Development of a Dynamic Cushioning System for Running Shoes

2007-08 SAIF Final Report

Submitted by:

John A. Mirth, Ph.D. Professor

Department of Mechanical and Industrial Engineering University of Wisconsin – Platteville

mirth@uwplatt.edu

August 22, 2008

SAIF 2007-08 – page 1

Development of a Dynamic Cushioning System for Running Shoes Abstract

This proposal describes a project to perform prototype testing on a novel cushioning system

for use in running shoes. The project involved the design and testing of a number of

configurations. The goal was to produce a design that would effectively transfer the impact

forces associated with running into a motion that flexes the forefoot of a running shoe. Designs

considered include those based on four-bar and six-bar geometries. The final design is

distinctive in that it appears to allow for a combination of energy return and shoe flex within a

relatively compact volume. The proposed design appears to be unique enough that a patent

could be pursued for the design even though a few issues are not fully resolved.

Introduction

The goal of the project outlined in this report was to perform prototype testing on a novel

shock absorption system for athletic shoes. The design under development relies on the ability to

effectively adapt a “compliant linkage” into the shock absorbing system for a running shoe. This

is a unique design in the realm of running shoes with the opportunity to pursue a patent for the

shock absorption system along with possible commercial development.

The following subsections provide some background for the project with a brief

introduction to running shoe technology and compliant linkages.

Running Shoe Technology

The running shoe industry is a 2.5 billion dollar industry with approximately 55 million

shoes sold each year in the United States [1]. Over the last 30 years running shoes have

developed from a simple foam cushioning system to today’s sophisticated cushioning systems

designed to stabilize the foot while providing some combination of cushioning and flexibility.

SAIF 2007-08 – page 2

A significant challenge in the design of running shoes is providing a proper balance between

cushioning, stability and flexibility while minimizing the amount of energy lost during ground

contact [7]. Innovations designed to meet these needs include “Nike Air”, “Asics Gel”, “Nike

Shox”, and the “Varus Wedge”, among others. A number of patents exist which reveal attempts

to provide more “energy return” in running shoes. References 2-6 provide a small sample of

these with one of the less practical systems shown in Fig. 1 [2]. No patent claims have been

found where a single, compact system

addresses the issues of cushioning, energy

return and flexibility in a manner similar to

the design developed in the current project.

The use of a compliant linkage in a running

shoe appears to have significant potential to

unify some of these conflicting design goals.

Compliant Mechanisms

A compliant mechanism is defined as a mechanism that gains some or all of its mobility from

the bending of flexible members. For example, Fig. 2 shows two positions of a mechanism that

achieves mobility from a set of rigid links connected to one another with revolute (pin) joints.

The same mechanism is shown in Fig. 3 with thin flexible members (flexural pivots) replacing

the joints. The mechanism shown in Fig. 3 has a number of possible advantages including lower

cost (fewer parts), and the ability to absorb and store energy as it moves.

The field of compliant mechanisms is relatively new. While flexible joints have been

utilized for many years [8-9], their application to linkages is more recent. Relevant works in this

SAIF 2007-08 – page 3

a) Initial Position b) Deflected Position

Figure 2: A pin-jointed mechanism in two positions

Figure 3: The fully compliant equivalent of Fig. 2a

area include papers that develop the mobility conditions and equations for compliant linkages

[10-16] and those relating methods for the fabrication of compliant linkages [17].

The use of compliant linkages in running shoe design seems to be a good application for

compliant linkage technology. A compliant linkage can both store energy and provide flexural

motion when subjected to an input force. The flexural pivots can also be “tuned” to provide

necessary stability without undue loss of flexibility.

The research completed in this project focused on the development of a compliant linkage

geometry that uses the ground impact forces of the running motion to cushion and flex a running

shoe. The project included several phases. The first was to determine the necessary complexity

of the compliant mechanism to produce the desired motion. This included trials with both four

and six-bar based geometries. Each trial included the development of a pin-jointed model, an

equivalent compliant mechanism, and a physical prototype of the compliant mechanism. The

following sections present the results of this testing for several four and six-bar geometries.

SAIF 2007-08 – page 4

Development of Mechanism Geometry – Four-bar based designs

The challenge of mechanism complexity is to define a mechanism with the simplest possible

geometry that is still capable of producing the desired motion. In the realm of mechanisms, this

typically begins by examining “four-bar” configurations. These configurations, such as the one

shown in Fig. 4, contain 3 moving links and a stationary (or ground) link. Several four-bar

geometries were examined during the development process. These are shown in Figures 4

through 8.

The mechanism shown in Figures 4 through 6 is perhaps the simplest available geometry

capable of producing the flexing motion needed for a running shoe. An applied vertical force is

capable of flexing the forefoot through an angle of approximately 45 degrees, as shown in Fig. 4.

In addition to being simple, the geometry has the advantage of flexing for any force applied to

the top links. Thus, any landing or toe-off force (heel, midfoot, or forefoot) is capable of

providing the desired shoe flex.

Figure 4: A pin-jointed 4-bar mechanism with good motion characteristics.

SAIF 2007-08 – page 5

The pin-jointed mechanism in Figure 4 is converted to the compliant linkage in Figure 5 by

replacing the pin joints with flexible compliant segments. One significant challenge in this

conversion is determining the proper lengths of the flexible segments. In this case, the lengths

were kept relatively short to provide better motion control. The one exception is the joint that

goes under the ball of the foot on the top of the mechanism. This joint has to be somewhat

longer to “wrap around” the foot to avoid any sensation of pinching as the shoe flexes.

Figure 5: The compliant equivalent of the mechanism from Fig. 4.

The physical prototype of the compliant mechanism in Fig. 5 quickly revealed some

shortcomings of this particular geometry. Because the compliant segments do not provide the

same rigid center of rotation as a pin joint, the motion of a compliant linkage can be dependent

upon the combination of forces applied. This is shown in Fig. 6. The desire is to produce a

flexing motion under the application of a vertical force. Such a force applied to this model

simply “squishes” the mechanism without any flexing as shown in Fig. 6a. Figure 6b shows the

combination of forces that must be applied to get the desired flexing of the mechanism.

SAIF 2007-08 – page 6

Figure 6: The motion of the compliant mechanism under applied loads.

The inadequacies of the above design led to the development of a second four-bar geometry.

This is shown in Fig. 7. The physical prototype of this model demonstrated fairly good motion

characteristics under an applied force. This motion is shown in Fig. 8. The primary shortcoming

of this mechanism is that the forefoot area is a single, solid link. A vertical force applied in the

forefoot region will not actuate the mechanism. One of the design goals is to produce a design

where a force applied to the forefoot will flex the mechanism. As such, the design shown in Fig.

8 is adequate, but less than optimal.

The four-bar mechanisms presented in this section provide a sample of the results from

testing various four-bar geometries. The test results suggest the need for a more complex

mechanism geometry. The next section presents the development of one such geometry.

SAIF 2007-08 – page 7

Figure 7: A second four-bar design and its compliant equivalent.

Figure 8: The response of the mechanism to an applied vertical force.

SAIF 2007-08 – page 8

Development of Mechanism Geometry – Six-bar based designs

A six-bar mechanism contains five moving links and one fixed link, as shown in Fig. 9.

More joints and links provide better opportunity to develop a design where compression in the

rear, middle, or front of the sole produces a flexing motion in the forefoot area of the shoe.

A number of six-bar geometries were designed and simulated. The simulations all pointed

toward a couple of necessary guidelines to produce the desired motion. These were:

1. The designs have two motion loops, one under the heel and one under the forefoot.

2. The designs have a short, somewhat vertical, link under the forefoot to actuate the

forefoot motion.

The best design found with the above characteristics is shown below in Figures 9 through 11.

Figure 9 shows the pin-jointed geometry and its motion. Figure 10 shows the compliant

equivalent and Figure 11 shows the motion of the compliant mechanism under loading.

One significant note related to figures 9 and 10 is the question of whether or not these are

actually equivalent mechanisms. The mechanism in Figure 9 contains six links and seven joints.

The one shown in Fig. 10 contains 5 rigid segments (instead of the expected 6) and 6 flexible

segments (instead of the expected 7). The short red colored link in Fig. 9 is actually missing

from Fig. 10. This link is replaced by a single compliant segment in Fig. 10. As a result, the

mechanism in Fig. 10 appears to have no mobility. However, the compliant nature of the

flexural segments allows for short links to be replaced by a compliant segment without changing

the mobility characteristics of the mechanism. The net result is that the mechanisms do produce

the same approximate motion.

SAIF 2007-08 – page 9

Figure 9: A pin-jointed 6-bar mechanism with good motion characteristics.

Figure 10: The compliant equivalent (???) of the mechanism from Fig. 9.

SAIF 2007-08 – page 10

The testing of the compliant mechanism produced reasonably good results. Samples of the

tests are shown in Fig. 11. These demonstrate the effect of equivalent loading at various points

along the shoe. The more that a runner’s weight is transferred forward on the shoe, the more

flexing that occurs in the shoe. The prototype also demonstrates a small amount of compression

in the forefoot area so that the flexing is not lost as the runner rolls from heel to toe-off.

Figure 11: Deflections resulting from a variety of applied forces.

SAIF 2007-08 – page 11

While the mechanism shown in Figures 9 through 11 demonstrates good promise, it too has

some shortcomings. The mechanism requires about an extra half inch of height for the sole of a

running shoe. The mechanism will also require some additional cushioning system, such as a

foam layer between some of the mechanism links, to fully absorb the impact forces associated

with running. Experiments have not yet been conducted to determine how such a cushioning

layer would alter the flexural behavior of the mechanism.

Conclusions and Recommendations for Further Study

The goal of this project was to develop a mechanism to convert the impact forces in a

running shoe into a motion that flexes the forefoot of the shoe. A six-bar style mechanism has

been produced that appears to satisfy this goal. The development produced good results and is

perhaps at a point where a patent application should be considered. The mechanisms produced

have successfully demonstrated the ability to use a compliant mechanism to convert a vertical

force into a flexing motion consistent with that found in a typical running shoe.

Full development of the concept requires some further study in several areas, including:

1. A study on the effect of adding additional cushioning between the members of the

mechanism. This cushioning may alter the motion characteristics of the mechanism.

2. A study on the effect of short links. As noted above, the final prototype was

effectively missing one link. In retrospect, this suggests that design options for

compliant mechanisms are not limited to the same options (four-bar, six bar) required

for pin-jointed mechanisms. A truly optimal solution may lie in a five or seven bar

mechanism that cannot be simulated by a pin-jointed mechanism.

Even with the above areas of uncertainty, the research has demonstrated the viability of the

proposed concept.

SAIF 2007-08 – page 12

References 1. Pribut, Stephen; and Richie, Douglas, 2004, “Separating the Buzz from the Biomechanics:

A Guide to Athletic Shoe Trends & Innovations,” Podiatry Management, Oct. 2004, pp 85-97.

2. Rennex, Brian G., 1990, “Energy Efficient Running Shoe”, US Patent No. 4936030. 3. Schmid, Rainer K., 2005, “Energy Return Sole for Footwear”, US Patent No. 6944972. 4. Gallegos, Alvaro, Z., 1995, “Spring Athletic Shoe,” US Patent No. 5435079. 5. Derderian, Thomas; Frederick, Edward C.; Gross, Alexander L., 1983, “Shock Absorbing

Sole Layer,” US Patent No. 4535553. 6. 8. Marvin, William; Christiansen, Brian; Litchfield, Paul E., and McInnis, William, 2006,

“Cushioning Sole for an Article of Footwear,” US Patent No. 7080467 7. Cavanaugh, Peter (editor), 1990, Biomechanics of Distance Running, Human Kinetics,

Champaign, IL. 8. Tuttle, S.B., 1967, Mechanisms for Engineering Design, Chapter 8: Semifixed Flexural

Mechanisms, John Wiley and Sons, Inc., New York, New York. 9. Stein, P.K., 1964, Measurement Engineering, Chapter 11: Flexural Devices in Measurement

Systems by R.N. Motsinger, Stein Engineering Services, Phoenix, Arizona. 10. Hetrick, J. A., and Kota, S., 1999, “An Energy Formulation for Parametric Size and Shape

Optimization of Compliant Mechanisms,” ASME Journal of Mechanical Design, Vol. 121, No. 2, pp. 229-234.

11. Howell, L. L., and Midha, A., 1994, “A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots,”, ASME Journal of Mechanical Design. Vol. 116, No. 1, pp. 280-290.

12. Larry L. Howell, Compliant Mechanisms, Wiley, 2001 13. Howell, L.L., and Midha, A., 1994, "The Development of Force-Deflection Relationships

for Compliant Mechanisms," Machine Elements and Machine Dynamics, DE-Vol. 71, 23rd ASME Biennial Mechanisms Conference, pp. 501-508.

14. Howell, L.L., Midha, A., and Norton, T.W., 1996, "Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms," ASME Journal of Mechanical Design, Vol. 118, No. 1, pp. 126-131.

15. Salamon, B.A., and Midha, A., 1992, "An Introduction to Mechanical Advantage in Compliant Mechanisms," Advances in Design Automation, (Ed.: D.A. Hoeltzel), DE-Vol 44-2, 18th ASME Design Automation Conference, pp. 47-51.

16. Frecker, M.I, Kikuchi, N., and Kota, S., 1996, "Optimal Synthesis of Compliant Mechanisms to Meet Structural and Kinematic Requirements-Preliminary Results," Proceedings of the 1996 ASME Design Engineering Technical Conferences, 96-DETC/DAC-1497.

17. Mortensen, C.R., Weight, B.L., Howell, L.L., and Magleby, S.P., 2000, "Compliant Mechanism Prototyping," Proceedings of the 2000 ASME Design Engineering Technical Conferences, DETC2000/MECH-14204.

18. Mattson, C.A., Howell, L.L., Magleby, S.P., “Development of Commercially-Viable Compliant Mechanisms Using the Pseudo-Rigid-Body Model: Case Studies of Parallel Mechanisms,” Journal of Intelligent Material Systems and Structures, Vol. 15, No. 3, pp. 195-202, March 2004.

19. http://www.et.byu.edu/~llhwww