US3864586A - Vibrator and vibratory system - Google Patents

Vibrator and vibratory system Download PDF

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Publication number
US3864586A
US3864586A US396675A US39667573A US3864586A US 3864586 A US3864586 A US 3864586A US 396675 A US396675 A US 396675A US 39667573 A US39667573 A US 39667573A US 3864586 A US3864586 A US 3864586A
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Prior art keywords
vibratory
arms
central
vibrator
magnet
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US396675A
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English (en)
Inventor
Hiroshi Saito
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Seikosha KK
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Seikosha KK
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Priority claimed from JP9230172A external-priority patent/JPS5336747B2/ja
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    • G—PHYSICS
    • G04—HOROLOGY
    • G04C—ELECTROMECHANICAL CLOCKS OR WATCHES
    • G04C3/00—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means
    • G04C3/08—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means wherein movement is regulated by a mechanical oscillator other than a pendulum or balance, e.g. by a tuning fork, e.g. electrostatically
    • G04C3/10—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means wherein movement is regulated by a mechanical oscillator other than a pendulum or balance, e.g. by a tuning fork, e.g. electrostatically driven by electromagnetic means
    • G04C3/101—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means wherein movement is regulated by a mechanical oscillator other than a pendulum or balance, e.g. by a tuning fork, e.g. electrostatically driven by electromagnetic means constructional details
    • G04C3/102—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means wherein movement is regulated by a mechanical oscillator other than a pendulum or balance, e.g. by a tuning fork, e.g. electrostatically driven by electromagnetic means constructional details of the mechanical oscillator or of the coil
    • G—PHYSICS
    • G04—HOROLOGY
    • G04C—ELECTROMECHANICAL CLOCKS OR WATCHES
    • G04C3/00—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means
    • G04C3/08—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means wherein movement is regulated by a mechanical oscillator other than a pendulum or balance, e.g. by a tuning fork, e.g. electrostatically
    • G04C3/10—Electromechanical clocks or watches independent of other time-pieces and in which the movement is maintained by electric means wherein movement is regulated by a mechanical oscillator other than a pendulum or balance, e.g. by a tuning fork, e.g. electrostatically driven by electromagnetic means
    • G—PHYSICS
    • G04—HOROLOGY
    • G04C—ELECTROMECHANICAL CLOCKS OR WATCHES
    • G04C5/00—Electric or magnetic means for converting oscillatory to rotary motion in time-pieces, i.e. electric or magnetic escapements
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K33/00—Motors with reciprocating, oscillating or vibrating magnet, armature or coil system
    • H02K33/02—Motors with reciprocating, oscillating or vibrating magnet, armature or coil system with armatures moved one way by energisation of a single coil system and returned by mechanical force, e.g. by springs
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K33/00—Motors with reciprocating, oscillating or vibrating magnet, armature or coil system
    • H02K33/02—Motors with reciprocating, oscillating or vibrating magnet, armature or coil system with armatures moved one way by energisation of a single coil system and returned by mechanical force, e.g. by springs
    • H02K33/10—Motors with reciprocating, oscillating or vibrating magnet, armature or coil system with armatures moved one way by energisation of a single coil system and returned by mechanical force, e.g. by springs wherein the alternate energisation and de-energisation of the single coil system is effected or controlled by movement of the armatures
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K7/00—Arrangements for handling mechanical energy structurally associated with dynamo-electric machines, e.g. structural association with mechanical driving motors or auxiliary dynamo-electric machines
    • H02K7/06—Means for converting reciprocating motion into rotary motion or vice versa
    • H02K7/065—Electromechanical oscillators; Vibrating magnetic drives
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
    • H03H9/24—Constructional features of resonators of material which is not piezoelectric, electrostrictive, or magnetostrictive

Definitions

  • a vibrator comprises a vibratory unit composed of re silient sheet material and having two main vibrator [2]] Appl' 396675 arms disposed in spaced parallel relationship and in terconnected at their ends by two connecting end por- [30] Foreign Application Priority Data tions.
  • a pair of central vibratory arms extend inwardly seph 14 972 Japan H 471M301 from each connecting end portion in a direction to- Oct 20, 1972 Japan H 47405064 wards each other and the central arms and the main arms all lie in a common plane.
  • the vibratory system 52 us.
  • Cl 310/21, 310/22, 310/25 comprises the vibrator in Combination with a driving 58/23 v 58/23 D magnet connected to one of the central arms thereof 51 Int. Cl. H02k 7/06 and a driving coming with the driving magnet to 5 pick f Search 310/21 25 58/23 R, alternately drive same to effect flexural vibration of 53 23 TF 23 v 23 34 409 457; 331 15 the central arm accompanied by vibration of the main vibratory arms.
  • a driven magnet is connected to ei- 5 References Cited ther the same central arm or the other central arm of UNITED STATES PATENTS the vibrator and coacts with a magnetic follower wheel to rotationally drive the follower wheel in an ina il termittent manner in accordance with the vibratory 314913257 1/1970 ogie' 'fffIIIIIIIIIIIIIIIIIIIIII 310/25 X move of the main vibratory 9 Claims, 12 Drawing Figures PATENTED 3.864.586
  • the present invention relates generally to mechanical vibrators and more particularly, to a mechanical vibrator especially designed for use in a timepiece or as a mechanical filter.
  • tuning fork vibrator has proven to be especially suitable and reliable for use in timepieces.
  • One type of tuning fork which is widely used in the art has three tines or prongs and has a driving magnet secured to the free end of the central tine and a set of weighting or balancing masses affixed to the free ends of the other two tines.
  • the central tine moves through an arc of a circle during use of the vibrator and consequently, sufficient clearance must be provided between the path of travel of the driving magnet and the interior of the driving coil.
  • tuning fork vibrator is of the cantilever type wherein all the vibratory arms are secured at one end to a support and are free at their other ends and this type of vibrator readily undergoes vibrational mode changes and is susceptible to vibrating in spurious vibrational modes rather than the intended normal vibrational mode.
  • the present invention eliminates the aforementioned disadvantages of the conventional tuning fork vibrator.
  • the vibrator of the invention is composed of resilient sheet material and has two main vibratory arms which are interconnected at their ends by respective connecting end portions and the vibrator has two central vibratory arms which each project inwardly from one of the connecting end portions towards each other and terminate in spaced opposed relationship from each other.
  • a driving magnet is secured to one of the central arms and is magnetically driven during use of the vibrator to vibrate the central arm and accordingly vibrate the two main vibratory arms in a predetermined normal vibrational mode.
  • the free end of the driven central arm pivots about the corresponding connecting end portion of the vibrator and once the main vibratory arms begin to vibrate, they in turn pivot about a pivot located at the other connecting end portion and as a result of the different directions of pivotal movement of the central arm and the main arms, the driving magnet undergoes substantially linear alternating movement.
  • the hollow driving coil which is used to electromagnetically drive the magnet may be disposed very close to the path of travel of the magnet thereby increasing the driving efficiency of the vibratory system.
  • FIG. I is a plan view of one embodiment of a vibrator constructed in accordance with the principles of the invention.
  • FIG. 2 is a plan view of the vibrator shown in FIG. I along with additional components which make up the vibratory system;
  • FIG. 3 is a sectional view taken along lines IIIIII in FIG. 2;
  • FIG. 4 is a right side view of the vibratory system shown in FIG. 2;
  • FIG. 5 is one embodiment of an electric drive circuit usable with the vibrator of the invention.
  • FIG. 6 is another embodiment ofan electric drive circuit for use in driving the vibrator of the invention.
  • FIGS. 7A and 7B are explanatory diagrams depicting the normal vibrational mode of the vibrator
  • FIG. 8 is a series ofexplanatory diagrams comparing the normal vibrational mode with the spurious vibra tional modes
  • FIG. 9 is a plan view of another embodiment of a vibratory system according to the invention.
  • FIG. 10 is a sectional view taken along the section line XX in FIG. 9.
  • FIG. 11 is a right side view ofthe embodiment shown in FIG. 9.
  • the vibrator comprises a vibratory unit 1 composed of resilient sheet material having a constant modulus of elasticity.
  • the vibratory unit I has a pair ofmain vibratory arms 2,2 which extend in parallel and spacedapart relationship and which are interconnected at one end by a connecting end portion 3 and at the other end by another connection end portion 4.
  • a pair of central vibratory arms 5 and 6 are connected to respective ones of the connecting end portions 3 and 4 and extend inwardly towards each other as shown in FIG. 1.
  • the dis tal ends of these central arms 5 and 6 are spaced-apart from each other to enable the arms to move independently of each other.
  • a pair of supporting arms 7 and 8 extend outwardly from the connecting end portion 4 and the supporting arms are connected to a fastening portion 9.
  • a pair of holes 10,10 are provided in the fastening portion 9 and by such a construction, the vibratory unit is fastened to and supported upon a suitable support member during use of the vibratory unit.
  • a driving magnet 14 is affixed to the free end of the central vibratory arm by means of a supporting member 15.
  • the driving magnet 14 has a cylindrical contig uration and is supported so as to extend perpendicularly with respect to the plane of the vibratory unit 1 and the longitudinal axis of the driving magnet lies along a center line L.
  • An adjusting screw 16 is threaded into the supporting member and the screw is selectively threaded into or out of the supporting member to accordingly regulate the frequency of vibration of the vibrator.
  • a driven magnet 20 is secured to the other side ofthe central arm 5 by means of a supporting member 21. As seen in H08. 3 and 4, the driven magnet 20 is mounted along the center line L and the magnet 20 has the configuration on a yoke having two generally parallel arms which are connected at one end to the supporting member 21 and which terminate at their other ends in a pair of arm extensions 22,22. The arm extensions ex tend toward each other and are spaced-apart to define a small gap therebetween.
  • a magnetic follower wheel 23 is mounted for rotation adjacent the yoke such that the periphery of the follower wheel passes through the gap and the arm extensions 22,22 function as magnetic poles and coact with the follower wheel 23 to rotationally drive same in an intermittent manner in response to vibration of the vibratory unit 1.
  • the follower wheel 23 has a plurality of circumferentially spaced-apart peripheral teeth 24 and a corresponding plurality of apertures 25 dis posed radially inwardly from the teeth 24.
  • the combi* nation of the teeth 24 and the elongated apertures 25 define a wavy magnetic track on the follower wheel 23 and the track is magnetically coupled with the mag netic poles 22,22.
  • a balancing mass 26 is secured to the free end portion of the other central arm 6 and the balancing mass is suitably located to insure that the center of gravity of the vibrator lies along the center line L and is located in the plane of the vibrator.
  • FIG. 5 One embodiment of an electric drive circuit is shown in FIG. 5 and the drive circuit comprises an electric power source El having its positive terminal connected to one side of the pickup-and-driving coil 18 and the negative terminal of the power source is connected to the emitters of transistors Trl and Tr2.
  • the other end of the pickup-and-driving coil 18 is connected through a resistor R3 to the base ofthe transistor Trl.
  • the positive terminal of the power source is also connected to the collector of the transistor Trl through a resistor R2.
  • the collector of the transistor Trl is connected to the base of the Tr2 through a capacitor C2.
  • An R-C biasing network comprising a capacitor C1 shunted by a resistor Rl is connected between the base and collector ofthe transistor Trl.
  • a resistor R4 is coupled between the base and the collector of the transistor Tr2 and this resistor is provided to regulate the frequency ofthe drive circuit.
  • the frequency of the drive circuit is adjusted to be a little lower than the natural frequency of the vibrator l.
  • the circuit functions such that as the vibrator l vibrates, a voltage is induced in the pickup-and-driving coil causing the transistor Tr2 to turn on thereby delivering driving current to the coil 18 to drive the driving magnet.
  • FIG. 6 Another embodiment of an electric drive circuit is shown in FIG. 6 and in this embodiment, the single pickup-and-driving coil 18 is separated into a driving coil 18a and a pickup coil 1811.
  • An electric power source E2 has its positive terminal connected to the emitter of a transistor Tr3 and the negative terminal of the power source is connected to the collector of the transistor Tr3 through the driving coil [80.
  • the base of the transistor Tr3 is connected to the negative terminal of the power source E2 through an R-C biasing network composed of a capacitor C3 which is shunted by a resistor R5 and the biasing network is in series with the pickup coil l8b which in turn is connected to the negative terminal of the power source.
  • This drive circuit functions in a manner similar to that shown in FIG.
  • the leftward movement of the free end of the vibrator is the result of the small degree of pivotal movement of the vibrator about the supporting arms 7 and 8 whereas the rightward movement of the free end of the central vibratory arm 5 is due to the small degree of pivotal movement it undergoes about its pivotal point which is located at the connecting end portion 3 of the vibrator.
  • the two displacements of the free end of the vibrator and the free end of the central arm 5 almost cancel each other out and therefore the driving magnet 14 and the driven magnet 20 move basically linearly in an upward direction in one sense along the center line L.
  • the other central vibratory arm 6 flexes downward in the opposite sense and this condition is shown in FIG. 7A which depicts the position of the various elements at the end of one vibratory stroke.
  • FIG. 7B depicts the position of the same elements at the end of the other vibratory stroke wherein the vibratory arms 2 and 3 are resiliently flexed downward causing the free end of the vibrator 1 to move leftward a small distance a.
  • the central vibratory arm 5 bends downward and its free end moves rightward almost the same distance. The two displacements cancel each other out as aforementioned to ef fect substantially linear downward movement of both the driving magnet 14 and the driven magnet 20 along the center line L.
  • the other central vibratory arm 6 is flexed upward.
  • the dimensions of the vibrator itself as well as the dimensions and configurations of the driving and driven magnets and the balancing mass 26 are designed to effectuate this purpose.
  • the adjusting screw 16 is carefully adjusted to obtain a fine adjustment of the balance of the vibrator thereby ensuring that the driving magnet 14 reciprocates along a linear axis defined by the center line L.
  • the normal vibrational mode A was l28 Hz and the various vibratory arms vibrated in the manner shown.
  • One spurious vibration mode A had a frequency of 85 Hz and another spurious vibration mode 1;, had a frequency of 173 Hz and the vibrational pattern of the vibratory arms was as shown in the drawing. From such an example, it may be readily seen that the frequency of the vibrator when operating in the normal vibration mode A, may be fully segregated from the frequencies of the spurious vibration modes A and A thereby ensuring that the vibrator vibrates in the normal vibrational mode.
  • the quality factor Q of the vibrator was 2,000.
  • FIGS. 9-11 Another embodiment of the vibratory system is shown in FIGS. 9-11 and in this embodiment, the parts similar to those shown and described with reference to the embodiment of FIGS. 2-4 have corresponding reference numerals except that they are increased by 100.
  • the driven magnet 120 is mounted upon the central vibratory arm 106 by means of a supporting member 127 and the driving magnet 114 is mounted upon the central vibratory arm 105.
  • both the driving and driven magnets were secured to the same central arm whereas in this embodiment, the respective magnets are mounted on different ones of the central vibratory arms.
  • the supporting member 127 has two brackets 128,128 extending in parallel and each connected together at one of their end portions to form another supporting member 129.
  • An adjusting screw 130 is threaded into the supporting member 129 and is used to regulate the balance of the vibrator.
  • the dimensions and configurations of the various parts are so constructed such that the center of gravity of the moving parts lies along a linear center line as in the former embodiment.
  • the driving magnet moves essentially linearly thereby making it possible to reduce the air gap between the driving magnet and the coil to a minimum value.
  • the normal vibrational mode varies very little even if the orientation of the vibrator is varied and this is due to the fact that the center of gravity of the moving parts moves in essentially a linear manner and is not influenced by the attitude ofthe vibrator.
  • the main vibratory arms 2,2 and one central vibratory arm bend in opposite directions, the vibrational energy cancels out at the supporting arms so that very little leakage of the vibrational energy occurs at the point of fastening.
  • the linear movement of the driving magnet causes a very stable corresponding movement of the driven magnet and hence the follower wheel is accurately rotated.
  • the vibrator and vibratory system of the invention is especially suitable for use as a precision frequency source for a timepiece or the like and though obvious modifications and changes will become apparent to those skilled in the art, the present invention is intended to cover all such obvious modifications and changes which fall within the spirit and scope of the invention as defined in the appended claims.
  • a mechanical vibrator for a timepiece or the like comprising: a vibratory unit composed of resilient sheet material and having two main vibratory arms disposed in spacedapart generally parallel relationship, two connecting end portions each interconnecting adjacent ends of said two main vibratory arms, and two central vibratory arms connected to respective ones of said connecting end portions and extending inwardly towards each other, and configured to vibrate, when supported at one said connecting end portion and suitably energized, in a normal vibrational mode wherein said two main vibratory arms along with the one central vibratory arm which is located remote from said one con necting end portion all flexurally vibrate in the same sense about their respective ends of connection while the other central vibratory arm which is connected to said one connecting end portion flexurally vibrates in the opposite sense about its end of connection such that the free end of said one central vibratory arm undergoes substantial linear vibratory movement; and means including a magnet secured to the free end of said one central vibratory arm for energizing said vibra tory unit in its normal vibrational mode.
  • a vibratory system comprising: a mechanical vibrator composed of resilient sheet material and having two main vibratory arms disposed in spaced-apart generally parallel relationship, two connecting end portions each interconnecting adjacent ends of said two main vibratory arms, and two central vibratory arms connected to respective ones of said connecting end portions and extending inwardly towards each other; supporting means connected to one of said connecting end portions for supporting said mechanical vibrator at said one connecting end portion to enable same to vibrate thereabout; a driving magnet secured to a free end of one of said central vibratory arms; means coacting with said mechanical vibrator and magnetically coupled with said driving magnet for magnetically driv ing said magnet to effect vibration of said mechanical vibrator in a normal vibrational mode wherein said free end of said one central vibratory arm alternately flexes about its corresponding connecting end portion accompanied by alternate flexing of said two main vibratory arms about said one connecting end portion such that said driving magnet alternately moves along a substantially linear path of travel; a rotatable output member; and means responsive to vibration of said mechanical vibrator for rotation
  • said means for magnetically driving said magnet includes an energizeable coil having a hollow space in the center thereof which is disposed along said path of travel of said driving magnet and dimensioned to receive therein with a minimum clearance therebetween said driving magnet during linear alternating movement thereof along said path of travel.
  • said means responsive to vibration of said mechanical vibrator includes a driven magnet secured to the free end of said one central vibratory arm on the opposite side thereof from said driving magnet and vibrationally driven by said one central vibratory arm during vibration of said mechanical vibrator.
  • a vibratory system according to claim 6', wherein said means responsive to vibration of said mechanical vibrator includes a driven magnet secured to the free end of the other of said central vibratory arms and vibrationally driven thereby during vibration of said mechanical vibrator.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Electromagnetism (AREA)
  • Acoustics & Sound (AREA)
  • Apparatuses For Generation Of Mechanical Vibrations (AREA)
  • Reciprocating, Oscillating Or Vibrating Motors (AREA)
  • Electromechanical Clocks (AREA)
  • Electric Clocks (AREA)
  • Jigging Conveyors (AREA)
US396675A 1972-09-14 1973-09-13 Vibrator and vibratory system Expired - Lifetime US3864586A (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
JP9230172A JPS5336747B2 (enrdf_load_stackoverflow) 1972-09-14 1972-09-14
JP10506472A JPS553677B2 (enrdf_load_stackoverflow) 1972-09-14 1972-10-20

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US3864586A true US3864586A (en) 1975-02-04

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US396675A Expired - Lifetime US3864586A (en) 1972-09-14 1973-09-13 Vibrator and vibratory system

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US (1) US3864586A (enrdf_load_stackoverflow)
JP (1) JPS553677B2 (enrdf_load_stackoverflow)
AU (1) AU472494B2 (enrdf_load_stackoverflow)
CA (1) CA977161A (enrdf_load_stackoverflow)
CH (1) CH615072GA3 (enrdf_load_stackoverflow)
DE (1) DE2346397A1 (enrdf_load_stackoverflow)
ES (1) ES418739A1 (enrdf_load_stackoverflow)
FR (1) FR2200560B1 (enrdf_load_stackoverflow)
GB (1) GB1420664A (enrdf_load_stackoverflow)
IT (1) IT994235B (enrdf_load_stackoverflow)
NL (1) NL7312373A (enrdf_load_stackoverflow)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4793199A (en) * 1985-12-19 1988-12-27 Messerschmitt-Bolkow-Blohm Gmbh Electromagnetic precision rotary drive
US20140103750A1 (en) * 2012-04-10 2014-04-17 Hosiden Corporation Vibrator
US20150177696A1 (en) * 2013-12-23 2015-06-25 The Swatch Group Research And Development Ltd Regulating device
US10033249B2 (en) * 2013-10-14 2018-07-24 Sunrising Eco-Friendly Tech. Co., Ltd. Mobile induction and power-generation device

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3360704A (en) * 1965-04-22 1967-12-26 Kohlhagen Walter Spring-type electromechanical oscillator
US3448304A (en) * 1965-10-07 1969-06-03 Portescap Le Porte Vibrator device
US3491257A (en) * 1967-05-12 1970-01-20 Centre Electron Horloger Resonance motor for portable timekeepers

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3360704A (en) * 1965-04-22 1967-12-26 Kohlhagen Walter Spring-type electromechanical oscillator
US3448304A (en) * 1965-10-07 1969-06-03 Portescap Le Porte Vibrator device
US3491257A (en) * 1967-05-12 1970-01-20 Centre Electron Horloger Resonance motor for portable timekeepers

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4793199A (en) * 1985-12-19 1988-12-27 Messerschmitt-Bolkow-Blohm Gmbh Electromagnetic precision rotary drive
US20140103750A1 (en) * 2012-04-10 2014-04-17 Hosiden Corporation Vibrator
US10033249B2 (en) * 2013-10-14 2018-07-24 Sunrising Eco-Friendly Tech. Co., Ltd. Mobile induction and power-generation device
US20150177696A1 (en) * 2013-12-23 2015-06-25 The Swatch Group Research And Development Ltd Regulating device
US9389591B2 (en) * 2013-12-23 2016-07-12 The Swatch Group Research And Development Ltd Regulating device

Also Published As

Publication number Publication date
CA977161A (en) 1975-11-04
FR2200560B1 (enrdf_load_stackoverflow) 1977-08-12
AU5988373A (en) 1975-03-06
ES418739A1 (es) 1976-06-16
NL7312373A (enrdf_load_stackoverflow) 1974-03-18
JPS553677B2 (enrdf_load_stackoverflow) 1980-01-26
GB1420664A (en) 1976-01-07
CH615072GA3 (en) 1980-01-15
CH615072B (fr)
AU472494B2 (en) 1976-05-27
DE2346397A1 (de) 1974-03-21
IT994235B (it) 1975-10-20
FR2200560A1 (enrdf_load_stackoverflow) 1974-04-19
JPS4964467A (enrdf_load_stackoverflow) 1974-06-21

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