(12) United States Patent
`Pepin et al.
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 8,093,767 B2
`Jan. 10, 2012
`
`USO08093767B2
`
`(54)
`(76)
`
`(*)
`
`(21)
`(22)
`(65)
`
`(60)
`
`(51)
`
`(52)
`
`(58)
`
`(56)
`
`LINEAR-RESONANT VIBRATION MODULE
`
`Notice:
`
`Inventors: Brian Marc Pepin, Oakland, CA (US);
`Robin Elenga, Seattle, WA (US)
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 0 days.
`Appl. No.: 12/782,697
`Filed:
`May 18, 2010
`
`Prior Publication Data
`US 2010/0289346A1
`Nov. 18, 2010
`
`Related U.S. Application Data
`Provisional application No. 61/179,109, filed on May
`18, 2009.
`
`Int. C.
`(2006.01)
`HO2K33/00
`(2006.01)
`HO2K. 4I/02
`(2006.01)
`HO2K. 4I/00
`(2006.01)
`HO2K 700
`U.S. C. ........... 310/15; 310/12.15; 310/13:310/14;
`31 Of 19
`Field of Classification Search .............. 310/13–15,
`310/19, 12.15
`See application file for complete search history.
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`5,955,799 A * 9/1999 Amaya et al. ................... 310,36
`6,323,568 B1 * 1 1/2001 Zabar ...........
`... 310, 17
`6,326,706 B1* 12/2001 Zhang ........................ 310,1231
`
`6,809,427 B2 * 10/2004 Cheung et al. ................ 290.1 R
`2005/0231045 A1 * 10/2005 Oba et al. ........................ 310, 19
`2005/0275508 A1* 12/2005 Orr et al. ....
`... 340/407.1
`2006/0138875 A1
`6/2006 Kim et al. ....................... 310, 15
`2006/0208600 A1* 9/2006 Sahyoun ...
`... 310,254
`2008/0174187 A1* 7/2008 Erixon et al. ................... 310, 15
`
`FOREIGN PATENT DOCUMENTS
`10164809 A
`6, 1998
`JP
`11018395 A
`1, 1999
`JP
`98.19383 A1
`5, 1998
`WO
`* cited by examiner
`
`Primary Examiner — Quyen Leung
`Assistant Examiner — Jose Gonzalez Quinones
`(74) Attorney, Agent, or Firm — Olympic Patent Works
`PLLC.
`
`(57)
`
`ABSTRACT
`
`Various embodiments of the present invention comprise lin
`ear-resonant vibration modules that can be incorporated in a
`wide variety of appliances, devices, and systems to provide
`vibrational forces. The vibrational forces are produced by
`linear oscillation of a weight or member, in turn produced by
`rapidly alternating the polarity of one or more driving elec
`tromagnets. Feedback control is used to maintain the vibra
`tional frequency of linear-resonant vibration module at or
`near the resonant frequency for the linear-resonant vibration
`module. Linear-resonant vibration modules can be designed
`to produce vibrational amplitudeffrequency combinations
`throughout a large region of amplitudeffrequency space.
`
`5 Claims, 15 Drawing Sheets
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`Jan. 10, 2012
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 2 of 15
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`Exhibit 1027 - Page 3 of 22
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 3 of 15
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`Jan. 10, 2012
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 5 of 15
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`Exhibit 1027 - Page 6 of 22
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`U.S. Patent
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`Jan. 10, 2012
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`Jan. 10, 2012
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`Sheet 8 of 15
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`Jan. 10, 2012
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 10 of 15
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`US 8,093,767 B2
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`Jan. 10, 2012
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`Sheet 11 of 15
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 12 of 15
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`US 8,093,767 B2
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 13 of 15
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`US 8,093,767 B2
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 14 of 15
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`US 8,093,767 B2
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`U.S. Patent
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`Jan. 10, 2012
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`Sheet 15 Of 15
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`US 8,093,767 B2
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`

`

`US 8,093,767 B2
`
`1.
`LINEAR-RESONANT VIBRATION MODULE
`
`CROSS-REFERENCE TO RELATED
`APPLICATION
`
`This application claims the benefit of Provisional Patent
`Application No. 61/179,109, filed May 18, 2009.
`
`TECHNICAL FIELD
`
`The present invention is related to vibration-generating
`devices and, in particular, to vibration modules that can be
`incorporated into a wide variety of different types of electro
`mechanical devices and systems to produce vibrations of
`selected amplitudes and frequencies over a wide range ampli
`tudeffrequency space.
`
`10
`
`15
`
`BACKGROUND
`
`2
`tional force, it is generally not possible to achieve linear
`oscillation. In many cases, time path traced by the shall center
`may be close to circular. The frequency of vibration of the
`unbalanced electric motor is equal to the rotational frequency
`of the electric-motor shaft, and is therefore constrained by the
`rate at which the motor can rotate the shaft. At low rotational
`speeds, little vibration is produced.
`While effective in producing vibrations, there are many
`problems associated with the unbalanced-electric-motor
`vibration-generating units, such as that shown in FIG. 1A,
`commonly used in the various devices, systems, and applica
`tions discussed above. First, unbalancing the shaft of an elec
`tric motor not only produces useful vibrations that can be
`harnessed for various applications, but also produces destruc
`tive, unbalanced forces within the motor that contribute to
`rapid deterioration of motor parts. Enormous care and effort
`is undertaken to precisely balance rotating parts of motors,
`vehicles, and other types of machinery, and the consequences
`of unbalanced rotating parts are well known to anyone famil
`iar with automobiles, machine tools, and other such devices
`and systems. The useful lifetimes of many devices and appli
`ances, particularly hand-held devices and appliances, that
`employ unbalanced electric motors for generating vibrations
`may range from a few tens of hours to a few thousands of
`hours of use, after which the vibrational amplitude produced
`by the devices declines precipitously as the electric motor and
`other parts deteriorate.
`A second problem with unbalanced electric motors is that
`they are relatively inefficient at producing vibrational motion.
`A far greater amount of power is consumed by an unbalanced
`electrical motor to produce a given vibrational force than the
`theoretical minimum power required to produce the given
`vibrational three. As a result, many hand-held devices that
`employ unbalanced electric motors the generating vibrations
`quickly consume batteries during use.
`A third problem with unbalanced electric motors, dis
`cussed above, is that they generally produce elliptical vibra
`tional modes. Although Such modes may be useful in particu
`lar applications, many applications can better use a linear
`oscillation, with greater directional concentration of vibra
`tional forces. Linear oscillation cannot generally be produced
`by unbalanced electric motors.
`A fourth, and perhaps most fundamental, problem associ
`ated with using unbalanced electric motors to generate vibra
`tions is that only a very limited portion of the total vibrational
`force/frequency space is accessible to unbalanced electric
`motors. FIG.3 shows a graph of vibrational three with respect
`to frequency for various types of unbalanced electric motors.
`The graph is shown as a continuous hypothetical curve,
`although, of course, actual data would be discrete. As shown
`in FIG. 3, for relatively low-power electric motors used in
`hand-held appliances, only a fairly narrow range of frequen
`cies centered about 80 Hz (302 in FIG. 3) generate a signifi
`cant vibrational force. Moreover, the vibrational force is rela
`tively modest. The bulk of energy consumed by an
`unbalanced electric motor is used to spin the shaft and unbal
`anced weight and to overcome frictional and inertial threes
`within the motor. Only a relatively small portion of the con
`Sumed energy is translated into desired vibrational forces.
`Because of the above-discussed disadvantages with the
`commonly employed unbalanced-electric-motor vibration
`generation units, designers, manufacturers, and, ultimately,
`users of a wide variety of different vibration-based devices,
`appliances, and systems continue to seek more efficient and
`
`25
`
`30
`
`35
`
`40
`
`45
`
`Vibration-inducing motors and mechanisms have been
`used for many years in a wide variety of different consumer
`appliances, toys, and other devices and systems. Examples
`include vibration signals generated by pagers, vibration
`driven appliances, such as hair-trimming appliances, electric
`toothbrushes, electric toy football games, and many other
`appliances, devices, and systems. The most common electro
`mechanical system used for generating vibrations is an inten
`tionally unbalanced electric motor.
`FIGS. 1A-B illustrate an unbalanced electric motor typi
`cally used liar generating vibrations in a wide variety of
`different devices. As shown in FIG. 1A, a small, relatively
`low-power electric motor 102 rotates a cylindrical shaft 104
`onto which a weight 106 is asymmetrically or mounted. FIG.
`1B shows the weight asymmetrically mounted to the shaft,
`looking down at the weight and shaft in the direction of the
`axis of the shall. As shown in FIG. 1B, the weight 106 is
`mounted off-center on the electric-motor shaft 104. FIGS.
`2A-13 illustrate the vibrational motion produced by the
`unbalanced electric motor shown in FIGS. 1A-B. As shown in
`FIGS. 2A-B, the asymmetrically-mounted weight creates an
`elliptical oscillation of the end of the shall, normal to the shaft
`axis, when the shall is rotated at relatively high speed by the
`electric motor. FIG. 2A shows displacement of the weight and
`shall from the stationary shall axis as the shall is rotated,
`looking down on the weight and shaft along the shall axis, as
`in FIG. 1B. In FIG. 2A, a small mark 202 is provided at the
`periphery of the disk-shaped end the of electric-motorshall to
`illustrate rotation of the shaft. When the shalt rotates at high
`speed, a point 204 on the edge of the weight traces an ellipsoid
`206 and the center of the shaft 208 traces a narrower and
`50
`smaller ellipsoid 210. Were the shaft balanced, the center of
`the shaft would remain at a position 212 in the center of the
`diagram during rotation, but the presence of the asymmetri
`cally-mounted weight attached to the shaft, as well as other
`geometric and weight-distribution characteristics of the elec
`tric motor, shall, and unbalanced weight together create
`forces that move the end of the shaft along the elliptical path
`210 when the shaft is rotated at relatively high speed. The
`movement can be characterized, as shown in FIG. 2B, by a
`major axis 220 and minor axis 222 of vibration, with the
`direction of the major axis of vibration equal to the direction
`of the major axis of the ellipsoids, shown in FIG. 2A, and the
`length of the major axis corresponding to the amplitude of
`vibration in this direction. In many applications, in which a
`linear oscillation is desired, designers seek to force the major
`axis-amplitude/minor-axis-amplitude ratio to be as large as
`possible, but, because the vibration is produced by a rota
`
`55
`
`60
`
`65
`
`Exhibit 1027 - Page 17 of 22
`
`

`

`US 8,093,767 B2
`
`3
`capable vibration-generating units for incorporation into
`many consumer appliances, devices, and systems.
`
`SUMMARY
`
`Various embodiments of the present invention comprise
`linear-resonant vibration modules that can be incorporated in
`a wide variety of appliances, devices, and systems to provide
`vibrational forces. The vibrational forces are produced by
`linear oscillation of a weight or member, in turn produced by
`rapidly alternating the polarity of one or more driving elec
`tromagnets. Feedback control is used to maintain the vibra
`tional frequency of linear-resonant vibration module at or
`near the resonant frequency for the linear-resonant vibration
`module. Linear-resonant vibration modules can be designed
`to produce vibrational amplitudeffrequency combinations
`throughout a large region of amplitudeffrequency space.
`
`10
`
`15
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`4
`anced electric motors. The linear nature of the LRVM vibra
`tion-inducing motion allows the problems associated with
`unbalanced-electric-motor vibrators, discussed above, to be
`effectively addressed. An oscillating linear motion does not
`produce destructive forces that quickly degrade and wear out
`an unbalanced electric motor. A linearly oscillating mecha
`nism is characterized by parameters that can be straightfor
`wardly varied in order to produce vibrations of a desired
`amplitude and frequency over a very broad region of ampli
`tudeffrequency space. Combining a linearly oscillating vibra
`tion-inducing mechanism with feedback control, so that the
`frequency of vibration falls close to the resonant frequency of
`the LRVM, results in optimal power consumption with
`respect to the amplitude and frequency of vibration produced
`by the LRVM. Clearly, linear oscillation within a LRVM
`translates into highly direction vibrational forces produced by
`an appliance or device that incorporates the LRVM.
`FIGS. 4A-G illustrate one particular LRVM, and operation
`of the particular LRVM, that represents one embodiment of
`the present invention. FIGS. 4A-G all use the same illustra
`tion conventions, next discussed with reference to FIG. 4A.
`The LRVM includes a cylindrical housing 402 within which
`a Solid, cylindrical mass 404, or weight, can move linearly
`along the inner, hollow, cylindrically shaped chamber 406
`within the cylindrical housing or tube 402. The weight is a
`magnet, in the described embodiment of the present inven
`tion, with polarity indicated by the "+" sign 410 on the right
`hand end and the “-” sign 412 on the left-hand end of the
`weight 404. The cylindrical chamber 406 is capped by two
`magnetic disks 414 and 416 with polarities indicated by the
`“+' sign 418 and the “-sign 419. The disk-like magnets 414
`and 418 are magnetically oriented opposite from the mag
`netic orientation of the weight 404, so that when the weight
`moves to either the extreme left or extreme right sides of the
`cylindrical chamber, the weight is repelled by one of the
`disk-like magnets at the left or right ends of the cylindrical
`chamber. In other words, the disk-like magnets act much like
`springs, to facilitate deceleration and reversal of direction of
`motion of the weight and to minimize or prevent mechanical
`impact forces of the weight and the end caps that close off the
`cylindrical chamber. Finally, a coil of conductive wire 420
`girdles the cylindrical housing, or tube 402 at approximately
`the mid-point of the cylindrical housing.
`FIGS. 4B-G illustrate operation of the LRVM shown in
`FIG. 4A. When an electric current is applied to the coil 420 in
`a first direction 422, a corresponding magnetic force 424 is
`generated in a direction parallel to the axis of the cylindrical
`chamber, which accelerates the weight 404 in the direction of
`the magnetic force 424. When the weight reaches a point at or
`close to the corresponding disk-like magnet 414, as shown in
`FIG. 4C, a magnetic force due to the repulsion of the disk-like
`magnet 414 and the weight 404, 426, is generated in the
`opposite direction, decelerating the weight and reversing its
`direction. As the weight reverses direction, as shown in FIG.
`4D, current is applied in an opposite direction 430 to the coil
`420, producing a magnetic force 432 in an opposite direction
`from the direction of the magnetic. force shown in FIG. 4B,
`which accelerates the weight 404 in a direction opposite to the
`direction in which the weight is accelerated in FIG. 4B. As
`shown in FIG. 4E, the weight then moves rightward until, as
`shown in FIG. 4F, the weight is decelerated, stopped, and then
`accelerated in the opposite direction by repulsion of the disk
`like magnet 416. An electrical current is then applied to the
`coil 420 in the same direction 434 as in FIG. 4B, again
`accelerating the Solid cylindrical mass in the same direction
`as in FIG. 4B. Thus, by a combination of a magnetic field with
`rapidly reversing polarity, generated by alternating the direc
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`FIGS. 1A-B illustrate an unbalanced electric motor typi
`cally used for generating vibrations in a wide variety of dif
`ferent devices.
`FIGS. 2A-B illustrate the vibrational motion produced by
`the unbalanced electric motor shown in FIGS. 1A-B.
`FIG. 3 shows a graph of vibrational force with respect to
`frequency for various types of unbalanced electric motors.
`FIGS. 4A-G illustrate one particular LRVM, and operation
`of the particular LRVM, that represents one embodiment of
`the present invention.
`30
`FIGS.5A-B illustrate an H-bridge switch that can be used,
`in various embodiments of the present invention, to change
`the direction of current applied to the coil that drives linear
`oscillation within a linear-resonance vibration module
`(“LRVM).
`FIG. 6 provides a block diagram of the LRVM, illustrated
`in FIGS. 4A-G, that represents one embodiment of the
`present invention.
`FIGS. 7A-C provide control-flow diagrams that illustrate
`the control program, executed by the CPU, that controls
`operation of an LRVM that represents one embodiment of the
`present invention.
`FIG.8 represents the range of frequencies and vibrational
`forces that can achieved by different implementations of
`LRVM and LRVM control programs that represent embodi
`45
`ments of the present invention.
`FIG. 9 shows a plot of the amplitude/frequency space and
`regions in that space that can be operationally achieved by
`unbalanced electrical motors and by LRVMs that represent
`embodiments of the present invention.
`FIGS. 10-17 show a variety of different alternative imple
`mentations of LRVMs that represent different embodiments
`of the present invention.
`FIG. 18 illustrates an enhancement of the embodiment of
`the present invention shown in FIG. 16.
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`DETAILED DESCRIPTION
`
`Embodiments of the present invention include various
`types of linear-resonant vibration modules (“LRVMs) that
`can be used within a wide variety of different types of appli
`ances, devices, and systems, to generate vibrational forces.
`The LRVMs that represent embodiments of the present inven
`tion are linear in the sense that the vibrational forces are
`produced by a linear oscillation of a weight or component
`within the LRVM, rather than as a by-product of an unbal
`anced rotation, as in the case of currently employed unbal
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`Exhibit 1027 - Page 18 of 22
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`US 8,093,767 B2
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`tion of current applied to the coil, and by the repulsive forces
`between the weight magnet and the disk-like magnets at each
`end of the hollow, cylindrical chamber, the weight linearly
`oscillates back and forth within the cylindrical housing 402,
`imparting a direction force at the ends of the cylindrical
`chamber with each reversal in direction.
`Clearly, the amplitude of the vibration and vibrational
`forces produced are related to the length of the hollow cham
`ber in which the weight oscillates, the current applied to the
`coil, the mass of the weight, the acceleration of the weight
`produced by the coil, and the mass of the entire LRVM. All of
`these parameters are essentially design parameters for the
`LRVM, and thus the LRVM can be designed to produce a
`wide variety of different amplitudes.
`The frequency of the oscillation of the solid, cylindrical
`mass is determined by the frequency at which the direction of
`the current applied to the coil is changed. FIGS. 5A-B illus
`trate an H-bridge switch that can be used, in various embodi
`ments of the present invention, to change the direction of
`current applied to the coil that drives linear oscillation within
`an LRVM. FIGS. 5A-B both use the same illustration con
`ventions, described next with respect to FIG. 5A. The
`H-bridge switch receives, as input, a directional signal d502
`and direct-current (DC) power 504. The direction-control
`signal d502 controls four switches 506-509, shown as tran
`sistors in FIG. 5A. When the input control signal d502 is
`high, or “1,” as shown in FIG. 5A, switches 508 and 509 are
`closed and switches 506 and 507 are open, and therefore
`current flows, as indicated by curved arrows, such as curved
`arrow 510, from the power-source input 504 to ground 512 in
`a leftward direction through the coil 514. When the input
`control signal d is low, or “0” as shown in FIG. 5B, the
`direction of the current through the coil is reversed. The
`H-bridge switch, shown in FIGS.5A-B, is but one example of
`various different types of electrical and electromechanical
`35
`switches that can be used to rapidly alternate the direction of
`current within the coil of an LRVM.
`FIG. 6 provides a block diagram of the LRVM, illustrated
`in FIGS. 4A-G, that represents one embodiment of the
`present invention. The LRVM, in addition to the cylindrical
`housing, coil, and internal components shown in FIG. 4A,
`includes a power Supply, a user interface, generally compris
`ing electromechanical buttons or Switches, the H-bridge
`switch, discussed above with reference to FIGS. 5A-B, a
`central processing unit ("CPU), generally a small, low-pow
`ered microprocessor, and one or more electromechanical sen
`sors. All of these components are packaged together as an
`LRVM within a vibration-based appliance, device, or system.
`As shown in FIG. 6, the LRVM 600 is controlled by a
`control program executed by the CPU microprocessor 602.
`The microprocessor may contain Sufficient on-board memory
`to store the control program and other values needed during
`execution of the control program, or, alternatively, may be
`coupled to a low-powered memory chip 604 or flash memory
`for storing the control program. The CPU receives inputs
`front the user controls 606 that together comprise a user
`interface. These controls may include any of various dials,
`pushbuttons, Switches, or other electromechanical-control
`devices. As one example, the user controls may include a dial
`to select a strength of vibration, which corresponds to the
`current applied to the coil, a Switch to select one of various
`different operational modes, and a power button. The user
`controls generate signals input to the CPU 608-610. A power
`Supply 612 provides power, as needed, to user controls 614, to
`the CPU 616 and optional, associated memory, to the
`H-bridge switch 618, and, when needed, to one or more
`sensors 632. The voltage and current supplied by the power
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`6
`Supply to the various components may vary, depending on the
`operational characteristics and requirements of the compo
`nents. The H-bridge switch 620 receives a control-signal
`input d 622 from the CPU. The power supply 612 receives a
`control input 624 from the CPU to control the current Sup
`plied to the H-bridge switch 618 for transfer to the coil 626.
`The CPU receives input 630 from one or more electrome
`chanical sensors 632 that generate a signal corresponding to
`the strength of vibration currently being produced by the
`linearly oscillating mass 634. Sensors may include one or
`more of accelerometers, piezoelectric devices, pressure-sens
`ing devices, or other types of sensors that can generate signals
`corresponding to the strength of desired vibrational forces.
`FIGS. 7A-C provide control-flow diagrams that illustrate
`the control program, executed by the CPU, that controls
`operation of an LRVM that represents one embodiment of the
`present invention. FIG. 7A provides a control-Bow diagram
`for the high-level control program. The program begins
`execution, in step 702, upon a power-on event invoked by a
`user through a power button or other user control. In step 702,
`various local variables are set to default values, including the
`variables: (1) mode, which indicates the current operational
`mode of the device; (2) strength, a numerical value corre
`sponding to the current user-selected strength of operation,
`corresponding to the electrical current applied to the coil; (3)
`lv10, a previously sensed vibrational strength; (4) liv11, a cur
`rently sensed vibrational strength; (5) freq, the current fre
`quency at which the direction of current is alternated in the
`coil: (6) d, the control output to the H-bridge switch; and (7)
`inc, a Boolean value that indicates that the frequency is cur
`rently being increased. Next, in step 704, the control program
`waits for a next event. The remaining steps represent a con
`tinuously executing loop, or event handler, in which each
`event that occurs is appropriately handled by the control
`program. In certain implementations of the control program,
`events may be initiated by interrupt-like mechanisms and
`stacked for execution while, in more primitive implementa
`tions, certain events that overlap in time may be ignored or
`dropped. In the implementation illustrated in FIGS. 7A-C,
`two timers are used, one for controlling the change in direc
`tion of the current applied to the coil, at a currently established
`frequency, and the other for controlling a monitoring interval
`at which the control program monitors the vibrational force
`currently produced. Rather than using a formal timer mecha
`nism, certain implementations may simply employ counted
`loops or other simple programming techniques for periodi
`cally carrying out tasks. When an event occurs, the control
`program begins a series of tasks, the first of which is repre
`sented by the conditional step 706, to determine what event
`has occurred and appropriately handle that event. When the
`frequency timer has expired, as determined in step 706, the
`value of the output signal d is flipped, in step 708, and output
`to the H-bridge switch, with the frequency timer being reset to
`trigger a next frequency-related event. The frequency-timer
`interval is determined by the current value of the variable freq.
`Otherwise, when the event is a monitor timer expiration
`event, as determined in step 710, then a routine “monitor is
`called in step 712. Otherwise, when the event corresponds to
`a change in the user input through the user interface, as
`determined in step 714, the routine “control is called in step
`716. Otherwise, when the event is a power-down event, as
`determined in step 718, resulting from deactivation of a
`power button by the user, then the control program appropri
`ately powers down the device, in step 720, and the control
`program terminates in step 722. Any other of various types of
`events that may occur are handled by a default event handler
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`Exhibit 1027 - Page 19 of 22
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`7
`724. These events may include various error conditions that
`arise during operation of the device.
`FIG. 7B provides a control-flow diagram for the routine
`“monitor” called in step 712 of FIG. 7A. In step 730, the
`routine “monitor converts the sensor input to an integer
`representing the current vibrational force produced by the
`LRVM and stores the integer value in the variable liv11. Next,
`in step 732, the routine “monitor determines whether or not
`the LRVM is currently operating in the default mode. In the
`default mode, the LRVMuses continuous feedback control to
`optimize the vibrational force produced by the LRVM by
`continuously seeking to operate the LRVMata frequency as
`close as possible to the resonant frequency for the LRVM.
`Other, more complex operational modes may be handled by
`various more complex routines, represented by step 734 in
`FIG. 7B. More complex vibrational modes may systemati
`cally and/or periodically alter the frequency or produce vari
`ous complex, multi-component vibrational modes useful in
`certain applications, appliances, devices, and systems. These
`more complex modes are application dependent, and are not
`further described in the control-flow diagrams. In the case
`that the operational mode is the default mode, in which the
`control program seeks to optimize the vibrational force gen
`erated by the device, in step 736, the routine “monitor deter
`mines whether the local variable i