Court Opinion

ID: 773245
Source: CourtListenerOpinion
Date Created: 2012-04-18 11:24:31+00
Date Added: 2024-06-11T17:56:09.828989
License: Public Domain

249 F.3d 1314 (Fed. Cir. 2001)
LOCKHEED MARTIN CORPORATION,  Plaintiff-Appellant,v.SPACE SYSTEMS/LORAL, INC.,  Defendant-Appellee.
00-1310
United States Court of Appeals for the Federal Circuit
DECIDED:  April 30, 2001

Appealed from: U.S. District Court for the Northern District of California  Judge Susan Illston Robert B. Smith, Skadden, Arps, Slate, Meagher & Flom, LLP, of New York, New York, argued for plaintiff appellant. With him on the brief were Edward V. Filardi, of New York, and David W. Hansen, of Palo Alto, California.
Gregory R. Lyons, Wiley, Rein and Fielding, of Washington, DC, argued for defendant-appellee. With him on the brief were James H. Wallace, Jr., John B. Wyss. and Scott E. Bain.
Before SCHALL, Circuit Judge, FRIEDMAN, Senior Circuit Judge, and GAJARSA, Circuit Judge.
GAJARSA, Circuit Judge.

DECISION

1
Lockheed Martin Corporation ("Lockheed") is the assignee of United States  Patent 4,084,772 ("the '772 Patent"), which discloses an apparatus and  method for steering a satellite. In 1995, Lockheed's predecessor, Martin  Marietta Corporation, brought this patent infringement action against Space  Systems/Loral, Inc. ("SSL"), alleging that certain SSL satellites infringe  the '772 Patent. On March 7, 2000, the United States District Court for the  Northern District of California ("District Court") determined that certain  limitations required by claim 1 of the '772 Patent are not present in SSL's  Intelsat VII satellites either literally or under the doctrine of  equivalents, and granted SSL's motion for summary judgment. Lockheed Martin  Corp. v. Space Systems/Loral, Inc., 88 F. Supp. 2d 1095, 1102 (N.D. Cal.  2000). Lockheed appeals that judgment.

2
For the reasons discussed below, we affirm.

I. BACKGROUND

3
The '772 Patent, entitled "Roll/Yaw Body Steering for Momentum Biased  Spacecraft," claims a structure and method for reducing the pointing errors  of a satellite that has entered into an inclined orbit by varying the speed  of the satellite's transverse momentum wheel in a sinusoidal manner.

A. Introduction

4
A communications satellite typically orbits the earth in a geosynchronous  equatorial orbit, circling the earth once every twenty-four hours in the  equatorial plane. A geosynchronous orbit in the equatorial plane allows a  satellite to maintain the same position relative to fixed points on the  earth's surface, and is often referred to as "geostationary." A satellite  in geostationary orbit, when viewed from the ground, appears to remain  stationary in the sky. Therefore, a geostationary orbit enables a  communications satellite to maintain a constant relationship with  transmitters on earth. In addition to preserving a geosynchronous  equatorial orbit, a communications satellite must also maintain a proper  "attitude," or pointing direction, so that its antennae remain pointed at  the desired target on the earth.

5
While in orbit, however, a satellite is subject to various destabilizing  forces such as the gravitational effects of the sun and the moon. Such  forces may cause a satellite to drift out of its equatorial orbit, into an  "inclined" north-south orbit. A satellite in an inclined orbit may still  orbit the earth in a geosynchronous manner (once every twenty-four hours),  but may no longer appear stationary in the sky to an earthbound observer.  The following diagram, Figure 2 of the '772 Patent specification, depicts  an inclined orbit relative to an equatorial orbit: [Tabular or Graphical Material Omitted]

6
Therefore, in an inclined orbit, the antennae of a communications satellite  point north of the equator for half of the orbit and south of the equator  for half of the orbit. Unless the satellite corrects for solar and lunar  gravitational effects, the orbit of a geosynchronous satellite acquires an  inclination at the rate of about 0.8 degrees annually.

7
The '772 Patent discloses a system for allowing a communications satellite  to continue to operate effectively after entering an inclined orbit. It  does so by changing the attitude, or pointing direction, of the satellite  when the satellite is north and south of the equator. The method described  by the '772 Patent rotates the satellite so that its antennae point north  or south, and remain pointed at the same earth target over the course of  twenty-four hours.

8
The attitude of satellites is described in terms of movement and rotation  about three axes. The "pitch" axis lies in a north-south direction, the  "roll" axis points in the direction of satellite orbital movement, and the  "yaw" axis points to the center of the earth. In an inclined orbit, roll  pointing error occurs when a satellite is north or south of the equator.  There is no roll pointing error when a satellite crosses the equator twice  each orbit (depicted above in diagram 2 at points B and D). Conversely, yaw  pointing error is greatest when a satellite crosses the equator. There is  no yaw pointing error when a satellite is furthest north or south of the  equator (depicted above in diagram 2 at points A and C).

9
The structure and method described by the '772 Patent rotates a satellite  around its roll axis such that its antennae point to the south when the  satellite is north of the equator, and point to the north when the  satellite is south of the equator. In this manner, even though a satellite  is moving north and south during its orbit, it remains pointed at the same  earth target, and behaves as if it were still in geostationary orbit.

B. The '772 Patent Technology

10
Many communication satellites employ at least one "momentum" or "reaction"  wheel centered on the pitch axis of a satellite ("pitch wheel") powered by  an electric motor. A spinning momentum wheel creates angular momentum, or  "stiffness," and opposes any satellite rotation about the roll or yaw axis.  In other words, the spinning pitch wheel acts like a gyroscope, resists  external forces, and keeps the pitch axis pointed in a north-south  direction.

11
In addition to this resistance effect, momentum wheels also cause a  satellite to rotate around its axes by taking advantage of the physical law  of conservation of angular momentum. When a momentum wheel increases speed  in one direction, it causes the entire satellite to spin in the opposite  direction along the same axis in order to conserve angular momentum. Thus,  through careful control of momentum wheels centered on different axes, a  proper satellite attitude can be maintained.

12
As discussed above, the invention described by the '772 Patent is a  structure and method for spinning a second momentum wheel centered on a  satellite's yaw axis. This wheel is referred to as the "yaw" wheel or  "transverse" wheel. When the yaw wheel is accelerated, it creates angular  momentum about the yaw axis. In response, the pitch wheel and the entire  satellite must rotate about the roll axis in order to compensate and cancel  the angular momentum created by the yaw wheel, thereby adjusting the north-  south pointing direction of the antennae.

13
As described by the '772 Patent, the amount of north-south roll pointing  attitude adjustment varies with the speed and spin direction of the yaw  wheel. When the yaw wheel is not spinning, the satellite does not rotate  about its roll axis. However, increased yaw wheel speed in one direction  points the satellite to the north; increased yaw wheel speed in the other  direction points the satellite to the south.  In short, by varying the  speed and direction of the yaw wheel, the satellite can be steered about  its roll axis, adjusting and correcting for the north-south roll pointing  errors described above.

14
The following diagram, Figure 3 of the '772 Patent specification, depicts  the pointing direction resulting from this roll pointing attitude  adjustment. As depicted, by rotating the satellite around its roll axis by  (tm) degrees, the satellite points at the equator:

15
[Tabular or Graphical Material Omitted]

16
The speed of the yaw wheel varies in a "sinusoidal" manner based on the  orbital angle of inclination and the satellite's distance from the equator.  That is, the yaw wheel spins slowly after the satellite crosses the  equator, and spins at a maximum velocity when the satellite is furthest  north or south in relation to the equator. As the satellite again  approaches the equator, the yaw wheel slows down. As the satellite crosses  the equator, the yaw wheel slows, stops, and reverses direction. The rate  of change of yaw wheel spinning velocity is based on a sinusoidal variation  over twenty-four hours.

17
The following diagram, Figure 4 of the '772 Patent specification, depicts a  block diagram of the control system described by the '772 Patent:

18
[Tabular or Graphical Material Omitted]

19
The intentional north-south attitude adjustment described in the  specification of the '772 Patent creates an additional control problem  which must be resolved. Prior art satellites employed an "earth horizon" or  "roll" sensor in order to keep the yaw axis pointed at the center of the  earth during equatorial orbit. If the earth sensor described by the '772  Patent determines that the yaw axis is not pointed at the center of the  earth, it activates the magnetic torquer (64) or roll thruster (66) in an  attempt to reorient the satellite. During inclined orbit, however, the  satellite is intentionally rotated about its roll axis. Unless the  satellite is otherwise "fooled," the earth sensor would activate the  magnetic torquer or roll thruster in an attempt to undo the intentional  attitude adjustment.

20
The '772 Patent discloses a structure and method for "fooling" the earth  sensor. A tachometer (52) generates a signal representing the speed and  direction of the yaw wheel. This signal, representing the angle of  intentional roll, is subtracted from the signal generated by the earth  sensor (56) by a "summer" (58), and effectively "fools" the earth sensor  from undoing the intentional attitude adjustment.

C. The '772 Patent Claims

21
Claim 1, the only independent claim in the '772 Patent at issue, reads as  follows:

22
A control system for an orbiting pitch momentum biased satellite, said satellite having a pitch, roll, and yaw axis, and wherein the momentum of said satellite is defined by a momentum vector,

23
said satellite being adapted to be placed in an orbit defining a plane that is inclined relative to a plane containing a geo-synchronous orbit, said inclination inherently causing roll and yaw pointing errors with respect to said geo-synchronous orbit, comprising:

24
a. a transverse wheel mounted parallel to said yaw axis and adapted for bi-directional rotation and varying speed,

25
b. means for rotating said wheel in accordance with a predetermined rate schedule which varies sinusoidally over the orbit at the orbital frequency of the satellite whereby the attitude of said satellite is offset in response to the effect of said rotating wheel by the direction of the pitch axis being changed with respect to said momentum vector, the direction of said pitch axis with respect to the inclined orbit normal varying sinusoidally at the orbital frequency to null said roll pointing error due to said orbit inclination, the momentum vector being maintained perpendicular to the plane of the geo-synchronous orbit to null said yaw pointing error due to said orbit inclination,

26
c. means responsive to said transverse wheel when rotating for generating a signal indicative of the speed and direction of said wheel,

27
d. attitude sensing means for generating an attitude error signal indicative of an error in desired role attitude relative to said inclined orbit,

28
e. means responsive to said roll attitude error signal to orient said satellite by altering the inertial direction of said momentum vector,

29
f. said orientation means including means responsive to said wheel speed and direction signal for modifying said attitude error signal to be non-responsive to said offset in attitude generative by said transverse wheel, said attitude offset being in addition to said roll attitude errors,

30
said attitude offset due to said rotating transverse wheel having a predetermined relation to said inclination, whereby the yaw pointing errors due to said inclination are substantially reduced to zero by said momentum vector being repositioned to be perpendicular to the plane of said geo-synchronous orbit, and  whereby the roll pointing errors due to said inclination are reduced substantially to zero by the rotation action of said transverse wheel.

31
(emphasis added)

32
The transverse wheel of limitation [a] is the yaw wheel discussed  above.1 The structure corresponding to the means recited in  limitation [b] is the sine generator (46) and wheel electronics (48) noted  in Figure 4 above. When the satellite enters inclined orbit, the sine  generator commands the wheel electronics to rotate the yaw wheel (22) in a  sinusoidal manner as described above. The structure corresponding to the  means recited in limitation [c] is the tachometer (52) and difference  amplifier (54). The "signal" referred to in limitation [c] represents the  angle of intentional roll adjustment. The structure corresponding to the  means recited in limitation [d] is the "earth horizon" or "roll" sensor  (56) discussed above. The structure corresponding to the means recited in  limitation [e] is the magnetic torquer (64) and/or the roll thruster (66)  discussed above. Finally, the structure corresponding to limitation [f] is  the "summer" (58) discussed above, which subtracts the angle of intentional  roll from the roll pointing error signal generated by the earth sensor.

D. The Accused SSL Satellites

33
Lockheed asserts that SSL's Intelsat VII satellites infringe claim 1 of the  '772 Patent. As discussed above, the '772 Patent describes a yaw wheel used  in conjunction with a pitch wheel. The SSL satellites do not use a single  pitch wheel centered on the pitch axis of the satellite. Instead, the SSL  satellites use a pair of "V-Wheels" that straddle the pitch axis in a V-  shape; each V-Wheel operates in a single direction. The attitude of the SSL  satellites is controlled by altering the relative speed of the two V-Wheels  ("V-Mode").

34
In addition to the V-Wheels, the SSL Intelsat VII satellites include a yaw  wheel centered on the yaw axis of the satellite, referred to as an "L-  Wheel." According to SSL, the L-Wheel is activated only when one of the two  V-Wheels fails. The L-Wheel rotates in one direction if one V-Wheel fails  ("L1-Mode"), and the other direction if the other V-Wheel fails ("L2-  Mode"). However, the L-Wheel does not operate in both directions during an  orbit. That is, the L-Wheel does not slow down to zero speed and reverse  direction during an orbital period. Furthermore, while in operation, the L-  Wheel never spins more slowly than a certain "bias" speed in order to  offset the partial yaw momentum of the functioning V-Wheel.

35
The SSL satellites continuously monitor and correct roll and pitch pointing  errors detected by the earth sensor. While operational, therefore, the  speed of the L-Wheel changes continuously during orbit because it responds  to actual errors detected while in orbit. The attitude control system of  the SSL satellites is also designed to operate effectively during inclined  orbit by compensating for the roll pointing error created by inclined  orbit. During inclined orbit, the "roll bias generator" and "yaw momentum  bias generator" of the SSL satellites vary the speed of the V-Wheels or the  L-Wheel, intentionally causing the satellite to point north or south.

36
The SSL satellites also include a mechanism to "fool" the satellite from  attempting to correct the intentional roll pointing error detected by the  earth sensor. As discussed above, if the SSL satellite earth sensor detects  a roll pointing error while the L-Wheel is operational, the speed of the L-  Wheel changes in order to correct the detected error. However, when the  satellite is intentionally rolled during an inclined orbit, the angle of  intentional roll is summed with the roll error output signal of the earth  sensor, and the satellite is effectively "fooled" from correcting for the  intentional attitude adjustment.

E. Procedural Background

37
On March 10, 1999, the District Court held a Markman hearing in order to  construe the phrases "adapted for bi-directional rotation" and "varies  sinusoidally" contained in limitations [a] and [b] of claim 1 of the '772  Patent. The District Court subsequently issued its claim construction order  regarding these phrases. See Lockheed Martin Corp. v. Space Systems/Loral, 88 F.Supp.2d 1095(N.D. Cal. Mar. 12, 1999). Of particular  importance, the District Court concluded that the phrase "varies sinusoidally" used in limitation [b] means "a sine-shaped variation that  passes through zero." Id. at 1099. Relying on intrinsic evidence alone, it  ruled that the phrase means "variation that passes through zero and changes  direction, or sign." Id. at 1099. Furthermore, the District Court "decline[d]  to construe 'varies sinusoidally' to include variations that do not pass  through zero," and determined that additional inputs are "more  appropriately addressed under the doctrine of equivalents." Id. at 1100-01.

38
On March 7, 2000, the District Court granted summary judgment of non-  infringement for SSL. Lockheed, 88 F. Supp. 2d at 1102. First, the District  Court ruled that the SSL satellites do not literally infringe claim 1 of  the '772 Patent. Consistent with its construction of the phrase "varies  sinusoidally," the District Court reasoned that, "[i]t is undisputed that  the speed of the accused reaction wheel does not slow to zero and reverse  direction." Id. at 1099. Furthermore, the District Court stated that, "[i]t  is also undisputed that the speed of the Intelsat VII reaction wheel varies  according to a rate schedule that is not purely sinusoidal, providing an  additional basis for finding that this limitation is not literally met."  Id.

39
The District Court also ruled that the SSL satellites did not infringe  under the doctrine of equivalents. The District Court applied the  "function-way-result" analysis to determine the appropriate scope of  limitation [b] under the doctrine of equivalents. Id. (referencing Warner-  Jenkinson Co., Inc. v. Hilton Davis Chem. Co., 520 U.S. 17, 40 , 41 USPQ2d  1865, 1875 (1997)). Under the doctrine of equivalents, a finding of  infringement is appropriate if each element of the accused device performs  substantially the same function, in substantially the same way, to achieve  substantially the same result.  Id. The District Court determined that the  function of limitation [b] is a means for "rotating said wheel," by way of  using a "predetermined rate schedule which varies sinusoidally," with the  result that "the attitude of said satellite is offset . . . to null said  roll pointing error due to said orbit inclination." Lockheed, 88 F. Supp.  2d at 1100.

40
The District Court then ruled that there was a factual dispute as to  whether the function and result of the accused SSL L-Wheel are  substantially the same as that claimed by limitation [b] of claim 1 of the  '772 Patent. However, based on its prior claim construction, the District  Court noted that, "it is undisputed that the transverse wheel of the  Intelsat VII does not pass through zero twice per orbit." Id. at 1101.  Therefore, the District Court granted summary judgment of non-infringement  for SSL because it determined that the "way" the SSL L-Wheel operated was  not substantially similar as that claimed in the '772 Patent.  Id. The  District Court held that any other theory of equivalence would vitiate the  claim limitation "varies sinusoidally" recited in limitation [b]. Id.  (citing Tronzo v. Biomet, Inc., 156 F.3d 1154, 1160, 47 USPQ2d 1829, 1834  (Fed. Cir. 1998)).

41
As an additional basis for granting summary judgment, the District Court  ruled the SSL satellites do not infringe limitation [f] of claim 1 of the  '772 Patent, either literally or through the doctrine of equivalents. Id.  at 1102. The District Court stated that, "[t]he limitation requiring  element [f] to be responsive to a wheel direction signal is simply not  met." Id.

F. Arguments on Appeal

42
Lockheed does not challenge the District Court's claim construction that  "varies sinusoidally" means "a variation in a sine-shaped curve that passes  through zero." Accordingly, Lockheed concedes that there can be no literal  infringement of limitation [b]. However, Lockheed posits that the grant of  summary judgment was improper because a factual dispute exists as to  whether the SSL satellites contain an equivalent to limitation [b].  Lockheed relies on the testimony of its expert witness, Dr. Alfriend, for  the proposition that the SSL Intelsat VII satellites have a means to rotate  their L-Wheel purely sinusoidally. Moreover, Lockheed disagrees with the  construction of the phrase "varies sinusoidally" insomuch as it precludes  additional, insubstantial inputs.

43
Finally, Lockheed maintains that the District Court failed to conduct a  complete infringement analysis as to limitation [f]. Although the District  Court examined the SSL tachometers and ground-based computer processors,  Lockheed argues that the District Court failed to consider whether the SSL  "roll bias generator" satisfies the requirements of limitation [f].

II. STANDARD OF REVIEW

44
We review the grant of a motion for summary judgment de novo, drawing all  reasonable factual inferences in favor of the non-moving party. Anderson v.  Liberty Lobby, Inc., 477 U.S. 242, 255 (1986); Festo Corp. v. Shoketsu  Kinzoku Kogyo Kabushiki Co., 234 F.3d 558, 585, 56 USPQ2d 1865, 1886 (Fed.  Cir. 2000) (en banc). Summary judgment "shall be rendered forthwith if the  pleadings, depositions, answers to interrogatories, and admissions on file,  together with the affidavits, if any, show that there is no genuine issue  as to any material fact and that the moving party is entitled to a judgment  as a matter of law." Fed. R. Civ. P. 56(c); Newbanks v. Cent. Gulf Lines,  Inc., 64 F. Supp. 2d 1, 4 (D. Mass. 1999).

45
The determination of infringement is a two-step process. First, the court  construes the claims to correctly determine the scope of the claims.  Second, it compares the properly construed claims to the accused device.  Cybor Corp. v. FAS Techs., Inc., 138 F.3d 1448, 1454, 46 USPQ2d 1169, 1172  (Fed. Cir. 1998) (en banc). Claim construction is a matter of law that we  review de novo, without deference to the District Court. Id. at 1456, 46  USPQ2d at 1172-73. Hence, claim construction of a "means plus function"  limitation, as contemplated by 35 U.S.C. § 112 ¶ 6 (1994 ed., Supp. V), is  also a question of law to be reviewed de novo. Chiuminatta Concrete  Concepts, Inc. v. Cardinal Indus., Inc., 145 F.3d 1303, 1308, 46 USPQ2d  1752, 1755-56 (Fed. Cir. 1998).

46
However, a determination of infringement, both literal and under the  doctrine of equivalents, is a question of fact. Insituform Techs., Inc. v.  Cat Contracting, Inc., 161 F.3d 688, 692, 48 USPQ2d 1610, 1614 (Fed. Cir.  1998). Thus, viewing the facts and inferences in the light most favorable  to Lockheed, summary judgment is proper only if "no reasonable jury could  return a verdict for the nonmoving party." Anderson, 477 U.S. at 255 .  Finally, the determination of infringement under the doctrine of  equivalents is limited by two primary legal doctrines: (1) prosecution  history estoppel and (2) the "all elements" rule. The application of these  legal limitations is reviewed by this court de novo. Festo, 234 F.3d at  586, 56 USPQ2d at 1886.

III. DISCUSSION

47
1. Claim Construction: Limitation [b]

48
Both parties agree that limitation [b] of claim 1 of the '772 Patent is  written as a "means-plus-function" claim limitation. A means-plus-function  limitation recites a function to be performed rather than definite  structure or materials for performing that function. Chiuminatta, 145 F.3d  at 1307, 46 USPQ2d at 1755. Such a limitation must be construed to cover  the corresponding structure, material, or acts described in the  specification and equivalents thereof. 35 U.S.C. § 112 ¶ 6.

49
The first step in analyzing a claim written in means-plus-function form is  to identify the claimed function. Chiuminatta, 145 F.3d at 1308, 46 USPQ2d  at 1756. The District Court determined that limitation [b] recites a means  having the function of "rotating said wheel." Lockheed, 88 F. Supp. 2d at  1100. SSL maintains that the District Court improperly broadened the  function of limitation [b] by "reading out" the remaining claim  limitations. We agree with SSL.

50
Once a court establishes that a means-plus-function limitation is at issue,  it must identify and construe that limitation, thereby determining what the  claimed function is, and what structures disclosed in the written  description correspond to the "means" for performing that function. The  phrase "means for" generally invokes 35 U.S.C. § 112 ¶ 6, and is typically  followed by the recited function and claim limitations. Greenberg v.  Ethicon Endo-Surgery, Inc., 91 F.3d 1580, 1584, 39 USPQ2d 1783, 1786-87  (Fed. Cir. 1996). In identifying the function of a means-plus-function  claim, a claimed function may not be improperly narrowed or limited beyond  the scope of the claim language. Micro Chem. Inc. v. Great Plains Chem.  Co., 194 F.3d 1250, 1258, 52 USPQ2d 1258, 1263 (Fed. Cir. 1999).  Conversely, neither may the function be improperly broadened by ignoring  the clear limitations contained in the claim language. The function of a  "means plus function" claim must be construed to include the limitations  contained in the claim language.

51
In this case, the District Court erred by improperly broadening the scope  of the claimed function by "reading out" the limitations contained in the  claim language. The function of limitation [b] is properly identified as  "rotating said wheel in accordance with a predetermined rate schedule which  varies sinusoidally over the orbit at the orbital frequency of the  satellite." The function is properly identified as the language after the  "means for" clause and before the "whereby" clause, because a whereby  clause that merely states the result of the limitations in the claim adds  nothing to the substance of the claim.  Texas Instruments Inc. v. United  States Int'l Trade Comm'n, 988 F.2d 1165, 1172, 26 USPQ2d 1018, 1023-24  (Fed. Cir. 1993).

52
Having identified the function of limitation [b], we next construe the  meaning of the words used to describe the claimed function, using ordinary  principles of claim construction. The District Court construed the phrase  "varies sinusoidally" to mean "a variation in a sine-shaped curve that  passes through zero." Lockheed, 88 F. Supp. 2d at 1099. In its claim  construction order, the District Court explained that the "rate" or "speed"  of the wheel itself must pass through zero. See Lockheed, 88 F.Supp.2d at 1100-01. The District Court determined that this construction "is  consistent with the other limitations in the claims themselves regarding  the capacity of the transverse momentum wheel to accelerate in one  direction, slow to zero, and rotate in the opposite direction." Id.

53
Neither party disputes the District Court's construction of this phrase,  and we find no fault in the District Court's careful analysis. The meaning  of the remaining language of limitation [b] is clear from the plain  language of the claim and is consistent with the intrinsic evidence. See  Vitronics Corp. v. Conceptronic, Inc., 90 F.3d 1576, 1582-83, 39 USPQ2d  1573, 1576-77 (Fed. Cir. 1996). The wheel must rotate in accordance with a  "predetermined rate schedule." According to the written description, the  rate schedule is produced by the sine generator and is dependent on the  orbital period as well as the angle of orbital inclination. '772 Patent,  col. 7, ll. 28-64. It is undisputed that the "orbital frequency of the  satellite" is twenty-four hours; the written description specifically  states that the pointing errors change "at the orbital frequency, which for  a spacecraft in a synchronous altitude orbit, is one day." '772 Patent,  col. 4, l. 29. Furthermore, it is clear from the written description that  the rate schedule is "predetermined" insomuch as the sine generator  produces a sine wave with an amplitude that changes "on a continuous basis"  and that is "related to the inclination deviation" angle. '772 Patent, col.  7, l. 28 - col. 8, l. 33.

54
After identifying the function of the "means plus function" limitation and  construing the meaning of the claim language, we look next to the written  description to identify the structure corresponding to the function. Micro  Chemical, 194 F.3d at 1258, 52 USPQ2d at 1263. It is undisputed that the  structures disclosed in the '772 Patent which correspond to the function of  limitation [b] are the sine generator and wheel electronics noted in Figure  4 above. As discussed, the sine generator operates by producing a sine wave  signal whose amplitude varies based on the orbital angle of inclination.  The wheel electronics are responsive to signals from the sine generator and  the tachometer, and generate a signal to the yaw wheel such that the wheel  generates a sinusoidal variation of momentum. '772 Patent, col. 8, ll. 15-  25.

55
2. Infringement: Limitation [b]

56
Literal infringement of a § 112 ¶ 6 claim requires that the relevant  structure in the accused device perform the identical function recited in  the claim and be identical or equivalent to the corresponding structure in  the specification. WMS Gaming, Inc. v. Int'l Game Tech., 184 F.3d 1339,  1347, 1350, 51 USPQ2d 1385, 1390, 1392-93 (Fed. Cir. 1999); Odetics, Inc.  v. Storage Tech. Corp., 185 F.3d 1259, 1267, 51 USPQ2d 1225, 1229 (Fed.  Cir. 1999). Lockheed concedes that there can be no literal infringement of  limitation [b] because the SSL satellite L-Wheel rotates about a non-zero  bias speed. That is, the SSL L-Wheel does not perform the identical  function of limitation [b] as properly construed. However, Lockheed  contends that a factual dispute exists as to whether the SSL Intelsat VII  satellites meet the requirements of limitation [b] under the doctrine of  equivalents. An accused structure that does not literally infringe a "means  plus function" claim may nevertheless infringe under the doctrine of  equivalents. See Kemco Sales, Inc. v. Control Papers Co., 208 F.3d 1352,  1364, 54 USPQ2d 1308, 1315-16 (Fed. Cir. 2000). Specifically, Lockheed  asserts that the testimony of its expert, Dr. Alfriend, raises a genuine  issue of material fact as to whether the SSL satellites contain an  equivalent to the claimed means for rotating the transverse wheel about  zero speed.

57
Lockheed relies on the testimony of its expert, Dr. Alfriend, for the  proposition that the SSL satellite L-Wheel "varies according to a sine-  shaped curve that passes through zero and changes direction twice per day."  According to Dr. Alfriend, "[t]he only difference is that, in the Intelsat  VII satellite, when the sinusoidal input is added, the yaw wheel is already  spinning at a bias speed, whereas in the '772 exemplary embodiment the  wheel is initially stationary." Furthermore, Dr. Alfriend posits that the  SSL satellite "has the capability to be operated in inclined orbit with a  purely sinusoidal roll bias if desired." Even when other inputs are used,  Dr. Alfriend states that, "the bias signal would be predominantly  sinusoidal." It is true that an accused device may infringe under the doctrine of  equivalents if each element performs substantially the same function, in  substantially the same way, to achieve substantially the same result.  Warner-Jenkinson, 520 U.S. at 40 , 41 USPQ2d at 1875. However, this court  must first determine whether the scope of the doctrine of equivalents, as  applied to the claim limitations of limitation [b], has been narrowed by  the legal doctrine of prosecution history estoppel or proscribed by the  "all elements" rule. Festo, 234 F.3d at 586, 56 USPQ2d at 1886. These  determinations are made de novo. Id.

58
The scope of the doctrine of equivalents may be limited by prosecution  history because a patentee cannot recapture subject matter surrendered  during the prosecution of the patent. Warner Jenkinson, 520 U.S. at 31 -32,  41 USPQ2d at 1872-73. Estoppel may arise by amendments made to overcome  prior art rejections, or by argument made to secure allowance of a claim.  Festo, 234 F.3d at 586, 56 USPQ2d at 1886. The first step in a prosecution  history estoppel analysis is to determine which claim limitations are  alleged to be met by equivalents.  Id. Lockheed argues that limitation [b]  is met by equivalents because the rotation of the SSL satellite L-Wheel is  substantially the same as the sinusoidal variation described by the '772  Patent.

59
This court must next determine whether an amendment was made concerning the  limitation at issue during the prosecution of the patent.  Festo, 234 F.3d  at 586, 56 USPQ2d at 1886. If the claim limitation at issue was amended,  this court must determine whether the amendment narrowed the literal scope  of the claim.  Id. If so, prosecution history estoppel will bar the  application of the doctrine of equivalents to the claim limitation, unless  the patent holder establishes that the amendment was made for a purpose  unrelated to patentability. Id.

60
In this case, limitation [b] was amended twice during prosecution of the  patent. As originally filed, the pertinent language of limitation [b]  stated, "means for rotating said wheel in accordance with a predetermined  sinusoidal variation." The examiner first rejected the application on  obviousness grounds, based on four prior art references. In response, the  applicant amended limitation [b] to state, "means for rotating said wheel  in accordance with a predetermined rate schedule which varies sinusoidally  over the orbit." (added language underlined). Thus, the phrase "sinusoidal  variation" was changed to "rate schedule which varies sinusoidally over the  orbit." The examiner again rejected the claim. The applicant again amended  the claim by adding the phrase "at the orbital frequency of the satellite"  such that limitation [b] appeared as it ultimately issued. Lockheed argues  that the two amendments to limitation [b] "had nothing to do with  sinusoidal operation about zero speed, or with purely sinusoidal  operation." Instead, Lockheed asserts that the amendments were made to  distinguish the period of sinusoidal variation described in the prior  references. Specifically, Lockheed asserts that the claim was rejected  because the prior references disclosed sinusoidal variation over a period  of "nutation" (several minutes). Lockheed argues, therefore, that the  amendments merely distinguished that the period of sinusoidal variation  disclosed in limitation [b] occurs "over the orbit at the orbital frequency  of the satellite" (twenty-four hours).

61
In short, Lockheed argues that this court should follow the "flexible bar"  approach in determining the proper scope of equivalents. Lockheed asserts  that the amendments to limitation [b] were directed only at the period of  sinusoidal variation. Therefore, Lockheed reasons that prosecution history  estoppel does not act as a complete bar to the application of the doctrine  of equivalents as to the sinusoidal variation claimed in limitation [b].  However, our decision in Festo comprehensively and explicitly rejects such  a "flexible bar" approach. 234 F.3d at 574-78, 56 USPQ2d at 1877-80. We  reasoned that the notice function of patent claims has become paramount,  and the need for certainty as to the scope of patent protection has been  emphasized. Id. By rejecting the flexible bar approach, we enforce the  disclaimer effect of a narrowing claim amendment, and best serve the notice  and definitional function of patent claims. Id. In short, we held that,  "prosecution history estoppel acts as a complete bar to the application of  the doctrine of equivalents when an amendment has narrowed the scope of a  claim for a reason related to patentability." Id. at 574, 56 USPQ2d at 1877  (emphasis added).

62
In this case, even Lockheed admits that, "the two amendments to claim  element [b] were to specify more narrowly the period of the sinusoidal  variation, i.e., to specify that the sinusoidal variation occurred once per  day." (emphasis in original). Therefore, the entire claim limitation [b]  was amended to define further the characteristics of the sinusoidal  variation. The first amendment wholly replaced the phrase "sinusoidal  variation" with the language "rate schedule which varies sinusoidally over  the orbit." This amendment illustrates that the entire limitation of  limitation [b] was changed- not that a completely separate limitation,  unrelated to sinusoidal variation, was added. Thus, the amendment narrowed  the literal scope of limitation [b].

63
"No scope of equivalents can be afforded to a claim element that was  narrowed because of patentability concerns." Festo, 234 F.3d at 576, 56  USPQ2d at 1878. As discussed, the amendments narrowed the literal scope of  limitation [b]. Additionally, it is undisputed that the amendments were  made for purposes of patentability. Therefore, because the applicant  limited the scope of limitation [b] to "a predetermined rate schedule which  varies sinusoidally over the orbit," there is no range of equivalents  available to show infringement of limitation [b]. Thus, "prosecution  history estoppel [bars] the application of the doctrine of equivalents" to  limitation [b]. Festo, 234 F.3d at 586, 56 USPQ2d at 1886. Moreover,  because Lockheed's claim of infringement must fail, we need not discuss the  all elements rule, nor examine whether the SSL satellites meet the  limitations of limitation [f].

IV. CONCLUSION

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For the reasons discussed, the District Court's grant of summary judgment  of non-infringement in favor of SSL is

65
AFFIRMED.

COSTS

66
No costs.

Notes:

1
  The District Court and the parties use the term "element"   to  refer to subcategories of claim language.  However, "[i]t is preferable to The District Court and the parties use the term "element"   use the  term  'limitation'  when  referring  to  claim  language and the termle to The District Court and the parties use the term "element"   'element' when referring to the accused device."  Festo  Corp.  v.  Shoketsuhe District Court and the parties use the term "element"   Kinzoku Kogyo Kabushiki Co., 234 F.3d 558, 564 n.1, 56 USPQ2d 1865, 1868 (Fed.   Cir. 2000).  We, therefore, use the term "limitation" in this opinion.