Patent application title: SHAPE MEMORY ALLOY (SMA) ACTUATORS AND DEVICES INCLUDING BIO-INSPIRED SHAPE MEMORY ALLOY COMPOSITE (BISMAC) ACTUATORS
Alexis A. Villanueva (Blacksburg, VA, US)
Colin Smith (Blacksburg, VA, US)
Shashank Priya (Blacksburg, VA, US)
IPC8 Class: AF01B2910FI
Class name: Power plants motor operated by expansion and/or contraction of a unit of mass of motivating medium mass is a solid
Publication date: 2012-07-12
Patent application number: 20120174571
An actuator comprising a flexible spring affixed at a separation distance
from a shape memory alloy or artificial muscle element amplifies strain
developed by the shape memory alloy or artificial muscle element while
maintaining a substantial fraction of the force developed during
activation of the shape memory alloy or artificial memory element. A
plurality of such actuators positioned relative to each other by
encapsulation or attachment to a body of material such as a terminal hub
can emulate a wide variety of biological movements such as for providing
gripping in the manner of an opposed human thumb or propulsion in the
manner of a jellyfish.
1. An actuator comprising, in combination, a flexible spring beam, a
shape memory alloy or artificial muscle element, and a connection between
said flexible spring beam and said shape memory alloy or artificial
muscle element maintaining a separation distance therebetween over a
length of said actuator.
2. The actuator as recited in claim 1, further including stand-off structures for establishing said separation distance.
3. The actuator as recited in claim 1, wherein stiffness of said beam is locally modified to control shape of said actuator when said shape memory alloy or artificial muscle element is activated.
4. The actuator as recited in claim 3, wherein said beam is modified in thickness or width to control stiffness.
5. The actuator as recited in claim 4, wherein said beam is shaped to control shape of said actuator when said shape memory alloy or artificial muscle element is not activated.
6. The actuator as recited in claim 5, wherein said shape memory alloy or artificial muscle element has a parent shape, when activated, such that activation from an unactivated state emulates a biological motion.
7. The actuator as recited in claim 5, wherein a combination of said bean and said shape memory alloy or artificial muscle element has a parent shape, when activated, such that de-activation from an activated state emulates a biological motion.
8. The actuator as recited in claim 1, wherein said beam is modified in thickness or width to control stiffness.
9. The actuator as recited in claim 8, wherein said beam is shaped to control shape of said actuator when said shape memory alloy or artificial muscle element is not activated.
10. The actuator as recited in claim 9, wherein said shape memory alloy or artificial muscle element has a parent shape, when activated, such that activation from an unactivated state emulates a biological motion.
11. The actuator as recited in claim 9, wherein a combination of said bean and said shape memory alloy or artificial muscle element has a parent shape, when activated, such that de-activation from an activated state emulates a biological motion.
12. An apparatus comprising a plurality of actuators, wherein an actuator of said plurality of actuators comprises a flexible spring beam, a shape memory alloy or artificial muscle element, and a connection between said flexible spring beam and said shape memory alloy or artificial muscle element maintaining a separation distance therebetween over a length of said actuator, and a body for locating said plurality of actuators in a desired relationship to each other.
13. The apparatus as recited in claim 12, wherein said body is a rigid body.
14. The apparatus as recite inn claim 12, wherein said body is a terminal hub.
15. The apparatus as recited in claim 14, further including an umbrella shaped bell and said plurality of said actuators are arranged to contract said umbrella-shaped bell.
16. The apparatus as recited in claim 15, wherein said umbrella-shaped bell encapsulates said plurality of actuators.
17. The apparatus as recited in claim 12, wherein said shape memory alloy or artificial muscle element has a parent shape, when activated, such that activation from an unactivated state emulates a biological motion.
18. The apparatus as recited in claim 12, wherein a combination of said bean and said shape memory alloy or artificial muscle element has a parent shape, when activated, such that de-activation from an activated state emulates a biological motion.
CROSS-REFERENCE TO RELATED APPLICATIONS
 This application claims benefit of priority of U S. Provisional Application 61/421,847, filed Dec. 10, 2010, which is hereby incorporated by reference in its entirety.
FIELD OF THE INVENTION
 The present invention generally relates to actuators employing shape memory alloy (SMA) elements and, more particularly, to bio-inspired shape memory alloy composite (BISMAC) actuators and devices employing them including a propulsion system for a submersible vessel emulating a species of fish such as an Aurelia aurita species of jellyfish.
BACKGROUND OF THE INVENTION
 During the progress of science in regard to materials and their physical properties, many new materials have been developed that exhibit unusual physical properties. Some of these properties will have been the object of development of the material, itself and important applications of the material will already exist while other applications may be developed later. Occasionally, unexpected physical properties are developed; for some of which practical applications may be abundantly evident while other properties may remain little more than a scientific curiosity for many years.
 Shape memory alloys (SMAs) fall into the latter classification and the property of being able to return to a given shape after being deformed or bent upon application of heat or a magnetic field was reportedly discovered by accident in regard to a nickel-titanium alloy presumably developed to produce other improved properties compared to other metal alloys. The potential for use in actuators (e.g. as materials that change shape, stiffness, position, natural or resonant frequency or other mechanical characteristics in response to temperature or magnetic fields), in general, may have been more or less immediately apparent but devices to which such materials provided a significant advantage compared to other commonly used materials in known devices were much less readily evident. New designs have been developed for some applications that allow SMAs to be used to advantage such as a so-called variable geometry chevron device that reduces aircraft engine noise, pipe connections for oil pipelines, vibration dampers for structural supports for buildings, bridges and the like, valves for low pressure pneumatic systems, anti-scalding valves (largely due to their response speed being very much higher than, for example, bi-metallic actuators), focusing and image stabilization arrangements for optical systems and eyeglass frames and various medical devices, generally for attachment of implanted devices, guidance of probes and orthodontal appliances. Few, if any, new devices have been developed that uniquely exploit the properties of SMAs for useful purposes. For example, while the light weight of SMA materials and the smooth, easily controllable forces that SMA materials can develop, which are similar to those produced by muscle tissue, suggest uses in robotics and prosthetic devices, few, if any, successful applications have been developed, even for devices of known types for robotic or prosthetic applications.
 SMA materials achieve the shape memory function by undergoing a phase change of the alloy at a transition temperature while in the solid state (e.g. without melting). Many different SMA materials are known and are commercially available. For a nickel-titanium SMA (often referred to as Nitinol), the low temperature phase is referred to as martensite in which the position of particles within the crystal structure of the solid can be rearranged by applied mechanical forces. Thus, in the low temperature, martensite phase, the material is malleable and can be bent and deformed at will. A "parent" shape is developed by holding the material in a particular desired shape and heating the SMA material to about 500° C. The high temperature causes the atoms of the SMA material to assume the most compact and regular arrangement possible, resulting in a rigid cubic arrangement referred to as the austenite phase. The shape thus developed persists after the SMA material is cooled and returns to the malleable and flexible martensite phase. When the SMA material is again heated, above the transition temperature (which can vary between about -50° C. and 160° C., depending on the particular composition of thee SMA, which is much lower than the temperature at which the "parent" shape is established) the SMA material reverts to the austenite phase and the "parent" shape. (The terms "austenite" and "martensite" and other grammatical forms thereof will be used hereinafter in a manner consistent with the usage in regard to Nitinol even though other names may be applied to particular phases of alloys of other compositions.) This cycle can be repeated millions of times if only elastic deformation of the martensite phase is employed or plastic deformation is not excessive although repeated plastic deformation of the SMA material may lead to a shift of the characteristic transformation temperatures; an effect referred to as functional fatigue since it is related to changes of microstructural and functional properties of the SMA material.
 Perhaps one reason for the lack of development of new applications is the fact that while SMA materials can recover up to about 8% of plastic deformation when bent, only about 4% elastic strain can be developed in the change from the martensite phase to the austenite phase (substantially corresponding to the degree of compaction of the crystal lattice in the austenite phase when the "parent" shape is established). In comparison, the amount of contraction of which muscle tissue is capable often exceeds 50% by a substantial margin. For mechanical actuators, the required motion is often a substantial fraction of the overall actuator size. To obtain larger degrees of motion from the shape memory effect, itself, the elastic deformation must be augmented by recoverable plastic deformation from a force developed externally to the SMA material, generally requiring the use of another powered actuator which largely defeats the advantages to be derived from use of an SMA material and still yields only a relatively small motion. Further, the rapidity with which the shape memory function can be repeated is largely a function of the rate of cooling of the SMA material after the phase transition to the austenite phase. Additionally, while the required transition temperature can be chosen in accordance with an application (e.g. slightly above body temperature for a prosthetic device) the temperature excursion above the transition temperature to produce the shape memory effect in a suitably short time may be difficult to accommodate. These problems of application of SMA materials appear to have largely precluded development of novel structures that can optimally exploit their properties.
SUMMARY OF THE INVENTION
 It is therefore an object of the present invention to provide an actuator employing a SMA material in which the range of motion can be amplified.
 It is another object of the invention to provide an actuator utilizing shape memory effects that can provide a range of motion comparable to biological muscle tissue.
 It is a further object of the invention to provide an efficient propulsion system for a water-borne vehicle.
 In order to accomplish these and other objects of the invention, an actuator is provided comprising, in combination, a flexible spring beam, a shape memory alloy or artificial muscle element, and a connection between the flexible spring beam and the shape memory alloy or artificial muscle element maintaining a separation distance therebetween over a length of said actuator.
 In accordance with another aspect of the invention, an apparatus is provided comprising a plurality of actuators, wherein an actuator of the plurality of actuators comprises a flexible spring beam, a shape memory alloy or artificial muscle element, and a connection between the flexible spring beam and the shape memory alloy or artificial muscle element maintaining a separation distance therebetween over a length of the actuator, and a body for locating the plurality of actuators in a desired relationship to each other.
BRIEF DESCRIPTION OF THE DRAWINGS
 The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which:
 FIGS. 1A and 1D are cross-sectional and side views of a generalized preferred form of an actuator in accordance with the invention, respectively,
 FIGS. 2A and 2B are top and side views of possible exemplary modifications of the spring beam of an actuator in accordance with the invention for obtaining more complex actuator shapes when actuated, respectively,
 FIGS. 3A and 3B are side views of the SMA element and an actuator in accordance with the invention illustrating modifications of the SMA element and effects thereof, respectively,
 FIG. 4 is a side view of an actuator having two SMA elements,
 FIGS. 5A, 5B, 5C and 5D illustrate application of actuators in accordance with the invention to a device capable of gripping an object,
 FIGS. 6A, 6B, 6C and 6D depicts application of actuators in accordance with the invention to produce a propulsion device for a water-borne vehicle in the form of a species (Aurelia aurita) of jellyfish,
 FIGS. 6E and 6F illustrate a preferred inner bell surface configuration of the propulsion apparatus in accordance with the invention,
 FIGS. 7A, 7B and 7C illustrate motion of a jellyfish during swimming a comparison with the movement produced by the invention and an exemplary inclusion of an actuator in accordance with the invention into an artificial jellyfish bell,
 FIG. 8 compares measured jellyfish motion with the motion achieved by the invention, and.
 FIG. 9 depicts a preferred waveform for operating the propulsion device and vehicle of FIG. 6A-6F.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION
 Referring now to the drawings, and more particularly to FIGS. 1A and 1B, a generalized form of an actuator in accordance with the invention is shown in cross-sectional and side views, respectively. For simplicity of illustration, all of FIGS. 1B, 2B, 3A, 3B and 4 are assumed to be cantilevered from the rightmost end thereof as depicted in FIG. 12. In its simplest form, the actuator 100 in accordance with the invention comprises only three elements: a spring beam 110 (hereafter sometime simply "beam"), an SMA element 120 and an encapsulation body 130. The beam 110 is preferably a highly flexible material such as spring steel and having a rectangular cross-section tending to flex in a preferential direction determined by its thickness relative to its width to constrain and define the motion of the actuator. The SMA element 120 can be any known or foreseeable SMA material and is preferably in the form of a wire of circular cross-section in order to minimize effects on actuator shape other than along its length, as is usually preferred. The encapsulation body 130 may be of any cross-sectional shape and dimensions and is preferably formed of a material which is both adhesive and flexible without being excessively compressible since it is the principal function of the encapsulation body to maintain a given separation, d, between the beam 110 and the SMA element 120 and adhering them to each other. Other properties of the may be freely chosen in consideration of the application of the actuator. However, choice of thermal conductivity may be of some importance for cooling the SMA element after actuation and/or controlling heat transfer between the SMA element 120 and the beam 110.
 It may be helpful to observe that many familiar demonstrations of the shape memory effect involve starting with a straight, elongated body of SMA material, such as a wire, bending (e.g. causing plastic deformation) the wire into a contorted shape and heating the wire and observing the wire returning to the straight, elongated shape. The basic principle of the invention, however, exploits the fact that when the wire is heated and returns to its straight, elongated shape, it also returns to the compacted austenitic phase and is reduced in length by about 4%, as alluded to above, which is not apparent in familiar demonstrations of the shape memory effect. Rather, the basic principle of the invention is to exploit the change in length of the SMA material, whether the SMA material is either plastically or elastically deformed during the martensitic phase, and amplify the movement caused by the shape memory effect. Secondarily, the SMA material is exploited by establishing a desired shape for the austenitic phase to which the SMA material will return upon heating above the transition temperature and using a spring beam to cause elastic and possibly a small degree of recoverable plastic deformation of the SMA material in the martensitic phase.
 As alluded to above, during actuation, when the SMA element is heated to a temperature above the transition temperature, preferably by resistive heating developed by passing a current from power source 150 through the SMA element 120 over connections 160, an austenitic phase of the SMA material is achieved, the strain that can be achieved by the crystal lattice assuming a cubic, compacted form is only about 4%. (Such a level of strain is also comparable to the strain exhibited by so-called artificial muscle materials such as conducting polymer, ionic polymer metal composite, piezoelectric polymer, shape memory magnetic polymer, carbon nanotube yarns and the like, any of which can be substituted for the SMA element in any of the actuators or applications which will be discussed below. However, SMA materials are preferred for the force levels they can develop corresponding to the strain levels they exhibit as well as the ability to establish any desired shape to be assumed in the austenitic phase.) However, by adhering the SMA element 120 to a substantially incompressible spring beam 110, the disparity in elemental length and the force, f, associated with the strain corresponding to the opposing tensile force in the SMA and the compressive force in the Spring beam due to contraction in length of the SMA element, when neutral fibers of the beam 110 and SMA element 120 are separated by a distance, d, causes a bending moment, M=f×d and substantial curvature of actuator 100 along its length will occur as illustrated at dashed outline 140. In other words, the structure of the actuator 100, through use of encapsulation body 130 to maintain distance d substantially constant over the length of the actuator, regardless of the shape the actuator assumes, effectively amplifies the motion or strain that the SMA element can produce. The strain produced in the SMA element as it seeks to contract in the austenitic phase against the relatively incompressible beam from which it is separated by a distance d causes a bending moment causing the actuator to assume a radius of curvature which is dependent on the separation distance, d. The motion amplification rises sharply as d is increased. The amplification is a function of distance d, the length of the actuator and the amount of strain, in shear, that can occur in the encapsulation material and which should generally be minimized by choice of material for the encapsulation body. It is preferred to employ spaced stand-off structures 135 along the length of the actuator to accurately establish separation distance, d, as desired. An optionally or alternatively provided web element of a somewhat less compressible material (or the same encapsulation material of different density) can be employed to maintain d and resist shear, if desired at the location indicated by reference numeral 135.
 By the same token, the force that can be applied by the actuator in accordance with the invention is reduced by the same factor as the amplification of motion. However, since the force that can be generated by the SMA element assuming the austenitic phase is on the order of several tens of Megapascals, motion can be amplified by a factor of ten to fifteen to be comparable to the contraction of biological muscle tissue while maintaining the force developed to be well in excess of one to two Megapascals which is certainly usable in some applications, as will be discussed below. The trade-off between force developed and motion application can be varied as needed for a given application. The range of motion obtained from the actuator can also be extended somewhat by modification of the shape of the beam 110 or the SMA element 120 as will be discussed below. Thus, when actuator 100 is activated and the SMA element 120 heated above the transition temperature, the actuator will assume curved shape 140. Upon termination of activation and cooling, the actuator will be drawn back into another shape 170 by the spring force applied by the beam 110.
 Referring now to FIGS. 2A-2C, the beam can be modified in several ways that affect the shape of the actuator in active (e.g. actuated) and/or passive (e.g. unactivated) states. (In FIGS. 2A 2C, only the beam 120 of actuator 100 is shown for clarity of illustration.) For example, the stiffness of the beam may be reduced by forming a notch 210 on one or both lateral sides of the beam. If only one notch is formed, that portion of the beam will be asymmetrically located relative to the SMA element and will result in a compound motion having a lateral component as shown in FIG. 2C when the actuator is in the actuated state. The formation of one notch or two opposing, symmetrical notches will cause a reduction in stiffness and result in increased curvature of the actuator in the activated state as shown at 230 of FIG. 2B.
 Conversely, the stiffness of the beam in a desired are can be increased by increasing the thickness thereof in a symmetrical or asymmetrical manner as shown at 220. Such an increase in beam stiffness will cause a reduction in curvature in the activated state, as shown at 240 of FIG. 2B. It should be understood that localized increases or decreases in stiffness of beam 110 can also be achieved by localized alteration of composition, heat treatment or the like. In general, these effects will be relatively slight when the SMA material is in the activated state due to the large force developed by the SMA material in the austenitic phase unless the beam is configured to be of very substantial stiffness. However, such localized modifications of beam stiffness could be useful in modifying the intermediate shapes assumed by the actuator during transition between the austenitic and martensitic phases. It should also be understood and appreciated that radius of curvature of the actuator, when activated, can also be altered and adjusted locally or throughout the actuator by alteration of the separation distance, d, between the SMA element 120 and the beam 110, either alone or in combination with beam modifications as discussed above.
 Additionally, the shape of the beam need not be straight but could be shaped or bent as shown at 250 at one or more locations 260. Since the shape of the actuator is a function of both the shape of the beam and the strain developed in the SMA material, such shaping will generally modify both the activated and unactivated states of the actuator as shown in FIG. 2B. (The embodiments of the invention shown in FIGS. 1A and 1B assume a straight, elongated shape for SMA element 120. In the embodiments of FIGS. 2A and 2B, the SMA element may be either straight or bent similarly to the beam, if bent to a shape other than straight.)
 Referring now to FIGS. 3A and 3B, the influence of the shape of the SMA element 120 will now be discussed. FIG. 3A depicts a "parent" shape that can be established for the SMA element. It should be understood that the SMA element can be shaped as desired in accordance with any arbitrary shape. However, the shape 310 shown in FIG. 3A has particular utility in connection with the propulsion system provided in accordance with an embodiment of the invention as will be discussed below. It should also be appreciated that so-called two-way SMA materials are known which will assume one shape above a given temperature but will assume a second, different shape, represented by dashed outline 340, below another given temperature independent of any influence of a beam element on the shape. The second, different shape can be different from an unactivated shape substantially established by the beam shape, as discussed above. The invention can be practiced without resorting to such two-way SMA materials but such two-way SMA materials can also be used as a potential alternative to beam 110 or advantageously used in combination therewith in some applications.
 FIG. 3B illustrates an actuator using a linear beam 110 in combination with an SMA element shaped as shown in FIG. 3A. In the unactivated state, shape 320 is a result of the forces exerted by the beam 110 on the SMA element in the martensitic phase of the SMA element. Conversely, shape 330 is a similar result of the beam forces acting on the shaped SMA element of FIG. 3A but in the activated state where the austinitic phase is developed.
 A further exemplary modification of actuator 100 is illustrated in FIG. 4. Any number of actuators, with or without variations described above can be combined into a compound actuator to provide additional flexibility and control of shape of the compound actuator. For example, using splices 410, 420, one actuator can be attached to and cantilevered from the end of another in any mechanically robust but electrically insulative fashion; allowing the individual actuators to be activated independently of each other. The beam 110 and SMA element may be similarly oriented in both portions of the compound actuator, in which case, splice 420 is preferably omitted and beam 110 formed to extend in one piece through the compound actuator. Such a configuration allows an activated shape of the SMA element to be achieved in either or both portions of the compound actuator. Alternatively, the relative locations of the beam 110 and SMA element 120 can be reversed or otherwise differently oriented to achieve a combination of movements of the respective portions of the compound actuator. Such a reversal might be particularly useful in an application where the angle of orientation of the surface of the compound actuator may be important such as in gripping an object where the surface in contact with the object would be advantageously maximized by being substantially parallel. Undulating motions can also be achieved by activating the actuators in a suitable, possibly overlapping sequence and can possibly be advantageously enhanced by overlapping portions of the actuators along their lengths.
 Referring now to FIGS. 5A-5D, another form of compound actuator capable of, for example, gripping an object will now be discussed. In this case, the actuators form a compound actuator and are arranged in and "H" shape with two actuators 510, 520, oriented generally parallel to each other and a third actuator 530 joining the parallel-oriented actuators. In this case, all three actuators of the compound actuator preferably are formed on a single, unitary, "H"-shaped beam 540. FIGS. 5A and 5B are cross-sectional and plan views, respectively, of the compound actuator with none of the actuators activated. FIG. 5C shows alteration of the cross-sectional shape of the compound actuator by activation of actuator 530, bringing actuators 510, 520, into a geometry where they oppose each other, much in the manner that a thumb may be brought into opposition with another finger of the human hand. Thus, as shown in FIG. 5D, actuators 510 and 520 can be activated while actuator 530 remains activated such that the actuators 510, 520, assume shapes 550 to grip object 560. It should be understood and appreciated that additional actuators can be added to the simplified example of FIGS. 5A-5D to obtain other relative positions for actuators 510, 520 which may also be constituted by compound actuators as discussed above in connection with FIG. 4. Thus operations of a keyboard, walking and other types of human or animal (e.g. bio-inspired shape memory alloy composite or BISMAC) activities can be simulated or emulated using actuators in accordance with the invention.
 Referring now to FIGS. 6A-6D, a high-efficiency BISMAC propulsion device in accordance with the invention will now be discussed. There has been significant recent interest in developing water-borne or submersible vehicles that develop high efficiency propulsion in the manner of animals which have evolved such efficient techniques of propulsion over many thousands if not millions of years. For example, squids can develop substantial propulsive forces by ejecting a jet of water by contraction of an internal organ. Rays or skates develop substantial propulsive swimming forces by relatively small movements of large surfaces. Either of these types of propulsion can be emulated easily with actuators in accordance with the invention consistent with maintaining a vessel shape substantially consistent with their biological counterparts.
 The inventors have discovered that one of the most efficient techniques of propulsion, at least for low speed movement or maintaining position against ambient current is that of the jellyfish. The inventors have also appreciated that emulation of jellyfish is a near optimal environment for use of actuators in accordance with the invention and exploitation of the properties of SMA materials and mode of production and useful application of the shape memory effect.
 Specifically, the method of propulsion developed by the jellyfish is performed essentially by contracting a large, umbrella-shaped body or "bell" to force a current of water from the open side of the bell, propelling the jellyfish body in the opposite direction with the umbrella contracted to reduce drag. The bell is again opened or extended and then contracted again to further propel or accelerate the jellyfish body in a motion sometimes referred to as rowing.
 The degree of contraction of the umbrella has been found by the inventors to be approximately 55% which is well within the range of motion amplification achieved by actuators in accordance with the invention and consistent with preserving sufficient force for contracting against the enclosed water. Reduced force due to amplification of actuator motion is not particularly critical since the result of reduced available force is principally manifested in a reduced speed of contraction of the bell against the water inside the bell. The repetition rate of this motion is not critical other than for the fact that larger jellyfish or vessels must have an increased repetition rate to reach equivalent speeds compared to smaller jellyfish or vessels. Repetition rates of about 0.5 to 2.0 seconds are generally sufficient for adequate speeds to be obtained over a wide variety of vessel sizes based on the modeling of jellyfish motions.
 Of fairly great importance, however, is the heat sinking capability of the surrounding water which allows nearly instantaneous reversion from the activated/austenitic state to the unactivated and martensitic state of the SMA material which can substantially increase possible repetition rate and maintain the contraction function substantially constant since little increase in actuator temperature can occur in the actuator even at maximum repetition rates. The small increase in actuator temperature that does occur can be exploited to increase efficiency as will be discussed below.
 The basic principles of actuators in accordance with the invention and the substantial freedom of physical design have been discussed above. A rigorous analysis of the forces available and the motion amplification provided by actuators in accordance with the invention is provided in "Modeling of Artificial Aurelia aurita Bell Deformation" by Joshi et al. published in the Marine Technology Journal, Volume 45, Number 4, July/August 2011, pp. 165-180(16) which forms a part of the provisional application incorporated by reference above and is, also hereby incorporated by reference herein. That article also contains analyses of various alternative structures and their functional differences that may be used in the propulsion apparatus in accordance with the invention but which are unnecessary to an understanding of the principles of the invention or the successful practice thereof to provide propulsion for a water-borne or submersible vehicle.
 FIGS. 6A-6D appear in the above-incorporated article and illustrate various views of a preferred form of the bell 600 of the propulsion system in accordance with the invention. FIG. 6A illustrates an isometric view, FIG. 6B is a top view, FIG. 6C is a side view and FIG. 6D is a cross-sectional view through an opposed pair of actuators 100 located with radial symmetry around the bell. The bell 600 is thus divided into eight substantially identical radial sectors. However, the number of sectors provided is not important to the successful practice of the invention but even numbers of sectors are convenient for purposes of control and at least six sectors are considered to be consistent with a generally circular overall shape as is best seen in FIG. 6B.
 The bell 600, itself, is preferably constructed of inner and outer contoured shells of flexible material such as a silicone rubber which are preferably molded, preferably by shape-deposition manufacturing in which a printer-like apparatus deposits successive layers of material in a fluid form to a mold surface and the space between them is preferably molded of a soft material to form a water-tight common encapsulation body 130 for all (eight) actuators 100 subsequent to installation of the actuators on the inner or outer shell. Alternatively, the molds can be fabricated in such a manner, the actuators installed on the molds and the molds assembled together and filled with soft, gel-like (e.g. silicone) material and the resulting integral shape suitably finished and/or coated.
 The interior contour of the bell 600 is considered to be of a significant degree of importance to the efficiency and correct operation of the invention but is not critical thereto. FIGS. 6E and 6F illustrate the preferred contour which causes the bell 600 to be sharply reduced in thickness at locations 100' between the actuators 100. This reduced thickness forms an effective hinge while the decreased thickness between actuators causes the bell to fold in a desirable fashion between the actuators to move water more uniformly when the bell is contracted. These joint or hinge structures are also present in the biological A. aurita jellyfish and other species, as well, and are basically wedge-like cavities that vary in shape with bell height. The mid-bell profile is taken as:
This function describes the joint shape across a two-dimensional plane with height, j, half-width, k, and curvature, δ, as parameters. The joint structure can be described as a piece-wise function representing two symmetric sides of a single function, mirrored about the y-axis. Thus, this function can be used to model the actual joint structure of a wide variety of biological species.
 As shown in FIG. 6F, the actuators, substantially configured as discussed above in connection with FIGS. 3A and 3B, are preferably cantilevered from a terminal hub, preferably formed of an acrylic material and of a length to reach the outer periphery of bell 600. The terminal hub can also be used for attachment of a vessel body or hull, a side of which is schematically indicated by dashed line 620. In devices emulating other biological motions, a hub is not necessary and any body of flexible or rigid material can be used to position actuators in a desired relationship to each other. The shape and construction of hull 620 is of no importance to the successful practice of the invention as long as its configuration does not mechanically interfere with bell contraction. The entire assembly of the bell and hull should be preferably ballasted to be of substantially neutral or only very slightly negative buoyancy and balanced such that the orientation of the vessel without activation of the actuators maintains the bell 600 above the hull 620.
 FIG. 7A illustrates, in cross-section, measured movements of a biological A. aurita jellyfish with the fully expanded and fully contracted positions being illustrated. FIG. 7B shows details of an exemplary embedding of an actuator in accordance with the invention in an artificial jellyfish bell. FIG. 7c compares the axial and radial positions of the biological and artificial jellyfish bells during a cycle of contraction and re-expansion/relaxation. It can be seen that the biological jellyfish movements are quite accurately mimicked by the artificial jellyfish model in accordance with the invention. The similarity of these movements can be even further improved by shaping of the beam and/or SMA element and/or varying the separation distance, d, between the beam and SMA element along the length of the actuator. Experimental data for a refined model is compared in FIG. 8, showing an extremely close match between the movements of biological and artificial jellyfish.
 It should also be appreciated from the above discussion in connection with FIGS. 6A-8 that actuators in accordance with the invention are applicable to not only very accurate modeling of the motions of the A. aurita and other species of jellyfish but, as indicated in the above discussion of FIG. 5, are very well suited to modeling other types of biological motions. For example, the contraction of any structure capable of containing a fluid can produce a jet of fluid for propulsion as alluded to above in regard to a biological squid. If the bell structure is omitted, a radial array of actuators can also provide a walking type of motion as employed, for example, by a crab, lobster, spider or any of a wide variety of insects for propulsion over land or in the water, particularly if the actuators are embodied as described above in connection with FIGS. 2C or 4 to provide compound motions. Such vehicles are referred to as micro air vehicles (MAV). Applicability to provide flexure to wide surfaces can readily emulate swimming or "flying" motions of fish or rays or even birds up to a repetition rate of 3 to 4 repetitions per second. The actuators in accordance with the invention can be fabricated at virtually any size and are scalable up to very large sizes as may be required for any of a wide variety of applications.
 FIG. 9 illustrates an exemplary and preferred waveform for operation of the jellyfish emulating propulsion system in accordance with the invention. Similar waveforms could be used for any other biological emulation. In the case of the jellyfish, it should be appreciated that maximum propulsion force will be produced when all actuators are activated and de-activated concurrently. However, substantial guidance of the artificial jellyfish model can be achieved while producing substantial propulsive force by activating and deactivating less than all of the actuators. Differentially timed activation would also be appropriate to walking and swimming/flying motions. In the current waveform of FIG. 9, three initial current spikes are preferably applied for rapid heating of the SMA by ohmic resistance. The peaks vary in amplitude principally due to the change in electrical resistance of the SMA element as temperature increases. Several sets of these pulses may be necessary to achieve and maintain full actuator flexure or contracting force during the first few cycles of activation following any relatively long period without activation since the entire apparatus will have been cooled to a low temperature by the surrounding water. Even though current amplitude is substantial, only a short series of very brief pulses need be applied and full development of the shape memory effect takes place within about 0.1 seconds. Therefore the power consumption during the high current pulses is kept low by the low duty cycle and short duration of this phase of activation. The thermal resistance of the bell material that encapsulates the SMA element should be sufficient to retain heat generated by these pulses.
 Once full deformation is achieved in any given activation cycle, the current level can be greatly reduced, as shown from 0.1 seconds to 0.7 seconds. This phase of activation corresponds to the time the SMA element is held in the austenitic state and the force produced thereby initiates contraction of the bell 600 which continues to contract and apply force against the water within the bell to expel it and provide propulsion. Increased thermal resistance of the bell material will allow the current level during this phase of activation to be minimized.
 When the contraction of bell 600 is complete (at about 0.7 seconds) the current can be reduced to zero and the SMA material allowed to cool and revert to the martensite phase which the beam can then deform to the relaxed state of the actuator. The thermal resistance of the bell/encapsulation material should be kept low enough that such cooling can occur relatively quickly to prepare the actuator for another cycle of activation. Cooling will progress rapidly as additional water enters bell 600 as the actuators begin to resume the martensitic state.
 In view of the foregoing, it is seen that the invention provides an actuator configuration that allows amplification of the small strain that is developed by SMA materials and artificial muscle such as conductive polymer while maintaining a usable fraction of the large force developed by the shape memory effect. The actuator(s) in accordance with the invention can be modified to have many shapes and assume desired shapes upon developing the shape memory effect that are useful in various applications such as a gripping or walking mechanism or BISMAC propulsion system such as that of the exemplary jellyfish as discussed above or emulation of any motion of any biological species, including plants (e.g. phototropism).
 While the invention has been described in terms of a single preferred embodiment, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the appended claims.
Patent applications by Shashank Priya, Blacksburg, VA US
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