Angular Rate Sensor Apparatus

Referring to the drawing, wherein like numerals represent like parts throughout the several views:

FIG. 1 is a perspective view illustrating a first embodiment of an angular rate sensor apparatus constructed according the principles of this invention, and illustrating application of the invention with piezoelectric bender element vibrating members;

FIG. 2 is a side elevational view of the angular rate sensor apparatus illustrated in FIG. 1;

FIG. 3 is a top plan view of the angluar rate sensor apparatus illustrated in FIG. 1;

FIG. 4 is a graphic illustration of the transfer function and phase response of a typical resonant element;

FIG. 5 is a graphic illustration of the demodulated system response for a piezoelectric sensor system having identical drive and sensor elements with the transfer functions of FIG. 4;

FIG. 6 is an expanded representation of FIG. 5 illustrating the distortion that results in the demodulated system response when the sense resonance changes by only one percent;

FIG. 7 is a graphic illustration of the distortion in the demodulated system response for a piezoelectric sensor system similar (but not expanded) to that of FIG. 6, wherein the resonance of the sense element is different from that of the drive element; and

FIG. 8 is a diagrammatic view of the sensor assembly of FIGS. 1-3, illustrating various dimension parameters for the respective bender elements.

This invention employs a new configuration of vibratory elements sized, arranged and configured in a manner so as to provide an improved vibrating element angular rate sensor. The sensor structure employs two identical, opposed vibrating elements mounted and driven so as to vibrate in direct opposition to one another, similar in outward appearance to the opposed mounting arrangement employed in a tuning-fork structure. The vibrating elements may, for example, comprise piezoelectric bender members such as piezoelectric ceramic or crystal members as discussed in more detail hereinafter. The vibrating elements are preferably secured at one end by a mounting mechanism and project outwardly therefrom in generally parallel, cantilevered manner toward a "free" end. The vibratory elements are matched and are generally lightweight and susceptible to controlled active motion at their respective free ends in response to an applied oscillatory drive signal. The vibratory elements are driven (vibrated) in an oscillation plane in opposition to each other about a mounting or nodal axis of symmetry. The matched vibrating elements are sized and closely spaced (hereinafter described in more detail) and arranged to be driven for motion in direct opposition to one another, such that their combined vibrational forces reflected back to the mounting base form an acoustic node at the mounting base axis of symmetry, resulting in essentially no externally transmitted vibrational acoustic energy as a result of the motion of the vibrating elements. Conversely, any external vibration noise that would otherwise be transmitted through the mounting base to the vibrating elements (e.g. in prior art structures having only a single vibrating element) or which is acoustically received by the vibrating elements is equally applied to both of the opposed vibrating elements. Since the vibrating elements are moving in direct opposition to one another, the effect of any such received vibrational noise is nulled out and does not affect operation of the sense element portions of the vibrating elements.

A preferred embodiment of the invention is diagrammatically illustrated in FIGS. 1 through 3. The preferred embodiment illustrates application of the invention to a sensor structure using piezoelectric vibratory elements. Referring to FIGS. 1 through 3, a pair of piezoelectric vibrating elements, generally designated at 10, are constructed for operation in the manner generally described in my referenced article "Piezoelectric Vibrating Beam Rate Gyro", and in my co-pending patent application "Resonance Drive Oscillator Circuit", Ser. No. 280,500 filed July 6, 1981. To the extent that the disclosures of my referred article and co-pending patent application are applicable to defining the piezoelectric elements or their mode of operation, the disclosures of the referred materials are herein incorporated by reference. It will be understood that the illustrations of FIGS. 1-3 are not to scale but are diagrammatically illustrated for enhancing depiction of detail of the vibratory elements. In particular, the vibrating elements 10 are much longer and are much more closely spaced to one another than illustrated in the Figures. In the preferred embodiment, each of the vibrating elements 10 comprises a pair of rectangular piezoelectric ceramic bender members longitudinally aligned end to end but rotated 90.degree. from one another. It will be understood that while ceramic piezoelectric bender members are used in the preferred embodiment, that other piezoelectric bender members such as crystals could also be employed. The secured bender member (hereinafter described in more detail) is the "drive" bender member and is designated at 10A in the Figures. The second bender member is referred to as the "sense" member and is designated at 10B in the Figures. The drive member 10A and the sense member 10B are fixedly butted end to end to one another and are mounted for alignment about a "sense" axis (S), by means of an appropriate bonding agent such as epoxy, generally designated at 11.

The pair of vibrating bender members 10 are constructed to be as identical to one another as possible in physical construction mass, and in the natural resonances of their respective and analogous bender elements. One end of each of the drive bender elements 10A is fixedly mounted to a base or mounting piece generally designated at 15. The base piece 15 illustrated in the figures is symmetrically configured about a mouting or nodal axis, generally designated at 20. The mounting base illustrated comprises first and second mounting members respectively indicated at 15A and 15B. The material of the mounting base 15 should have an acoustic stiffness equal to or greater than that of the bender members 10 so as to reduce tuning errors of the bender members. As is well known in acoustic design art, material stiffness is a property relating to the propensity of the material to lose acoustic or vibrational energy (i.e. the "Q" of the material). The stiffer a material is (i.e. the higher Q that material has), the lower are its vibrational losses. In the preferred construction illustrated, the mounting piece material 15 is brass; however, any other material having the desired stiffness and vibrational damping ability could be used (as described in more detail hereinafter). The first mounting member 15A defines a generally "U"-shaped (as viewed from above) channel defining a pair of flat vertically oriented land surfces 16 (see FIG. 3), configured for uniformly engaging one side surface of the drive bender member 10A. The second mounting member 15B is "T"-shaped and sized to fit within the "U"-shaped channel of the first mounting piece 15A. The mounting member 15B has a pair of flat vertically oriented land surfaces 17 configured for uniformly engaging and sandwiching the retained ends of the drive bender members 10A between the opposed land areas 16 and 17 (see FIG. 3). An electrically insulating layer 12 is interposed between the mating surfaces of the first and second mounting members 15A and 15B and extends behind the secured ends of the drive bender members 10A, to insulate such ends from electrical contact with the mounting member 15A and to electrically isolate mounting pieces 15A and 15B from each other.

In the embodiment illustrated, the mounting pieces 15A and 15B also function as electrodes or conductors for transmitting electrical signals to and from the drive bender members 10A. In a preferred construction of the sensor apparatus the opposing flat surfaces of the drive bender members 10A are soldered in place to the flat land areas 16 and 17 of the first and second mounting members 15A and 15B respectively (FIGS. 1 and 3). The solder connections provide both electrical and mechanical connections for the drive bender members 10A to the mounting members 15A and 15B. It will be understood that the secured ends of the drive bender members 10A need not be secured by an electrode structure as illustrated, but could also be directly secured in place by appropriate bonding agents such as epoxy or glue which would form a solid mounting base with good damping characteristics. In such a configuration, the electrical connections to the drive elements thereto could be made by small wires or other electrical engagement means. Alternatively, the dimensions and tolerances of the mating portions of the first and second mounting pieces 15A and 15B could be such that the retained ends of the drive members 10A would be fixedly, frictionally held therebetween, and possibly even provide electrical contact to the drive members through such frictional engagement. Other mounting and electrical connection schemes will be readily apparent to those skilled in the art. To avoid stresses in the retained ends of the drive members 10A, it is preferrable that uniform conductive engagement be made between the land surfaces 16 and 17 of the electrode mounting pieces 15A and 15B and the engaged sides of the drive members 10A.

The first mounting piece 15A longitudinally extends outwardly along the nodal axis 20 to a "T"-shaped mounting bar, generally designated at 18, the end posts (18a) of which are secured to an appropriate base substrate 19 which could, for example, comprise a printed circuit board, housing or chassis of the sensor apparatus. The free end of the second mounting piece 15B also extends longitudinally outward along the nodal axis 20 to a mounting post, generally designated at 21, which is also secured to the substrate 19. The mounting connection of the electrode posts 21 and 18a provide electrical paths and/or contacts for the electrode base members 15A and 15B to a resonance drive oscillator circuit (diagrammatically illustrated at 30 in FIG. 2) located on or attached to or through circuit patterns forming a part of the base substrate 19. The resonance drive oscillator 30 may be of any configuration suitable for driving (i.e. vibrating) the drive members 10A at their natural resonance. However, for the sensor configuration illustrated herein a resonance drive circuit of the type described in my referenced co-pending patent application Ser. No. 280,500 is preferred.

As illustrated in the Figures, the mounting piece 15, as secured to the substrate 19 by the mounting posts 21 and 18a, suspends the vibrating bender members 10 in closely spaced cantilevered manner about their respective "sense" axes (S), symmetrically about the nodal axis 20, and above the upper surface of the substrate 19. A number of interrelated factors and considerations combine to determine the physical size and spacing considerations for the bender elements 10 within the system.

The spacing of the vibrating bender elements 10 about the nodul axis 20 (i.e. the distance between the sense axes (S)) determines the sensitivity of the sensor apparatus to acoustic noise and its propensity to radiate acoustic noise. This dimension is illustrated at "X" in FIG. 8. Using acoustic wave propagation theory related to destructive interference of wave fronts of closely spaced wave front emitters, in order to cancel 90 percent of the radiated acoustic energy from the sensor apparatus, the bender element spacing "X" should preferably be less than 0.008 wavelengths, wherein the wavelength is determined by the resonance drive frequency of the drive elements 10A. As pointed out above, the drive elements 10A are driven at their natural resonance, which is selected to be at a suitable frequency for accomodating the application in which the sensor apparatus will be used. For example, when used in angular rate sensor applications for aircraft, minimum system frequency specifications are provided for insuring that the aircraft-produced vibration forces do not interfere with operation of the angular rate sensor. Such minimum operational frequencies are generally stated for different types or classes of aircraft according to the type of engine propelling the aircraft. For piston-powered civilian aircraft, for example, the typical specified maximum vibration spectra reaches 55 Hz. For turbine-powered civilian aircraft, the typical specified maximum vibration spectra is 500 Hz. Military rocket applications may have vibration specifications as high as 2000 Hz. In a preferred embodiment of the invention as applicable to turbine-powered civilian aircraft, the drive bender elements 10A have been selected to have a drive resonance of 560 Hz. Accordingly, the bender element spacing "X", in air, is determined to be approximately 0.200 inches in order to cancel 90 percent of the radiated acoustic energy. As will become apparent upon further description of the invention, setting of the "X" dimension necessarily has an effect upon the physical width ("w" in FIG. 8) dimensions of the bender elements, which must be sized small enough so as to prevent physical interference of the ends of the sense elements 10B when in operative motion about the nodal axis 20.

In the preferred construction of the sensor apparatus illustrated, the mounting base 15 is constructed of brass, which also provides the desired electrical conductivity for the conductor/electrode function of the mounting piece; however, as described above it is understood that other materials could equally well be used within the spirit and intent of this invention. Similarly, while the mounting piece 15 has been illustrated as serving an electrode function, it will be understood that either or both of the mounting pieces 15A or 15B could be employed as electrode members, or, alternatively, that neither might serve as electrodes, but that electrical connection to the drive elements could be made by other means as, for example, through soldered wire connections.

Similarly, while a specific configuration of the mounting base 15 has been illustrated with respect to this embodiment of the invention, it will be understood that other configurations could equally well be employed within the scope of this invention. The primary consideration in the design of such mounting base is that when the vibrating sensor elements are operatively mounted thereby, they will be symmetrically mounted about the nodal axis 20 for opposing vibration relative to one another thereabout, as will be described in more detail hereinafter. An advantage of the mounting configuration illustrated in description of the preferred embodiment of invention, and particularly with respect to the "T" configuration of the mounting extension 18, is that such "three-point" mounting structure provides for expansion along the nodal axis 20 due to temperature variations, imperfections in the mounting to the substrate 19 and the like, which expansion may relieve stress reflection back to the bender members 10.

As above described, the drive members 10A are energized through the electrode base members 15A and 15B at their secured ends. Electrical signals generated by the piezoelectric sense members 10B caused by bending thereof in response to detected angular motion, are carried from the sense members by means of fine insulated wires 25 soldered to the opposed broad surfaces of the sense members. The wires 25 are mounted along the bending axes of the drive members 10A back toward the mounting piece 15, and are secured to or through circuitry (not illustrated) on or attached to or through the base substrate 19. The wires 25 may be interconnected by means of the external circuitry in any desired manner so as to analyze and use the signals generated by the sense members 10B. In the preferred construction, the wires 25 are interconnected by the external circuitry to electronically connect the sense members 10B in "parallel". In such arrangement, wires 25a and 25b are commonly connected as one terminal of the dual sensor arrangement, and wires 25b and 25c are connected to form the second terminal of the sense members 10B. As will be appreciated by those skilled in the art, the external connection could alternately be configured for connecting the sense member signals in "series", or to directly feed the respective signals from each of the sense members 10B into appropriate "mixing" circuitry.

If connected in series, the structure illustrated in FIGS. 1-3 could be externally wired such that wires 25b and 25d were connected to one another, with wires 25a and 25c providing the "output" terminals of the dual sense member structure. Alternatively, wires 25a and 25c could be connected to one another, with wires 25b and 25d providing the "output" terminals.

As will become apparent from a full reading of this specification, it is not necessary to electrically connect the sense members 10B of "both" bender members 10. While both drive members 10A should be energized to obtained the desired vibrational results of the entire sensor structure, it may be possible to obtain adequate "sensed" information from a single one of the sense bender members 10B.

As electrically connected, in the preferred embodiment, the opposing oscillatory motion of the sense members 10B, caused by an angular "rate" motion to which the sensor apparatus is subjected, will produce signals from the sense members 10B which "add" together, such that common mode motions caused by acceleration or the like will be subtracted from one another, and thus cancel.

It will be understood that appropriate drive, sensing and detection circuitry (not illustrated herein) can be operatively connected to the electrode terminals of the mounting piece 15 and to the output terminals of the sensing wires 25 to provide the desired functions, as is well-known in the art. See for example my co-pending patent application entitled Resonance Drive Oscillator Circuit, previously cited herein.

The sense wires 25 are mounted along the planes of symmetry of the mounting system. Fine wires are used, to reduce as far as possible any undesirable radiation from or collection by the wires, of vibrational energy.

As previously stated, the pair of bender members 10 are matched as closely as possible in their respective physical and electrical properties. In the preferred embodiment the matching between the respective sense and drive members on either side of the nodal axis 20 is preferably within one hertz. While the drive members 10A and sense members 10B may be selected such that they have the same natural resonance, the prefered configuration provides for different resonant frequencies respectively for the drive and sense bender members 10A and 10B. Experimentation has shown that with the physical parameters of the preferred embodiment configuration, the preferred frequency separation occurs when the sense and drive natural resonance frequencies are separated by a factor of approximately 4/3 times the desired output response bandwidth. Therefore, in the preferred embodiment configuration described above, wherein the resonant drive frequency was selected to be 560 Hz, a sense resonance frequency of 800 Hz within a system Q of approximately 25 provides a useful output bandwidth response of over 180 Hz. The desirability of providing separation between the sense and drive resonance frequencies can be illustrated more clearly with reference to FIGS. 4-7.

In general, angular rate sensors in the art that use vibrating elements, have a resonance characterized by a high peak of response at the resonant frequency of the vibrating element, as illustrated by the transfer function of FIG. 4. For angular rate sensor configurations such as described in this specification, wherein there are both "drive" and "sense" elements, there would be two such response curves as illustrated in FIG. 4, one for the drive response and one for the sense response. The transfer function illustrated in FIG. 4 is a typical transfer function for a piezoelectric bender element of the type illustrated herein, having a resonance of 800 Hz and a Q when mounted in the sensory system of 25. It will be appreciated that while the "natural" (unmounted) Q of the bender element may be much larger (e.g. as high as 500), due to the damping characteristics of the means for operatively mounting the bender element, its Q as operatively "mounted" is generally significantly lower. It should be noted, that while the remaining discussion will describe the sensor apparatus with respect to a system Q of 25, that the invention is not limited to such "low Q" systems (i.e. Q range of 10 to 100), but that the invention applies equally well to systems having significantly higher Q values, even greater than 300.

As described more fully hereinafter, the "sense" response of the system is an important quality of the sensor apparatus. The peak of the sense response occurs at the resonant frequency of the sense axes motions. The energy from drive member (i.e. along the drive axis), which is imposed on the sense axis by angular rotations, is placed on the sense response curve at the drive resonance frequency. Most prior art angular rate sensor configurations and teachings suggest that the best arrangement is to design the sense and drive elements to have the same resonant frequencies, since it would appear at first glance that the best signal gain can be achieved in this manner. However, and as described herein, this approach does not account for "practical" implementation factors that occur in the design and operation of angular rate sensor structures.

A first consideration relates to bender element turning matching limitations. A typical "Q" for a practical piezoelectric sensor system can be 25. This figure is based on the materials used in fabrication of the preferred embodiment described herein. Using this value as a worst case and a resonant frequency (based on convenient component sizes and typical vibration noise spectra) of 800 Hz for both the drive and sense modes of operation, the turning of the bender elements must be performed to accuracies of much less than one percent in order to match the operating responses and phase of the curves (e.g. FIG. 4) adequately.

In terms of dynamic response, the energy transferred from the drive to the sense bender elements is divided into two equal parts and is placed on the sense response curve at the drive frequency plus and minus the input excitation frequency. This is a heterodyne response producing upper and lower sidebands. Using the previous frequencies (800 Hz) and Q (25), FIG. 5 illustrates the resulting system response as "lagging" by 90 degrees and as having a maximum obtainable bandwidth of 10 Hz at -3 db. Such response is not usable in any practical stabilization or navigation system. The fact that the D.C. response contains almost a 90 degree phase shift indicates that the output is actually more an integration of the angular rate (i.e. the output from an angular rate input will contain a strong component of angular displacement).

Since the match in sense and drive frequencies will have a finite error through age, over temperature, and as a result of other factors, and since there is such a strong inflection in response near resonance (for resonant systems), there will be strong variations in the response envelope and phase. This fact is illustrated in FIG. 6, wherein the sense resonance has been plotted on the expanded response curve of FIG. 5, but displaced by only one percent. The upper curve ("A") of FIG. 6 represents the expanded response curve of FIG. 5 wherein the sense resonance frequency is 800 Hz (also see Table 1), and the lower curve ("B") of FIG. 6 represents the response curve wherein the only parameter change is that the sense resonance frequency was changed by one percent, to 808 Hz (also see Table 2). The resulting distortion between the "A" and "B" curves shows nearly a 10 percent loss of gain and a phase shift of approximately 26 percent. This distortion makes the system unusable, since the actual piezoelectric elements used in such systems typically vary not only by one percent, but by as much as .+-.20 percent over the operable temperature range and are typically not matchable by any closer than 2 percent.

Accordingly, as pointed out by the above shortcomings of the prior art, in order to produce a wider usable bandwidth, there should be a difference between the sense and drive resonances. In operation, the sense member (i.e. 10B) of a vibrating angular rate sensor is more vulnerable to error from external vibrations than is the drive member. Because of this practical effect, the sense resonance should be at a higher frequency that that of the drive resonance. As stated earlier, experimentation associated with this invention has shown that the sense and drive frequencies should be separated by approximately 4/3 times the desired output response bandwidth. This result is illustrated in FIG. 7 and tabulated in Table 3. Referring to FIG. 7 and Table 3 it will be noted that for a drive resonance of 560 Hz, a sense resonance of 800 Hz, and a system Q of 25, that the output is reasonably usable to over 180 Hz (i.e. the phase is still stable and the gain is still at a low enough level wherein it can be practically controlled by standard filtering techniques. It will be noted that the tabulated data of Table 3B (i.e. for a one percent change of sense resonance), when plotted on FIG. 7 is so close to that of Table 3A that the curves appear superimposed on one another with practically no measurable response error between them. Therefore, as a result of the frequency separation of the drive and sense resonances, the sensitivity to shifts in resonances of the sense and drive elements is greatly reduced, yielding a practical form of implementing the invention.

To accomplish the above sense and drive resonance relationships in the configurations described in FIGS. 1-3 (i.e. wherein the drive resonance is 560 Hz, the sense resonance is 800 Hz, and the Q is 25), the sense member 10B should be approximately twice as long as the drive member 10A, with their respective cross-sectional dimensions being identical. As discussed above with respect to selecting the inter-element spacing "X", the width dimension ("w" of FIG. 8) of the sense and drive members is limited by the physical interference of the sense member ends when in operative motion. Referring to FIG. 8, the "w" dimension must be small enough such that the "y" dimension is large enough to prevent the inner edges of the sense members 10B from interfering with one another during operative motion. The thickness dimension ("t" in FIG. 8) is generally determined by availability of standard bender element parts. In the preferred embodiment sensor configuration, the dimensions for the sense and drive members 10B and 10A respectively are as follows: sensor member length "L2" is 0.625 inches; drive member length "L1" is 0.312 inches; width "w" is 0.062 inches; and thickness "t" is 0.020 inches. It will be understood that while the above dimensions have been used for providing a system having a drive frequency of 560 Hz and a sense resonance of 800 Hz for a particular type of ceramic piezoelectric bender material, that such dimensions would appropriately be changed to accommodate other sense or drive resonant frequency system parameters or other piezoelectric materials.

The opposed arrangement for mounting the vibrating members provides a simple and fully effective means of accurately tuning the "Drive" and "sense" proportions of the vibrating members for significantly reducing most of the error sources encountered in vibrating element angular rate sensors. The energy of vibration of the vibrating elements 10 is conserved by the symmetry of the system, and virtually no vibrational energy (i.e. linear or torsional energy) is dispersed by the mounting structure to the substrate. Such structure significantly differs from known prior art angular rate sensor mounting configurations wherein energy leaving such prior art systems is typically reflected back into the system in varying amounts. Such reflective energy generally affects the sense bender member and causes erroneous and unstable readings. The structure of this invention also rejects externally generated vibrational energy by reason of its unique compensating opposing symmetrical arrangement and due to the matching of masses, stiffness and frequencies of the respectively opposed vibrating members of the system.

Sensitivity of the present invention is preserved, since it is only the lightweight sensing bender members (10B) themselves that are providing sensed readings, as opposed to those prior art sensing systems which measure oscillatory torque of the entire sensing assembly about a "general" sense axis. With the present invention, a relatively high resonant frequency can be obtained, providing increased bandwidth.

The present invention produces only a minor amount of torsional forces, yet keeps the sensitivity of the sense members 10B high. The sense members 10B are "whipped" by the drive members 10A, so that most of the vibrational energy appears at the "free" ends of the sense members. The sense members are spaced as close as possible (i.e. the "y" dimension of FIG. 8) so as to allow for a significant amount of "whip" motion with the minimum amount of operative clearance therebetween. The free ends of the sense members are driven about their respective sense axes (S) as illustrated at (D) in FIG. 3, in the oscillatory plane in which the sense axes (S) lie. The drive members 10A drive the sense members 10B in a manner such that their respective movements are in direct opposition to one another (i.e. both simultaneously move respectively toward and away from the nodal axis 20 at the same time and at exactly the same rate). The cummulative vibrational forces from such movement which is reflected back through the drive member 10A to the mounting base 15 is virtually zero, due to the "cancelling" effect of the opposing motions at the nodal axis.

The sense members respond to an "angular rate" movement (i.e. to a force perpendicular to both the angular motion and the "driven" motion) applied to the free ends of the sense members. The "forces" applied to the free ends of the two sense members 10B caused by the sensed angular motion, are in opposite directions, which forms a "couple" that results in a vibrational torsion about the nodal axis 20. Since the spacing of the "couple" is small, and since very small forces are involved due to the low mass of the bender members, the resulting torque reflected to and through the mounting base 15 is negligible. The presence of such "forces", does, however, produce a larger "bending" moment on the individual sense members 10B which is approximately ten times larger than the reflected system torque, and which causes the piezoelectric bender elements to generate electrical signals proportional to the magnitude of the bending moments of the sense member. The large bending moments on the sense members provides improved system sensitivity while reducing radiated vibration and acoustic disturbance to practically zero.

While the invention has been above described with respect to a preferred embodiment, as applicable to piezoelectric vibrational sensor members, the principles of the invention apply equally well to other types of vibrational elements as well as to other modes of detection.

From the foregoing description, it will be appreciated that the present invention solves many of the problems or deficiencies associated with prior art vibrating element angular rate sensor configurations. It will be understood that while a specific application for the present invention, as used in association with piezoelectric bender element vibration systems has been disclosed, the invention is also applicable to other actuator/mass configurations and to other forms of drive and sensing modes of operations. For example, structures for sensing the stimulation of the vibrating elements employing electroptics or capacitance sensing modes could be easily adapted to the present invention. Further, while specific configurations of mounting and drive structures have been illustrated with respect to the piezoelectric embodiment of the invention, it will be understood that other configurations employing the symmetrical opposed mounting concept for the vibrational elements could equally well be employed.

Other modifications of the invention will be apparent to those skilled in the art in view of the foregoing descriptions. This description is intended to provide specific examples of an embodiment which clearly disclose the present invention. Accordingly, the invention is not limited to the described embodiment or to use of the specific elements, dimensions, materials or configurations contained therein. All alternative modifications and variations of the present invention which fall within the spirit and broad scope of the appended claims are covered.