Vanderbilt University

Sr. Design Project

Group 7: Athletic Shoe Development

Date Due: 04/25/06

Group Members:

Michael CannamelaCaroline de Monasterio

Robin GiannattasioBrandon JacksonPhillip O'Bannon

Dan Thomas

Abstract

50% of runners every year will acquire significant injuries such as Plantar Fasciitis, Iliotibial Band Syndrome, Achilles Tendonitis, and Patellofemoral Pain Syndrome which are a direct result of overuse and hyperpronation. Running shoes help to prevent injury and make the running gait more efficient, making a running shoe the most important piece of equipment a runner possesses. Shoes must be able to absorb shock, control motion, be flexible, and be durable. However, because of the complexity of biomechanics and the range of pronation between different individuals, it is difficult to find the perfect shoe to find all foot types. Our group proposed to create an adjustable running shoe that would be able to correct pronation and thereby reduce running injuries. By using a rigid plate and spring model developed in Matlab, we were able to implement a design that incorporated a suspension system as well as a tilt of the upper plate of the shoe to induce pronation control. Furthermore, we tested our design against the top of the line model shoe on the market today as well as a normal running shoe to see how it compared to various competitors for pronation control and Ground Reaction Force (GRF). We were able to correct rearfoot pronation of our test subject, however, there was a higher GRF during the toe-off as a result of the firm springless sole at the toe.

Introduction

Running is the primary exercise for 40 to 50 million people in the United States each year; however, significant injuries will occur in 50% of runners. Injuries vary from the foot and ankle, all the way up to the lower back. The main risk factors in running related injuries are overuse and hyperpronation. Biomechanical studies in running evaluate movement alternating between pronation and supination throughout the gait cycle. Pronation is defined by the simultaneous movement of calcaneal eversion, abduction of the forefoot, and dorsiflexion of the foot such that the sole of the foot moves away from the medial line. Supination is defined by simultaneous calcaneal inversion, adduction of the forefoot, and plantar flexion of the foot occurring together in a movement that causes the soles of the foot to turn inward toward the medial line. A runner will cycle between supination and pronation depending on what point of the cycle they are in; for normal gait, at midstance there is a transition from the dorsiflex position to a plantar flex position. From midstance to push off, the subtalar joint, the keystone to normal foot function and the site of pronation, will supinate. This helps to lock the foot into a rigid lever that the midtarsal joint can use for efficient propulsion. From the loading response right before the heel strike to midstance, the subtalar joint pronates causing the metatarsal joint to unlock and allow shock absorption.

Even slight deviation from the normal gait cycle can cause problems for runners along the biomechanical chain. When a person has an excessive angle of pronation, misalignment in the biomechanical chain will occur. Hyperpronation causes the "down and in" phenomenon to the

Figure 1: The left leg shows hyperpronation at the subtalar joint and the right leg shows a normal line of action of the subtalar joint.

normal line of action; the hip becomes internally rotated and the knees and knee caps bend inward and become flexed. This internal rotation causes injuries from the foot all the way up to the lower back.

The Posterior Tibialias runs from the back of the leg and helps to maintain the arch of the foot. The major action of the Posterior Tibialias is to invert the foot in the open kinetic chain and evert the foot when there is a loading response. The posterior tibialias will contract eccentrically such that the maximum stretch is in the pronated position. The Proneous Longus sits on the lateral side of the fibula, wraps under the foot, and attaches to the first metatarsal so that it pulls in to eccentrically control eversion. During overpronation, the Proneous Longus continually attempts to stabilize the foot and the Posterior Tibialias becomes overstretched so that there is a chronic abusing of both tendons leading to inflammation and tendonitis.

The Plantar Fascia, which runs along the bottom of the foot from the calcaneus to the metatarsal, normally lengthens and shortens depending on the angle of pronation. Since the subtalar joint stays in an unlocked relaxed position during pronation, hyperpronation will prevent the subtalar joint from entering supination so that it will not be rigid enough for propulsion. The Plantar Fascia responds by staying rigid in order to compensate for the lack of supination causing it to became abused and inflamed leading to Plantar Fasciitis.

In the pronated position, the normal amount of dorsiflexion causing a functional shortening of the calf muscles and a strain on the subtalar joint. This shortening results in a smaller range of motion for the ankle when walking and running which will displace the Achilles tendon into an incorrect position. The chronic micotrauma over time caused by the abuse of the tendon causes micro tears and the insidious onset of Achilles tendonitis. Furthermore, insufficient dorseiflexion prevents the tibia from traversing over the talus and causes the knee to overextend to correct for the ankle position. This pain from over extension is one cause of Patellofemoral Pain Syndrome.

Since the knee is flexed due to the internal rotation of the tibia and the femur, the quadriceps muscles become lengthened in response. The Vastus Medialis Oblique, the part of the quadriceps that is responsible for stabilizing the patella, becomes weak and can longer cause proper tracking of the patella. This will strain the patellar tendon resulting in its inflammation as well as the inflammation of the bursa, the sack of fluid between the tendon and the bone. Intrapatellar Bursitis and Patellar Tendonitis are another two contributing factors of Patellofemoral Pain Syndrome.

The abdominals are also lengthened and weakened by pronation since the pelvis becomes internally rotated and misaligned. The abdominals become too weak to posteriorly tilt the pelvis into the correct position; therefore, the hamstrings attempt to dynamically stabilize the pelvis by shortening their length. During the heel strike of the gait cycle, the hamstring needs to fully extend but this is prevented by their role as preferential dynamic stabilizer of the pelvis. Therefore, the perpetual quick stretch of the hamstring during the gait cycle will cause chronic micro tears in the muscle leading to a hamstring strain.

The ileotibial band is a ligament over the trochanter of the hip that attaches to the fascialatae. The anterior tilt of the pelvis during pronation causes the ITB complex to shorten which will squeeze down on the bursa between the ITB and the trochanter. Since the bursa is meant to help reduce friction by promoting gliding of the ligament over the bone, the constant pounding on the trochanter causes the bursa to become aggravated in an injury known as Iliotibial Band Friction Syndrome.

Finally, since overpronation causes misalignment all the way up the biomechanical chain, the internally rotated anterior tilt of the pelvis will increase lordosis of the spine causing an increase in the amount of shearing forces on the weight bearing lumbar vertebrae. This is especially stressful for the L5 vertebrae since its already precarious position juts out even further. Since the position of the pelvis is changed by the angle of pronation, the gaps between the sacrum and inominate bones through which the nerves and ligaments run can increase or decrease size. Sciatica can be caused by the pinching of sciatic nerve when it is run through a smaller than normal gap.

The numbers of running injuries that are caused by a deviation of the normal angle of pronation are vast and it is imperative for athletes to ensure that they are running correctly to prevent overuse injuries. A shoe can be used as an orthotic to support and effect weak joints and muscles in order to enhance performance by correcting the angle of pronation. By effectively changing the hyperpronation to a normal degree of pronation, the injuries that are caused by the misalignment of the biomechanical chain and overuse will automatically decrease because the source of the injury has been eliminated. However, the pronation angle fluctuates from person to person as well as other variables including the type of terrain and the current gait. Therefore, a shoe would ideally adjust to whatever the current angle of pronation was. The Adidas 1 is currently the only shoe on the market that dynamically adjusts to correct for pronation. Furthermore, the Adidas 1 is a very expensive option, $250, and it is not found in stores so it must be specially ordered from the company. Additionally, the ideal running shoe is lightweight so that it will not impede with running performance. A normal running shoe weighs 12 ounces, whereas the Adidas 1 weighs 15.3 ounces. Taking into account the drawbacks of the Adidas 1 and the amount of people affected by the various running injuries, there is limited competition and a large target market for such a device.

Methods

In order to achieve the goal of correcting overpronation and thus reduce injuries the shoe design had to accommodate the runner’s individual bio-mechanics and running preferences/styles. Upon research into the anatomy of a running shoe the decision was made to focus on the midsole region which is essentially the shoes suspension system. A running shoe is composed of four components: the upper, midsole, the last and the outsole. The upper is the part of the shoe that wraps around the foot and is usually constructed from a combination of lightweight nylon mesh and synthetic materials. Some parts of the upper contribute to midfoot support, motion control or provide torsional stability; however, its main purpose is comfort and friction prevention. The midsole is considered the most important part of the running shoe since its main purpose is to provide cushioning, stability and motion control. In most shoes, the midsole incorporates materials of various densities positioned in strategic places to achieve the desired effect.

Commonly used materials are EVA (ethyl-vinyl acetate), polyurethane, air, gel and firm plastic. The last refers to shape and construction. The outsole is what comes into contact with ground and is usually made of carbon rubber, blown rubber or a combination of both. The outsole resists wear and provides traction. It may also have transverse flex grooves or longitudinal split grooves to enhance shoe flexibility while potentially sacrificing a degree of stability.

Before developing a prototype, a QFD was developed in order to determine the most important features of the design to ensure that it would meet all of our qualifications. Our primary goal was to create a shoe that was able to decrease the amount of injuries sustained because of running by adjusting the runner's angle of pronation and fixing the suspension of the midsole making stability control and adjustability key elements on the product planning matrix. Since many runners acquire high mileage throughout the year, running shoes can wear out the shock absorption of the midsole contributing to further running problems. Therefore, it is important that the shoe be durable so that it will continue to fix the problem instead of aggravating it. Finally, the main competition on the market for our prototype is the Adidas 1, which are too heavy and too expensive. By making our prototype cost effective and lightweight, it provides an edge to the current competition in the market.

The preliminary idea for an adjustable shoe suspension involved a series of inflatable air bladders. These bladders would be attached to a micro-pump located in the heel of the shoe so that upon heel strike air would be driven into the bladders positioned on either side of the shoe. Based on the resistance of each bladder (such as how open the exhaust valves were) one side would be stiffer than the other. In addition this design would provide viscous damping effects when the bladder was impacted by the runner’s foot. This approach never advanced past initial concept and some rough sketches because it was quickly discovered that the idea of integrating an inflatable air bladder into a shoe was extremely patented. Examples of these patents are #4263728 and #5179792.

The concept of combining piezoelectrics into the shoes midsole was another line of thought which was short-lived. The idea involved using PVDF (polyvinelydine fluoride) a piezoelectric polymer to recover some of the power lost in the process of running to drive an electrorheological fluid also located in the midsole. PVDF was chosen over any other available piezoelectrics because of its flexibility, high voltage output, good impact resistance and the fact that its small stiffness adds minimum local stiffening to the host structure. Dr. Goldfarb posed the idea of using this to interact with an electrorheological fluid which would stiffen into a semi-solid when subjected to the electric field. While the underlying theory was promising the idea proved to be too difficult to implement. There simply was not enough research or testing compiled to make it feasible. Furthermore, durability proved to be an important factor in our shoe prototype and the complexity of this particular design was likely to make the shoe's lifespan a short one.

For the final prototype design, we chose two rigid plates separated by springs. Stable spring placement was decided by using the two plate rigid shoe model developed in Matlab, although several methods of modeling were performed. The pressure map for the foot in Figure 2 shows areas of darker green where there is areas of high pressure and yellow where there is low pressure. Since the springs are used as a suspension, it is important for them to be placed at

areas of higher pressure in order to maximize their efficacy. This placement is shown in Figure 2 by the red stars. It was essential that the prototype followed the parameters entered into the model so that we could see if our prototype had the desired results. Rigid plates were chosen to provide a stable platform for the springs to rest on and to ensure accurate force calculations. For the upper shoe, we used a Shimano bike shoe because it had a rigid carbon fiber sole to add to the stability of the upper plate. To provide flexibility in the forefoot of the shoe, a cut was made on each bike shoe at the ball of the shoe across the width. In order to provide traction so the runner would not slip during testing, the sole from a pair of Nike Prestos was attached to the bottom of the metal plate.

To reduce shoe mass, aluminum mesh plates were used as the platforms for the springs. These plates were designed with length equal to the distance from the heel to the ball of the foot and wide enough to support to adjacent springs. Initially, the rigid plates were secured to the upper and to the rubber tread using epoxy; however, this proved unsuccessful due to lack of surface area on the mesh plates. To resolve this problem, three zip ties were used to secure the lower platform to the treads and one zip tie to secure the top plate to the upper. The springs were wrapped in duct tape with the adhesive facing outward to prevent lateral motion in the springs and plates. It was important that the springs were not permanently fixed to the metal plates in case we decided to use springs with different spring constants during the testing. To maintain vertical contact between the plates and the springs at the rear of the shoe, 2 zip ties were threaded through the rubber sole, two rigid plates then finally through the heel of the bike shoe and tightened. The forefoot region of the upper shoe and the treads were wrapped in duct tape. This also helped to secure the spring – plate system to the upper.

In order to reduce overpronation, the upper of the shoe was tilted outwards to counteract the eversion of the foot and reduce the pronation angle. To accomplish this, a zip tie was attached on the outside portion of the shoe at the middle of the foot. It was tightened enough to compress on side of the shoe, thereby tilting the shoe outwards while keeping the sole completely flat to the ground. The final prototype can be seen in Figure 3.

In order to test our shoes effectiveness we made use of the Belmont University motion analysis lab under charge of Dr Kevin Robinson. A plantar pressure analysis was made where the subject walked on pressure transducers that electronically measured the pressures in the foot so the areas

Figure 2: Pressure Map from heel to balls of feet, red stars indicate spring placements

of highest and lowest pressure could be identified. From plantar loading data the maximum and average pronation angle as well as the maximum and average deflection could be determined. This test was repeated for running. We also used Vicon computerized gait analysis where small reflective markers are taped to the subject’s feet (or shoes), legs and torso. Markers were located at the right and left bilateral ASIS (anterior superior iliac spine), right and left PSIS (posterior superior iliac spine), right and left lateral mid-femur, right and left lateral joint of the knee, right and

left lateral mid fore leg, right and left lateral mallelous, and in between the second and third metatarsal heads on both feet. Eight state of the art, high speed video cameras record the motion of these markers as the subjects walks or runs down a designated path. Then a 3-D model was generated on the computer. Gait analysis or motion analysis is a quantitative assessment of coordinated muscle function. It is intended to describe motion based on kinetic and dynamic measurements and visual recordings. Kinetics describes the mechanisms that cause movement. These are ground-reaction forces and joint movements. They require acquisition of joint motion and force plate data in order to be calculated. Once you have an analysis of specific gait characteristics you can describe patterns or abnormalities in motion. An AMTI-force platform collecting at 1000 Hz was mounted flush in the middle of a wooden track. Video data were also collected at 1000 Hz using eight infrared M2 cameras and Qualisys software. This particular orientation enables the markers to define the anatomical coordinate system. Following a standing calibration trial, the subject participated in a series of tests. One trial was barefoot, followed by the Adidas 1, the prototype and the Asics shoe. Each test was at a subject speed of 4.5 mph. A trial was considered as valid when the following criteria were met: a heel-strike pattern, running speed within the outlined boundaries, and no visual adjustment in gait pattern to contact the pressure plate.

Modeling

Running is a complicated kinematic process and much work has been done to model it. In this project, we chose to limit our scope to the pronation angle of the ankle joint, forgoing modeling the rest of the motion. There are several reasons for this approach. First, we were limited in both computational power and programming knowledge, so it was best that we kept the model as simple as possible. Furthermore, we wanted to be able to optimize the model using stochastic methods for which many simulations are necessary, so regardless of our ability to create a complex model the time required for each simulation had to be quite small. Second, we had the ability to map the pressures on the foot via a flat transducer and to track various angles on the person using motion capture. Since we had decided to place the focus of the design on the

Figure 3: Final Prototype

suspension of the shoe rather than support at the upper or ankle itself, it seemed natural to try and isolate this system from the plane of the pressure map on down. This was advantageous because it allowed us to avoid modeling contact between foot and sole. It presumes, however, that the pressure map can be taken as an input when in fact it is dependent on the dynamics of the shoe used when it was measured. This assumption was mitigated by using a shoe with a fairly even suspension as our benchmark. In the end, three approaches were considered; finite element methods, a MATLAB Simulink model, and a state space representation.

Finite element methods were one obvious possibility for modeling the suspension of the shoe. They are good at showing trends when properly executed and can deal with complex geometries and arbitrary inputs like our pressure maps. Also, one of our team members had some experience with FEM. Despite these advantages, this approach was not chosen. Speed of simulation was a concern as dynamic models tend to eat CPU time. Tuning the many parameters of such a model was also a concern, since the ability to model complexity necessarily brings complications with it. Not only must the model be tuned, but to optimize anything it must be changed programatically using the particular FEM package's scripting language. Our programming expertise was in MATLAB, and from past experience with ABAQUS and the Python scripting language it was known that getting the two programs to interact was not trivial for someone who does not know both languages. Finite element models can be quite finicky, and any instabilities or errors can quickly muddle the optimization algorithm or bring it to a halt altogether without good error checking. This is particularly frustrating if the optimization time is long. Thus, the difficulties involved with setting up this type of model were deemed too troublesome to go through for a project of this scope, although it could be appropriate if hefty processing power were available and the team had the programming know-how to interface their FEM package with their optimizer.

After excluding FEM, the next choice was a block diagram type model in MATLAB's Simulink. Specifically, Simulink has a module called SimMechanics for representing machines. Building a model in Simulink requires little programming knowledge, just a firm grasp of block diagrams and some functions for manipulating the block parameters. SimMechanics is a bit different from the rest of Simulink, however, and learning to use it took considerable time and effort. The block diagram representation is a double-edged sword; its simplicity is both its greatest strength and weakness. SimMechanics, for instance, can only model rigid bodies. Furthermore, these bodies have lumped parameters in the sense that the distribution of mass throughout the body is represented somewhat abstractly by a single inertia tensor, as opposed to FEM which concretely discretizes an arbitrarily shaped body. Noting however that most running shoes today have fairly rigid, nearly planar plates in the sole and that the inertance of the shoe is dominated by the compliance of its suspension, we felt that these limitations were not crippling and that we could give a fair approximation of the shoe as a rigid body with springs beneath it. SimMechanics has several built in blocks for representing compliant elements as well as the possibility to model custom elements using appropriate gains and feedback loops. One challenge was how to apply the input forces; we had a high-resolution pressure map but SimMechanics only allows for point force applications, and it is computationally infeasible to apply over 1000 point forces simultaneously. To work around this, we noted that in the pressure map there are a few critical regions which sustain the highest loads while other regions remain fairly untouched. These regions can roughly be described as the heel, the balls of the feet, and the toe. Thus, we would

attempt to discretize our pressure map by consolidating the pressures in these regions into a few manageable point loads. With these assumptions made, the modeling was begun. Immediately, complications arose and continued to crop up at every turn. There were degree-of-freedom issues with the joints in the SimMechanics models. During testing with sinusoidal forcing functions, the spring elements often went singular and these errors were difficult to find. Programmatic manipulation of the SimMechanics blocks was not as simple as it first appeared, and modeling variable compliance with the pre-made blocks proved to be impossible. This led us to abandon the spring element blocks and design our own using feedback loops and actuators acting directly on the body. This reduced the number of joints and blocks in the model and our feedback loops worked smoothly in initial testing, but ultimately these were simply too slow. Simulink could handle one or two of them, but any more than that succeeded only in bringing the CPU to a slow and painful grind by reducing the average step size to ~10 -4 or in the case of the variable compliance elements, 10-6 seconds. The result being that seconds of simulation turned into minutes or more often, a singularity error and a full stop near the end of the transient response. Various solvers and solver configurations available in Simulink were tried but none seemed to perform any better than the others. Thus, after 3 different builds of the model and many lessons learned, the Simulink model was scrapped entirely and we moved on to the realm of the tried and true state-space representation.

State-space is a reliable way to model linear time-invariant systems in a computer setting. The MATLAB control systems toolbox is well equipped for modeling these systems not only in state space but also in transfer function and zero-pole-gain representations. To model our shoe, we took two rotational and one translational equation of motion corresponding to plantar flexion and dorsiflexion, inversion and eversion, and vertical deflection, respectively. The equations of motion are

(1)

(2)

(3)

where are the rotations about the x and y axes, x and y are measured from the center of gravity of the plate for all i spring-dampers and all n forces of magnitude F, and z is the vertical deflection of the center of gravity. J1,2 are the moments of inertia about the x and y axes and m is the mass. States are chosen to be the rotations and their first deriviatives and the deflection and its first derivative. Inputs are all the terms on the RHS of equations (1)-(3). Outputs are are the rotations and deflections themselves. This choice of states, inputs and outputs leads to the following state space representation;

where and .

In practice, this means that we choose a number of springs i each with a different stiffness k and damping constant b to place beneath the plate, which is loaded with n forces obtained from each cell of the pressure map. In MATLAB, this system is easily implemented with the sys() function and evaluated for the arbitrary input with a call to the lsim() function.

This model turned out to be far more stable than the simulink model, and it is certainly fast. After testing the model for stability, we performed a targeted optimization on all three outputs. For a first test, the targets were chosen to be no more than 30 degrees of flexion in either direction and no more than 10 degrees of in/eversion. The vertical deflection target was set at 0.25 inches. The model had no trouble hitting the targets for angular displacement, but at the cost of a very low vertical deflection of 0.025 in. This was true at other targets too; getting enough rotational stiffness to

maintain stability necessitated a high translational stiffness as well. In the first optimization, the model was allowed to vary position and compliance of 3 compliant elements. In practice however, we did not have such general elements. Our springs had a stiffness of 450 lb/in and no damping, and no more than two would fit in the shoe at once. Therefore, the model was optimized given two springs of fixed stiffnesses but variable position. The optimized response and spring placement superposed onto the pressure map of the foot are shown in Figure 2 and Figure 4. Since our springs were undamped, the system response shows considerable oscillation.

The optimization itself was done using a particle swarm optimization algorithm. Swarm sizes of both 10 and 20 were tried, with no grossly apparent differences in performance. The algorithm typically found a good solution within 100 iterations, or 1000 calls to the state space model function. Thus, depending on the number of springs used and the range of their properties and degree of convergence desired, an optimization might take from 2 to 5 minutes beginning with random initial conditions. A good set of starting solutions would speed this up a good deal.

Results

The results of the experiment are summarized in Table 1 and the graphs for sample trials of each shoe are in the appendix. For each shoe, Asics, Prototype, and Adidas, three trials were taken using the motion capture cameras. The magnitude of the pronation angle was measured by subtracting from a given peak in the angle the

Shoe Prototype Asics Tiger Adidas 1Foot R L R L R LAverage Pronation 14.8 13.9 18.3 28.5 16.1 23.4S. Error 1.26 1.13 2.48 0.652 0.301 0.159t-score 1.56 1.88 1.86 1.53 0.303 0.347p-value* 0.090 0.067 0.080 0.085 0.384 0.367Table 1: Average pronation angle for Prototype, Normal Running Shoe, and Top of the line Model

Figure 4: Flexion in red, in/eversion in green, vertical deflection in blue.

preceding trough. Disregarding noise, measurements for all trials were averaged together for each foot. Differences amongst shoes were readily apparent, and t-tests between the mean pronation for each shoe show that the observed differences are significant, with the prototype controlling pronation the best. In addition to the pronation angle, the z deflection, or the ground reaction force (GRF), was measured for each shoe and barefoot while walking. Here the prototype had higher GRF than the other shoes for the toe-off, although the heel strike appeared to be somewhat lower. This could be the result of the relatively loose suspension in the back and hard, springless sole at the toe. This same construction might help to explain the pronation control; giving the heel the freedom to move allows the body to avoid pronation, while a more solid suspension beneath the heel forces pronation by holding the foot in place such that is has no place to go. The graphs showing the results of the GRF are also in the appendix.

Conclusions and Recommendations

There was no problem controlling the response of the model using variable compliance elements. Using the particle swarm optimization algorithm, the desired response could be obtained within minutes. In testing, the prototype we constructed succeeded in controlling the rearfoot pronation of our test subject. This was in contrast to his usual running shoe, a pair of Asics, and the top of the line Adidas 1. Qualitatively, his normal shoe was most comfortable to him and he did not like the Adidas. He found the prototype surprisingly comfortable and liked the novel feel of the suspension. While we did have optimal spring placements from the model, it is still unclear the extent to which the model represents the real kinematical situation of running. After this experiment, we hypothesize that it is our exceptionally loose rear suspension that controlled the pronation, allowing the heel to go where it needed to dissipate the impact of running without buckling. The very stiff suspension under the toe then allowed for a solid pushoff. As can be seen in Table 1, the pronation on the left foot tends to be larger than that of the right foot. This discrepancy is caused by the fact that our test subject has legs of two different lengths. In order to compensate for this in our shoe, we were able to manually fasten the side of the left prototype such that there was an increased pronation correction. This demonstrates the importance of tilting the upper in pronation correction. As far as the cost for our shoe, most of our materials were obtained as free samples or as donations. In fact, the most expensive element of our project was purchasing the Adidas 1 for testing purposes. However, since our design is relatively simple and modifications were primarily done only on the midsole, we speculate that the cost of manufacturing our shoe on a large scale would be comparable to the average running shoe on the market.

For future models, we would like to introduce some damping into the system as well as a variable stiffness element. The design and construction of such an element would be foremost for future incarnations of the shoe, as such a device is not readily available with high stiffness modulation and low power. It is hoped that damping elements in the system could also be used to produce the power necessary for stiffness modulation. The design of a suitable control system also remains a considerable challenge. Also, it would be a good idea to use a firm and light weight plastic to replace the aluminum rigid plates and springs can be permanently fixed in casings once the optimal placement and stiffness was found. Titling the upper plate also proved to fix pronation, so in future prototypes it would be wise to implement this facet of the design by using an adjustable strap allowing the runner to vary the degree of the pronation angle.

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Appendix

Budget

Adidas 1's- $275Glue, zip ties, fasteners- $20Shoes- freeSprings- free samples

An Alternative Approach from Dan ThomasThe initial mission for the prototype was to have adjustable cushioning, flexibility and motion control. The vision of the shoe is to make these three traditionally static variables tunable. The first prototype dabbled with an inflatable spiral-tube tube technology. The spiral design was intended to compete with Nike’s Air-Max technology (a foot-shaped bladder with seamless pillars built in) in providing a more a stable form of cushioning that is also adjustable. The mechanism was intended to more slowly redistribute air after impact by forcing the pushed air to ‘circle around’ instead of going only in one direction. ¼” medical latex tubing was wound in a spiral and sandwiched between the upper and outsole, where the midsole is traditionally located. The upper and outsole were taken from a Saucony running shoe. However, after experimenting with this prototype it became apparent that the air-redistribution design efforts did little to actually stabilize the platform. Further stabilization might have required strategic pillar reinforcement and the ability to vary channel size – however these solutions were beyond the scope of our fabrication and modeling abilities, so the concept was tossed.

Our model represented the shoe as a rigid platform, suspended by springs. With this in mind our first prototype incorporated a bike shoe with a rigid carbon fiber midsole. The tread of the shoe was shaved down and the carbon-fiber foot plate was cut at the perpendicularly from the lateral plantar fascia area to the medial plantar fascia. Given that the impact of heel strike is 3-5 times as much as the bodyweight, we then allocated springs from Smalley Spring Co. The spring rates were chosen considering the weight of our test runner and assuming that heel impact is bodyweight x 4 and toe-off is bodyweight x 3. While the wavesprings were advantageous in providing more deflection and less weight than coil-springs, these springs literally crumple under shear force and need side-support to restrict movement in the x and y direction. These springs are normally housed in cylindrical chambers. For the shoe, the springs were instead wrapped in duct tape and reinforced silicone rubber. Two springs (1” tall by 2” diameter) were strategically positioned: one beneath the heel rocker and one beneath the ankle rocker to optimize energy return in these area. In addition to springs, Dan contributed to motion control by implementing his dual-chamber adjustable motion (DCAMC) concept, in which two inflatable gum rubber tubes stabilize the medial and lateral sides of the foot. The tubes are sealed on one end by a gum rubber stopper and on the other with a Schrader valve allowing the bladder to inflate. This technology is allow’s the runner to increase both support in the medial or lateral foot areas to correct pronation or supination. Dan’s original design, used ¾” diameter gum rubber tubing, because the lighter, flexible latex rubber tubing could not withstand a suitable range of pressures. Silicon rubber was then used as the conduit for the entire midsole; it was predicted that the springy nature and flexibility would enhance the already energy-efficient shoe. However, the superfluous amount of silicone burdened the shoe.

A second prototype was then made using Polyurethane (PU) foam, donated from a local orthotics company, as the midsole component. This material, while not springy, is lighter and more stable than silicone rubber. Also a lighter football cleat was chosen for the upper, A cylindrical holes were bored at the spring locations. The piece of PU was then shaped using sanding and heating methods. Due to the constant tweaking necessary and the unforgiving time constraint of glue, zip ties were used to bind the upper to the midsole. After shaving down the cleat to a thin plastic platform, holes were drilled through the sole and sides, to accommodate the binding zip-ties. This model, while lighter was still quite heavy and too high. The team felt that excessive weight and height of the first two prototypes would cause the test runner to alter their stride and possibly skew the data.

The team decided not to accept Dan’s DCAMC technology because of the continuous and interdependent dynamic nature of the rubber tubing would interfere with the mathematical model of a rigid-plate/spring system.

Due to the incongruency of DCAMC with the rest of the report, Dan’s withheld his intellectual property from the report and covered the DCAMC development expenses himself. The DCAMC system , however in his free time Dan was able to make a practical prototype with a normal heel height and weight of 18 ounces. This super-shoe concept handles adjustable pronation by using removable Kevlar-fiber insoles which come in a variety of stiffness. The air-chambers were shortened and the springs removed to lower weight and height.

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