US3643037A - Separation control for record media transducer with transverse slots to supply ambient pressure - Google Patents

Separation control for record media transducer with transverse slots to supply ambient pressure Download PDF

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Publication number
US3643037A
US3643037A US815562A US3643037DA US3643037A US 3643037 A US3643037 A US 3643037A US 815562 A US815562 A US 815562A US 3643037D A US3643037D A US 3643037DA US 3643037 A US3643037 A US 3643037A
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Prior art keywords
tape
operating surface
tangency
media
transducer
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Expired - Lifetime
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US815562A
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English (en)
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Richard E Norwood
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International Business Machines Corp
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International Business Machines Corp
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    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B5/00—Recording by magnetisation or demagnetisation of a record carrier; Reproducing by magnetic means; Record carriers therefor
    • G11B5/127—Structure or manufacture of heads, e.g. inductive
    • G11B5/187—Structure or manufacture of the surface of the head in physical contact with, or immediately adjacent to the recording medium; Pole pieces; Gap features
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B15/00—Driving, starting or stopping record carriers of filamentary or web form; Driving both such record carriers and heads; Guiding such record carriers or containers therefor; Control thereof; Control of operating function
    • G11B15/60—Guiding record carrier
    • G11B15/62—Maintaining desired spacing between record carrier and head
    • G11B15/64—Maintaining desired spacing between record carrier and head by fluid-dynamic spacing

Definitions

  • the cocking tendency is caused by a region Of lower 3,533,058 10/1970 Platter ..l79/ 100.2 P than ambient pressure near the point where the media draws 3,161,120 1964 Tim 6 79/ 2 P away from the operating surface, and provides means for sup- ,2 1966 179/1002 P plying ambient pressure at that point.
  • the means comprises a transverse slot extending beyond 3,398,870 8/ 1968 Mullan et 81....
  • the present invention relates to magnetic transducer apparatus, and more particularly to flexible web record media transducers of the type which employ fluid bearings between the operating surface of the transducer and the moving media to reduce wear and control separation.
  • the patents further point out that the stability of the bearing and the uniformity of its .thickness are, in part, a function of the arc length over which it exists along the operating surface of the head.
  • the present invention is concerned with situations wherein it is desirable to provide a uniform fluid bearing over a length of operating sur- .face, but where the wrap angle and operating surface contour are such, with respect to the media involved, that a constant pair of generally flat surface portions that are inclined only a few degrees relative to one another and are joined by a small ,radius portion.
  • the record media assumes an angle of wrap over the radius portion and a bearing is generated, but, due to the short arc length involved, precise control and stability are difficult to achieve.
  • the bearing developed in this case often varies in thickness along the radius portion. It is also found that the point of closest proximity between the radius portion and the media shifts, depending upon the direction the media is travelling. If a transducing gap is located in the radius section, these variations can cause variations in the signals recorded on or read from the media by the gap. Unless the gap is located precisely midway between the points of closest proximity for each direction of media travel, a different separation is found at the gap for each direction of motion and different transducing action takes place. A magnetic tape read in the forward direction of tape motion in this situation will produce different signal strengths than when read in a backward direction.
  • the forward-backward ratio of transduced signal characteristics be maintained as nearly equal to 1:1 as possible for error-free operation. Accordingly, it is the principal object of this invention to provide, in a transducer having transducing gaps located in radius portions of its operating surface, means for stabilizing the fluid bearing between the moving record media and the radius surface, and for ensuring uniformity of its thickness. It is a particular object of the invention to improve the uniformity of the bearing thickness for both directions of motion of the media.
  • An important aspect of this invention is the discovery that a flexible record media of a given stiffness, such as a conventional magnetic tape, passing over a radius on an operating surface, generates fluid bearing pressure, the distribution of which is not symmetrical between the entry and exit points of tangency between the media path and the surface.
  • the moving mediadoes not leave the surface at the exit point of tangency determined byits wrap angle, but tends to follow the surface further than it should. Analysis of the pressure distribution between the mediaand the surface has shown that this situation results from the presence of a negative pressure region near the exit point of tangency.
  • This negative pressure region seems to be produced by the increase in the volume of the space between the media and the surface as the media leaves the surface, and an inability of the environmental fluid to till the space adequately under the conditions present.
  • the media is, accordingly, drawn toward the surface and cocked downstream.
  • the cocking contributes to nonuniformity' of separation over the distance between the entry and exit tangency points. It produces a varying separation that has a position of closest proximity nearer the exit tangent point than the entry tangent point.
  • This closest proximity position thus, differs for each direction of motion of the media and produces an undesirable forward-backward signal ratio, as earlier described, unless the transducing gap on the radius surface is positioned exactly midway between the two tangency points. Such fine positioning is difficult, if not impossible, to obtain.
  • the cocking problem is solved by providing a slot in the operating surface of the transducer at the position where the negative pressure region is found to have existed.
  • the slot extends transversely of the direction of motion of the media and communicates with the ambient fluid environment at the sides of the media. Its width and depth dimensions are sufficient to produce ambient pressure between the media and the surface at the exit tangency point, thus dissipating the negative pressure region and allowing the media to depart along the path dictated by the wrap angle. It has been found that, by provision of this slot, the tendency to cock is. eliminated and the fluid bearing over the length of operating surface between the entry and exit tangency points is greatly enhanced in terms of stability and uniformity of thickness. Criticality of location of the transducing gap is thus eliminated.
  • FIG. 1 is a schematic representation of a transducer having a transducing gap positioned in a radius portion of its operating surface, and illustrating the cocking tendency of a record tape passed thereover at a small wrap angle;
  • FIG. 2 is a plot of the fluid bearing pressure distribution between the transducer operating surface and the record tape of FIG. 1;
  • FIG. 3 is a plot of the separation between the tape and operating surface of FIG. 1;
  • FIG. 4 is a schematic representation of a transducer similar to that of FIG. I, but having slots provided in accordance with this invention
  • FIG. 5 is a plot of the fluid .bearing pressure distribution between the transducer operating surface and the record tape of FIG. 4;
  • FIG. 6 is a plot of the separation between the tape and operating surface of FIG. 4.
  • FIG. 7 is a schematic representation of a transducer having plural transducing gaps spaced along the direction of tape motion showing the provision of slots for each gap-containing area of the operating surface.
  • FIG. 1 shows an enlarged elevational view of the contour of a portion of a transducer 10 having an operating surface 12 over which a magnetic record tape is passed.
  • the surface 12 has a width dimension (into the plane of the paper) at least equal to and preferably greater than the width of the record tape and is generally smooth and continuous over the length shown.
  • the surface includes a radius portion 14 that blends at each end with two generally flat portions 16 and 18 that are inclined one to the other.
  • the radius portion 14 comprises a processing zone of the transducer structure and a transducing gap 20 is positioned within it.
  • the magnetic head element that forms the gap is partially shown in dotted outline at 22.
  • a magnetic record tape to be processed is passed over the operating surface along the path indicated by the solid line 24.
  • the path of the tape is such that a small wrap angle over the radius portion 14 is achieved.
  • the wrap angle is provided by means (not shown) that cause the tape to enter and leave the processing zone of the transducer at the angle shown.
  • the means may include tape guides or fluid pressure means that constrain the tape. Its specific configuration is not a part of this invention and will not be described herein.
  • passage of the tape along path 24 over the operating surface 12 produces a fluid foil bearing between the tape and the surface 12 from the environmental fluid in which the apparatus resides (for example, air).
  • the bearing produces a separation between the tape and the surface 12 that lubricates the system and prevents excessive wear on both elements.
  • the thickness of the bearing has been greatly exaggerated in the drawings for the purposes of illustration; it is, in reality, usually in the order of 30-100 microinches, depending upon the several parameters which control its generation.
  • the fluid bearing generated in the arrangement shown exists substantially over the arc length between the points where the tape path 24 becomes tangent to the radius portion 14 of the surface 12. These points are identified in FIG. 1 at the intersections 26 and 28 of radius lines R with the path 24. Depending upon the direction of travel of the tape, one of the points 26 or 28 is an entry point of tangency and the other is an exit point of tangency. These points of tangency are located with respect to the static or desired tape path determined by its wrap angle. It will be appreciated from the following description that the tape does not always follow the preferred path, however, and tends to enter and leave the processing zone at points which vary from the point of tangency.
  • the bearing between the points of tangency be stable and uniform in thickness so that the tape follows essentially the preferred path 24 and good uniform transducing action can be achieved between the tape and the gap 20. It has been found, however, that in arrangements such as is shown, where conventional tape is used and where the wrap angle is small (for example, in the order of about 10 or less) and the radius of curvature of the portion 12 is also small (for example, less than one inch), there is not a sufficient arc length between points 26 and 28 to ensure a good stable and uniform bearing over the processing zone. It has been discovered that, for a given direction of travel, the tape actually cocks downstream somewhat, assuming paths shown at 30 and 32 in FIG. 1. Path 30 is assumed for a left to right direction (arbitrarily called forward,” hereinafter) of travel, while path 32 is assumed for the reverse (backward) direction.
  • FIG. 2 The horizontal axis of the plot of FIG. 2 corresponds in scale to FIG. 1.
  • Curve 34 shows the pressure distribution for forward travel
  • curve 36 shows the distribution for backward travel. It will be seen that, for each direction, there exists a positive pressure region over a substantial length of the operating surface between the points of tangency 26 and 28, and then a negative pressure region (indicated by a dip of the curve below the horizontal axis) at about the exit point of tangency where the tape should pull away from the surface 12.
  • This negative pressure region seems to be produced by an inability of the ambient fluid to adequately flow into the increasing space beneath the tape under the conditions present when the tape is moving at high speed.
  • the net result is that the negative pressure region draws the tape down at the exit point and moves the point of tangency downstream.
  • the effect also tends to move the entry point of tangency downstream and results in the cocked condition shown by lines 30 and 32.
  • the extent of the cocking effect. and the exact position of the negative pressure region are a function, in part, of the tape stiffness and may vary somewhat for different tapes.
  • FIG. 1 The amount of cocking in each case is exaggerated in FIG. 1 for illustration purposes. It is more accurately shown by the tape-to-operating surface separation plot of FIG. 3.
  • the curves 38 and 40 illustrate the variation in separation of the tape for forward (curve 38) and backward (curve 40) travel with respect to the surface of portion 14.
  • the horizontal scale of FIG. 3 corresponds to that of FIGS. 1 and 2 to permit ready comparison.
  • Examination of FIG. 3 shows that, for each direction of travel, the separation distance varies widely between the entry and exit points of tangency, and includes a point of closest proximity that is not positioned midway between the tangency points, but is moved downstream toward the negative pressure region.
  • FIGS. 1 through 3 The problems discussed in connection with FIGS. 1 through 3 are solved in accordance with this invention by the provision of means to eliminate the substantial negative pressure region between the tape and the operating surface, and thereby eliminates the cocking tendency of the tape as it travels over the processing zone.
  • the means comprises a slot in the operating surface extending transversely of the directions of motion of tape travel.
  • FIG. 4 shows a transducer 10 like that of FIG. 1 having slots 44 and 46 provided therein for this purpose. Each slot 44 or 46 extends across the operating surface 12' of the transducer 10 a distance at least greater than the width of the tape and, preferably, from one side edge of the transducer to the other.
  • FIG. 7 shows, in perspective, the arrangements of such slots at 116, in a complete transducer assembly.
  • slots 44 and 46 The purpose of the slots 44 and 46 is to provide means to produce ambient fluid pressure at the points where the deleterious negative pressure is found to exist. Accordingly, they must be of sufficient depth and width to carry the volume of fluid required for this purpose and they must communicate with the ambient fluid at the sides of the tape. While two slots are shown in FIG. 4, it will be appreciated that, for a given direction of motion, the downstream slot is of primary interest. Thus, for forward motion, slot 46 provides the anticocking control, while slot 44 controls the effect for backward motion. The positioning of the slots is important. For each direction of motion, the slot must be within the area of the operating surface portion at which the negative pressure is found to have existed. Generally speaking, this is near the exit point of tangency. From the plot of FIG.
  • the negative pressure region extends upstream from the exit tangency point 28' (forward) or 26' (backward) somewhat, so it is useful to locate the upstream edge 44A or 46A of the slot somewhat inside that point. Some variation in positioning may be permitted so long as the slot's upstream edge 44A or 46A is within the negative pressure area and capable of equalizing the pressure enough to prevent cocking. Experimentation on a given operating surface contour to establish the negative pressure point will establish the proper position for that contour.
  • the presence of two slots 44 and 46 provides for elimination of the cocking problem in each direction of tape motion.
  • the upstream slot is not essential for a given direction and, in a transducer arranged only for unidirectional tape motion operation, it may be eliminated. It has been found, however, that such a slot is beneficial in that it tends to bleed off some of thefluid that is dragged beneath the tape to form the fluid bearing and aids in producing thin bearings that improve transducing action.
  • the bearing thickness is directly proportional to the radius of curvature of the operating surface in the area where the bearing is generated.
  • FIG. 5 shows the pressure distribution between the tape and operating surface in the embodiment of FIG. 4. It will be noted that the negative pressure region has been effectively eliminated by the slot 46 for forward motion (curve 34') and by the slot 44 for backward motion (curve 36'). Reference to FIG. 6 shows that the separation of the tape from the operating surface is substantially constant along the processing zone,
  • the slots 44 and 46 are a preferred means for supplying ambient fluid pressure beneath the tape at the negative pressure regions. It should be understood, however, that other equivalent means, such as holes in the operating surface at the points where the slots 44 and 46 are shown, would suffice. Such holes would, of course, communicate with a sourceof ambient pressure. v t
  • FIG. 7 of the drawings is a perspective illustration of a multitrack transducer 100 provided in accordance with the principles of this invention.
  • the transducer 100 has two transducing gaps 102 and 104 in each information chanhe] or track along its operating surface 106.
  • the purpose of the two gaps in each track is to permit simultaneous writing and reading operations, as is well understood in the art. The.
  • operating surface 106 is arranged to have a flat central portion 108 with flat leading and trailing portions 110 and l 12 extending outwardly in each direction at an angle thereto.
  • the portions and 112 are bind to the central portion by small curved portions "4 o radius r within which the transducing gaps are located.
  • the portions 114 correspond to the radius portions 14 of FIG. 4. Near the points where each radius portion 114 joins each of its adjacent flat portions, a slot ll6 is provided.
  • the slots 116 provide the functions described with respect to slots 44 and 46 of FIG. 4, and they are located near the points of tangency of the tape path with the radius portions 114 to relieve the negative pressures earlier described. In this transducer 100, the tape actually experiences the situation described with reference to FIG. 1 twice during its travel over the operating surface 106; once as it is wrapped over each radius portion "4 between the center flat surface 108 and one of the end flat portions 110 and I12.
  • slots 118 are seen in FIG. 7. These slots are coupled to a source of vacuum pressure and operate to load the tape (not shown) downwardly over the transducer 100 to create the wrap angle necessary for generation of fluid bearings at the radius portions 114 and control of the tape separation at the transducing gaps.
  • Longitudinal slots 120 extend toward the radius portions from the vacuum slots 118. These slots 120 are positioned to underlie the side edges of the tape as it passes over the transducer and exerta downward force to prevent any tendencyof the edges to curl upwardly.
  • Additional longitudinal intertrack slots 122 may be provided in a transducer 100 to provide a channelling action for a portion of the fluid bearings over the surfaces 114 to further reduce their thicknesses.
  • the function of the slots 122 in no way adversely affects the anticocking action of slots 116.
  • a magnetic tape transducer of the fluid bearing type which has an operating surface including a radius portion connecting inclined flat surface portions over which a length of magnetic tape, significant lengths of which appear flexible and short lengths of which appear rigid, having a fixed width is adapted to be moved in either of two directions, said tape being arranged to have an angle of wrap about the radius portion of the operating surface that produces spaced entry and exit points of tangency with said surface for each direction of movement, and wherein movement of the tape over said operating surface generates a fluid bearing between said tangency points
  • the improvement in means for providing a uniform bearing over a substantial portion of said operating surface between said points of tangency for each direction of tape motion comprising a slot, extending transversely of the direction of tape motion, immediately adjacent said exit point of tangency, within a distance from said exit point corresponding to a short length of apparently rigid tape, and substantially longer than the tape width for supplying ambient fluid pressure between the tape and the operating surface when the tape is moving in a direction toward said exit point of tangency from the
  • the magnetic tape is a conventional one-half-inch-wide record tape of average stiffness, wherein the radius portion of the operating surface has a radius of less than one inch, and wherein the angle of wrap is less than 10.

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  • Engineering & Computer Science (AREA)
  • Manufacturing & Machinery (AREA)
  • Magnetic Heads (AREA)
  • Slot Machines And Peripheral Devices (AREA)
  • Paper (AREA)
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US815562A 1969-04-14 1969-04-14 Separation control for record media transducer with transverse slots to supply ambient pressure Expired - Lifetime US3643037A (en)

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US81556269A 1969-04-14 1969-04-14

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US (1) US3643037A (enrdf_load_stackoverflow)
JP (1) JPS4932131B1 (enrdf_load_stackoverflow)
CA (1) CA939434A (enrdf_load_stackoverflow)
DE (1) DE2017407C3 (enrdf_load_stackoverflow)
ES (1) ES378552A1 (enrdf_load_stackoverflow)
FR (1) FR2041168A1 (enrdf_load_stackoverflow)
GB (1) GB1293205A (enrdf_load_stackoverflow)

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3859663A (en) * 1973-06-18 1975-01-07 Sperry Rand Corp Multichannel transducer with glass support elements
US3872507A (en) * 1972-02-04 1975-03-18 Matsushita Electric Ind Co Ltd Rotating air bearing head with shaped control slots
US4414593A (en) * 1981-10-08 1983-11-08 Archive Corporation Streaming cartridge tape drive
US4695909A (en) * 1983-11-10 1987-09-22 Hitachi, Ltd. Magnetic head assembly
US5574606A (en) * 1989-02-28 1996-11-12 Canon Denshi Kabushiki Kaisha Magnetic head having dust handling tape slide surface
US5867352A (en) * 1992-11-13 1999-02-02 U.S. Philips Corporation Magnetic tape apparatus having a magnetic head with at least one cleaning groove thereon
US5953184A (en) * 1997-09-30 1999-09-14 Storage Technology Corporation Transverse slotted magnetic tape head assembly
US5969912A (en) * 1997-12-10 1999-10-19 Cope; James Robert Bidirectional magnetic read/write recording head surface contour with plurality of Bernoulli Pocket cavities for generating very low media-to-head separations
US6122147A (en) * 1999-01-05 2000-09-19 Imation Corp. Negative pressure head contour in a linear tape recording system with tape deforming cavity
WO2002037478A3 (en) * 2000-10-30 2003-04-17 Storage Technology Corp Tape head contour utilizing enclosed through slots
US20050134989A1 (en) * 2003-12-18 2005-06-23 Carolyn Girvin Multi-format thinfilm head and associated methods
US9734854B2 (en) * 2014-08-20 2017-08-15 International Business Machines Corporation Tape heads with sub-ambient pressure cavities
US9984720B1 (en) * 2017-01-10 2018-05-29 International Business Machines Corporation Damping lateral tape motion disturbances

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3947887A (en) * 1975-04-03 1976-03-30 Storage Technology Corporation Transducer head contour and method of generating same
JPH01315061A (ja) * 1988-06-15 1989-12-20 Sony Corp ヘッドの安定板構造

Citations (7)

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US3161120A (en) * 1963-02-25 1964-12-15 Fma Inc Apparatus for bringing ribbon-type media together
US3273896A (en) * 1960-02-17 1966-09-20 Leesona Corp Tape recorder and tape storage magazine therefor
US3319238A (en) * 1963-07-16 1967-05-09 Ampex Magnetic head assembly with means for heat dissipation
US3398870A (en) * 1967-01-23 1968-08-27 Ibm Controlled air film bearing
US3435442A (en) * 1965-03-26 1969-03-25 Ampex Fluid lubricated magnetic tape transducer
US3533058A (en) * 1967-07-13 1970-10-06 Ibm Edge curl control for a flat vacuum head
US3582917A (en) * 1968-12-13 1971-06-01 Ibm Magnetic head having a continuously variable radius of curvature

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Publication number Priority date Publication date Assignee Title
US3273896A (en) * 1960-02-17 1966-09-20 Leesona Corp Tape recorder and tape storage magazine therefor
US3161120A (en) * 1963-02-25 1964-12-15 Fma Inc Apparatus for bringing ribbon-type media together
US3319238A (en) * 1963-07-16 1967-05-09 Ampex Magnetic head assembly with means for heat dissipation
US3435442A (en) * 1965-03-26 1969-03-25 Ampex Fluid lubricated magnetic tape transducer
US3398870A (en) * 1967-01-23 1968-08-27 Ibm Controlled air film bearing
US3533058A (en) * 1967-07-13 1970-10-06 Ibm Edge curl control for a flat vacuum head
US3582917A (en) * 1968-12-13 1971-06-01 Ibm Magnetic head having a continuously variable radius of curvature

Non-Patent Citations (3)

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Title
J. T. S. Ma, An Investigation of Self Acting Foil Bearings, Transactions of the ASME, Journal of Basic Engineering, Paper 65 Lubs 4, 1965. *
P. Magura, Channeled Magnetic Head, IBM Technical Disclosure Bulletin, July 1961, page 33. *
R. E. Norwood, Effects of Bending Stiffness in Magnetic Tape, IBM Journal of Research and Development, March 1969 pp.205 208 *

Cited By (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3872507A (en) * 1972-02-04 1975-03-18 Matsushita Electric Ind Co Ltd Rotating air bearing head with shaped control slots
US3859663A (en) * 1973-06-18 1975-01-07 Sperry Rand Corp Multichannel transducer with glass support elements
US4414593A (en) * 1981-10-08 1983-11-08 Archive Corporation Streaming cartridge tape drive
US4695909A (en) * 1983-11-10 1987-09-22 Hitachi, Ltd. Magnetic head assembly
US5574606A (en) * 1989-02-28 1996-11-12 Canon Denshi Kabushiki Kaisha Magnetic head having dust handling tape slide surface
US5867352A (en) * 1992-11-13 1999-02-02 U.S. Philips Corporation Magnetic tape apparatus having a magnetic head with at least one cleaning groove thereon
US5953184A (en) * 1997-09-30 1999-09-14 Storage Technology Corporation Transverse slotted magnetic tape head assembly
US5969912A (en) * 1997-12-10 1999-10-19 Cope; James Robert Bidirectional magnetic read/write recording head surface contour with plurality of Bernoulli Pocket cavities for generating very low media-to-head separations
US6122147A (en) * 1999-01-05 2000-09-19 Imation Corp. Negative pressure head contour in a linear tape recording system with tape deforming cavity
WO2002037478A3 (en) * 2000-10-30 2003-04-17 Storage Technology Corp Tape head contour utilizing enclosed through slots
US20050134989A1 (en) * 2003-12-18 2005-06-23 Carolyn Girvin Multi-format thinfilm head and associated methods
US7154691B2 (en) * 2003-12-18 2006-12-26 Quantum Corporation Multi-format thinfilm head and associated methods
US9734854B2 (en) * 2014-08-20 2017-08-15 International Business Machines Corporation Tape heads with sub-ambient pressure cavities
US9761259B2 (en) 2014-08-20 2017-09-12 International Business Machines Corporation Tape heads with sub-ambient pressure cavities
US9984720B1 (en) * 2017-01-10 2018-05-29 International Business Machines Corporation Damping lateral tape motion disturbances
US10553245B2 (en) 2017-01-10 2020-02-04 International Business Machines Corporation Damping lateral tape motion disturbances
US10832724B2 (en) 2017-01-10 2020-11-10 International Business Machines Corporation Damping lateral tape motion disturbances

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ES378552A1 (es) 1973-08-16
CA939434A (en) 1974-01-01
GB1293205A (en) 1972-10-18
FR2041168A1 (enrdf_load_stackoverflow) 1971-01-29
JPS4932131B1 (enrdf_load_stackoverflow) 1974-08-28
DE2017407A1 (enrdf_load_stackoverflow) 1970-10-29
DE2017407B2 (de) 1973-06-07
DE2017407C3 (de) 1974-01-10

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