10$years$of$experience.$About$63%$of$the$respondents$also$believe$that$they$can$heel$tap$longer.$The$result$from$this$survey$can$help$us$advertise$the$product$in$the$future.$

From$the$CBC$results,$we$can$also$see$that$users$prefer$their$pedal$to$be$lighter$and$more$portable,$and$also$for$the$price$to$be$as$cheap$as$possible.$These$results$can$help$us$identify$our$design$objectives.$

Years of experience

in drumming

Difficulty in using

toe pedal?

Do you think using a heel pedal will be harder than using a toe

pedal?

Speed'of'tapping'

Stamina'of'tapping'

Effects'of'pedal'on'technique'

Willingness'to'learn'new'technique'

0$ No$Heel$slightly$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ No$opinion$

0$ Slightly$Heel$slightly$easier$

Toe$tap$faster$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ No$opinion$

0$ Yes$Toe$much$easier$

Toe$tap$faster$

Toe$tap$last$longer$

Pedal$strongly$amplifies$technique$ No$opinion$

0$ No$Toe$slightly$easier$

Toe$tap$faster$

Toe$tap$last$longer$

Pedal$slightly$amplifies$technique$ Yes$

0$ Yes$Heel$slightly$easier$

About$the$same$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

1$ No$Heel$much$easier$

Heel$tap$faster$$

Toe$tap$last$longer$

Pedal$strongly$hinders$technique$ Yes$

1$ No$Toe$slightly$easier$

Toe$tap$faster$

Toe$tap$last$longer$

Pedal$slightly$amplifies$technique$ Yes$

4$ Slightly$Heel$much$easier$

About$the$same$

About$the$same$

Pedal$strongly$hinders$technique$ No$opinion$

9$ Yes$Heel$slightly$easier$

Toe$tap$faster$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

10$ No$Heel$slightly$easier$

Toe$tap$faster$

Toe$tap$last$longer$

Pedal$slightly$hinders$technique$ Yes$

12$ No$Toe$slightly$easier$

Toe$tap$faster$

Heel$tap$last$longer$$

Pedal$slightly$amplifies$technique$ Yes$

12$ No$Toe$slightly$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$slightly$amplifies$technique$ Yes$

12$ No$Heel$slightly$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

15$ No$Heel$slightly$easier$

Toe$tap$faster$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

16$ No$Heel$slightly$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

18$ No$Heel$slightly$easier$

Toe$tap$faster$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ No$$

20$ No$ No$difference$Toe$tap$faster$

Toe$tap$last$longer$ No$effects$ Yes$

20$ Slightly$Heel$slightly$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

21$ Yes$Heel$slightly$easier$

Toe$tap$faster$

Toe$tap$last$longer$

Pedal$slightly$hinders$technique$ Yes$

21$ Slightly$Heel$slightly$easier$

About$the$same$

Toe$tap$last$longer$

Pedal$slightly$hinders$technique$ Yes$

21$ Slightly$ No$difference$Toe$tap$faster$

Heel$tap$last$longer$$ No$effects$ Yes$

23$ Yes$Heel$much$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$strongly$hinders$technique$ Yes$

23$ No$Heel$slightly$easier$

About$the$same$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

24$ Slightly$Heel$slightly$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

26$ No$Toe$slightly$easier$

Toe$tap$faster$

Toe$tap$last$longer$

Pedal$slightly$amplifies$technique$ Yes$

31$ No$Heel$slightly$easier$

Heel$tap$faster$$

Heel$tap$last$longer$$

Pedal$slightly$hinders$technique$ Yes$

31$ Slightly$ No$difference$About$the$same$

Heel$tap$last$longer$$ No$effects$ No$opinion$

$

Drumming$Experience$in$years$

No$difficulty$

Faced$difficulty$

Toe$Easier$

Heel$Easier$

Toe$taps$faster$

Heel$taps$faster$

Toe$taps$longer$

Heel$taps$longer$

None$ 2/5$ 3/5$ 2/5$ 3/5$ 3/5$ 1/5$ 2/5$ 3/5$=<10$ 3/5$ 2/5$ 1/5$ 4/5$ 3/5$ 1/5$ 3/5$ 1/5$>10$ 10/17$ 7/17$ 3/17$ 11/17$ 7/17$ 7/17$ 4/17$ 13/17$Total$ 15/27$ 12/27$ 6/27$ 18/27$ 13/27$ 9/27$ 9/27$ 17/27$$

$

CBC'Results'Analysis'

CBC$System$$Multinomial$Logit$Estimation$

Copyright$1993Z2010$Sawtooth$Software$$Name/Description:$Logit$Run$04:34:50PM$Wednesday,$October$05,$2011$$Main$Effects$Tasks$Included:$All$Random$$$$$$Total$number$of$choices$in$each$response$category:$$$$$$$$$$$$$$1$$$$137$$33.83%$$$$$$$$$$$$$$2$$$$120$$29.63%$$$$$$$$$$$$$$3$$$$115$$28.40%$$$$$$$$$$$NONE$$$$$33$$$8.15%$$$$$$Files$built$for$27$respondents.$$$$$$$There$are$data$for$405$choice$tasks.$$$$$$Iter$$$$1$$Chi$Square$=$$$$$256.94051$$rlh$=$$$$$$$0.34332$$$$$Iter$$$$2$$Chi$Square$=$$$$$261.91324$$rlh$=$$$$$$$0.34544$$$$$Iter$$$$3$$Chi$Square$=$$$$$261.92813$$rlh$=$$$$$$$0.34544$$$$$Iter$$$$4$$Chi$Square$=$$$$$261.92813$$rlh$=$$$$$$$0.34544$$$$$Converged.$$$$$$LogZlikelihood$for$this$model$=$$$$Z430.48515$$$$$LogZlikelihood$for$null$model$=$$$$Z561.44922$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ZZZZZZZZZZZZ$$$$$$$$$$$$$$$$$$$$$$$$Difference$=$$$$$130.96407$$$Percent$Certainty$$$$$$$$$$$$$$$$$=$$$$$$23.32608$Consistent$Akaike$Info$Criterion$$=$$$$$938.01306$Chi$Square$$$$$$$$$$$$$$$$$$$$$$$$=$$$$$261.92813$Relative$Chi$Square$$$$$$$$$$$$$$$=$$$$$$23.81165$$$$$$$$$$$$Effect$$$$$$$$Std$Err$$$$$$$t$Ratio$$$$$$Attribute$Level$$$1$$$$$$$$1.05969$$$$$$$$0.12970$$$$$$$$8.17054$$$$1$1$Below$$100$$$2$$$$$$$$0.75570$$$$$$$$0.12955$$$$$$$$5.83309$$$$1$2$Between$$100$to$$200$

Appendix F

Appendix F-Force analysis

We explored other changes that can be made to our pedal. For example, we explored the possibility of shortening or removing the stock from our design, and changing the radius of the wheel. In order to facilitate our discussion, the locations and the list of symbols for the forces involved in the motion of the pedal is listed below. All the forces are measured in pounds.

Table 1: List of forces

Force Location Symbol

Weight of hammer head Center of gravity of hammer head Wh

Weight of handle attached to hammer Center of gravity of handle Ws Tension in chain Along chain T

Force experienced by user At edge of pedal F Weight of pedal Center of gravity of pedal Wp

Normal reaction at pin, horizontal direction At pin Rx

Normal reaction at pin, vertical direction At pin Ry Normal reaction at hinge, horizontal

direction At hinge Nx

Normal reaction at hinge, vertical direction At hinge Ny

Figure 1: Force notations

The force equations used were as follows:

Isolating the mallet, wheel, and the top part of the chain:

Taking moments about the center of the wheel: 𝑇 = 1𝑟

(𝑊𝑠�𝐿2−𝑟�

√2+ 𝑊ℎ(𝐿−𝑟)

√2)

Isolating the pedal, hinge, cam, and part of the chain (note: the presence or absence of the cam does not affect the results): Balancing forces in the vertical direction: F - T * sin(theta c) - Ry - Ny + Wp = 0 Balancing forces in the horizontal direction: Rx-T * cos(theta c)+ Nx = 0 Taking moments about the hinge, clockwise is positive: -Ry * Lp * cos(theta p) + Rx * Lp * sin(theta p) + F * La * sin(theta p) – T * Lp * (theta c+theta p) + Wp * La/2 * cos(theta p) =0 Taking moments about the pin, clockwise is positive: Ny * Lp * cos(theta p) – Nx * Lp * sin(theta p) + F * (La-Lp) * cos(theta p) + Wp * (La/2-Lp) * cos(theta p) =0 Taking moments about the location of F, clockwise is positive: Ny * La * sin(theta p) – Nx * La * cos(theta p) + T * (La-Lp) * sin(theta c + theta p) + Ry * (La-Lp) * cos(theta p) – Rx * (La-Lp) * sin(theta p) – Wp * La/2 * cos(theta p) =0 As we can see, T is directly solvable, and the 5 remaining unknowns (F, Nx, Ny, Rx, Ry) can be solved with the 5 equations above. Using the solve function in MATLAB, we can then obtain values for the unknowns given a certain set of inputs. From analyzing results for the normal reaction forces, we can compute the forces felt by the pin and hinge. They should not be too large, as too large a force will result in unnecessary wear and tear. It will also cause the joints to be vulnerable to fatigue failure.

We can also compute the tension force in the chain, which enables us to determine the type of chain to be used on our pedal.

Appendix G

APPENDIX G – Economic Analysis