Abstract
A controlled variable delivery external gear machine (VD-EGM). The VD-EGM includes a housing, an inlet, a drive gear, a driven gear, the drive gear configured to engage the driven gear in an angular mesh zone, an outlet, a first slider comprising a first longitudinal portion connected to a second longitudinal portion such that longitudinal forces applied to the first and second longitudinal portions substantially cancel each other thereby requiring between about 0 N to about 20 N to longitudinally moving the first slider, selective positioning of the first slider configured to vary net operational volumes of fluid communication between the inlet and the outlet, for a given rotational speed of the drive gear, and a first drive mechanism coupled to the first slider and configured to cause the first slider to slide in a longitudinal direction.
Claims
1. A controlled variable delivery external gear machine (VD-EGM), comprising: a housing; an inlet formed in the housing and configured to receive fluid from a supply; a drive gear disposed in the housing having a plurality of teeth; a driven gear disposed in the housing having a plurality of teeth and configured to be driven by the drive gear, the drive gear configured to engage the driven gear in an angular mesh zone, tooth space volumes defined by tooth spaces between each two consecutive teeth of the drive gear and each two consecutive teeth of the driven gear configured to receive volumes of fluid from the inlet as the corresponding teeth rotate about the inlet; an outlet formed in the housing and configured to receive at least some of the volume of fluid when the corresponding tooth space volumes in the angular mesh zone decrease as the corresponding teeth of the drive gear and driven gear come into contact with each other; a first slider disposed in the housing comprising a first longitudinal portion connected to a second longitudinal portion receiving longitudinal forces from fluid pressure applied to the first and second longitudinal portions substantially cancel each other thereby requiring between about 0 N to about 20 N to longitudinally moving the first slider, selective configured to vary net operational volumes of fluid communication between the inlet and the outlet, for a given rotational speed of the drive gear; and a first drive mechanism coupled to the first slider and configured to cause the first slider to slide in a longitudinal direction.
2. The VD-EGM of claim 1, wherein the first longitudinal portion of the first slider is connected to the second longitudinal portion at a distal end of the second longitudinal portion, and further comprising a foot connected to a proximal end of the second longitudinal portion, the foot having a cross-section such that when the foot of the first slider is coupled to a first lateral side of the drive gear and a first lateral side the driven gear, a high-pressure zone fluidly coupled to the outlet and a low-pressure fluidly coupled to the inlet are generated about the first and second longitudinal portions of the first slider.
3. The VD-EGM of claim 2, wherein the first drive mechanism includes one or more of a stepper motor, a solenoid, a lever, a cam, a hydraulic activation mechanism, and a pneumatic activation mechanism.
4. The VD-EGM of claim 3, wherein the longitudinal forces required to longitudinally move the first slider is governed by: F.sub.net1=P.sub.2.Math.(A.sub.11−A.sub.21)+P.sub.1.Math.(A.sub.31+A.sub.21), wherein F.sub.net1 is the net longitudinal force needed to move the first slider longitudinally, P.sub.2 is the pressure at the outlet, P.sub.1 is the pressure at the inlet, A.sub.11 is a cross-sectional of the first longitudinal portion of the first slider, A.sub.21 is a cross-sectional area of the second longitudinal portion of the first slider, and A.sub.31 is a cross-sectional area of the foot of the first slider.
5. The VD-EGM of claim 4, wherein the first and second longitudinal portions of the first slider are cylindrical in shape and cross-section of the foot of the first slider is rectangular.
6. The VD-EGM of claim 5, wherein F.sub.net1 is further governed by: F.sub.net1=P.sub.2.Math.((d.sub.11.sup.2−d.sub.21.sup.2).Math.π/4−L.sub.1.Math.W.sub.1)+P.sub.1.Math.(L.sub.1.Math.W.sub.1+d.sub.21.sup.2.Math.π/4), wherein d.sub.11 is the diameter of the first longitudinal portion of the first slider, d.sub.21 is the diameter of the second longitudinal portion of the first slider, L.sub.1 is the length of the foot of the first slider, and W.sub.1 is the width of the foot of the first slider.
7. The VD-EGM of claim 4, wherein the cross section of the first and second longitudinal portions of the first slider are elliptical in shape.
8. The VD-EGM of claim 7, wherein the cross-section of the foot of the first slider includes grooves.
9. The VD-EGM of claim 7, wherein the foot of the first slider has an elliptical cross-section.
10. The VD-EGM of claim 4, further comprising a second slider disposed in the housing separated from the first slider by the drive gear and the driven gear, comprising a first longitudinal portion connected to a second longitudinal portion such that longitudinal forces applied to the first and second longitudinal portions of the second slider substantially cancel each other thereby requiring between about 0 N to about 20 N to longitudinally move the second slider, selective positioning of the second slider configured to vary net operational volumes of fluid communication between the inlet and the outlet, for a given rotational speed of the drive gear and to balance lateral pressure forces acting on the drive gear and the driven gear; and a second drive mechanism coupled to the second slider and configured to cause the second slider to slide in a longitudinal direction.
11. The VD-EGM of claim 10, wherein the first longitudinal portion of the second slider is connected to the second longitudinal portion at a distal end of the second longitudinal portion, and further comprising a foot connected to a proximal end of the second longitudinal portion, the foot having a cross-section such that when the foot of the second slider is coupled to a second lateral side of the drive gear and a second lateral side the driven gear, the high-pressure zone and the low-pressure fluidly are formed about the first and second longitudinal portions of the second slider.
12. The VD-EGM of claim 11, wherein the second drive mechanism includes one or more of a stepper motor, a solenoid, a lever, a cam, a hydraulic activation mechanism, and a pneumatic activation mechanism.
13. The VD-EGM of claim 12, wherein the longitudinal forces required to longitudinally move the second slider is governed by: F.sub.net2=P.sub.2.Math.(A.sub.12−A.sub.22)+P.sub.1.Math.(A.sub.32+A.sub.22), wherein F.sub.net2 is the net longitudinal force needed to move the first slider longitudinally, P.sub.2 is the pressure at the outlet, P.sub.1 is the pressure at the inlet, A.sub.12 is a cross-sectional of the first longitudinal portion of the second slider, A.sub.22 is a cross-sectional area of the second longitudinal portion of the second slider, and A.sub.32 is a cross-sectional area of the foot of the second slider.
14. The VD-EGM of claim 12, wherein the first and second longitudinal portions of the second slider are cylindrical in shape and cross-section of the foot of the second slider is rectangular.
15. The VD-EGM of claim 14, wherein F.sub.net2 is further governed by: F.sub.net2=P.sub.2.Math.((d.sub.12.sup.2−d.sub.22.sup.2).Math.π/4−L.sub.2.Math.W.sub.2)+P.sub.1.Math.(L.Math.W.sub.2+d.sub.22.sup.2.Math.π/4), wherein F.sub.net2 is the net longitudinal force needed to move the second slider downward, P.sub.2 is the pressure at the outlet, P.sub.1 is the pressure at the inlet, d.sub.12 is the diameter of the first longitudinal portion of the second slider, d.sub.22 is the diameter of the second longitudinal portion of the second slider, L.sub.2 is the length of the foot of the second slider, and W.sub.2 is the width of the foot of the second slider.
16. The VD-EGM of claim 12, wherein the cross section of the first and second longitudinal portions of the first slider are elliptical in shape.
17. The VD-EGM of claim 16, wherein the cross-section of the foot of the first slider includes grooves.
18. The VD-EGM of claim 16, wherein the foot of the first slider has an elliptical cross-section.
19. The VD-EGM of claim 10, where the first drive mechanism and the second drive mechanism are the same drive mechanism.
20. The VD-EGM of claim 1, wherein the VD-EGM is selectively operated as a motor and a pump.
Description
BRIEF DESCRIPTION OF DRAWINGS
(1) FIG. 1 is a schematic of an external gear machine of the prior art depicting an exploded perspective view of various components including a drive gear and a driven gear each with a plurality of teeth.
(2) FIG. 2 is a schematic view of the drive and driven gear of FIG. 1 in coupling with each other depicting teeth in engagement with respect to each other.
(3) FIG. 3 is a schematic graph of tooth space volume vs. angular position of the engaged teeth of FIG. 2.
(4) FIG. 4 is a schematic of a controlled variable delivery external gear machine (VD-EGM) according to the present disclosure depicting an exploded perspective view of various components including a drive gear and a driven gear each with a plurality of teeth shown engaged therewith, a front cover, a back cover and casing having an inlet and an outlet, a first slider disposed in the front cover.
(5) FIG. 5 is a schematic cross-sectional view of various components of the VD-EGM of the present disclosure depicting the first slider in a juxtaposed position with respect to the drive and driven gears of FIG. 4, according to the present disclosure.
(6) FIG. 6 is a schematic perspective view of the first slider of FIG. 4, according to the present disclosure.
(7) FIG. 7A is a schematic collection of graphs of tooth space volume vs. angular position of the engaged teeth of FIG. 4 showing a trapped volume of fluid as the drive and driven gears rotate, according to the present disclosure.
(8) FIG. 7B is a schematic collection of graphs of tooth space volume vs. angular position of the engaged teeth of FIG. 4 showing changes in the tooth space volume as the position of the first slider changes, according to the present disclosure.
(9) FIG. 7C is a perspective schematic view of a front cover also shown in FIG. 4, according to the present disclosure, depicting insertion of the first slider into the front cover.
(10) FIG. 7D is a perspective schematic view of the front cover of FIG. 7C, according to the present disclosure, depicting the first slider fully inserted into the front cover with a top plate, also shown in FIG. 4 placed atop the front cover.
(11) FIG. 8 is a perspective schematic view of the front cover, slider, and the top place of FIG. 7D, according to the present disclosure, further depicting an actuator, also shown in FIG. 4 placed atop the top plate.
(12) FIG. 9 is a graph of flow (lpm) vs. pressure (bar) for various rotational speeds of the drive gear, with the slider kept at maximum displacement.
(13) FIG. 10 is a graph of flow (lpm) vs. pressure (bar) for various rotational speeds of the drive gear, with the slider kept at minimum displacement.
(14) FIG. 11 is a perspective view of a back cover and casing also shown in FIG. 4, depicting an inlet and outlet.
(15) FIG. 12 is a schematic of another controlled variable delivery external gear machine (VD-EGM) according to the present disclosure depicting an exploded perspective view of various components including a front cover, a back cover, a casing having an inlet and an outlet, a first slider disposed in the front cover, and a second slider disposed in the back cover, the casing configured to receive a drive gear and a driven gear (not shown) each having a plurality of teeth (not shown), engaged therewith, the first slider and the second slider configured to balance pressure between lateral sides of the drive and driven gears.
(16) FIGS. 13A and 13B are front and perspective views, respectively, of a slider according to another embodiment, where the foot of the slider includes grooves.
DETAILED DESCRIPTION
(17) For the purposes of promoting an understanding of the principles of the present disclosure, reference will now be made to the embodiments illustrated in the drawings, and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of this disclosure is thereby intended.
(18) In the present disclosure, the term “about” can allow for a degree of variability in a value or range, for example, within 10%, within 5%, or within 1% of a stated value or of a stated limit of a range.
(19) In the present disclosure, the term “substantially” can allow for a degree of variability in a value or range, for example, within 90%, within 95%, or within 99% of a stated value or of a stated limit of a range.
(20) Referring to FIG. 4, an exploded perspective view of a variable displacement external gear machine (VD-EGM) 400 according to one embodiment of the present disclosure is provided. The VD-EGM 10 includes a flange 401, a back cover and casing 402 having an outlet 422 and an inlet 424, a lateral plate 403, a drive gear 404A and a driven gear 404B, a front cover 405, a front cover top plate 406, a slider 407, an actuator 408, and a plurality of fastening members 410. It should be appreciated that the lateral plate 403 shown is optional for improved surface mating and is not required in all embodiments according to the present disclosure. While not intended to be a limiting factor of the VD-EGM 400 of the present disclosure, one difference between the VD-EGM 400 of the present disclosure and the EGM of the prior art for high pressure applications (e.g., with reference to FIG. 1), is the VD-EGM 400 of the present disclosure does not require axial compensations; therefore, the lateral grooves controlled by the sliders 120A and 120B (FIG. 1) can be realized directly on the front cover 405 of the VD-EGM 400. The actuator 408 is mechanically coupled to the slider 407 and is configured to force the slider up and down in the respective cavities of front cover 405 and front cover top plate 406 as will be discussed in more detail below. The outlet 422 is configured to eject fluid at a selective variable flow rate and the inlet 424 is configured to receive fluid at a selective variable flow rate. The drive gear 404A is coupled to and driven by a drive shaft 412 that passes through and is supported by collars 414 and 416 of the back cover and casing 402 and the flange 401, respectively, and by a corresponding collar (not numbered) on the front cover 405. The driven gear 404B is similarly supported by collars (not shown) in the back cover and casing 402 and the flange 401, respectively, and by a corresponding collar (not numbered) on the front cover 405. Both the drive gear 404A and the driven gear 404B are received in a cavity in the back cover and casing 402 (see cavity 420 in FIG. 11, discussed below). The fastener members 410 pass through the front cover 405 and the back cover and casing 402 and thread into the flange 401 in order to bring these components in fluid operations together.
(21) The design of the slider 407 represents an important aspect of the VD-EGM 400. One of the goals realized by the design of the slider 407 is to minimize the longitudinal forces (i.e., vertical forces in FIG. 4) acting on the slider resulting from the fluid pressure. This requirement is to permit a low force actuation of the VD-EGM 400, so that the flow can be varied without significant energy consumption. This arrangement permits a low energy actuation by the actuator 408. While a stepper motor is depicted in FIG. 4 for the actuator 408, it should be appreciated that other electromechanical and electrohydraulic approaches, including motors, cams, belts, and/or chains, known to a person having ordinary skill in the art, and electrohydraulic approaches known to a person having ordinary skill in the art can be used to effect the up and down motion of the slider 407.
(22) The slider 407 is now discussed in relationship with FIGS. 5, 6, 7A, 7B, 7C, 7D, and 8. FIG. 5 is a schematic view of the slider 407 disposed in the front cover 405 and coupled to the drive and driven gears 404A and 404B. The slider 407 is an L-shaped member with three zones of interest. The bottom (right side of the foot of the slider 407) is a low-pressure zone 516 (marked in FIG. 5 as “LP”). The central portion of the slider 407 (left side of the foot of the slider 407) is situated in high-pressure zones 514 and 512, having the same high pressure side as the outlet 422 (see FIG. 4). The top 510 of the slider 407 protruding out of the top plate 406 is mechanically coupled to the actuator 408. A seal 508 (e.g., an O-ring) dynamically seals the slider 407 against the front cover 405 and the top plate 406. The high-pressure zones 512 and 514 are designed to generate opposing forces (high-pressure zone 512 generates longitudinal force F1 which is pressure times the area of the high-pressure zone 512 while high-pressure zone 514 generates longitudinal force F2 which is pressure times the area of the high-pressure zone 514, opposite F1). Depending on the application in which the VD-EGM 400 used, e.g., whether the low-pressure is at atmosphere or below or above atmospheric pressure, the low-pressure zone 516 generates longitudinal force F3 which is pressure times the area of the low-pressure zone 516. The slider 407 is thus designed such that F1+F3−F2 is about zero. F3 can be ignored if the low-pressure is atmosphere. While no force is shown acting on the top 510, a force can be used (either from atmospheric pressure, or an external force other than the actuator). If so, that force (e.g., F4) would be used in the algebraic relationship provided above between the other forces with the appropriate sign depending on the direction of the force.
(23) Referring to FIG. 6, a perspective view of the slider 407 is provided. The slider 407 comprises two longitudinal portions 608 having a larger outer dimension and 610 having a smaller outer dimensions. While a cylindrical-shaped slider with a rectangular foot is discussed above and shown in the figures of the present disclosure, it should be appreciated that other shapes, e.g., elliptical and non-rectangular foot shapes, are also within the scope of the present disclosure.
(24) The longitudinal portion 608 is sealingly coupled to the front cover 405 via the seal 508 (see FIG. 5). The longitudinal portion 608 has an outer diameter 607 (d1 which is r1.Math.2). The longitudinal portion 610 has an outer diameter 609 (d2 which is r2.Math.2). Force F1 (see FIG. 5) is defined by high-pressure acting on an area A1 defined in the embodiment shown by (d1.sup.2−d2.sup.2).Math.π/4. The longitudinal portion 610 terminates in a foot 606 defined by dimensions length 614 (L) and width 612 (W). Force F2 (see FIG. 5) is defined by high-pressure acting on an area A2 defined in the embodiment shown by L.Math.W. Force F3 (see FIG. 5) is defined by low-pressure acting on an area A3 defined in the embodiment shown by L.Math.W+d2.sup.2.Math.π/4. Therefore, from manufacturing considerations, the following approximation applies:
W×L≈π(R.sup.2−r.sup.2) (1)
(25) The longitudinal force required to move the slider 407 downward is thus defined by:
F.sub.net=P.sub.2.Math.(A1−A2)+P.sub.1.Math.(A3), wherein
F.sub.net is the net longitudinal force needed to move the first slider 407 downward,
P.sub.2 is the pressure at the outlet 422,
P.sub.1 is the pressure at the inlet 427. In the embodiment shown, Eq (1) can be re-written as
F.sub.net=P.sub.2.Math.((d1.sup.2−d2.sup.2).Math.π/4−L.Math.W)+P.sub.1.Math.(L.Math.W+d2.sup.2.Math.π/4), wherein
d.sub.1 is the diameter of the longitudinal portion 608,
d.sub.2 is the diameter of the longitudinal portion 610,
L is the length of the foot 606, and
W is the width of the foot 606.
(26) It should be appreciated that fluid disposed atop the foot 606 is in fluid communication with the outlet 422 (see FIG. 4) and fluid disposed below the foot 606 is in fluid communication with the inlet 424. Similar to the tooth space volume shown in FIG. 2, the location of the foot 606 with respect to the drive gear 404A and 404B (see FIG. 4) determines the volumetric selection of fluid transfer from the inlet 424 to the outlet 422. Referring to FIG. 7A a schematic overview effect of slider position on fluid flow is provided. As shown in the top panel, with the slider position centrally within a mesh zone 700 of the drive gear and the drive gear 404A and driven gear 404B, the tooth space volume has a minimum trapped volume M. As shown in the middle panel, “D” representing the beginning of the trapped volume is equidistantly shown on the tooth space volume graph from “M” as is “M” from the end of the trapped volume (“S”). In the position of the slider 407 shown in FIG. 7A, maximum fluid flow is established from the inlet 424 to the outlet 422.
(27) Referring to FIG. 7B, a schematic overview effect of slider movement on fluid flow is shown. As shown in the left panel (similar to FIG. 7A), when the foot 606 (shown in dashed lines) of the slider 407 (also shown in dashed lines) is centrally positioned with respect to the mesh zone 700, the point “M” is centrally positioned between maximum allowed fluid input from the inlet 424 and fluid output out of the outlet 422. However, when the slider 407 is moved downward, the maximum allowed fluid input from the inlet 424 is decreased thereby decreasing the volumetric fluid flow through the VD-EGM 400. It should be noted that if the slider 407 is allowed to travel downward beyond a threshold, the inlet 424 will be connected to the outlet 422, thereby rendering the VD-EGM 400 inoperative (i.e., no fluid flow). While not shown, if the slider 407 was to move upward from the position shown in the left panel of FIG. 7B, the maximum allowed fluid output out of the outlet 422 is decreased thereby decreasing the volumetric fluid flow through the VD-EGM 400. Similarly, it should be noted that if the slider 407 is allowed to travel upward beyond a threshold, the inlet 424 will be connected to the outlet 422, thereby rendering the VD-EGM 400 inoperative (i.e., no fluid flow).
(28) Referring to FIG. 7C, a schematic representation of insertion the slider 407 into the front cover 405 is shown. In FIG. 7C, a sliding chamber 720 and two receiving collars 730 for the drive shaft and a shaft on which the driven gear is mounted are shown.
(29) Referring to FIG. 7D, a partially assembled VD-EGM 400 is shown with the slider 407 in place through the top plate 406 and the front cover 405.
(30) Referring to FIG. 8, the actuator 408 is provided on top of the top plate 406 and coupled to the slider 407. The seal 508, provides a dynamic seal between the slider 407 and the front cover 405 and the top plate 406. The actuator 408 is activated by cables 810.
(31) The actuator 408 (stepper, or other actuators as discussed below) control precisely the position of the slider, so that the flow of the VD-EGM 400 can be electronically set. The actuator utilizes negligible power (between about 0 and 0.1 W) when it is not actuated. This means that the electronic controller will consume energy only when the slider has to be moved to realize a different flow through the VD-EGM 400.
(32) Referring to FIGS. 9 and 10, flow vs pressure curves are provided based on measurements for several rotational speeds with the slider kept at maximum displacement and minimum displacement, respectively. With reference to FIG. 9, at maximum displacement, the resulting derived displacement is about V.sub.d,max=8.87 cm.sup.3/rev—the displacement is the y-intercept divided by the speed as provided in the legend, where the y-intercept gives flow rate at zero pressure which when divided by angular speed provides displacement. With reference to FIG. 10, similar experiments were performed with the slider kept at minimum displacement position, see the right panel of FIG. 7B. The resulting displacement is about V.sub.d,min=6.31 cm.sup.3/rev.
(33) FIG. 11 shows a schematic perspective view of the back cover and casing 402 showing the inlet 424 and the outlet 422 in relationship to each other and to the back cover and casing 402. The cavity 420 is shown in the back cover and casing 402 that is configured to receive drive gear 404A and the driven gear 404B.
(34) FIG. 12 depicts another embodiment of a variable displacement external gear machine (VD-EGM) 500 where two sliders are used, one identified as 407A in the front cover 405A, as shown in FIG. 4, and one identified as 407B in a back cover 405B. A casing 402A is shown, having an outlet 422A and an inlet (not shown). Also, while not shown, a drive gear and driven gear are configured to be received within a cavity 420A disposed within the casing 402A. Also, while not shown, either a separate electrical actuation, or as discussed earlier with respect to the actuator 408 other electromechanical or electrohydraulic actuators known to a person having ordinary skill in the art, can be utilized to actuate the second slider 407B or the same electrical actuation used for the first slider 407A. The purpose for use of two sliders 407A and 407B is to provide a pressure balancing between the inlet 424 and the outlet 422. In other words, in high pressure applications, use of only one slider can generate lateral forces on the drive gear 404A and the driven gear 404B, resulting in pre-mature failure of internal components of the VD-EGM 400. In particular, the two-slider implementation shown in VD-EGM 500 causes the pressure distribution on the two lateral surfaces of the gears to be uniform. This ensures there is no lateral moment resulting from lateral forces and the gears are laterally balanced, thereby maintaining a lateral lubricating gap (not shown) which is sufficient and thus allows the internal components to bear the resulting load. At high pressures this lateral gap needs to be controlled to minimize leakages and to prevent contact between the gears lateral surface and the front and back covers 405A and 405B, thus resulting in low wear and longer life.
(35) As discussed above, while an electrical actuation in the form of a stepper motor is described, herein, it should be appreciated that other types of actuation are within the scope of the present disclosure. For example, alternate actuation technologies include electrical (e.g., solenoid), manual, mechanical, e.g. using a lever or a cam, pneumatic, hydraulic, as well as other actuation techniques known to a person having ordinary skill in the art.
(36) Referring to FIGS. 13A and 13B, front and perspective views, respectively, of a slider 507 according to another embodiment, of the present disclosure are presented. The slider 507 is similar to the slider 407 shown in FIG. 6, with one difference that the foot of the slider 507 includes grooves. In other aspects, not shown, the foot of the slider can have an elliptical cross section instead of a rectangular (as shown in FIG. 6) or a pseudo-rectangular as shown in FIGS. 13A and 13B. In yet other aspects, not shown, the foot of the slider can have a hybrid cross-section. The important aspect of the foot design is that when the foot of the slider 407 or 507 is coupled to a lateral side of the drive gear 404A and the driven gear 404B—or when the foot of the first slider 407A is coupled to a first lateral side of the drive gear 404A and a first lateral side of the driven gear 404B and the foot of second slider 407B is coupled to a second lateral side of the drive gear 404A and a second lateral side of the driven gear 404B—that a high-pressure zone coupled to the outlet 422 and a low-pressure zone coupled to the inlet 424 be generated about the first and second longitudinal portions of the respective slider(s), thereby generating the counterbalancing forces about these longitudinal portions requiring only a longitudinal force of between about 0 N and about 20 N to longitudinally move the respective slider.
(37) In the present disclosure a combination of the front cover, the rear cover, and the back cover and casing are used synonymously as a housing.
(38) While the variable delivery external gear machine (VD-EGM) of the present disclosure is described generally as a pump, it should be appreciated the VD-EGM of the present disclosure can be selectively operated as a pump or a motor.
(39) Those having ordinary skill in the art will recognize that numerous modifications can be made to the specific implementations described above. The implementations should not be limited to the particular limitations described. Other implementations may be possible.
