Method of making actuators based on unbalanced moments of inertia

Methods and computer-readable mediums are provide that, in some embodiments maximize bending of an actuator and, in other embodiments, minimize bending of the actuator. For example, in one embodiment, a method is provided that designs and determines a Ratio1 for a first component. Ratio1 is a modulus of inertia for the first component divided by a Young's Modulus for the first component. Thereafter, a second component is designed that has a Ratio2 substantially equal to the Ratio1 of the first component. Ratio2 is a modulus of inertia for the second component divided by a Young's Modulus for the second component. Thereafter, the first component and the second component can be used to make an actuator that is spun into fiber to make products (e.g., batting material, woven material, a suture, a thermostat needle, a gel, etc.). Other embodiments are provided that utilize computer-readable medium.

BACKGROUND

Field of the Invention

Embodiments of the present invention generally relate to actuators and more specifically to tailoring the moments of inertia of at least two components, of the actuator, to enhance or suppress bending.

Description of the Related Art

It has long been known that two sheets of metal with different coefficients of thermal expansion (“CTE”) will bend with changes in temperature. The traditional approach to this technology is illuminated by the “bi-metallic spring.” The general relationship for when the two metals (i.e., in a bi-metallic strip) are of the same thickness is analyzed in Timoshenko, S., Analysis of Bi-metal Thermostats, J. Opt. Soc. Am. (1925), 11(2), pp. 233-255 (hereinafter “Timoshenko”).

Timoshenko analyzed the bending of a bi-metal thermostat of rectangular cross-section and concluded:The curvature is proportional to the difference in elongation of the two metals and inversely proportional to the thickness of the strip. It is seen that the magnitude of the ratio [of the Young's moduli of the two metals] does not produce any substantial effect on the curvature of the strip. See Timoshenko at page 235.

A bi-metallic strip100is provided inFIG. 1. Specifically, the bi-metallic strip100includes a first component102and a second component104. The first component102is made of a different metal than the second component104. The first component102and second component104have the same dimensions and different coefficients of linear expansion and moments of inertia. Heating the bi-metallic strip100causes bending of the bi-metallic strip100.

Equations are provided below for calculating the temperature of budding, the complete travel during buckling, and the temperature of buckling in a backward direction. By using these equations, the dimensions of the bi-metallic strip100for a given temperature of operation and a given complete range of temperature can be calculated. It has long been known that two sheets of metal with different coefficients of thermal expansion (“CTE”) will bend with changes in temperature. The general relationship for the two metals (i.e., components102and104) are of the same thickness (as provided by Timoshenko) is provided by Equation 1:

where the CTEs of the two materials are α1(component102) and α2(component104), the change in temperature is ΔT, h is the combined thickness of components102and104, n is the ratio of the mechanical moduli of components102and104, the radius of curvature is ρ, and the “curvature” is

Note that Equation (1) can alternatively be expressed as Equation (2) below.

where

1ρrect
is the curvature of the strip100, h is the height or diameter of the fiber, α2is the coefficient of thermal expansion for component104, α1is the coefficient of thermal expansion for component102, n is the ratio of the Young's moduli of the components102and104, and m is a ratio of the thickness of components102and104. Note that setting m=1 in Equation (2) yields Equation (1).

According to the analysis in Timoshenko, the bending of the bonded metal sheets (i.e., components102and104combined) is not a strong function of the mechanical modulus of the component metals. E1and E2are the elastic moduli of components102and104, respectively. It is seen that the magnitude of

n=E1E2
does not produce any substantial effect on the curvature of the strip. For example, when n=1, then Equation (1) above is reduced to Equation (3).

where the CTEs of the two materials are α1(component102) and α2(component104), the change in temperature is ΔT, h is the combined thickness of components102and104, the radius of curvature is ρ, and the “curvature” is

Similarly, when

n=12
or n=2 then Equation (1) is reduced to Equation (4) below.

where the CTEs of the two materials are α1(component102) and α2(component104), the change in temperature is ΔT, h is the combined thickness of components102and104, the radius of curvature is ρ, and the “curvature” is

“For a ratio of Young's moduli of 2, the “difference . . . [in curvature] is only about 3 percent.” See Timoshenko at page 236.

However, many combinations of materials that could be useful have mechanical moduli which can vary by a factor or ten or more. Based on these same equations the bending would be reduced by about one third. If the mechanical moduli differ by two orders of magnitude the bending is reduced to only 15% of the amount of bending that would be seen in the case where mechanical moduli are equal.

Examples of materials with very different mechanical moduli are polymers above and below their glass transition temperatures. Amorphous polymers above their glass transition temperature (i.e., in a rubbery state) usually have much higher CTEs than those below their glass transition temperature (i.e., in a glassy state) and would make good candidates for bending in response to temperature changes to act as a thermostat or a temperature adaptive insulation. Unfortunately, a decrease in modulus of about 3 orders of magnitude occurs at the glass transition making this combination of materials essentially useless.

Many materials of current technological interest such as gels, amorphous metals, shape memory polymers, and nanocomposites have mechanical moduli which vary by orders of magnitude limiting the combinations of materials that can be used.

However, for polymeric materials, the elastic modulus can change by three orders of magnitude below and above the glass transition temperature (Aklonis and McKnight, 1983). It is just such a combination of a polymer above its glass transition temperature and one below its glass transition temperature (or in a crystalline form) that gives the greatest difference in coefficients of thermal expansion.

The prior art (e.g., U.S. Pat. No. 4,115,620 issued Sep. 19, 1978) discloses an even polymer blend (i.e., extruded at 50:50 ratio) and doesn't adjust the ratio of the two components to optimize bending.

Other prior art (e.g., U.S. Pat. No. 8,389,100 B2 issued Mar. 5, 2013 (“Rock et al.”)) utilizes two different types of components (i.e., a polyethylene and a polypropylene). However it appears that Rock et al. utilizes about 50:50 ratio of these components in a side-by-side relationship.

Although U.S. Pat. No. 4,315,881 (issued Feb. 16, 1982) discloses that the ratio by weight of extruded fiber components is 30:70 to 70:30 and 40:60 to 60:40 it does not appear that these ranges are used (or manipulated) to optimize bending of the extruded material.

Generally, the prior art does not use the moments of inertia of the components to determine the ratio of those components (in an extruded material) and manipulate the shape of the extruded material to maximize bending. In addition, it does not appear that the prior art adjusts the ratio (of the moments of inertia to the Young's Modulus), of the components, so that they are substantially equal to one another to optimize bending nor does it appear that the prior art uses/manipulates the ratios to optimize bending of extruded material(s).

Thus there is a need to use a wider selection of materials of significantly different mechanical moduli. There is also a need to tailor the moments of inertia of at least two components, in an actuator, to enhance or suppress bending.

SUMMARY

Embodiments herein generally relate to actuators and more specifically to tailoring the moments of inertia of at least two components, of the actuator, to enhance or suppress bending.

Some embodiments herein generally relate to techniques optimizing the thermal response by knowing the characteristics of the materials used to make an actuator. For example, by knowing the characteristics (e.g., the ratio of the moment of inertia to the Young's Modulus (“Ratio1”) of one component a second component having known characteristics (e.g., the ratio of the moment of inertia and the Young's Modulus (“Ratio2”)) can also be selected. The amount of material used for the second component can be tailored so that that Ratio1 is substantially equal to Ratio2. In various embodiments, either/both of the components can have at least one cavity therein. The amount of the material used in either component, the materials selected, the shape of the actuator, whether to have at least one cavity in either/both components, and the size of the cavity/cavities (if any) are designed based upon making Ratio1 and Ratio2 substantially equal to one another.

Other embodiments herein generally relate to actuators with at least two components, where at least one of the components has at least one cavity within and to tailoring the moments of inertia of the components of the actuator to enhance or suppress bending.

For example, in one embodiment, a method is provided that acquires a first ratio of a modulus of inertia for a first component that contains at least one cavity to a Young's Modulus for the first component. The method also acquires a second ratio of a modulus of inertia for a second component to a Young's Modulus for the second component. Thereafter, the method provides an actuator (which includes at least one of the components having at least one cavity therein). The actuator has a cross-sectional shape such that the first ratio substantially equal to said second ratio.

In another embodiment, a method is provided that designs and determines a Ratio1 for a first component. Ratio1 is a modulus of inertia for the first component divided by a Young's Modulus for the first component. Thereafter, a second component is designed that has a Ratio2 substantially equal to the Ratio1 of the first component. Ratio2 is a modulus of inertia for the second component divided by a Young's Modulus for the second component. Thereafter, the first component and the second component can be used to make an actuator that is spun into fiber to make products (e.g., batting material, woven material, a suture, a thermostat needle, a gel, etc.).

In yet another embodiment, a computer-readable medium is provided that is used to design and determine a Ratio1 for a first component. Ratio1 is a modulus of inertia for the first component divided by a Young's Modulus for the first component. Thereafter, a second component is designed that has a Ratio2 substantially equal to the Ratio1 of said first component. Ratio2 is a modulus of inertia for the second component divided by a Young's Modulus for the second component. Thereafter, the first component and the second component can be used to make an actuator that is spun into fiber to make products (e.g., batting material, woven material, a suture, a thermostat needle, a gel, etc.).

Other embodiments of the invention are provided that include other methods, apparatuses, and computer-readable mediums having features similar to the method described herein.

To facilitate understanding, identical reference numerals have been used, wherever possible, to designate identical elements that are common to the figures.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth to provide a more thorough understanding of the invention. As will be apparent to those skilled in the art, however, various changes using different configurations may be made without departing from the scope of the invention. In other instances, well-known features have not been described in order to avoid obscuring the invention. Thus, the invention is not considered limited to the particular illustrative embodiments shown in the specification and all such alternate embodiments are intended to be included in the scope of the appended claims.

In short, embodiments of the invention make the ratio of the moment of inertia to the Young's Moduli for a first component equal to the ratio of the moment of inertia to the Young's Moduli for a second component. One way to make the two ratios equal is to provide a shape (i.e., the ratio) for the combination of the two components such that there is less of one component than the other component. Exemplary shapes are provided inFIGS. 2 and 3. It is to be understood that the shaped provided herein are for illustrative purposes only and not intended to limit the scope of the invention (i.e., limit the invention to the exemplary shapes).

Some of the commercial applications of embodiments of the invention include, but are not limited to, temperature adaptive insulation, stimuli responsive textiles, self-tightening sutures and switches/thermostats.

For illustrative purposes only, aspects of the invention are described herein as maximizing the bending of the actuators. However, these descriptions are not intended to limit the invention in any way. For example, aspects of the invention also include limiting the bending of the actuators.

For illustrative purposes only, aspects of the invention are described herein using polymers. However, these descriptions are not intended in any way to limit the scope of the invention nor are they intended to limit the scope of the materials which can be used.

One application of the invention is an adaptive thermal insulation for clothing and equipment that provides greater insulation at low temperatures and less at high temperatures. Clothing that adapts to changes in environmental conditions means that fewer items will be required to effectively protect soldiers over a wide range of operating temperatures.

For illustrative purposes only, embodiments of the invention are described herein with respect to temperature adaptive insulation. For example, soldiers must adapt their clothing to a wide variety of weather and climate conditions. This often means adding or subtracting garments and providing more or less ventilation by using openings in the clothing. The insulation required for thermal balance can change rapidly especially in mountainous regions as soldiers move from one altitude to another or encounter climatic variables. If the insulation level is too low it may result in hypothermia or frostbite leading to degraded performance (loss of dexterity and fine motor control). If the insulation level is too high it can result in unnecessary sweating which collects within the insulation, degrading the insulation and increases water consumption, which in turn may lead to dehydration.

Although the term “extrusion” is used herein that use is for illustrative purposes only and not intended, in any way, to limit the scope of the invention. For example, in various embodiments, compounds are bonded, secured, attached, or coupled to each other.

In aspects of the invention, moments of inertia of the components are tailored such that the response of materials with very different mechanical moduli is accommodated. As an example, one implementation of this is a bi-component fiber of triangular cross section (depicted inFIG. 2). InFIG. 2, a first component202is depicted as the “top” of the triangular shaped extrusion200while the second component204is the “bottom” of the triangular shaped extrusion200(note that the second component204has a trapezoidal shape).

Experimentally it is found that considerably greater bending can be seen in configurations with the first component202composed of a higher modulus material than the second compound204(rather than a reverse configuration with the second compound204on top).

FIG. 2also depicts a length (“b”) of one dimension206of first component202and a length (“c”) of one dimension208of second component204. First component202and second component204include heights a11and a22, respectively. The curvature for triangular cross section200is provided in Equation (5), as follows:

where

1ρtri
is the radius of curvature of the triangular cross-section200, h is the total height or diameter of the components202and204, α2is the coefficient of thermal expansion for component204, α1is the coefficient of thermal expansion for component202, n is the ratio of the Young's moduli of the components202and204, and m is a ratio of the thickness of components202and204, a1is the height of the component202, and a2is the height of component204. Note that a1+a2=1 and that a2=1−a1has been substituted into Equation (5).

Calculation of the moment of inertia for first component202is provided by Equation (6).

where I1is the moment of inertia for first component202, a11is the height of the first component202, and b is the length of one of the dimensions (i.e., the base) of the first component202.

Calculation of the moment of inertia for the second component204is provided by Equation (7).

where I2is the moment of inertia for second component204, a22is the height of the second component204, and b and c are lengths of the upper and lower sides (of the trapezoid) of the second component204.

Equation (5) is simplified to Equation (8) when m=1.

where

1ρtri
is the radius of curvature of the triangular shaped extrusion200, h is the total height of the triangular shaped extrusion200, α2is the coefficient of thermal expansion for component204, α1is the coefficient of thermal expansion for component202, n is the ratio of the Young's moduli of the components202and204.

FIG. 3depicts another embodiment 300 of the invention. Specifically,FIG. 3depicts a substantially circular shaped cross-section300. The substantially circular shaped cross-section300includes a first component302(at an upper portion of the cross-section300) and a second component304(at a lower portion of the cross-section300).

The first component302includes a height308(a11) and a dimensional length306(b). The second component304includes a height310(a22). Extrusion300includes a diameter314(depicted in dashed lined). Angle θ312is taken from the diameter314(and center of cross-section300) and is the angle formed between the diameter314and dashed lines316extending from the center of the extrusion300to the ends of dimensional length306.

The curvature for circular shaped cross-section300is provided below in Equation (9), (10), (11), and (12) (when components302and304are of unequal height).

where X is used as a substitution to simplify Equation (12).

where F is used as a substitution to simplify Equation (12).

where A1represents the cross-sectional area of the first component302and A2represents the cross-sectional area of the second component304.

where

1ρcirc
is the radius of curvature of the circular cross-section300, h is the total height or diameter of the circular cross-section300, α2is the coefficient of thermal expansion for component304, α1is the coefficient of thermal expansion for component302, n is the ratio of the Young's moduli of the components302and304, m is a ratio of the thickness of components302and304, X is provided by Equation (9), F is provided by Equation (10), k is the ratio of cross-sectional areas of the first component302to the second component304, and B and C are functions of the geometry of the circle and are used as a substitute for variables to simply Equation (12a).

where

1ρcirc
is the radius of curvature of the circular cross-section300, h is the total height or diameter of the circular cross-section300, α2is the coefficient of thermal expansion for component304, α1is the coefficient of thermal expansion for component302, n is the ratio of the Young's moduli of the components302and304, m is a ratio of the thickness of components302and304, X is provided by Equation (9), F is provided by Equation (10), k is the ratio of cross-sectional areas of the first component302to the second component304, and B and C are functions of the geometry of the circle and are used as a substitute for variables to simply Equation (12b).

Equation (12a) can be simplified to Equation (13) when the areas of the two components are equal (i.e., when θ=π and k=1).

where

1ρcirc
is the radius of curvature of the circular cross-section300, h is the total height or diameter of the circular cross-section300, α2is the coefficient of thermal expansion for component304, α1is the coefficient of thermal expansion for component302, n is the ratio of the Young's moduli of the components302and304, and m is a ratio of the thickness of components302and304.

Embodiments of the invention use the ratio of the moment of inertia to the Young's Moduli for a first component equal to the ratio of the moment of inertia to the Young's Moduli for a second component to create shaped fibers that bend in response to temperature. The shaped fibers are multi-component fibers (e.g., bi-component or tri-component fibers). Multi-component spinning can be used as a cost effective way of producing large quantities of fibers that bend as the temperature changes.

One way to use such fibers is to create a loose mat or batting. Battings are commonly used as insulation in, for example, jackets and sleeping bags. In various embodiments, the polymeric fibers (e.g., bi-component or tri-component polymeric fibers having circular or triangular cross-sections) are used to provide insulation which changes thickness in response to temperature. The polymeric fibers have at least two components with different coefficients of thermal expansion (CTE). As the temperature changes polymeric fibers are temperature responsive and curl as the temperature is decreased. Curling of the polymeric fibers (in response to the decrease temperature) causes the insulation thickness to increase providing greater thermal insulation.

As indicated above, bi-component and tri-component fibers can spun from commercially available polymers of widely differing coefficients of thermal expansion. Some combination of polymers and fiber geometry results in changes of more than two orders of magnitude (>1.5×10−2per ° C.).

Fibers can be spun to create a temperature adaptive thermal insulation using a tri-component fiber extruder. One of the purposes of a third component (depicted inFIG. 7) is to limit the interfacial shear between the high and low CTE components.

In some embodiments of the invention, thickness changes by more than 1.5% per ° C. (30% over a temperature range from approximately 20° C. to 0° C.).

FIG. 4depicts a plot400of the temperature response (i.e., curvature) using Equation (1). Specifically, graph400includes a curvature402(parallel to a “Z axis”), a ratio of moduli

(E1E2)
404(parallel to a “Y axis”), and an upper rectangle height fraction406(parallel to an “X axis”). The graph400depicts plot408which shows that when the ratio of the moduli are equal to 1 then the optimum bending occurs at 50% of each component. The maximum bending at any ratio of the moduli404from 0-10 is different depending upon the composition of the fiber.

FIG. 5shows a graph500of the temperature response for a series when the area fraction of the base of the triangle is systematically varied. Specifically, graph500includes a curvature402(parallel to a “Z axis”), a ratio of moduli

(E1E2)
404(parallel to a “Y axis”), and an upper segment height fraction504(parallel to an “X axis”). The graph500depicts plot502which shows that when compared to a rectangular cross-section (e.g., in the plot408) that a circular cross-section provides a potential for greater bending of the fiber (in various embodiments) and greater suppression of bending of the fiber (in other embodiments). In addition, plot502also shows that the components used can be at a higher ratio of the moduli than taught in the prior art.

FIG. 6depicts a graph600of the temperature response for a systematically varied area fraction of the base of the triangle in accordance with embodiments of the invention. Specifically, graph600includes a curvature402(parallel to a “Z axis”), a ratio of moduli

(E1E2)
404(parallel to a “Y axis”), and an upper triangle height fraction604(parallel to an “X axis”). The graph600depicts plot602which shows that when compared to a rectangular cross-section (e.g., in the plot408) that a triangular shaped cross-section provides a potential for greater bending of the fiber (in various embodiments) and greater suppression of bending of the fiber (in other embodiments). In addition, plot602also shows that the components used can be at a higher ratio of the moduli than taught in the prior art.

It appears from plot604that the batting is stronger for decreasing area fraction of the bottom section (i.e., second component204) of a triangular shaped cross-section of a fiber. The results are consistent with the analytical model. Some Fiber samples show a change in the thickness of 1.8% per ° C. while the lowest response is about 0.3% or less. In some embodiments, an area fraction of 0.3 is the approximate lower limit for the fiber spinning apparatus. Plot604indicates an optimum response at a level that is a function of the ratio of the mechanical moduli of the components in a two component system.

In various embodiments of the invention, isotactic and syndiotactic polypropylene (i-PP, s-PP) are the components used in the fibers. The isotactic polymer is of a relatively high crystallinity and has a relatively high modulus and low coefficient of thermal expansion. In contrast, the syndiotactic polymer crystallizes slowly and is expected to have a high CTE and a low modulus.

Values for polypropylene can be taken from Uehara, H., Yamazaki, Y. and Kanamoto, T. Tensile Properties of Highly Syndiotactic Polypropylene. 1996, Vol. 37, 1, pp. 57-64 (hereinafter “Uehara”) for calculation and comparison of values obtained during testing. For example, drawn isotactic polypropylene presumed to have a fiber modulus of 20 GPa while well drawn syndiotactic polypropylene had a fiber modulus of 3 GPa and a ratio of 6.67-to-1. A typical CIL for an amorphous polymer is around 10−4m/m ° C. Crystalline and highly oriented polymeric fibers can have a negative CTE along the length of the fiber. The chain axis CTE for isotactic PP crystals is negative, −1×10−5m/m ° C.

In various embodiments of the invention, fibers are spun from commercial grades of polypropylene. In various embodiments, spun fibers have an edge length of approximately about 50 microns. In various embodiments, fibers are spun with a draw ratio of about 2.5-to-1 and collected onto rolls of about 15 cm diameter. Crystalline and highly oriented polymeric fibers can have a negative CTE along the length of the fiber. The chain axis CTE for isotactic PP crystals is negative, −1×10−5m/m ° C.

In various embodiments, the CTE and modulus in the fiber direction of each component is a function of the level of crystallinity and the orientation of the crystal, amorphous and intermediate phases.

FIG. 7depicts a triangular cross-section of a fiber700in accordance with embodiments of the invention. The fiber700includes a first component702, a center section704, and a second component706.

In various embodiments, the first component702is s-PP, the second component706is i-PP, and the center section704includes a small amount of dye added to a random ethylene propylene copolymer (co-EP) with a low modulus to limit interfacial stress between the first component702and the second component706but with a coefficient of thermal expansion similar to s-PP.

In various embodiments, a high modulus polymer of the second component706provides a modulus ratio of 1/6.67 or 0.15. From the equations above (e.g., Equations (5), (6), (7), and (8)), for a system with this modulus ratio, the maximum curvature is predicted to occur when the fraction of the first component702is between about 0.8 and about 0.85 (second component fraction between about 0.2 and about 0.15). A micrograph708of actual fibers is also depicted inFIG. 7. “Table 1” below provides examples of fibers (e.g., Fiber 1) and component ratios.

Fibers cut from rolls are spontaneously curled to form batting. The curling is the result of relaxation of stresses from the spinning process and the change in length as the fibers are cooled from the spinning temperature.

The battings can then die cut into samples for testing (e.g., cut into about 20 in2(129 cm2) circular samples). The thickness of the samples can be measured in a temperature controlled chamber by compressing the samples with a pressure of about 0.02 psi. The thickness of the samples can first measured be at room temperature then in an environmental chamber cooled to zero ° C.

FIG. 8depicts a plot800of a temperature response for an exemplary cross-section of an actuator in accordance with embodiments of the invention. Specifically,FIG. 8shows the change in thickness of batting per ° C.802(parallel to the “Y-axis”) where the area fraction of the base of the triangle804(parallel to the “X-axis”) is systematically varied. The results are consistent with the analytical model. For example,FIG. 8depicts a change in thickness of 1.8% per degree C. while the lowest response is about 0.3% or less. An area fraction of about 0.3 is the approximate lower limit for the fiber spinning apparatus.

An analysis of the thermally-induced curvature of bi-component fibers of various cross-sections with respect to the ratio of the moduli of the components and the fraction of the cross-section that each component occupies is provided. Graphical analysis of these functions supports qualitatively that to achieve maximum curvature of the fibers, the design space of interest resides along the “spine” of the surfaces. Quantitatively, the functions allow the proportions of the components to be selected to maximize the fiber curvature for a given pair of polymers. Experimental fibers of varying component fractions were spun, formed into mats and their thickness measured at various temperatures. The experimentally measured thickness changes are in good agreement with the analytical results for fiber bending. Based on a one dimensional heat transfer model the change in thickness appears to be sufficient for a practical adaptive thermal insulation.

FIG. 9depicts an embodiment of a method900in accordance with embodiments of the invention. The method900begins at step902and proceeds to step904.

At step904, a ratio (i.e., “Ratio1”) is determined between the moment of inertia and the Young's modulus for a first component. Thereafter, the method900proceeds to step906.

At step906, a ratio (i.e., “Ratio2”) is determined between the moment of inertia and the Young's modulus for a second component. Thereafter, the method900proceeds to step908.

At step908, an actuator is formed (e.g., spun fibers or adhesion) using the first component and the second component. Ratio1 and Ratio2 determine the amounts of the first component and the second component used. The amount of each component is adjusted until the ratios I/E (of each component) are substantially the same. So that Ratio1 and Ratio2 are substantially equal the actuators can have non-rectangular shapes (e.g., triangular or circular). After formation of the actuators, the method900proceeds to and ends at step912.

In various embodiments, the method900proceeds to optional step910. At optional step910the actuators (when the actuators are spun fibers) are formed into batting. After optional step910, the method proceeds to and ends at step912.

FIG. 10depicts an embodiment of a high-level block diagram of a general-purpose computer architecture1000for an actuator in accordance with embodiments of the invention. For example, the general-purpose computer1000is suitable for use in performing the methods ofFIGS. 9, 15, 16, and 17. The general-purpose computer ofFIG. 10includes a processor1010as well as a memory1004for storing control programs and the like.

In various embodiments, memory1004also includes programs (e.g., depicted as an “actuator cross-section”1012for creating actuators having a cross-sectional shape such that a ratio of the moment of inertia to Young's modulus for a first component is substantially equal to the moment of inertia to Young's modulus for a second component) for performing the embodiments described herein.

In other embodiments, the memory1004includes programs (not shown) for designing a first component having a Ratio1 for that first component. Ratio1 is a modulus of inertia for the first component divided by a Young's Modulus for the first component. The program is also used to design a second component that has a Ratio2 substantially equal to the Ratio1 of the first component. Ratio2 is a modulus of inertia for the second component divided by a Young's Modulus for the second component. When instructed these programs can place at least one cavity in the first component and/or the second component while still making Ratio1 substantially equal to Ratio2. Thereafter, the first component and the second component can be used to make an actuator that is spun into fiber to make products (e.g., batting material, woven material, a suture, a thermostat needle, a gel, etc.).

The processor1010cooperates with conventional support circuitry1008such as power supplies, clock circuits, cache memory and the like as well as circuits that assist in executing the software routines1006stored in the memory1004. As such, it is contemplated that some of the process steps discussed herein as software processes can be loaded from a storage device (e.g., an optical drive, floppy drive, disk drive, etc.) and implemented within the memory1004and operated by the processor1010. Thus, various steps and methods of the present invention can be stored on a computer readable medium. The general-purpose computer1000also contains input-output circuitry1002that forms an interface between the various functional elements communicating with the general-purpose computer1000.

AlthoughFIG. 10depicts a general-purpose computer1000that is programmed to perform various control functions in accordance with the present invention, the term computer is not limited to just those integrated circuits referred to in the art as computers, but broadly refers to computers, processors, microcontrollers, microcomputers, programmable logic controllers, application specific integrated circuits, and other programmable circuits, and these terms are used interchangeably herein. In addition, although one general-purpose computer1000is depicted, that depiction is for brevity on. It is appreciated that each of the methods described herein can be utilized in separate computers.

FIG. 11depicts an embodiment of a system1100in accordance with material disclosed herein.

The system1100includes an extruder11021and extruder11022. Each of the extruders11021and11022are adapted to receive a different component (e.g., one polymer is poured into extruder11021and a different polymer is poured into extruder11022). Illustratively, the polymer poured into extruder11021is one of isotactic polypropylene, a polyethyleneterephthalate (PET) and polyester; and the polymer poured in extruder11022is one of an amorphous polymer, a syndiotactic polypropylene, and a polycarbonate. After polymers are poured into the extruders11021and11022, the extruders11021and11022melt the polymers.

After the polymers melt, the extruders11021and11022force the polymers through metering pumps11041and11042. Each metering pumps11041and11042regulate the amount of melted polymer that passes through the metering pump11041and11042to a dye1106. A ratio of a modulus of inertia to a Young's Modulus for each component (illustratively referred to hereinafter as the “first ratio” and “second ratio” respectively) is acquired. The metering pumps11041and11042regulate the amount of each polymer that passes through the dye1106. The dye1106has an internal periphery which shapes and combines the two polymers. The metering pumps11041and11042regulate the amount of polymer passing through each respective pump such that the amount extruded through the dye1106results in the first ratio being substantially equal to the second ratio. In addition, the internal periphery (of the dye1106) forces an actuator (not shown) (i.e., a combination of the two polymers) passing through the dye1106to have the internal periphery of the dye1106. The resulting actuator has a cross-sectional shape (e.g., a triangular cross-section or a substantially circular cross-section) where the first ratio is substantially equal to said second ratio.

After an actuator is formed (i.e., as fibers), the fibers are spun onto cylindrical drum11081. In various embodiments, the system1100includes multiple cylindrical drums11081,11082, . . . and1108n.

Illustratively,FIG. 11depicts a bi-component extruder. However, that depiction is not intended in any way to limit the scope of the invention. For example, embodiments of the invention can be used in conjunction with tri-component extruders.

In various embodiments of the invention can be utilized with Micro-Electro-Mechanical-Systems (“MEMS”). Embodiments of the invention can be used to design/build actuators by machining, Computer Numerical Controlled machining (“CNC”), and micromachining processes. Even at the micron or nanometer level aspects of the invention can be used to make an actuator.

FIG. 12depicts an exemplary embodiment of a substantially triangular cross-section, of an actuator1200, in accordance with material disclosed herein. The actuator1200includes a first component1202and a second component1204. For illustrative purposes only, the first component1202is depicted, inFIG. 12, (and described below) as including one cavity1210. However, it is appreciated that in various embodiments, the first component1202has more than one cavity (or no cavity) and/or the second component1204includes no cavity or at least one cavity.

Note that “cavity” and “void” are interchangeably used herein.

A “Y-axis”1206and an “X-axis”1208are placed against the first component1202. Alphanumeric character “a2” designates the maximum height of the first component1202along the “Y-axis”1206. Alphanumeric character “a1” designates the maximum height of the second component1204along the “Y-axis”1206. Alphanumeric character “b” designates the maximum length of the first component1202and the second component1204along the “X-axis”1206.

Inside the first component1202is a cavity1210. The cavity1210has a centroid1212. Alphanumeric character “CY”1214designates the coordinate of the centroid1212along the “Y-axis”1206. Alphanumeric character “CX”1216designates the coordinate of the centroid1212along the “X-axis”1204.

The cavity1210is illustratively depicted as having a substantially rectangular shape. However, that depiction is not intended to limit the scope of the material taught herein in any way. It is appreciated that in various embodiments the cavity1210has another shape (e.g., a substantially circular shape, a substantially triangular shape, etc.).

When a component(s) includes a void, the centroid of the void moves as the void is moved up or down (i.e., vertically) within the component. An equation for the distance of the centroid from the X-axis is a variable of both, the size of the void and location within the component (i.e., the void centered along the X-axis).

Below, the moment of inertia is calculated for the first component1202without the cavity1210. Thereafter, the moment of inertia is calculated for the area occupied by the cavity1208.

For simplicity, calculations below regardingFIG. 12are considered in three parts. For example, a first part relates to calculations on the first component1202without consideration of the cavity1208. Variables relating to the first part include an “I” in the subscript of the variable.

A second part relates to calculations involving the first component1202minus the cavity1208. Variables relating to the second part include an “II” in the subscript of the variable.

A third part relates to calculations involving the cavity1208. Variables relating to the third part include an “III” in the subscript of the variable. The calculations below acquire the moment of inertia for the first part, the moments of inertia for the third part, and subtract the moments of inertia of the third part from the moments of inertia from the first part to obtain the moments of inertia of the second part (i.e., the moments of inertia of the component1202with cavity1208).

where “A” is the length of the cavity1210along the “Y-axis”1206, “fa” is the ratio of the cavity height to the first component height, and “a” is the maximum height of the component1202along the “Y-axis”1206.
B=fbbEquation (15)

where “B” is the length of the cavity1210along the “X-axis”1208, “fb” is the ratio of the cavity length to the component length, and “b” is the maximum length of the component1202along the “X-axis”1208.

(A2<Cy<a-A2)⁢⁢where,(0<fa,fb<1)⁢⁢and⁢⁢fa2<fc<(1-fa2)Equation⁢⁢(16)
where “Cy” is the distance from the “Y-axis”1206to the centroid1212of the cavity1210, “A” is the length of the cavity1210along the “Y-axis”1206, and “a” is the maximum height of the component1202along the “Y-axis”1206.

As indicated above, the centroid1212location will move as the cavity1210is moved up or down within the section, so:

yc=ab⁡(a2)-ABCyab-AB=a⁡(1-2⁢fa⁢fb⁢fc)2⁢(1-fa⁢fb)Equation⁢⁢(17)
where “yc” is the distance of the centroid1210from the “X-axis”1208, “a” is the maximum height of the component1202along the “Y-axis”1206, “b” is the maximum length of the component1202along the “X-axis”1208, “A” is the length of the cavity1210along the “Y-axis”1206, where “B” is the length of the cavity1210along the “X-axis”1208, “Cy” is the distance from the “Y-axis”1206to the centroid1212, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

For example, when fc=0.5 in Equation (17) then:

where “yc” is the distance of the centroid1210from the “X-axis”1208and “a” is the maximum height of the component1202along the “Y-axis”1206.

With this relation for ycthe moment of inertia can be found:
AI=abEquation (19)
where “AI” is the area of the upper component1202, “a” is the maximum height of the component1202along the “Y-axis”1206, and “b” is the maximum length of the component1202along the “X-axis”1208.
AIII=ABEquation (20)

where “AIII” is area of the cavity1210, “A” is the length of the cavity1210along the “Y-axis”1206, and “B” is the length of the cavity1210along the “X-axis”1208.
AII=AI−AIII=ab−AB=ab−faafbb=ab(1−fafb)  Equation (21)

where “AII” is the area of the first component1202, “AI” is the area of the first component1202and the cavity1210, “AIII” is area of the cavity1210, “a” is the maximum height of the component1202along the “Y-axis”1206, “b” is the maximum length of the component1202along the “X-axis”1208, “A” is the length of the cavity1210along the “Y-axis”1206, “B” is the length of the cavity1210along the “X-axis”1208, “fa” is the ratio of the cavity height to the first component height, and “fb” is the ratio of the cavity height to the component height.
IIx=IIIx/IIIIx,  Equation (22)

where “IIx” is the moment of inertia of the first component1202and the cavity1210, “IIIx” is the moment of inertia for the first component1202, and “IIIIx” is the moment of inertia for the cavity1210.

where “IIx” is the moment of inertia of the first component1202and the cavity1210, “a” is the maximum height of the component1202along the “Y-axis”1206, and “b” is the maximum length of the component1202along the “X-axis”1208.

where “IIIIx” is the moment of inertia for the cavity1210, “A” is the length of the cavity1210along the “Y-axis”1206, “B” is the length of the cavity1210along the “X-axis”1208, and “Cy” is the distance from the “Y-axis”1206to the centroid1212.
IIIx=IIx−IIIIxEquation (25)

where “IIx” is the moment of inertia of the first component1202and the cavity1210, “IIIx” is the moment of inertia for the first component1202, and “IIIIx” is the moment of inertia for the cavity1210.

Substituting Equation (23) and Equation (24) into Equation (25) algebraically provides Equation (26) and Equation (27).

where “IIIIx” is the moment of inertia of the first component1202, “a” is the maximum height of the component1202along the “Y-axis”1206, “b” is the maximum length of the component1202along the “X-axis”1208, “A” is the length of the cavity1210along the “Y-axis”1206, “B” is the length of the cavity1210along the “X-axis”1208, and “Cy” is the distance from the “Y-axis”1206to the centroid1212.

where “a” is the maximum height of the component1202along the “Y-axis”1206, “b” is the maximum length of the component1202along the “X-axis”1208, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “f0” is the ratio of “Cy” to the first component height.

Equation (27) can be further simplified into Equation (28).

where “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.
IIIc=IIIx−AII(yc)2Equation (29)

where “IIIc” is the moment of intertia of the first component relative to its centroid, “IIIx” is the moment of inertia for the first component1202, “AII” is the area of the first component1202, and “yc” is the distance of the centroid1210from the “X-axis”1208.

where “a” is the maximum height of the component1202along the “Y-axis”1206, “b” is the maximum length of the component1202along the “X-axis”1208, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

where “a” is the maximum height of the component1202along the “Y-axis”1206, “b” is the maximum length of the component1202along the “X-axis”1208, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of Cy to the first component height.

FIG. 13depicts an exemplary embodiment of a substantially triangular cross-section, of an actuator1300, in accordance with material disclosed herein. The actuator1300includes a first component1302and a second component1304. For illustrative purposes only, the first component1302is depicted (inFIG. 13) and described below as including one cavity1316. However, it is appreciated that in various embodiments, the first component1302has more than one cavity (or no cavity) and/or the second component1304includes at least one cavity.

The actuator1300includes a height1310. Height is measured along the “Y-axis.” In addition, the first component1302includes a maximum height1306(also indicated inFIG. 13by alphanumeric character “a1”) and the second component includes a maximum height1308(also indicated inFIG. 13by alphanumeric character “a2”).

Length is measured along the “X-axis”1312. The first component1302includes a length1312.

As indicated above, the first component1302includes cavity1316. The cavity1316has a maximum length indicated by an alphanumeric character “B” and a maximum height indicated by an alphanumeric character “A.” The maximum height “A” is illustratively twice the length of the maximum length “B.” The cavity1316includes a centroid1324. “Cy”1322is the distance from the “Y-axis”1314to the centroid1324. “Cx”1318is the distance from the “X-axis”1312to the centroid1324.
A=faaEquation (32)

where “A” is the height of the cavity1316along the “Y-axis”1314, “fa” is the ratio of the cavity height to the first component height, and “a” is the maximum height of the first component1302along the “Y-axis”1314.
B=fabEquation (33)

where “B” is the length of the cavity1316along the “X-axis”1312, “fb” is the ratio of the cavity length to the first component length, and “b” is the maximum length of the component1302along the “X-axis”1312.

where “Cy”1322is the distance from the “Y-axis”1314to the centroid1324, “fc” is the ratio of Cy to the first component height, “a” is the maximum height of the component1202along the “Y-axis”1206, “A” is the height of the cavity1316along the “Y-axis”1314, “fa” is the ratio of the cavity height to the first component height, and “fb” is the ratio of the cavity height to the component height.

where “AI” is the area of the upper component1302, “a” is the maximum height of the component1302along the “Y-axis”1314, and “b” is the maximum length of the first component1302along the “X-axis”1312.

where “AIII” is area of the cavity1316, “A” is the height of the cavity1316along the “Y-axis”1314, and “B” is the length of the cavity1316along the “X-axis”1312.

where “AII” is the area of the first component1302, “AI” is the area of the first component1302and the cavity1316, “AIII” is area of the cavity1316, “a” is the maximum height of the component1302along the “Y-axis”1314, “b” is the maximum length of the component1302along the “X-axis”1312, “A” is the height of the cavity1316along the “Y-axis”1314, “B” is the length of the cavity1316along the “X-axis”1312, “fa” is the ratio of the cavity height to the first component height, and “fb” is the ratio of the cavity height to the component height.
IIx=IIIx+IIIIxEquation (38)

where “IIx” is the moment of inertia of the first component1302and the cavity1316, “IIIx” is the moment of inertia for the first component1302, and “IIIIx” is the moment of inertia for the cavity1316.

where “IIx” is the moment of inertia of the first component1302and the cavity1316, “a” is the maximum height of the component1302along the “Y-axis”1314, and “b” is the maximum length of the component1302along the “X-axis”1312.

where “IIIIx” is the moment of inertia for the cavity1316, “A” is the height of the cavity1316along the “Y-axis”1314, “B” is the length of the cavity1316along the “X-axis”1312, and “Cy” is the distance from the “Y-axis”1314to the centroid1324.
IIIx=IIx−IIIIxEquation (41)

where “IIIx” is the moment of inertia for the first component1302, “IIx” is the moment of inertia of the first component1302and the cavity1316, and “IIIIx” is the moment of inertia for the cavity1316.

Substituting Equation (39) and Equation (40) into Equation (41) algebraically provides Equation (42), Equation (43), and Equation (44).

where “a” is the maximum height of the component1302along the “Y-axis”1314, “b” is the maximum length of the component1302along the “X-axis”1312, “A” is the height of the cavity1316along the “Y-axis”1314, “B” is the length of the cavity1316along the “X-axis”1312, and “Cy” is the distance from the “Y-axis”1314to the centroid1324.

where “a” is the maximum height of the component1302along the “Y-axis”1314, “b” is the maximum length of the component1302along the “X-axis”1312, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

where “a” is the maximum height of the component1302along the “Y-axis”1314, “b” is the maximum length of the component1302along the “X-axis”1312, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

where “a” is the maximum height of the component1302along the “Y-axis”1314, “b” is the maximum length of the component1302along the “X-axis”1312, “A” is the height of the cavity1316along the “Y-axis”1314, “B” is the length of the cavity1316along the “X-axis”1312, “C)” is the distance from the “Y-axis”1314to the centroid1324, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

For example, in Equation (45)

where “IIIc” is the moment of intertia of the first component relative to its centroid, “IIIx” is the moment of inertia for the first component1302, “AII” is the area of the first component1302, and “yc” is the distance of the centroid1324from the “X-axis”1312.

where “IIIc” is the moment of intertia of the first component relative to its centroid, “a” is the maximum height of the component1302along the “Y-axis”1314, “b” is the maximum length of the component1302along the “X-axis”1312, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

where “IIIc” is the moment of intertia of the first component relative to its centroid, “a” is the maximum height of the component1302along the “Y-axis”1314, “b” is the maximum length of the component1302along the “X-axis”1312, “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

Upon substituting the above, the equivalent equation to Equation (8) becomes:

“1ρ”
is the radius of curvature of a cross-section of1300, “h” is the total height of the cross-section1300, “α2” is the coefficient of thermal expansion for component1304, “α1” is the coefficient of thermal expansion for component1302, “t−to” is the change in temperature, “n” is the ratio of the Young's moduli of the components1302and1304; and “U” and “L” are functions of the size and location of the cavity1316:

where “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.
L=(1−fafb)  Equation (51)

where “fa” is the ratio of the cavity height to the first component height, “fb” is the ratio of the cavity height to the component height, and “fc” is the ratio of “Cy” to the first component height.

for instance, in the case where

where

“1ρ”
is the radius of curvature of a cross-section of1300, “α2” is the coefficient of thermal expansion for component1304, “α1” is the coefficient of thermal expansion for component1302, “t−to” is the change in temperature, “h” is the total height of the cross-section1300, and “n” is the ratio of the Young's moduli of the components1302and1304

In various embodiments, a component has a shape different than a cavity contained within the component.FIG. 14depicts an illustrative example, of a component having a shape (e.g., a substantially triangular shape) different than a cavity (e.g., a substantially circular shape) within the component.

Specifically,FIG. 14depicts an exemplary embodiment of a substantially triangular cross-section, of an actuator1400, in accordance with material disclosed herein. The actuator1400includes a first component1402and a second component1404. For illustrative purposes only, the first component1402is depicted (inFIG. 14) and described below as including one cavity1416. However, it is appreciated that in various embodiments, the first component1402has more than one cavity (or no cavity) and/or the second component1404includes at least one cavity.

The actuator1400includes a height1410. Height is measured along the “Y-axis”1414. In addition, the first component1402includes a maximum height1406(also indicated inFIG. 14by alphanumeric character “a1”) and the second component includes a maximum height1408(indicated inFIG. 14by alphanumeric character “a2”).

Length is measured along the “X-axis”1412. The first component1402includes a length indicated by alphanumeric character “b.”

As indicated above, the first component1402includes cavity1416. The cavity1416includes a centroid1424. The centroid1416has a diameter “d”1420. “Cy”1422is the distance from the “Y-axis”1414to the centroid1424. “Cx”1420is the distance from the “X-axis”1412to the centroid1324.
D=faaEquation (53)

where “D” is the diameter of the cavity1416, “fa” is the ratio of the cavity height to the first component height, and “a” is the maximum height of the first component1402.

where “Cy”1422is the distance from the “Y-axis”1414to the centroid1424, “fc” is the ratio of Cy to the first component height, “a” is the maximum height of the component1402along the “Y-axis”1414, and “D” is the diameter of the cavity1416.

where “fa” is the ratio of the cavity height to the first component height and “fc” is the ratio of “Cy” to the first component height.

where “A1” is the area of the first component1402, “a” is the maximum height of the component1402along the “Y-axis”1414, and “b” is the maximum length of the first component1402along the “X-axis”1412.

where “AIII” is area of the cavity1402, “π” is the circumference of a circle (i.e., the circumference of cavity1416), and “D” is the diameter of the cavity1416.

where “AII” is the area of the first component1402, “AI” is the area of the first component1402and the cavity1416, “AIII” is area of the cavity1416, “a” is the maximum height of the component1402along the “Y-axis”1414, “b” is the maximum length of the component1402along the “X-axis”1412, “π” is the circumference of a circle (i.e., the circumference of cavity1416), “D” is the diameter of the cavity1416, and “fa” is the ratio of the cavity height to the first component height.

where “AII” is the area of the first component1402, “a” is the maximum height of the component1402along the “Y-axis”1414, “b” is the maximum length of the component1402along the “X-axis”1412, “π” is the circumference of a circle (i.e., the circumference of cavity1416), and “fa” is the ratio of the cavity height to the first component height.

where “IIx” is the moment of inertia of the first component1402and the cavity1416, “a” is the maximum height of the component1402along the “Y-axis”1414, and “b” is the maximum length of the component1402along the “X-axis”1412.

where “IIIIc” is the moment of inertia of the cavity with respect to the cavity centroid and “D” is the diameter of the cavity1416.

where “IIIIx” is the moment of inertia for the cavity1416, “IIIIc” is the moment of inertia of the cavity with respect to the cavity centroid, “AIII” is area of the cavity1402, “Cy” is the distance from the “Y-axis”1414to the centroid1424, “π” is the circumference of a circle (i.e., the circumference of cavity1416), “D” is the diameter of the cavity1416, “fc” is the ratio of “Cy” to the first component height, “a” is the maximum height of the component1402along the “Y-axis”1414, and “fa” is the ratio of the cavity height to the first component height.

where “IIIx” is the moment of inertia for the first component1302, “IIx” is the moment of inertia of the first component1402and the cavity1416, “IIIIx” is the moment of inertia for the cavity1416, “a” is the maximum height of the component1402along the “Y-axis”1414, “b” is the maximum length of the component1402along the “X-axis”1412“it” is the circumference of a circle (i.e., the circumference of cavity1416), “D” is the diameter of the cavity1416, “fa” is the ratio of the cavity height to the first component height, “fc” is the ratio of “Cy” to the first component height.

where “yc” is the distance of the centroid1424from the “X-axis”1412, “a” is the maximum height of the component1402along the “Y-axis”1414, “b” is the maximum length of the component1402along the “X-axis”1412, “π” is the circumference of a circle (i.e., the circumference of cavity1416), “D” is the diameter of the cavity1416, “Cy”1422is the distance from the “Y-axis”1414to the centroid1424, “fa” is the ratio of the cavity height to the first component height, and “fc” is the ratio of “Cy” to the first component height.

FIG. 15depicts an exemplary embodiment of a method1500in accordance with material disclosed herein. The method1550begins at step1502and proceeds towards step1504.

At step1504, form at least one cavity in a first component and/or a second component. An overall size is selected for an actuator. As the size of the actuator is decreased, the actuator will have an ability to bend greater. As indicated above, the cavity (or cavities when there are multiple cavities) can have various shapes (e.g., a substantially rectangular or substantially triangular shape). After the cavity (or cavities when there are multiple cavities) is formed, the method1500proceeds towards step1506.

At step1506, a ratio1

I1E1
(i.e., the ratio of the moment of inertia to the Young's Modulus) for the first component is acquired. A rate at which the first component is extruded from the die, is in accordance with ratio1. It follows that the rate at which the first component is extruded also depends upon the material used for the first component because the moment of inertia and the Young's Modulus for the second component are specific to the material used to make the second component. Thereafter the method1500proceeds towards step1508.

At step1508, a ratio2

I2E2
(i.e., the ratio of the moment of inertia to the Young's Modulus) for the second component is acquired. A rate at which the first component is extruded from the die, is in accordance with ratio2. It also follows that the rate at which the second component is extruded also depends upon the material used for the second component because the moment of inertia and the Young's Modulus for the second component are specific to the material used to make the second component. Thereafter the method1500proceeds towards step1510.

At step1510, an actuator is formed/provided that includes the first component and the second component. The actuator is in the form of fiber. The actuator has a cross-sectional where

I1E1
of the first component is substantially equal

I2E2
of the second component. In various embodiments, I1+I2is equal to a fixed total value. Thereafter the method1500proceeds to and ends at step1518.

In various embodiments, the method1500includes optional steps1512,1514, and1516.

For example, in one embodiment, after step1510the method1500proceeds to optional step1512. At optional step1512the actuator is used to form batting material. Thereafter, the method1500proceeds to and ends at step1518. Alternatively, after optional step1512, the method1500proceeds to step1516. At step1516, the batting is used to make a product (e.g., the batting is placed between two layers of material as an insulator).

As another example, in another embodiment of the method1500, after step1510the method1500proceeds towards step1514. At step1514, the actuator is used to make a weave material. After step1514, the method1500proceeds to and ends at step1518. In alternative embodiments, after step1514, the method1500proceeds to step1516. At step1516, the weave material is used to make a product. After step1516, the method1500proceeds to and ends at step1518.

FIG. 16depicts an exemplary embodiment of a method1600in accordance with material disclosed herein. The method1600begins at step1602and proceeds towards step1604.

At step1604, for a predetermined moment of inertia a first component is selected and formed to have at least one cavity. Thereafter, the method1600proceeds towards step1604.

At step1604, a ratio1

I1E1
(i.e., the ratio of the moment of inertia to the Young's Modulus) for the first component is acquired. Thereafter, the method1600proceeds towards step1608.

At step1608, a second component is formed having a ratio2

I2E2
(i.e., the ratio of the moment of inertia to the Young's Modulus) that is substantially equal to the ratio1

I1E1
of the first component (acquired in step1604). Thereafter the method1600proceeds towards step1610.

At step1610, an actuator is formed from the first component and the second component. The extrusion rates of the first component and the second component so that ratio1 is substantially equal to ratio 2. The formed actuator has a cross-sectional shape such that ratio1 is substantially equal to ratio2. After step1610, the method1600proceeds towards and ends at step1610.

In various embodiments, the method1600includes steps other than those describe above. For example, in one embodiment, after step1610the method1600proceeds towards optional step1612. At optional step1612, the actuator is used to form batting material. After optional step1612, the method1600proceeds towards and end at step1618. In yet other embodiments of method1600, after optional step1612, the method1600proceeds towards optional step1616. At optional step1616a product is made using the batting material. After optional step1616, the method proceeds towards and ends at step1618.

In various embodiments of the method1600, after step1610, the method1600proceeds towards optional step1614. At optional step1614, the actuator is used to form a weave material. In various embodiments, after optional step1614, the method1600proceeds towards and ends at step1618. In yet other embodiments, after optional step1614, the method1600proceeds towards optional step1616. At optional step1616a product is made using the weave material. After optional step1616, the method1600proceeds towards and ends at step1618.

FIG. 17depicts an exemplary embodiment of a method1700in accordance with material disclosed herein. Method1700begins at step1702and proceeds towards step1704.

At step1704, a first component is designed so that it has at least one cavity therein. Thereafter, the method1700proceeds towards step1706.

At step1706, a Ratio1

I1E1
for the first component is acquired. After the ratio1 is acquired for the design of the first component, the method1700proceeds towards step1708.

At step1708, a second component is designed having a Ratio2

I2E2
(i.e., the ratio of the moment of inertia to the Young's Modulus) that is substantially equal to the ratio1

I1E1
of the first component. In various embodiments, the design of the second component includes at least one cavity. After designing the second component, the method1700proceeds to and ends at step1718.

In other embodiments, the method1700includes optional steps. For example, after step1708, the method1700proceeds towards optional step1710.

At optional step1710, an actuator is formed/provided that includes the first component and the second component designed in steps1704and1706, respectively. The actuator has a cross-sectional shape such that Ratio1 is substantially equal to Ratio2. In one embodiment, after optional step1710, the method1700proceeds to and ends at step1718.

In other embodiments, the method1700proceeds towards optional step1714after performing optional step1710. At optional step1714the actuator is used to produce a woven material. After optional step1714, the method1700proceeds towards optional step1716. At optional step1716, the woven material is used to make a product. After optional step1716, the method1700proceeds to and ends at step1718.

In various embodiments, an actuator can be designed by one entity and actually manufactured by another entity.