Substantial energy return shoe with optimal low-impact springs and tuned gear change

• US 20160302521A1
• Filed: 04/16/2015
• Published: 10/20/2016
• Est. Priority Date: 04/16/2015
• Status: Abandoned Application

• Current Assignee: Brian George Rennex
• Original Assignee: Brian George Rennex
• Inventors: Rennex, Brian George
• Application Number:
  US14/545,274
• Publication Number:
  US 20160302521A1
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: A43B 13/141 with a part of the sole being flexible, e.g. permitting articulation or torsion
• CPC Class Codes: A43B 13/145 Convex portions, e.g. with a bump or projection, e.g. 'Masai' type shoes
• CPC Class Codes: A43B 13/183 Leaf springs
• CPC Class Codes: A43B 13/184 the structure protruding from the outsole
• CPC Class Codes: A43B 3/34 with electrical or electronic arrangements
• CPC Class Codes: A43B 3/38 with power sources
• CPC Class Codes: F16F 3/02 with springs made of steel or of other material having low internal friction
• CPC Class Codes: F16F 3/0876 and of the same shape
• CPC Class Codes: Y10S 901/01 Mobile robot

Abstract

The optimized shoe invention comprises five embodiments and two methods to optimize both the performance and comfort of footwear for walking and running and for robotics, prosthetics and orthotics. First, there are three versions of enhanced heel-lift shoes for energy return much higher than that of just “springs in shoes.” Second, to minimize foot impact shoe there are ten enhanced optimal springs with 1% hysteresis loss. Third, for ankle and knee joints there is a rotating-arms enhanced optimal spring. Fourth, said enhanced optimal springs are incorporated into conventional shoes. Fifth, there is an automatic gear change mechanism to change the sole spring stiffness so that the sole is always close to full compression—so that the performance and comfort is always optimal. The optimal force curve method features a pre-loaded constant force curve tuned to a particular use. The shoe tuning method provides precise sole energies by slicing springs.

Claims

1. An optimized shoe for walking and running by humans and robots, wherein the applications for humans include normal human use, prosthetics, and orthotics, wherein the stance period is divided into a compression period and an expansion period, wherein the entity wearing and using the shoe is called the user, wherein said expansion period comprises a heel-lift period and a toe-off period, wherein said optimized shoe comprises a heel-pop shoe which comprises

a compressible sole,

a top load surface on the upper side of said compressible sole further comprising a footplate hingeably connected to a toe plate by a toe hinge,

a bottom load surface called a groundplate on the lower side of said compressible sole, wherein said compressible sole further comprises

a toe section,

a forefoot section, and

a heel section, wherein said compressible sole further comprises

a spring system which resists compression and which stores the impact energy of compression and

a heel-pop mechanism also called an enhanced heel-lift mechanism to lift said heel section during said heel-lift period by a distance that is substantially greater than the distance over which said heel section is compressed during said compression period which distance is called herein enhanced heel-lift, wherein said heel-pop mechanism provides energy return that is substantially greater than that of conventional shoes which do not have said heel-pop mechanism, wherein the significance of said energy return is that the metabolic energy cost of running is substantially reduced.

2. The optimized shoe of claim 1 wherein the resilient elements of said optimized spring system are made of fiberglass composite, wherein fiberglass is the significantly preferred material because it has very low mechanical hysteresis loss of approximately one to two percent as compared to approximately 20-50% for injection moldable materials such as thermoplastic polyurethanes (for example, pellethane 2363 or PEBAX 5533), wherein any other material with critical parameters for flexibility and bending strength which are similar to those of fiberglass can also be used, wherein the critical parameter for flexibility for said arch springs is the elongation limit of either the fiber or of the geometrical construction of the fiber.

3. The optimized shoe of claim 1 wherein said spring system comprises an optimal spring system with an optimal force curve, wherein the force-curve optimization goal for said optimal force curve is to maximize the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein the first part of a method to achieve a desired optimal force curve is to pre-load it and the second part is to vary the spring structure and shape so as to achieve a softer, more constant force curve, wherein the components of said optimal spring system are pre-loaded so that the force at the beginning of the optimal spring compression is a predetermined value (for example one-third the force value at full spring compression), wherein the work done by said spring system is the area under the curve of the force versus the spring deflection, wherein said work is accomplished with a reduced value of the maximum force point value as compared with the maximum force value point when there is no pre-load and as compared with a linear force curve, wherein said pre-load is accomplished with a physical restraint such as a tether or such as a structural restraint wherein the first criterion for said optimal force curve is to pre-load said spring system and the second criterion for said optimal force curve is to create a geometry so that the slope of the force curve decreases or even approaches zero throughout the latter said sole compression.

4. The optimized shoe of claim 1 wherein said spring system comprises a set of enhanced arch springs each of which is constructed from one or more arch spring types, wherein each said arch spring type represents a combination of elemental curved springs in different orientations, wherein said elemental curved spring is also called a curved arm and it is a curved spring which substantially flattens to a flat plate under full compression, wherein the first arch spring type is said elemental curved spring, wherein the end of said curved arm (which is horizontal and approximately parallel to the adjacent base load surface) is called the base end and the end of said curved arm that is approximately perpendicular to or diagonal with respect to the adjacent tip load surface is the tip end, wherein the full compression thickness at full compression of said elemental curved spring is the thickness of said curved arm, wherein the approximate shape of said elemental curved spring is a quarter of a circle although the curvature may be somewhat different, wherein the elemental spring height of said elemental curved spring is approximately the radius of said quarter of a circle, wherein said elemental full compression thickness is substantially smaller than the elemental spring height possible by a factor of ten to twenty, wherein the first arch spring type is simply said elemental curved spring, wherein said tip load surface freely translates horizontally with respect to said base load surface, wherein the spring strength comparisons for said elemental curved spring are as follows, wherein the spring strength using fiberglass composite is approximately ten times stronger than the spring strength using carbon fiber, wherein the spring strength using fiberglass composite is approximately sixteen times stronger than the spring strength using said injection moldable materials, wherein the spring weight using fiberglass composite is approximately twelve times lighter than the spring weight using carbon fiber composite, wherein the spring weight for fiberglass composite is approximately eight times lighter than the spring weight using said injection moldable materials.

5. The optimized shoe of claim 1 wherein said spring system comprises one of more said arch spring types, wherein the second said arch spring type is called an arch spring in which two said elemental curved springs are combined to form the shape of an arch, wherein the left side of said elemental curved spring is the mirror image of the right side of said elemental curved spring constructed about the vertical line at the junction of the opposing said base ends, wherein the arch center is located where the base ends of the opposing said elemental curved springs join, wherein the third said arch spring type is called a mirrored arch spring in which case the upper concave downward said arch spring is mirrored about the horizontal line just below the opposing said tip ends of the upper said arch spring, wherein the said arch centers of the upper and lower said arch springs are loaded by their adjacent mirrored load surfaces causing the opposing said tip ends to move outward horizontally as said mirrored arch spring fully flattens, wherein said mirrored load surfaces do not translate horizontally with respect each other and instead they move vertically and directly toward each other during said spring compression, wherein the fourth said arch spring type is called a rolling mirrored arch spring in which case the top and bottom of said mirrored arch springs have a circular shape in which case said rolling mirrored arch spring can roll somewhat while it is being loaded by two surfaces which are translating horizontally with respect to one another, wherein the fifth said arch spring type is called a half mirrored arch spring in which case said mirrored arch spring is cut in half along a vertical line though its center when viewed from the side, wherein the sixth said arch spring type is called a curly v-spring in which case said elemental curved spring is combined with its mirrored image also called an inverted said elemental curved spring to form said curly v-spring which looks like the letter V turned on its side with each of its arms being curled in the shape of said elemental curved spring, wherein the seventh said arch spring type is called nested arch springs in which one or more said arch spring types is or are nested within another arch spring type to form a nested arch spring at one or more levels of nesting, wherein the base of said elemental arch springs are offset in the vertical direction with respect to each other so that when said nested arch spring fully compresses, each component said elemental curved spring is approximately horizontal along its entire length, wherein the total spring strength of said nested arch spring is increased over that of a single said arch spring albeit at the cost of an increase in the thickness of said nested arch spring at full compression, wherein all above said arch spring types and more complex variations made from them have similar force curves and behaviors to the force curves of said elemental curved springs of which they are constructed.

6. The optimized shoe of claim 5 wherein said arch spring types comprise

spring elements,

linkage elements, and

hinges, wherein said spring elements and said linkage elements are connected to each other with hinges, wherein one or more said hinges are conventional cylindrical hinges comprising shafts and bearings.

7. The optimized shoe of claim 3 wherein said optimal spring system comprises an enhanced optimal spring system which is constructed of said arch spring types, wherein said enhanced optimal spring system is designed to optimize the force curve for devices such as footwear where it is advantageous to minimize the maximum force point along the force curve (especially when there is an impact force) on said user, on the structural elements of said spring system and on the device within it is incorporated, wherein the force-curve optimization goal for said force curve optimized spring is to maximum the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein the first part of a method to achieve a desired optimized force curve is to pre-load it and the second part is to vary the spring structure and shape so as to achieve a softer, more constant force curve, wherein these changes in force curve can reduce said maximum force value by 25% to approximately 40% as compared to a spring system with a linear force curve, wherein there are two classes of enhanced optimal spring systems, namely an enhanced fully optimal spring system where the force curve becomes approximately constant during the latter part of compression and namely an enhanced partly optimal spring system where the slope of the force curve decreases to approximately half of its initial value during the latter part of compression, wherein when a non-linear finite element analysis is done to determine the maximum allowable thickness (and hence the maximum possible force) of said curved arms within the stress limits of the material of which said curved arms are made, the total energy absorbed (work done) per unit area by each said arch spring is linearly proportional to the full deflection value which is the deflection at full compression so that it is easy to achieve a particular total energy absorbed by simply choosing the corresponding said full deflection value, which means that the only way to change said total energy absorbed (work done) per unit area is to change said full deflection value, wherein the impact energy of running is absorbed by the compression of said compressible sole with the sole compression energy and by the compression of the leg of said user with the leg compression energy, wherein the third criterion for optimization of said sole compression energy is to determine the optimal sole compression energy by experiment and then to realize said optimal sole compression energy by choosing the corresponding particular said deflection value, wherein one or more said hinges are necked-down living hinges which permit a continuous monolithic construction between adjacent ones of said linkages elements and said spring elements.

8. The optimized shoe of claim 7 wherein said enhanced fully optimal spring system comprises first enhanced fully optimal spring system which is also called an internal linkage mirrored arch spring system which comprises

monolithic mirrored arches, wherein said monolithic mirrored arches belong to a tension spring class of tensioned springs which comprise said elemental curved springs and tension band springs,

mirrored spreader linkage, wherein said mirrored spreader linkage belongs to a class of spreader linkages which spread said tension springs, wherein the force curve for the loading of said spreader linkages first increases and then bends over to eventually go to zero at full spreading when the links of said spreader linkage become aligned, wherein this linkage spreading loading qualifies said first enhanced fully optimal spring system as a said enhanced fully optimal spring system,

one or more parallel auxiliary springs, and

one or more series auxiliary springs, wherein said parallel auxiliary springs act in parallel and in combination with monolithic mirrored arches to increase the combined force curve to become approximately constant as full compression is approached, wherein each of said monolithic mirrored arches further comprises a monolithic arch hinge which is a necked-down living hinge and which pivotally connects the top half of said monolithic mirrored arch to its mirrored image bottom half, wherein said mirrored spreader linkage further comprises on the top and on the bottom

center links,

mostly vertical links, and

impinger links, wherein said center links are pivotally connected to said mostly vertical links by monolithic corner hinges, where said mostly vertical links are pivotally connected to said impinger links by monolithic impinger hinges, wherein said series auxiliary springs are positioned between said center links and the centers of said top half and said bottom half of said monolithic mirrored arches, wherein said parallel auxiliary springs are positioned between the opposing said center links of said internal linkage mirrored arch spring, wherein both said series auxiliary springs and said parallel auxiliary springs may be positioned in pairs spaced horizontally away from each other to provide a restoring force to keep said center links horizontal during compression, wherein said impinger links push outward against said monolithic arch hinges to flatten said monolithic mirrored arches, wherein said series auxiliary springs control and moderate the initial spreading of said monolithic mirrored arch by said mirrored spreader linkage, wherein the linkage force curve of the vertical compression force on said monolithic mirrored arches is for the force that would be applied if there were no parallel auxiliary springs and it first increases and then bends over and goes to zero during compression, wherein the force of said parallel auxiliary springs increases as said linkage force curve decreases so as to make sum of these two force curves approximately constant, wherein this sum is called the first combined force curve which is for said first enhanced fully optimal spring system, wherein said first combined force curve meets the requirements of said enhanced fully optimal spring system, wherein said auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height, wherein said monolithic mirrored arches optionally comprise one or more nested monolithic mirrored arches nested within each other, wherein the strength of said internal linkage mirrored arch spring is increased significantly by the addition of each additional nested monolithic mirrored arch since its thickness is decreased only slightly.

9. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a second enhanced fully optimal spring system which is also called a link-spread curved spring system which comprises a link-spread curved spring and one or more second auxiliary springs, wherein said link-spread curved spring comprises

a second spreader linkage which comprises two or three links,

a second curved spring, and

link hinges, wherein said links are pivotally connected by said link hinges one to the other and at either end to the ends of said second curved spring via spring hinges, wherein the top one of said links is called the top link and it connects to the next link by the top link hinge, wherein the total length of the links comprising said second spreader linkage equals the length of said second curved spring so that said link-spread curve spring can fully flatten at full compression, wherein said top link hinge contacts said top load surface at the contact compression distance, wherein said contact compression distance can be adjusted by changing the lengths of the links of said second spreader linkage, wherein said second auxiliary springs comprise both an above top link hinge partial spring located between said top link hinge and top load surface and an adjust spring located adjacent to said second spreader linkage so as to be loaded directly between said top load surface and said bottom load surface, wherein said above top link hinge partial spring controls and moderates the initial spreading of said second curved spring, wherein the force curve of the vertical compression force on said link-spread curved spring is called the second force curve and it first increases and then bends over and goes to zero during compression, wherein the force of said above top link hinge partial spring increases as said second force curve decreases so as to make the combined second force curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said second auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

10. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a third enhanced fully optimal spring system which comprises a combined monolithic tensioned mirrored curved spring which comprises a monolithic tensioned mirrored curved spring and one or more third auxiliary springs which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said monolithic tensioned mirrored curved spring comprises an external quad linkage which is oriented like a diamond and which further comprises four monolithic quad links monolithically at the top and bottom connected by monolithic vertical necked-down vertices and on the two sides by monolithic horizontal necked-down vertices and a double mirrored curly v-spring tension element which further comprises four monolithic tension curved springs each of which is monolithically connected to monolithic horizontal necked-down vertices via a side vertex connection and each of which curves up (or down) until it is approaching vertical to connect to its mirrored image at the center via said monolithic vertical necked-down vertices, wherein said monolithic horizontal necked-down vertex further optionally comprises

a first necked restraint,

a monolithic loop, and

a retainer pin, wherein said monolithic loop is a monolithic continuation between said monolithic quad link and said side vertex connection and said retainer pin is inserted from the side through said monolithic loop, wherein said first necked restraint encloses said monolithic loop to reinforce it to withhold the considerable force exerted by said side vertex and said monolithic quad link via said monolithic horizontal necked-down vertex, wherein the third force curve for the vertical force needed to pull apart said double mirrored curly v-spring tension element first increases and then reduces to zero, wherein the vertical force imparted by said third auxiliary springs increases as said third force curve decreases so as to make the combined third force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said third auxiliary springs are preferentially said mirrored arch springs in which case all elements of said combined monolithic tensioned mirrored curved spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

11. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a fourth enhanced fully optimal spring system which comprises a combined band tensioned linkage spring which comprises a band tensioned linkage spring and one or more fourth auxiliary springs, which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said band tensioned linkage comprises

a quad linkage which is oriented like a diamond and which further comprises four quad links connected at the top and bottom by vertical hinges and on the two sides by horizontal hinges,

a tension band with band end loops on either end, and

a shaft, wherein both said band end loops and said quad links (near where they connect to said horizontal hinges) are slotted so as to interleave one through the other so that said shaft can be inserted through said horizontal hinges so as to connect said quad linkage to said tension band, wherein the fourth force curve for the vertical force needed to pull apart said tension band first increases and then reduces to zero, wherein the vertical force imparted by said fourth auxiliary springs increases as said fourth force curve decreases so as to make the combined fourth force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said fourth auxiliary springs are preferentially said mirrored arch springs in which case all elements said combined band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

12. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a fifth enhanced partly optimal spring system which is called a monolithic tensioned mirrored arch spring which comprises

an outer top-loaded arch spring comprising a top extended arch and a bottom extended arch each of which comprises an extended flat section at its center and an outer tip section where it connects to the other,

an inner side-loaded arch spring on the top half which connects to said outer-tip section on either end via inner tip section and via inter-arch section,

a pair of inner tension-loaded curly v-springs on the bottom half which connect to each other at the center via inter curly v-spring tip section and which connect to said outer-tip section on either end via said inner tip section and via said inter-arch section, and

a pair of outer-tip spacers which space apart said outer-tip sections so that said outer top-loaded arch spring can fully flatten without interference with said inner side-loaded arch spring or said inner tension-loaded curly v-spring, wherein said outer-tip sections are clamped to said outer-tip spacer by outer clamps and said inner-tip sections are clamped to their mirrored image said inner-tip sections via said inner clamps, wherein both said inner side-loaded arch spring and said inner tension-loaded curly v-spring are equivalent as inner tension elements and can be substituted for the other but only said inner side-loaded arch spring is mentioned the further explanation here, wherein said inner side-loaded arch spring is located inside of and pulls on said outer top-loaded arch spring via said inter-arch section, wherein these three elements form a continuous monolithic structure and they are interconnected via necked-down living hinges, wherein the slope of the fifth force curve—

for the vertical compression force needed both bend said outer top-loaded arch spring and to pull apart said inner side-loaded arch—

decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

13. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a sixth enhanced partly optimal spring system which comprises a tensioned band mirrored arch spring which comprises

a second tension band with second band end loops on either end,

a pair of mirrored band arches each comprising a center arch section and arch tips which impinge their mirrored image arch tips via said second tension band,

a second band retainer pin, and

a pair of band pivots, wherein said second band retainer pin is slid from the side through said second band end loops so as to prevent second band end loops from sliding through said arch tips which are compressing said second tension band, wherein the slope of the sixth force curve—

for the vertical compression force needed both bend said mirrored band arches and stretch said second tension band—

decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said tensioned band mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

14. The optimized shoe of claim 9 wherein said link-spread curved spring system comprises a seventh enhanced fully optimal spring system which comprises a combined tensioned links rotating arms curved spring system which comprises a tensioned links rotating arms curved spring and a seventh auxiliary spring, wherein said tensioned links rotating arms curved spring comprises

a top arm,

a bottom arm,

an arm hinge which connects said top arm and said bottom arm, and

a pair of said link-spread curved springs which are mirrored images of each other to form a configuration analogous to said curly v-spring, wherein said seventh auxiliary spring is positioned between said top arm and said bottom arm so as to engage them when they are partially folded, wherein on one end said spring hinges hingeably connect to said top arm and said bottom arm at mirrored positions, wherein on the other end said spring hinges hingeably connect and impinge each other, wherein the pivotal connection of these said second curved springs is preferentially achieved by a curved arch pivot which is a necked-down living hinge, wherein when the mirrored ones of said top link hinges impinge each other by the loaded folding of said top arm and said bottom arm about said arm hinge, the mirrored said spreader linkages straighten the mirrored said second curved springs, wherein the torque curve of said loaded folding is called the first torque curve and it first increases and then bends over and goes to zero during said loaded folding, wherein the torque exerted by said seventh auxiliary spring to resist said loaded folding increases as said torque curve decreases so as to make the combined torque curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said seventh auxiliary spring is preferentially said curly v-spring in which case all elements of said combined tensioned links rotating arms curved spring system flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

15. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises an eighth enhanced partly optimal spring system which comprises an end-refined curved spring which comprises a solid initial section and a stiffness-changing rotating end section, wherein said solid initial section is oriented at its base primarily horizontally and said solid initial section curves upward for a solid portion of said elemental spring height to rigidly or monolithically attach to said stiffness-changing rotating end section, wherein said curved end-refined curved spring is loaded at its bottom by said bottom load surface and at its top by said top load surface which freely translates horizontally with respect to said bottom load surface, wherein during the initial portion of said spring compression the spring deflection is primarily due to the flattening of said solid initial section, wherein during the latter portion of said spring compression said spring deflection is primarily due to the compression and flattening of said stiffness-changing rotating end section as it rotates, wherein the stiffness of said stiffness-changing rotating end section can be independently parameterized to be weaker, wherein the force curve for compression of said end-refined curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section, after which said force curve bends over to become softer, which meets the requirements of said enhanced partly optimal spring system.

16. The optimized shoe of claim 15 wherein said end-refined spring system comprises a ninth enhanced partly optimal spring system which comprises a kite end curved spring, wherein said stiffness-changing rotating end section comprises a kite end section which splits (at the lower vertex) partway up said solid initial section into two kite arch arms which rejoin at the kite top end at the upper vertex at the top of said elemental spring height to form a kite arm mirrored arch which is eventually closed to flatten when the kite arm centers of said kite arms are directly loaded along the kite center line between the centers of the two said kite arms, wherein said kite end section has a vertex axis between said lower vertex and said upper vertex, wherein said vertex axis is oriented primarily vertically (although it might be somewhat diagonal) at the beginning of said spring compression, wherein said vertex axis rotates to be fully horizontal at the end of said spring compression, wherein the stiffness to bending of said kite end section is sufficient so that its bends only slightly or not at all during said initial portion of said spring compression, wherein said kite end section compresses during the latter portion of compression as said vertex axis rotates so that said kite end becomes more directly loaded along said kite line center so that the force required to compress said kite end section is reduced, wherein the force curve for compression of said kite end curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said kite end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said kite end curved spring can also be used to construct said set of arch spring configurations such as for said curly v-spring—

in like manner to how they were constructed for said elemental curved spring.

17. The optimized shoe of claim 15 wherein end-refined spring comprises a tenth enhanced partly optimal spring system which comprises an arrow head curved spring, wherein said stiffness-changing rotating end section comprises an arrow head end section comprising a rigid end rigidly attached to said solid initial section and an arrow curved spring the end of which is fixably attached to the tip end of said rigid end, wherein said arrow head curved spring is parallel to said rigid end at its attachment point, wherein said arrow head curved spring curves away from said rigid end as it extends to its arrow end, wherein said arrow head curved spring can be on one or both sides of said rigid end, wherein said arrow head curved spring is not in contact with its adjacent load surface at the beginning of spring compression but its tip end impinges its adjacent load surface during the latter portion of said spring compression so that said arrow head curved spring is completely compressed and flattened against said rigid end at full compression when said rigid end has rotated to be horizontal, wherein the force curve for compression of said arrow curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said arrow head end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said arrow head curved spring can be used to construct said set of arch spring configurations such as for said curly v-spring—

in like manner to how they were constructed for said elemental curved spring.

18. The optimized shoe of claim 7 wherein said enhanced optimal spring systems are configured to be in a multi-sided configuration in which there are one or more sides, wherein each side is preferentially wedge shaped to maximize the spring force.

19. The optimized shoe of claim 1 wherein said heel-pop mechanism comprises a generic parallelogram-like structure which further comprises a p-structure which comprises four p-elements which comprise said footplate as the A-top, said groundplate as the p-bottom, a p-front as the generic front side, a p-rear as the generic rear side, wherein said p-elements are pivotally interconnected via p-pivots, wherein said toe section comprises a toe plate, wherein said heel-pop mechanism functions as follows, wherein during the beginning of said heel-lift period the weight of said user holds down said toe plate which holds down said p-front even while said optimized spring system acts to p-expand said p-structure, wherein this p-expansion acts to lift the heel of said user upward by an enhanced distance substantially greater than the compression distance of the said heel section during said compression period, wherein the goal of said heel-pop mechanism is achieved.

20. The optimized shoe of claim 19 wherein said compressible sole comprises an anti-toe-sink mechanism which prevents said toe plate from further sinking during toe-off for the case when said compressible sole only partially compresses during said compression period.

21. The optimized shoe of claim 20 wherein said anti-toe-sink mechanism comprises

a toe parallelogram,

a ladder stop,

a toe stop on the bottom of said toe plate on either side, and

a toe spring, wherein said toe parallelogram comprises said a top toe link on the top side, a front toe link on the front side, a rear toe link on the rear side, and a bottom toe link on the bottom side, wherein said ladder stop also features ladder steps on its front side, wherein the shape of said ladder steps follows a path parallel to the track of said toe hinge during compression (forward and downward), wherein said anti-toe-sink mechanism functions as follows, during compression of said compressible sole, said toe spring weakly biases said toe plate to stay above said top toe link until said user weights said toe plate just before the beginning said heel-lift period at which time said toe stop impinges the nearest said ladder step thereby preventing toe sink, wherein this prevention can occur at any and all levels of partial compression of said compressible sole, wherein said user is also free to run on his or hers or its toes without undue toe sink.

22. The optimized shoe of claim 21 wherein said heel-pop shoe comprises a linkage-spread curved spring heel-pop shoe which comprises

a monolithic generic parallelogram-like structure,

a monolithic generic toe parallelogram-like structure,

said anti-toe-sink structure, and

one or more auxiliary p-springs, wherein said monolithic generic parallelogram-like structure comprises

a front double link-spread spring for said p-front which can optionally be a p-tension band,

a rear double link-spread spring for said p-rear which can optionally be a p-tension band,

a mid footplate link for said p-top,

a groundplate link for said p-bottom, and

an end footplate link,

wherein all just said links interconnect via monolithic, necked-down living hinges call mono pivots, wherein each said double link-spread spring comprises said double linkage and said curved spring, wherein said auxiliary p-springs comprise firstly one or more said above top link hinge partial springs located between said top link hinge and said top load surface and they comprise secondly one or more said adjust springs located adjacent to said front and rear spreader linkages so as to be loaded directly between said top load surface and said bottom load surface, wherein said above top link hinge partial springs control and moderate the initial spreading of said curved spring, wherein the force curve of the vertical compression force on the link-spread said curved spring is called the p-force curve and it first increases and then bends over and goes to zero during compression, wherein the force of said above top link hinge partial spring increases as said p-force curve decreases so as to make the combined p-force curve approximately constant, which meets the requirements of said enhanced optimal spring system, wherein said second auxiliary p-springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height, wherein said monolithic generic toe parallelogram-like structure comprises

a front footplate link,

a toe curved spring,

a spring plate on the bottom, and

a rear toe curved spring which is one and the same as said curved spring of said front double link-spread spring so this is the shared p-element between said monolithic generic parallelogram-like structure and said monolithic generic toe parallelogram-like structure—

as this sharing is what makes possible said enhanced heel-lift, wherein the purpose of said monolithic generic toe parallelogram-like structure is to maintain said front footplate link approximately horizontal during compression so that said toe stop does not rotate downward to engage on of said ladder steps until said user pushes her toe down just before said heel-lift begins, wherein said toe curved spring is only just strong enough to maintain said front footplate link so that the maximum said impact energy is stored in said front double link-spread spring, said rear double link-spread spring, and said auxiliary p-springs, which act as said spring system—

the combined energy of which provides said enhanced heel-lift, wherein the p-front and p-rear elements of said monolithic generic toe parallelogram-like structure feature curved springs which act as the structural links as well as spring elements to combine functions, wherein there is some seesaw rocking of said compressible sole, but this is sufficiently negligible as compared with the advantage of eliminating the need for a separate parallelogram in addition to the spring system.

23. The optimized shoe of claim 22 wherein said heel-pop shoe comprises a curved spring heel-pop shoe which comprises

a monolithic generic parallelogram-like structure,

a monolithic generic toe parallelogram-like structure,

and said anti-toe-sink structure, wherein said monolithic generic parallelogram-like structure comprises

a front curved spring for said p-front,

a rear curved spring for said p-rear,

a mid footplate link which serves as said p-top and which features an extension further rearward of said p-pivot for the connection between the top of said rear curved spring and said mid footplate link, and

a groundplate link for said p-bottom, wherein said p-pivots for the connections between said groundplate link and both said front curved spring and said rear curved spring are simply merged monolithic pivots in which said front curved spring and said rear curved spring curves become horizontal to merge with said groundplate link, wherein the same merged monolithic pivots are used for the connections between front curved spring and said rear curved spring and said footplate link, wherein conventional cylindrical hinges with shafts and bearings can also be used for these connections to said footplate link, wherein said monolithic generic toe parallelogram-like structure comprises said curved spring parallelogram-like structure, wherein the c-force curve of said curved spring heel-pop shoe is linear.

24. The optimized shoe of claim 22 wherein said heel-pop shoe comprises a parallelogram heel-pop shoe which comprises

a monolithic parallelogram structure,

a monolithic toe parallelogram structure,

said anti-toe-sink structure, wherein said monolithic generic parallelogram-like structure comprises

a front mono link for said p-front,

a rear mono link for said p-rear,

said footplate link which serves as said p-top and which features an extension further rearward of said p-pivot (which provides the connection between the top of said rear curved spring and said mid footplate link), and

said groundplate link for said p-bottom, wherein said p-pivots for the connections between said groundplate link and said front mono link and said rear mono link are simply merged monolithic pivots in which said front mono link and said rear mono link necks down and curves (close to their ends) to become horizontal to merge with said groundplate link and likewise for the connections to said footplate, wherein conventional cylindrical hinges with shafts and bearings can also be used for all these merged monolithic pivots, wherein said monolithic generic toe parallelogram-like structure comprises bottom toe link, front toe link, top toe link, and rear toe link (which is one and the same as said front mono link), wherein the sharing of this link is the requirement for said enhanced heel-lift, wherein monolithic pivots are preferentially used for all connections of the links of said parallelogram heel-pop shoe although conventional cylindrical hinges with shafts and bearings can be used as well, wherein said conventional cylindrical hinges guarantee that there is no seesawing of said compressible sole as the foot impact moves from the heel to the toe of said use, wherein said spring system comprises one or more of any said enhanced arch springs, which allow said top load surface to translate horizontally with respect to said bottom load surface, which can be used to achieve a linear force curve such as said rolling mirrored arch spring or said curly v-spring, wherein said spring system comprises one or more of any such said enhanced optimal springs—

which allow said top load surface to translate horizontally with respect to said bottom load surface and which can be used to achieve an optimal force curve, wherein these enhanced optimal springs include a rolling version of said internal linkage mirrored arch spring, said combined monolithic tensioned mirrored curved spring, said combined band tensioned linkage spring, a rolling version of said combined monolithic tensioned mirrored arch spring and a rolling version of said combined tensioned band mirrored arch spring, wherein rolling version means that such a spring starts tilted (rotated) back and then tilts forward during compression so that it is symmetrical oriented and fully flattened at full compression.

59. The optimized shoe of claim 1 wherein said spring system comprises an assembly of one or more component springs located anywhere under the foot or outside of the foot wherein each said component spring has its own distinct stiffness value and force curve, wherein the decision on how to use each component spring in the assembly depends on considerations of structural optimization, stability, and functionality issues such as pronation, wherein said component springs may be held together one to the other by bridging plates to form an insertable cartridge.

60. The optimized shoe of claim 59 wherein said component spring can be oriented at any angle.

25. An optimal spring system, which comprises

a set of enhanced optimal arch springs further comprising a set of enhanced arch springs each of which is constructed from one or more arch spring types, and

a fiberglass composite construction, wherein said optimal spring system has a optimal force curve, wherein the force-curve optimization goal for said optimal force curve is to maximize the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein one way to achieve a said optimal force curve is to vary the spring structure and shape so as to achieve a softer force curve, wherein said set of enhanced arch springs becomes said set of enhanced optimal arch springs when they have said optimal forces curves, wherein fiberglass composite is the significantly preferred material for the resilient spring elements of said enhanced arch springs because it has a very low mechanical hysteresis loss of approximately one to two percent as compared to approximately 20-50% for injection moldable materials such as thermoplastic polyurethanes (for example, pellethane 2363 or PEBAX 5533), wherein any other material with critical parameters for flexibility and bending strength which are similar to those of fiberglass can also be used, wherein the critical parameter for flexibility for said arch springs is the elongation limit of the fiber or of the geometrical construction of the fiber, wherein each said arch spring type represents a combination of elemental curved springs in different orientations, wherein said elemental curved spring is also called a curved arm and it is a curved spring which substantially flattens to a flat plate under full compression, wherein the end of said curved arm (which is horizontal and approximately parallel to the adjacent base load surface) is called the base end and the end of said curved arm that is approximately perpendicular to or diagonal with respect to the adjacent tip load surface is the tip end, wherein the full compression thickness at full compression of said elemental curved spring is the thickness of said curved arm, wherein the approximate shape of said elemental curved spring is a quarter of a circle, wherein the elemental spring height of said elemental curved spring is approximately the radius of said quarter of a circle, wherein said elemental full compression thickness is substantially smaller than the elemental spring height possibly by a factor of ten to twenty, wherein the first arch spring type is simply said elemental curved spring, wherein said tip load surface freely translates horizontally with respect to base load surface said elemental curved spring, wherein the spring strength comparisons for said elemental curved spring are as follows, wherein the spring strength using fiberglass composite is approximately ten times stronger than the spring strength using carbon fiber, wherein the spring strength using fiberglass composite is approximately sixteen times stronger than the spring strength using said injection moldable materials, wherein the spring weight using fiberglass composite is approximately twelve times lighter than the spring weight using carbon fiber composite, wherein the spring weight for fiberglass composite is approximately eight times lighter than the spring weight using said injection moldable materials.

26. The optimal spring system of claim 25 wherein said enhanced optimal arch springs are pre-loaded to improve said optimal force curve, wherein the force at the beginning of the optimal spring compression is a predetermined value (for example one-third the force value at full spring compression), wherein the work done by said spring system is the area under the curve of the force versus the spring deflection, wherein said work is absorbed with a reduced value of the maximum force value point as compared with the maximum force value point when there is no pre-load, wherein this improvement applies for both said optimal force curve and for a linear force curve, wherein the improvement due to pre-load is independent of the improvement due to a constant force curve so either improvement applies to said optimal force curve and the combination of both improvements also applies to said optimal force curve, wherein said pre-load is accomplished with a physical restraint such as a tether or such as a structural restraint, wherein the first criterion for said optimal spring system is to pre-load said optimal spring system, and the second criterion for said optimal spring system is to create a geometry so that the slope of said optimal force curve decreases or even becomes approximately constant throughout the latter said sole compression.

27. The optimal spring system of claim 26 wherein said optimal spring system comprises a set of enhanced arch springs each of which is constructed from one or more arch spring types, wherein each said arch spring type represents a combination of elemental curved springs in different orientations, wherein said elemental curved spring is also called a curved arm and it is a curved spring which substantially flattens to a flat plate under full compression, wherein the first arch spring type is said elemental curved spring, wherein the end of said curved arm (which is horizontal and approximately parallel to the adjacent base load surface) is called the base end and the end of said curved arm that is approximately perpendicular to or diagonal with respect to the adjacent tip load surface is the tip end, wherein the full compression thickness at full compression of said elemental curved spring is the thickness of said curved arm, wherein the approximate shape of said elemental curved spring is a quarter of a circle although the curvature may be somewhat different, wherein the elemental spring height of said elemental curved spring is approximately the radius of said quarter of a circle, wherein said elemental full compression thickness is substantially smaller than the elemental spring height possible by a factor of ten to twenty, wherein the first arch spring type is simply said elemental curved spring, wherein said tip end load surface freely translates horizontally with respect to said base load surface, wherein the spring strength comparisons for said elemental curved spring are as follows, wherein the spring strength using fiberglass composite is approximately ten times stronger than the spring strength using carbon fiber, wherein the spring strength using fiberglass composite is approximately sixteen times stronger than the spring strength using said injection moldable materials, wherein the spring weight using fiberglass composite is approximately twelve times lighter than the spring weight using carbon fiber composite, wherein the spring weight for fiberglass composite is approximately eight times lighter than the spring weight using said injection moldable materials.

28. The optimal spring system of claim 27 wherein said optimal spring system comprises one of more said arch spring types, wherein the second said arch spring type is called an arch spring in which two said elemental curved springs are combined to form the shape of an arch, wherein the left side of said elemental curved spring is the mirror image of the right side of said elemental curved spring constructed about the vertical line at the junction of the opposing said base ends, wherein the arch center is located where the base ends of the opposing said elemental curved springs join, wherein the third said arch spring type is called a mirrored arch spring in which case the upper concave downward said arch spring is mirrored about the horizontal line just below the opposing said tip ends of the upper said arch spring, wherein the said arch centers of the upper and lower said arch springs are loaded by their adjacent mirrored load surfaces causing the opposing said tip ends to move outward horizontally as said mirrored arch spring fully flattens, wherein said mirrored load surfaces do not translate horizontally with respect each other and instead they move vertically and directly toward each other during said spring compression, wherein the fourth said arch spring type is called a rolling mirrored arch spring in which case the top and bottom of said mirrored arch springs have a circular shape in which case said rolling mirrored arch spring can roll somewhat as it is being loaded by two surfaces which are translating horizontally with respect to one another, wherein the fifth said arch spring type is called a half mirrored arch spring in which case said mirrored arch spring is cut in half along a vertical line though its center when viewed from the side, wherein the sixth said arch spring type is called a curly v-spring in which case said elemental curved spring is combined with its mirrored image also called an inverted said elemental curved spring to form said curly v-spring which looks like the letter V turned on its side with each of its arms being curled in the shape of an elemental curved spring, wherein the seventh said arch spring type is called nested arch springs in which one or more said arch spring types is or are nested within another arch spring type to form a nested arch spring at one or more levels of nesting, wherein the base of said elemental arch springs are offset in the vertical direction with respect to each other so that when said nested arch spring fully compresses, each component said elemental curved spring is approximately horizontal along its entire length, wherein the total spring strength of said nested arch spring is increased over that of a single said arch spring albeit at the cost of an increase in the thickness of said nest arch spring at full compression, wherein all above said arch spring types and more complex variations made from them have similar force curves and behaviors to the force curves of said elemental curved springs of which they are constructed.

29. The optimal spring system of claim 28 wherein said arch spring types comprise

spring elements,

linkage elements, and

hinges, wherein said spring elements and said linkage elements are connected to each other with hinges, wherein one or more said hinges are conventional cylindrical hinges comprising shafts and bearings.

30. The optimal spring system of claim 26 which comprises an enhanced optimal spring system which is constructed of said arch spring types, wherein said enhanced optimal spring system is designed to optimize the force curve for devices such as footwear where it is advantageous to minimize the maximum force point along the force curve (especially when there is an impact force) on said user, on the structural elements of said spring system and on the device within it is incorporated, wherein the force-curve optimization goal for said force curve optimized spring is to maximum the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein the first part of a method to achieve a desired optimized force curve is to pre-load it and the second part is to vary the spring structure and shape so as to achieve a softer, more constant force curve, wherein these changes in force curve can reduce said maximum force value by 25% to approximately 40% as compared to a spring system with a linear force curve, wherein there are two classes of enhanced optimal spring systems, namely an enhanced fully optimal spring system where the force curve becomes approximately constant during the latter part of compression and namely an enhanced partly optimal spring system where the slope of the force curve decreases to approximately half of its initial value during the latter part of compression, wherein when a non-linear finite element analysis is done to determine the maximum allowable thickness (and hence the maximum possible force) of said curved arms within the stress limits of the material of which said curved arms are made, the total energy absorbed (work done) per unit area by each said arch spring is linearly proportional to the full deflection value which is the deflection at full compression so that it is easy to achieve a particular total energy absorbed by simply choosing the corresponding said full deflection value, which means that the only way to change said total energy absorbed (work done) per unit area is to change said full deflection value, wherein the impact energy of running is absorbed by the compression of said compressible sole with the sole compression energy and by the compression of the leg of said user with the leg compression energy, wherein the third criterion for optimization of said sole compression energy is to determine the optimal sole compression energy by experiment and then to realize said optimal sole compression energy by choosing the corresponding particular said deflection value, wherein one or more said hinges are necked-down living hinges which permit a continuous monolithic construction between adjacent ones of said linkages elements and said spring elements.

31. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises first enhanced fully optimal spring system which is also called an internal linkage mirrored arch spring system which comprises

monolithic mirrored arches, wherein said monolithic mirrored arches belong to a tension spring class of tensioned springs which comprise said elemental curved springs and tension band springs,

mirrored spreader linkage, wherein said mirrored spreader linkage belongs to a class of spreader linkages which spread said tension springs, wherein the force curve for the loading of said spreader linkages first increases and then bends over to eventually go to zero at full spreading when the links of said spreader linkage become aligned, wherein this linkage spreading loading qualifies said first enhanced fully optimal spring system as a said enhanced fully optimal spring system,

one or more parallel auxiliary springs, and

one or more series auxiliary springs, wherein said parallel auxiliary springs act in parallel and in combination with monolithic mirrored arches to increase the combined force curve to become approximately constant as full compression is approached, wherein each of said monolithic mirrored arches further comprises a monolithic arch hinge which is a necked-down living hinge and which pivotally connects the top half of said monolithic mirrored arch to its mirrored image bottom half, wherein said mirrored spreader linkage further comprises on the top and on the bottom

center links,

mostly vertical links, and

impinger links, wherein said center links are pivotally connected to said mostly vertical links by monolithic corner hinges, where said mostly vertical links are pivotally connected to said impinger links by monolithic impinger hinges, wherein said series auxiliary springs are positioned between said center links and the centers of said top half and said bottom half of said monolithic mirrored arches, wherein said parallel auxiliary springs are positioned between the opposing said center links of said internal linkage mirrored arch spring, wherein both said series auxiliary springs and said parallel auxiliary springs may be positioned in pairs spaced horizontally away from each other to provide a restoring force to keep said center links horizontal during compression, wherein said impinger links push outward against said monolithic arch hinges to flatten said monolithic mirrored arches, wherein said series auxiliary springs control and moderate the initial spreading of said monolithic mirrored arch by said mirrored spreader linkage, wherein the linkage force curve of the vertical compression force on said monolithic mirrored arches is for the force that would be applied if there were no parallel auxiliary springs and it first increases and then bends over and goes to zero during compression, wherein the force of said parallel auxiliary springs increases as said linkage force curve decreases so as to make sum of these two force curves approximately constant, wherein this sum is called the first combined force curve which is for said first enhanced fully optimal spring system, wherein said first combined force curve meets the requirements of said enhanced fully optimal spring system, wherein said auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height, wherein said monolithic mirrored arches optionally comprise one or more nested monolithic mirrored arches nested within each other, wherein the strength of said internal linkage mirrored arch spring is increased significantly by the addition of each additional nested monolithic mirrored arch since its thickness is decreased only slightly.

32. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a second enhanced fully optimal spring system which is also called a link-spread curved spring system which comprises a link-spread curved spring and one or more second auxiliary springs, wherein said link-spread curved spring comprises

a second spreader linkage which comprises two or three links,

a second curved spring, and

link hinges, wherein said links are pivotally connected by said link hinges one to the other and at either end to the ends of said second curved spring via spring hinges, wherein the top one of said links is called the top link and it connects to the next link by the top link hinge, wherein the total length of the links comprising said second spreader linkage equals the length of said second curved spring so that said link-spread curve spring can fully flatten at full compression, wherein said top link hinge contacts said top load surface at the contact compression distance, wherein said contact compression distance can be adjusted by changing the lengths of the links of said second spreader linkage, wherein said second auxiliary springs comprise both an above top link hinge partial spring located between said top link hinge and top load surface and an adjust spring located adjacent to said second spreader linkage so as to be loaded directly between said top load surface and said bottom load surface, wherein said above top link hinge partial spring controls and moderates the initial spreading of said second curved spring, wherein the force curve of the vertical compression force on said link-spread curved spring is called the second force curve and it first increases and then bends over and goes to zero during compression, wherein the force of said above top link hinge partial spring increases as said second force curve decreases so as to make the combined second force curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said second auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

33. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a third enhanced fully optimal spring system which comprises a combined monolithic tensioned mirrored curved spring which comprises a monolithic tensioned mirrored curved spring and one or more third auxiliary springs which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said monolithic tensioned mirrored curved spring comprises an external quad linkage which is oriented like a diamond and which further comprises four monolithic quad links monolithically at the top and bottom connected by monolithic vertical necked-down vertices and on the two sides by monolithic horizontal necked-down vertices and a double mirrored curly v-spring tension element which further comprises four monolithic tension curved springs each of which is monolithically connected to monolithic horizontal necked-down vertices via a side vertex connection and each of which curves up (or down) until it is approaching vertical to connect to its mirrored image at the center via said monolithic vertical necked-down vertices, wherein said monolithic horizontal necked-down vertex further optionally comprises

a first necked restraint,

a monolithic loop, and

a retainer pin, wherein said monolithic loop is a monolithic continuation between said monolithic quad link and said side vertex connection and said retainer pin is inserted from the side through said monolithic loop, wherein said first necked restraint encloses said monolithic loop to reinforce it to withhold the considerable force exerted by said side vertex and said monolithic quad link via said monolithic horizontal necked-down vertex, wherein the third force curve for the vertical force needed to pull apart said double mirrored curly v-spring tension element first increases and then reduces to zero, wherein the vertical force imparted by said third auxiliary springs increases as said third force curve decreases so as to make the combined third force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said third auxiliary springs are preferentially said mirrored arch springs in which case all elements of said combined monolithic tensioned mirrored curved spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

34. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a fourth enhanced fully optimal spring system which comprises a combined band tensioned linkage spring which comprises a band tensioned linkage spring and one or more fourth auxiliary springs, which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said band tensioned linkage comprises

a quad linkage which is oriented like a diamond and which further comprises four quad links connected at the top and bottom by vertical hinges and on the two sides by horizontal hinges,

a tension band with band end loops on either end, and

a shaft, wherein both said band end loops and said quad links (near where they connect to said horizontal hinges) are slotted so as to interleave one through the other so that said shaft can be inserted through said horizontal hinges so as to connect said quad linkage to said tension band, wherein the fourth force curve for the vertical force needed to pull apart said tension band first increases and then reduces to zero, wherein the vertical force imparted by said fourth auxiliary springs increases as said fourth force curve decreases so as to make the combined fourth force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said fourth auxiliary springs are preferentially said mirrored arch springs in which case all elements said combined band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

35. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a fifth enhanced partly optimal spring system which is called a monolithic tensioned mirrored arch spring which comprises

an outer top-loaded arch spring comprising a top extended arch and a bottom extended arch each of which comprises an extended flat section at its center and an outer tip section where it connects to the other,

an inner side-loaded arch spring on the top half which connects to said outer-tip section on either end via inner tip section and via inter-arch section,

a pair of inner tension-loaded curly v-springs on the bottom half which connect to each other at the center via inter curly v-spring tip section and which connect to said outer-tip section on either end via said inner tip section and via said inter-arch section, and

a pair of outer-tip spacers which space apart said outer-tip sections so that said outer top-loaded arch spring can fully flatten without interference with said inner side-loaded arch spring or said inner tension-loaded curly v-spring, wherein said outer-tip sections are clamped to said outer-tip spacer by outer clamps and said inner-tip sections are clamped to their mirrored image said inner-tip sections via said inner clamps, wherein both said inner side-loaded arch spring and said inner tension-loaded curly v-spring are equivalent as inner tension elements and can be substituted for the other but only said inner side-loaded arch spring is mentioned the further explanation here, wherein said inner side-loaded arch spring is located inside of and pulls on said outer top-loaded arch spring via said inter-arch section, wherein these three elements form a continuous monolithic structure and they are interconnected via necked-down living hinges, wherein the slope of the fifth force curve—

for the vertical compression force needed both bend said outer top-loaded arch spring and to pull apart said inner side-loaded arch—

decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

36. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a sixth enhanced partly optimal spring system which comprises a tensioned band mirrored arch spring which comprises

a second tension band with second band end loops on either end,

a pair of mirrored band arches each comprising a center arch section and arch tips which impinge their mirrored image arch tips via said second tension band,

a second band retainer pin, and

a pair of band pivots, wherein said second band retainer pin is slid from the side through said second band end loops so as to prevent second band end loops from sliding through said arch tips which are compressing said second tension band, wherein the slope of the sixth force curve—

for the vertical compression force needed both bend said mirrored band arches and stretch said second tension band—

decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said tensioned band mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

37. The optimal spring system of claim 32 wherein said link-spread curved spring system comprises a seventh enhanced fully optimal spring system which comprises a combined tensioned links rotating arms curved spring system which comprises a tensioned links rotating arms curved spring and a seventh auxiliary spring, wherein said tensioned links rotating arms curved spring comprises

a top arm,

a bottom arm,

an arm hinge which connects said top arm and said bottom arm, and

a pair of said link-spread curved springs which are mirrored images of each other to form a configuration analogous to said curly v-spring, wherein said seventh auxiliary spring is positioned between said top arm and said bottom arm so as to engage them when they are partially folded, wherein on one end said spring hinges hingeably connect to said top arm and said bottom arm at mirrored positions, wherein on the other end said spring hinges hingeably connect and impinge each other, wherein the pivotal connection of these said second curved springs is preferentially achieved by a curved arch pivot which is a necked-down living hinge, wherein when the mirrored ones of said top link hinges impinge each other by the loaded folding of said top arm and said bottom arm about said arm hinge, the mirrored said spreader linkages straighten the mirrored said second curved springs, wherein the torque curve of said loaded folding is called the first torque curve and it first increases and then bends over and goes to zero during said loaded folding, wherein the torque exerted by said seventh auxiliary spring to resist said loaded folding increases as said torque curve decreases so as to make the combined torque curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said seventh auxiliary spring is preferentially said curly v-spring in which case all elements of said combined tensioned links rotating arms curved spring system flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.

38. The optimal spring system of claim 30 said enhanced optimal spring system comprises an eighth enhanced partly optimal spring system which comprises an end-refined curved spring which comprises a solid initial section and a stiffness-changing rotating end section, wherein said solid initial section is oriented at its base primarily horizontally and said solid initial section curves upward for a solid portion of said elemental spring height to rigidly or monolithically attach to said stiffness-changing rotating end section, wherein said curved end-refined curved spring is loaded at its bottom by said bottom load surface and at its top by said top load surface which freely translates horizontally with respect to said bottom load surface, wherein during the initial portion of said spring compression the spring deflection is primarily due to the flattening of said solid initial section, wherein during the latter portion of said spring compression said spring deflection is primarily due to the compression and flattening of said stiffness-changing rotating end section as it rotates, wherein the stiffness of said stiffness-changing rotating end section can be independently parameterized to be weaker, wherein the force curve for compression of said end-refined curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section, after which said force curve bends over to become softer, which meets the requirements of said enhanced partly optimal spring system.

39. The optimal spring system of claim 38 wherein said end-refined spring system comprises a ninth enhanced partly optimal spring system which comprises a kite end curved spring, wherein said stiffness-changing rotating end section comprises a kite end section which splits (at the lower vertex) partway up said solid initial section into two kite arch arms which rejoin at the kite top end at the upper vertex at the top of said elemental spring height to form a kite arm mirrored arch which is eventually closed to flatten when the kite arm centers of said kite arms are directly loaded along the kite center line between the centers of the two said kite arms, wherein said kite end section has a vertex axis between said lower vertex and said upper vertex, wherein said vertex axis is oriented primarily vertically (although it might be somewhat diagonal) at the beginning of said spring compression, wherein said vertex axis rotates to be fully horizontal at the end of said spring compression, wherein the stiffness to bending of said kite end section is sufficient so that its bends only slightly or not at all during said initial portion of said spring compression, wherein said kite end section compresses during the latter portion of compression as said vertex axis rotates so that said kite end becomes more directly loaded along said kite line center so that the force required to compress said kite end section is reduced, wherein the force curve for compression of said kite end curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said kite end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said kite end curved spring can also be used to construct said set of arch spring configurations such as for said curly v-spring—

in like manner to how they were constructed for said elemental curved spring.

40. The optimal spring system of claim 38 wherein end-refined spring comprises a tenth enhanced partly optimal spring system which comprises an arrow head curved spring, wherein said stiffness-changing rotating end section comprises an arrow head end section comprising a rigid end rigidly attached to said solid initial section and an arrow curved spring the end of which is fixably attached to the tip end of said rigid end, wherein said arrow head curved spring is parallel to said rigid end at its attachment point, wherein said arrow head curved spring curves away from said rigid end as it extends to its arrow end, wherein said arrow head curved spring can be on one or both sides of said rigid end, wherein said arrow head curved spring is not in contact with its adjacent load surface at the beginning of spring compression but its tip end impinges its adjacent load surface during the latter portion of said spring compression so that said arrow head curved spring is completely compressed and flattened against said rigid end at full compression when said rigid end has rotated to be horizontal, wherein the force curve for compression of said arrow curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said arrow head end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said arrow head curved spring can be used to construct said set of arch spring configurations such as for said curly v-spring—

in like manner to how they were constructed for said elemental curved spring.

41. The optimal spring system of claim 30 wherein said enhanced optimal spring systems are configured to be in a multi-sided configuration in which there are one or more sides, wherein each side is preferentially wedge shaped to maximize the spring force.

42. The optimal spring system of claim 25 wherein said optimal spring system comprises an optimized conventional shoe wherein said enhanced optimal spring systems are used in conventional shoes, meaning shoes that do not have a heel-pop mechanism also called an enhanced heel-lift mechanism to lift said heel section during said heel-lift period by a distance that is substantially greater than the distance over which said heel section is compressed during said compression period which is called herein enhanced heel-lift, wherein said heel-pop mechanism provides energy return that is substantially greater than that of conventional shoes which do not have said heel-pop mechanism, wherein the significance of said energy return is that the metabolic energy cost of running is substantially reduced, wherein said optimized conventional shoe comprises

a compressible sole,

a top load surface on the upper side of said compressible sole further comprising a footplate hingeably connected to a toe plate by a toe hinge,

a bottom load surface called a groundplate on the lower side of said compressible sole, wherein said compressible sole further comprises

a toe section, wherein said toe section preferentially incorporates a conventional toe stop to elevate the take-off surface during toe-off,

a forefoot section, and

a heel section, wherein said compressible sole further comprises a spring system which resists compression and which stores the impact energy of compression.

43. The optimal spring system of claim 42 wherein the set of said enhanced optimal spring systems comprises a vertical compression subset, wherein said optimal spring system is loaded by said footplate against said groundplate, wherein for said vertical compression class of arch spring types said footplate does not translate horizontally with respect to said groundplate during the compression of said optimal spring system, wherein for said forward translating class of arch spring types said upper load surface does translate horizontally with respect to said lower load surface during the compression of said optimal spring system, wherein the following enhanced optimal spring systems belong to said vertical compression subset:

said internal linkage mirrored arch spring, said combined monolithic tensioned mirrored curved spring, said combined band tensioned linkage spring, said monolithic tensioned mirrored arch spring, said tensioned band mirrored arch spring, and said end-refined curved spring in curly v-spring configuration.

44. The optimal spring system of claim 43 wherein said spring system of said optimized conventional shoe comprises one or more members of said vertical compression subset of said enhanced optimal spring systems, wherein each said member is called an optimal shoe spring, wherein one or more said shoe springs may be located anywhere in said toe section, said forefoot section, or said heel section, wherein said optimal shoe springs may be oriented any way, wherein said optimal shoe springs may have small enough widths so as to be distributed across the width of said compressible sole, wherein said optimal shoe springs may be oriented at any angle, wherein the strength of said optimal shoe springs may vary across both the width and the length of said compressible sole, where said compressible sole may be of constant thickness or of tapered thickness, where said optimal shoe springs may be insertable or permanently attached.

45. The optimal spring system of claim 25 wherein said optimal spring system comprises an optimal force curve method which further comprises

a first means to determine both the user energy which is amount of impact energy absorbed by the legs and feet of said user and the sole energy which is the amount of impact energy absorbed by said compressible sole and

a second means to adjust said sole energy so that its value increases while said user energy decreases for a given total impact energy absorbed which corresponds to a reduction in the metabolic energy for running, wherein for said arch spring types and said enhanced arch springs and said enhanced optimal arch springs, the maximum shoe energy per unit area that can be absorbed at full spring compression is linearly proportional to the deflection value of said full spring compression—

in which case the desired value for said user energy can be realized by choosing the proper said deflection value (within the limits of how thick said compressible sole can practically be, of course).

46. The optimal spring system of claim 45 wherein said optimal force curve method comprises a precise tuning method which requires that said optimal sole energy is defined for the case when said sole energy at full compression is used as the target value for the manufacture of said optimal spring system for a particular user, wherein this means that said footwear is precisely tuned for said user for his or her chosen impact energy for the corresponding chosen gait.

47. The optimal spring system of claim 46 wherein said precise tuning method further comprises a precise manufacture means to realize a precise value of said optimal sole energy by simply slicing the elements of said optimal spring system to a precise value, wherein said arch spring types and said enhanced arch springs of which said optimal spring system are made are 2D springs which are uniform across their widths, wherein the spring strength of said 2D springs is determined by their widths so precise a manufacture means is easily achieved, wherein for a given shoe size there can be a multiplicity of said spring strengths for a range of said user energy values for diverse said users.

48. The optimal spring system of claim 46 wherein said precise tuning method further comprises the manufacture of changeable said 2D springs which can be removed from and inserted into said tuned spring system, wherein said 2D springs are easy to manufacture as changeable springs.

49. The optimal spring system of claim 46 wherein said a precise tuning method further comprises an impact force means to measure the ground reaction force of running or walking, wherein said impact force means further comprises the user'"'"'s weight, the user'"'"'s gait range, and measurement results from a force platform test.

50. The optimal spring system of claim 46 wherein said a precise tuning method further comprises a gear change mechanism, wherein the term gear change means that the spring stiffness of said tuned spring system is reset after every step so that there is close to full compression of said compressible sole on a continuous basis.

57. The optimal spring system of claim 34 wherein said tension band is made of a continuous wave composite (CWC), wherein said CWC comprises multiple layers which are laid down in sinusoidal waves transversely oriented within the plane of each layer, wherein said tension band of said CWC can be stretched considerably without breaking the fibers, wherein said tension band of said CWC has very low energy hysteresis loss of the order of 1-2%.

58. The optimal spring system of claim 37 wherein the pair of said link-spread curved springs are replaced by a pair of tension bands made of a continuous wave composite (CWC), wherein said CWC comprises multiple layers which are laid down in sinusoidal waves transversely oriented within the plane of each layer, wherein said tension band of said CWC can be stretched considerably without breaking the fibers, wherein said tension band of said CWC has very low energy hysteresis loss of the order of 1-2%.

51. A gear change mechanism in a shoe which comprises

a shoe upper,

a footplate,

a compressible sole, and

a gear change spring system, wherein said gear change mechanism comprises

gear springs,

an outside spring section of said compressible sole which is not directly under the foot of the user of said shoe and which uses said gear springs,

an underfoot spring section of said compressible sole which is directly under the foot of the user of said shoe and which uses said gear springs,

one or more outside springs in said outside spring section,

one or more underfoot springs in said underfoot section, wherein said underfoot springs are necessarily always compressed when said compressible sole is compressed, and

one or more outside springs, and

an outside spring engagement/disengagement mechanism for the purpose of engaging or disengaging said outside springs, wherein said user can be a human or a robot, wherein the human applications are normal, orthotics and prosthetics.

52. The gear change mechanism of claim 51 wherein when said user is a robot with a robotic foot said outside springs can comprise a centrally located section located in the center region of said robotic foot, wherein this is because said robotic foot can be divided into sections which do not fully and continuously cover said robotic foot, which is not the case for a human foot, wherein said compressible sole of said robotic foot can be compressed without said centrally located section being compressed.

53. The gear change mechanism of claim 51 wherein said outside springs and said underfoot springs are 2D springs, wherein said 2D springs are uniform across their widths so that they can be considered 2D springs, wherein the spring strength of said 2D springs is linearly proportional to their widths, wherein said spring strength can be very precisely selected, wherein said 2D springs can be rotated about shafts which extend across their widths from side to side, wherein said 2D springs can be sliced in any plane perpendicular to said shaft, wherein said 2D planes are also known as slicing planes.

54. The gear change mechanism of claim 51 wherein side spring engagement/disengagement mechanism comprises

a local force means to measure the ground reaction force of walking or running, wherein said local force means is located on said tuned shoe,

a microprocessor located on said shoe,

an actuator assembly,

an electrical connection means to electrically connect said local force means, said microprocessor, and said actuator assembly,

one or more sliced outside side springs, and

one or more engageable spring drive bars each of which engages and drives a particular one of said sliced outside springs, wherein if a particular one of said sliced outside springs is not instructed by said microprocessor to engage, then it is disengaged, wherein the output of said local force means is transmitted to said microprocessor right after toe-off of said tuned shoe, whereupon said microprocessor transmits its output to said actuator assembly telling it which engageable spring drive bars are to be engaged for the next step of said shoe, wherein the optimum number of said sliced outside springs is engaged for every next step based on the measured ground force of the previous step, wherein said compressible sole approximately achieves close to full compression on every step.

55. The gear change mechanism of claim 54 wherein said local force means is a force sensor positioned at the bottom of said compressible sole.

56. The gear change mechanism of claim 54 wherein said engageable spring drive bar comprises

a spring frame,

a drive shaft oriented in the sideways direction,

one or more drive bars oriented vertically,

a lock hole oriented in the front/back (lengthwise) direction in the top of said drive bar,

one or more bar holes oriented in the sideways direction, wherein each said bar hole is in the top of each of said drive bar, wherein said bar hole is oriented perpendicular to said lock hole,

a housing,

a shaft bar,

one or more lock shafts each of which is positioned directly in front of said lock hole in said drive bar so that said lock shaft moves through said lock hole as said length actuator moves said shaft bar in the lengthwise direction,

a length actuator oriented in the front/back direction, wherein said housing houses said length actuator, wherein said shaft bar is rigidly attached to the moving end of said length actuator, wherein said lock shafts are rigidly attached to said shaft bar and oriented in the front/back direction, wherein said spring frame is rigidly attached to the side of said footplate and extends upward to rigidly connect to said drive shaft which extends out toward the side of said compressible sole, wherein one or more of said drive bars is rotatably connected to said drive shaft via said bar hole and said drive bar hangs down from said drive shaft, wherein each said drive bar is located directly above said side sliced spring, wherein each said lock shaft is rigidly attached to one said shaft bar at staggered lengths so that each of them passes through its respective said lock hole (in said drive bar) at different times as said shaft bar is moved forward and backward by said length actuator, wherein when said lock shaft enters said lock hole, said drive bar is prevented from rotating out of the way of side sliced spring, in which case said drive bar drives said side sliced spring downward to its compressed state, wherein when said lock shaft does not pass through said lock hole then drive bar is free to rotate out of the way of said side sliced spring and said side spring engagement/disengagement mechanism has disengaged said side sliced spring from being compressed, wherein said gear change mechanism automatically changes gears so that it continuously ensures close to full compression of said compressible sole.