Patent Publication Number: US-6704256-B2

Title: Continuous flexible connection for miniature optical head

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. application Ser. No. 09/679,941, filed Oct. 4, 2000, which is commonly owned and incorporated by reference herein in its entirety. 
    
    
     COPYRIGHT NOTICE 
     A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 
     CROSS-REFERENCE TO CD-ROM APPENDIX AND APPENDIX A 
     A CD-ROM Appendix containing a computer program listing is submitted on a compact disc, which is herein incorporated by reference in its entirety. The total number of compact discs including duplicates is two. Appendix A, which is part of the present specification, contains a list of the files contained on the CD-ROM Appendix. 
     BACKGROUND 
     1. Field of the Invention 
     The present invention relates to a system that connects an optical head to additional electronics in an optical drive. 
     2. Description of Related Art 
     A conventional optical drive (e.g., a compact disk player) typically includes a stationary optical unit, a movable optical unit, and an actuator. The stationary optical unit generally includes a laser diode, a half mirror, and a photodetector. The laser diode generates a light beam that is reflected by the half mirror onto the movable optical unit. The movable optical unit typically includes an objective lens that focuses the light beam on a spinning optical disk. 
     The actuator aligns the movable optical unit with the tracks of the optical disk so that the light beam reflects off the lands and pits of the tracks. The reflected light beam travels back through the movable optical unit and back to the stationary optical unit. The light beam is transmitted through the half mirror onto the photodetector where the varying intensity of the light is changed to electrical signals. 
     Optical drives are becoming smaller so they can be integrated into portable devices including laptop computers and personal digital assistants (PDAs). Close arrangement and integration of components help to miniaturize optical drives. For example, the stationary and movable optical units described above can be integrated into a single component (an integrated optical head) called “optical pickup unit” or “OPU”. The OPU can be mounted on a small actuator arm that places the OPU over the tracks of the spinning medium with relatively small forces. 
     The miniaturization of the optical drive creates new design restraints on the flex circuit that carries signals to and from the OPU. Depending its shape and the location from which it departs from the actuator arm, the flex circuit may constrain or disturb the movement of the actuator arm carrying the OPU. Accordingly, what is needed is a system that connects the OPU to the remaining electronics of the optical drive without impinging on the motion of the actuator arm. 
     SUMMARY 
     In one embodiment of the invention, an optical assembly includes a base plate and an actuator arm. The actuator arm includes a tracking section pivotally mounted around a tracking axis to the base plate, and a focus section pivotally mounted around a focus axis to the tracking section. A proximate end of a service loop extends from the focus section while a distal end of the service loop is mounted to the base plate. When the tracking section rotates around the tracking axis, at least a portion of the service loop bends. When the focus section rotates around the focus axis, at least a portion of the service loop twists. 
     In another embodiment of the invention, a method predicts the shape of a service loop that does not rotate the actuator arm from a resting position. The method uses a number of beam elements deflected by the actuator arm to simulate the shape of the service loop. In order for the service loop not to rotate the actuator arm, the method assumes that the actuator arm applies an equivalent force through the rotation axis. A user provides a mounting point (the point where a first end of the service loop is mounted to a base plate), a mounting angle (the angle at which the first end of the service loop is mounted to the base plate), a departure point (the point where a second end of the service loop is mounted to the actuator arm), a departure angle (the angle at which the second end of the service loop is mounted to the actuator arm), the total number of the beam elements, and the beam stiffness. The user also provides initial values for the beam length and the magnitudes of the X and Y components of the force applied by the actuator arm. For each beam element, the method calculates a start position, a start angle (the angle at which the start of the beam is oriented), an end position, and a finish angle (the angle at which the end of the beam is oriented under deflection). If the end position and the finish angle of the last beam element do not match the desired end position and angle of the service loop, the method repeats the above steps with new values for at lest one of the beam length and the magnitudes of the X and Y components. 
     In yet another embodiment, a method calculates the restoring torque when the actuator arm is rotated away from its resting position. Unlike the above method, this method assumes that a moment exists around the rotation axis. In one implementation, the moment around the rotation axis is expressed as the product of the Y component and its X direction offset from the rotation axis. Thus, the user provides initial values for the offset of the Y component and the magnitudes of the X and Y components. The user also provides the mounting point, the mounting angle, the departure point, the departure angle, the total number of the beam elements, the beam stiffness, and the beam length. For each beam element, the method calculates a start position, a start angle, an end position, and a finish angle. If the position of the last beam element does not match the desired end position and angle of the service loop, the method repeats the above steps with new values for at least one of the offset of the Y component and the magnitudes of the X and Y components. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 illustrates a side view of an optical assembly. 
     FIG. 2A illustrates an exploded view of an optical assembly in one embodiment. 
     FIG. 2B illustrates a perspective side view of the assembly of FIG.  2 A. 
     FIG. 3 illustrates a side view of an optical pickup unit (OPU) of the assembly of FIG.  2 A. 
     FIGS. 4A,  4 B,  5 A, and  5 B illustrate cross sectional views of the assembly of FIG. 2A in various implementations. 
     FIG. 6 illustrates an exploded view of an optical assembly in another embodiment. 
     FIG. 7 illustrates a side view of the assembly of FIG.  6 . 
     FIG. 8 illustrates a perspective side view of an arm and a service loop of a flex circuit of an optical assembly. 
     FIGS. 9A and 9B illustrate perspective views of the bending of the service loop when the arm rotates clockwise and counterclockwise. 
     FIGS. 10A and 10B illustrate perspective views of the twisting of the service loop when the arm rotates up and down. 
     FIG. 11 illustrates a flow chart of a method for determining departure and mounting points of the service loop that do not cause the service loop to rotate the actuator arm away from a resting position in accordance with one embodiment of the invention. 
     FIG. 12 illustrates a top view of the actuator arm and the flex circuit used to explain the method of FIG.  11 . 
     FIG. 13 illustrates one of many beam elements used to predict the shape the service loop in the method of FIG.  12 . 
     FIG. 14 illustrates a flow chart of a method for determining the torque experienced by the actuator arm from the service loop when the actuator arm is rotated away from the resting position in accordance with one embodiment of the invention. 
    
    
     Use of the same reference symbols in different drawings indicates similar or identical items. 
     DETAILED DESCRIPTION 
     FIG. 1 illustrates an assembly  10  used to connect an OPU  20  to a printed circuit board  60  (or electronics of an optical drive). OPU  20  is mounted atop a copper plate  30  through a cutout of a fiberglass layer  40 . Fiberglass layer  40  includes pad  42 , pad  44 , and trace  46 . Pad  42  of fiberglass layer  40  is coupled to pad  22  of OPU  20  via a bond wire  25 . Plate  30  is mounted atop a flexible circuit  50  (or vice versa). Flexible circuit  50  includes pad  52 , trace  54 , and a connector  56 . Pad  44  of fiberglass layer  40  is coupled to pad  52  of flexible circuit  50  via a solder joint  35 . Flexible circuit  50  is next coupled to a printed circuit board  60  via connector  56 . 
     Assembly  10  has several disadvantages. Each of the wire bonds and solder joints in assembly  10  forms a point of failure that may break during use. Thus, the many wire bonds and solder joints in assembly  10  create multiple points of failure. Each of the wire bonds and solder joints must be formed during fabrication. Thus, the many wire bonds and solder joints increase fabrication cost. Solder joints also require large pads, thereby increasing the overall size of the fiberglass and flexible circuit layers. Assembly  10  is also constructed from multiple layers of silicon, fiberglass, copper, and flex circuit that increase the overall weight and volume of the optical drive. Accordingly, there is a need for a method and a system to connect the OPU to the remaining electronics of the optical drive while improving reliability and minimizing weight and volume. 
     FIGS. 2A and 2B illustrate an optical pickup assembly  100  in one embodiment. Assembly  100  includes an actuator arm  102  that places an optical pickup unit (OPU)  104  over the tracks of a spinning medium  330  (shown in FIG.  3 ). OPU  104  reflects a light beam off the tracks and converts the reflected light beam into electrical signals. A flexible circuit (flex circuit)  106  receives the electrical signals via a direct wire bond  116  to OPU  104  (shown in FIG.  2 B), thereby eliminating the use of an intermediate fiberglass layer and its associated wire bonds. Flex circuit  106  passes the electrical signals to a printed circuit board  120  (or any other electronics) for further processing. Flex circuit  106  also passes control and power signals from printed circuit board  120  to OPU  104 . A thermally conductive plate (heat sink)  108  is mounted to OPU  104  to dissipate heat generated by OPU  104  to the surroundings (e.g., the surrounding air and components). 
     As shown in FIG. 2B, flex circuit  106  is mounted atop plate  108 . Plate  108  can be made from various thermally conductive materials including aluminum, brass, carbon fiber composite, copper, gold, graphite, steel (stainless or otherwise with anti-corrosion treatment). One skilled in the art understands that plate  108  can also be made from alloys of the metals listed above. Flex circuit  106  is, for example, a conventional Kapton flex circuit with gold or copper traces. In some embodiments, flex circuit  106  is bonded to plate  108  using a thermally conductive adhesive  130 . Adhesive  130  includes pressure sensitive adhesives, acrylic adhesives, epoxies, structural epoxies, anaerobic adhesives, UV curable adhesives, gap filling adhesives, and wicking adhesives. Adhesive  130  may include a filler for thermal and/or electrical conductivity purposes (e.g., metal powders, metal fibers, carbon powders, and carbon fibers). In some implementations, flex circuit  106  and plate  108  are manufactured with respective alignment holes  109  and  111  (FIG. 2A) to properly position flex circuit  106  with respect to plate  108  during mounting. Flex circuit  106  and plate  108  are properly positioned when corresponding alignment holes  109  and  111  are aligned. 
     In some embodiments, flex circuit  106  includes a cutout  110  (FIG.  2 A). In these embodiments, OPU  104  is mounted atop plate  108  through cutout  110 . OPU  104  is, for example, bonded to plate  108  using a thermally conductive adhesive  132 . Thus, OPU  104  is fixedly attached to plate  108  and in a fixed position relative to flex circuit  106 . 
     As shown in FIG. 3, OPU  104  includes a light source  302  supported on a mount  304 . Light source  302  is, for example, an edge-emitting laser diode. Mount  304  in turn is mounted on a sub-mount (wafer)  306 . Sub-mount  306  is an integrated circuit chip formed in a semiconductor fabrication process to include photodetectors  332  for reading data and controlling the laser power and the servomechanism, and pads  114  and traces for wire bonding photodetectors  332 , laser  302 , and an optional oscillator chip (not shown) used to modulate laser  302 . 
     Above light source  302  is an OE (optical element) block  308 , which can include lenses, gratings, holograms and other optical components or devices. OE block  308  diffracts a fraction of the laser light to laser power control photodetectors (not shown) and optionally shapes the laser beam. Interposed between sub-mount  306  and OE block  308  are spacer blocks  310  and  312  where one side of spacer block  310  is provided with a  45  degrees turning mirror  314  that reflects the horizontal light beam produced by light source  302  to a vertical upward direction. 
     Mounted atop OE block  308  is a prism  316  made of a material that is transparent to the light beam emitted by light source  302 . Prism  316  is, for example, made of fused silica or flint glass (SF 2 ). The ends (lateral surfaces) of prism  316  are angled at about  45  degrees to the horizontal and are coated with a substantially reflective coating such as aluminum or silver to form turning mirrors  318  and  320 . Prism  316  also includes an internal polarization beam splitter surface (half mirror)  322  angled at about  45  degrees with respect to the horizontal. Beam splitter surface  322  is substantially reflective (i.e., acts as a mirror) for light of a first polarization and substantially transmissive for light of a second polarization. 
     Mounted atop prism  316  are a quarter-wave plate  324 , a lens spacer  326  and an objective lens  328 . Also shown in FIG. 3 is a section of an optical medium  330  positioned at a predetermined distance from objective lens  328 . As in conventional optical head units, the light beam emitted by light source  302  follows a forward path to optical medium  330 , where it is reflected along a return path to photodetectors  332  in sub-mount  306 . 
     In some embodiments, sub-mount  306  is first mounted atop plate  108  through cutout  110  of flex circuit  106 . A precision optical alignment tool can be used to position sub-mount  306  relative to plate  108  via tooling holes or reference surfaces formed in sub-mount  306  and plate  108 . Subsequently, the other components of OPU  104  described above are mounted atop sub-mount  306 . Again, a precision optical alignment tool can be used to position the components of OPU  104  during the assembly process. Additional details concerning OPU  104  are described in application Ser. No. 09/457,104, filed Dec. 7, 1999, entitled “Low Profile Optical Head”, and application Ser. No. 09/544,370, Apr. 6, 2000, entitled “System and Method For Aligning Components of Optical Head”, which are incorporated by reference herein in their entirety. 
     Referring back to FIGS. 2A and 2B, flex circuit  106  and OPU  104  include respective contact pads  112  and  114  for passing and receiving electrical signals via bond wires  116 . Traces on flex circuit  106  are used to carry data, control, and power signals between OPU  104  and printed circuit board  120  of the optical drive. Thus, bond wires  116  provides direct connection between flex circuit  106  and OPU  104 . 
     The use of the direct wire bond between OPU  104  and flex circuit  106  increases interconnection reliability because there are no wire bonds to an intermediate layers (e.g., fiberglass layer  40  in FIG. 1) that can break. The use of the direct wire bond also helps to eliminate the intermediate layer, thereby conserving the overall weight and volume of the miniature optical drive. The elimination of the intermediate layer further conserves the weight of OPU  104  so that it can be easily manipulated by actuator arm  102 . 
     Referring to FIG. 2A, OPU  104  is mounted to a fork  118  of actuator arm  102 . OPU  104  is, for example, bonded to fork  118  using a thermally conductive adhesive. In some embodiments, OPU  104  is placed in its mounting position by locating one or more edges of sub-mount  306 , OE block  308 , or prism  316  with respect to the mating surface on actuator arm  102  in the x and y directions, and by locating the top surface of flex circuit  106  or plate  108  relative to the mating surface on actuator arm  102  in the z direction. Portions of plate  108  and flex circuit  106  are mounted to the bottom surface of actuator arm  102 . For example, part  208  of plate  108  and part  206  of flex circuit  106  are bonded to the bottom surface of actuator arm  102  using a thermally conductive adhesive  134 . As plate  108  and flex circuit  106  are mounted to OPU  104 , they are properly positioned with respect to actuator arm  102  when OPU  104  is mounted to fork  118 . 
     In some implementations, part  206  has a different shape than part  208  and a portion of part  208  is covered by part  206  when part  206  is mounted atop part  208 . In these embodiments, thermally conductive adhesive  134  is applied over part  206  and the uncovered portion of part  208 . FIG. 4A is a cross-sectional view of one implementation of assembly  100  along a line A (FIG.  2 B). As shown in FIG. 4A, thermally conductive adhesive  134  provides a path  402  of thermal conduction between the uncovered portion of part  208  and actuator arm  102  when part  208  is bonded to the bottom surface of actuator arm  102 . Of course, heat is also conducted by a path  404  between the covered portion of part  208  and actuator arm  102  through part  206 . By forming conductive paths from OPU  104  to part  208  and actuator arm  102 , heat can dissipate to the surroundings through the surface area of plate  208  and actuator arm  102  (e.g., shown as paths  406 ). In one implementation illustrated in FIG. 4B, plate  208  (or any other portion of plate  108 ) may be provided with one or more protrusions or tabs  408  that pass through cutouts in part  206  (or any other portion of flex circuit  106 ) to directly contact actuator arm  102  in order to provide additional conduction paths between plate  108  and actuator arm  102 . 
     In other implementations, part  206  has a shape such that the entire part  208  is covered by part  206  when part  206  is mounted atop part  208 . FIG. 5A is a cross-sectional view of one implementation of assembly  100  along a line A (FIG.  2 B). As shown in FIG. 5A, part  208  only contacts actuator arm  102  through part  206 . Thus, heat from OPU  104  can be conducted in a path  502  from part  208  of plate  108  through part  206  of flex circuit  106  into actuator arm  102 . By forming conductive paths from OPU  104  to plate  108  and actuator arm  102 , heat can dissipate to the surroundings through the surface area of plate  108  and actuator arm  102  (e.g., shown as paths  506 ). In one implementation illustrated in FIG. 5B, plate  208  (or any other portion of plate  108 ) may be provided with one or more protrusions or tabs  408  that pass through cutouts in part  206  (or any other portion of flex circuit  106 ) to directly contact actuator arm  102  in order to provide additional conduction paths between plate  108  and actuator arm  102 . 
     FIGS. 6 and 7 illustrate an optical pickup assembly  600  in another embodiment. Although similar to optical pickup assembly  100 , the elements of optical pickup assembly  600  are arranged differently. A thermally conductive plate  608  is first mounted atop a flex circuit  606 . Plate  608  is, for example, bonded atop flex circuit  606  using a thermally conductive adhesive  630 . In some embodiments, flex circuit  606  and plate  608  are manufactured with respective alignment holes  609  and  611  to properly position flex circuit  606  with reference to plate  608  during mounting. 
     An OPU  604  is next mounted atop plate  608 . OPU  604  is, for example, bonded to plate  608  using a thermally conductive adhesive  632 . Thus, OPU  604  is fixedly attached to plate  608  and in a fixed position relative to flex circuit  606 . In some implementations, OPU  604  is constructed like OPU  104 . 
     Flex circuit  606  and OPU  604  include respective contact pads  612  and  614  for passing and receiving electrical signals via bond wires  616  (FIG.  7 ). In some embodiments, plate  608  includes cutouts  610  where bond wires  616  pass through to couple contact pads  612  and  614 . Traces on flex circuit  606  are used to carry data, control, and power signals between OPU  604  and printed circuit board  120  of the optical drive. 
     OPU  604  is mounted to a fork  618  of an actuator arm  602 . OPU  604  is, for example, bonded to fork  618  using a thermally conductive adhesive. Plate  608 , with flex circuit  606  attached, is mounted to the bottom surface of actuator arm  602 . For example, part  708  of plate  608  is bonded to the bottom surface of actuator arm  602  using a thermally conductive adhesive  634 . OPU  604 , flex circuit  606 , and plate  608  may be positioned relative to each other as described above in respect to assembly  100 . 
     FIG. 8 illustrates that actuator arm  102  includes a tracking section  804  pivotally mounted around a tracking axis  806  to a base plate  801 . Tracking section  804  is, e.g., mounted to base plate  801  through a bearing set  805 . A focus section  808  is pivotally mounted around a focus axis  810  to tracking section  804 . Focus section  808  is, e.g., engaged to tracking section  804  through a hinge  809 . OPU  104  is mounted at an end of focus section  808 . Tracking section  804  rotates around tracking axis  806  to place OPU  104  over the tracks of medium  330  (not shown) while focus section  808  rotates around focus axis  810  to focus OPU  104  on the tracks of medium  330 . Depending on the implementation, tracking axis  806  and focus axis  810  can intersect. Additional details concerning arm  102  are described in application Ser. No. 09/557,284, filed Apr. 25, 2000, entitled “TILT FOCUS METHOD AND MECHANISM FOR AN OPTICAL DRIVE”, which is incorporated by reference herein in its entirety. 
     In one implementation, the angle of rotation for tracking section  804  is 10 to 20 degrees in either direction (clockwise or counterclockwise) while the angle of rotation for focus section  808  is 0.25 to 1.5 degrees in either direction (up or down). In one implementation, the distance from tracking axis  806  to the objective lens of OPU  104  is 10 to 30 mm while the distance from focus axis  810  to the object lens of OPU  104  is 10 to 30 mm. 
     A service loop  802  of flex circuit  106  extends from arm  102 . Service loop  802  includes a proximate end  812  that extends from a departure point  1208  (see FIGS. 9A,  9 B, and  12 ) near axes  806  and  810 . In one implementation, proximate end  812  extends from departure point  1208  on focus section  808 . In some implementations, multiple service loops  802  can extend from arm  102 . Multiple service loops  802  may be necessary due to the number of signals to and from actuator arm  102  and the physical restraints imposed by the dimensions of the optical disk drive. 
     A distal end  814  of loop  802  is fixedly mounted to base plate  801  at a mounting point  1206  (see FIGS. 9A,  9 B, and  12 ) to cause loop  802  to have a curved shape (e.g., a catenary-like shape). Loop  802  is oriented so that its width (flex width) is vertical when focus section  808  is level. 
     FIGS. 9A and 9B illustrate that loop  802  bends and unbends when tracking section  804  rotates around tracking axis  806  in a first and a second direction, respectively. Loop  802  is preferably made of a material that has a low modulus of elasticity. Loop  802  is, e.g., made of polyimide such as a conventional Kapton flex circuit. The length of loop  802  is relatively large compared to its width and thickness. In one implementation, loop  802  is 26 mm long, 2.5 mm wide, and 0.07 mm thick. These characteristics allow loop  802  to bend easily (e.g., loop  802  has a low bending spring constant). Thus, loop  802  provides minimal constraint to the rotation of tracking section  804  around tracking axis  806 . 
     Proximate end  812  is also attached to arm  102  near tracking axis  806 . The placement of departure point  1208  gives loop  802  little mechanical advantage to exert a force on arm  102 . Thus, loop  802  does not disturb the motion of tracking section  804  around tracking axis  806 . 
     FIG. 10A illustrates how loop  802  twists when focus section  808  rotates around focus axis  810  in a first direction (e.g., up). When section  808  rotates up, proximate end  812  is raised while distal end  814  remains stationary. The movement of proximate end  812  twists loop  802 . Similarly, FIG. 10B illustrates how loop  802  twists when focus section  808  rotates around focus axis  810  in a second and opposite direction. When focus section  808  rotates down, proximate end  812  is lowered while distal end  814  remains stationary. Again, the movement of proximate end  812  twists loop  802 . 
     As described before, loop  802  preferably has a low modulus of elasticity and is relatively long. These characteristics allow loop  802  to twist easily (e.g., loop  802  has a low torsional spring constant). Thus, loop  802  does not constrain the rotation of focus section  808  around focus axis  810 . 
     Proximate end  812  is also attached to arm  102  near focus axis  810 . The placement of departure point  1208  gives loop  802  little mechanical advantage to exert a force on arm  102 . Thus, loop  802  does not disturb the motion of focus section  808  around focus axis  810 . 
     FIG. 11 shows a flow chart of a method  1100  used to determine a shape of service loop  802  that does not rotate actuator arm  102  away from a predetermined position (“resting position”) over medium  330 . The resting position is selected so that the tracking motor current required to rotate actuator arm  102  toward the inner diameter (ID) against service loop  802  is substantially equal to the tracking motor current required to rotate actuator arm  102  toward the outer diameter (OD) against service loop  802 . This minimizes the maximum current and maximum motor torque requirement for the tracking motor in the optical drive. In one implementation, the resting position places actuator arm  102  over the middle diameter (MD) on medium  330  (see FIGS.  9 A and  9 B). 
     Method  1100  starts a first end of service loop  802  at a predetermined point (“mounting point”) and angle (“mounting angle”). Method  1100  extends service loop  802  out in short sections to meet actuator arm  102  at a predetermined point (“departure point”) and angle (“departure angle”). Method  1100  treats each section as a simple beam element deflected by a force and moment applied to the end of said element under simple beam theory. By placing together many short beam elements, method  1100  is able to accurately predict the shape of service loop  802 . 
     As one skilled in the art understands, a force  1210  (FIG. 12) and a rotational moment  1211  applied by service loop  802  to actuator arm  102  at departure point  1208  can be replaced by an equivalent force and moment applied to any point on actuator  102  (e.g., force  1212  and moment  1213  at tracking axis  806 ). The magnitude and direction of force  1212  are constant while the magnitude and sign of moment  1213  will depend on the location of the chosen point. Method  1100  assumes that equivalent force  1212  and moment  1213  at tracking axis  806  consist of the constant force  1212  and a zero (0) value moment  1213  such that the combined effect of the two does not tend to rotate actuator arm  102  about tracking axis  806 . 
     For the purposes of calculating deflections of the simple beam elements which together comprise service loop  802 , a force  1214  and a rotational moment  1215  applied by actuator arm  102  to service loop  802  at departure point  1208  can be replaced by an equivalent force and moment applied to any point on service loop  802  (e.g., equivalent force  1216  and moment  1217  at point  1218 ). Force  1216  applied to service loop  802  at the location of any chosen simple beam element will be equal in magnitude and opposite in direction when compared with force  1212 . Moment  1217  applied to a chosen beam element can be calculated from force  1216  and the location of the simple beam element on service loop  802  chosen. Force  1216  and calculated moment  1217  applied to a chosen beam element in service loop  802  will cause the element to deflect. The complete curve of service loop  802  can thus be determined by calculating the deflection caused by force  1216  and calculated moment  1217  for each beam element in service loop  802 . 
     Method  1100  begins at the first end of service loop  802  and determines the deflection of the first comprising beam element by applying to said element force  1216  and calculated moment  1217 . Said deflected beam element is connected to the predetermined mounting point at the predetermined mounting angle. Method  1100  calculates the deflection of each beam element, connects said element to the second end of an immediately preceding beam element and sequentially repeats this process for each simple beam element comprising service loop  802 . 
     Further, method  1100  adjusts the magnitude and direction of force  1216  (e.g., by varying the magnitudes of the X and Y components of force  1216 ) and the common length of the individual simple beam elements (“beam length”) which together comprise service loop  802  to values that are consistent with the mechanical dimensions and characteristics of the material(s) constituting the service loop and the predetermined mounting point, mounting angle, departure point, and departure angle. 
     Generally, a user sets (1) the departure point (e.g., X and Y coordinates), (2) the departure angle, (3) the mounting point (e.g., X and Y coordinates), (4) the number of beam elements used to simulate service loop  802 , and (5) the bending modulus of the beam elements (e.g., stiffness of service loop  802 ). The user also provides initial values for (6) the beam length and (7) the magnitudes of the X and Y components of force  1216 . The initial values provided for the beam length and the magnitudes of the X and Y components are only guesses. A computer can vary one or more of the beam length and the magnitudes of the X and Y components in an iterative process to achieve a solution that places the end of service loop  802  at the predetermined departure point and angle. Typically, a large number of beam elements and a small beam length will produce an accurate prediction of the shape of service loop  802 . One implementation of method  1100  as a MATLAB™ computer program is provided in the CD-ROM Appendix. MATLAB™ is available from MathWorks of Natick, Mass. 
     Method  1100  starts in action  1102  (FIG.  11 ). In action  1102 , a user sets the departure point, the departure angle, the mounting point, the mounting angle, the number of beam elements, and beam stiffness. The user also provides initial values for the beam length and the magnitudes of the X and Y components of force  1216 . 
     In action  1104 , the computer determines if the beam element of the current iteration (“current beam element”) is the first beam element. If so, action  1104  is followed by action  1106 . Otherwise, action  1104  is followed by action  1110 . 
     In action  1106 , the computer sets the mounting point as the start position (e.g., point  1302  in FIG. 13) of the current beam element. In action  1108 , the computer sets the angle (“start angle”; e.g., θ s  in FIG. 13) at which the start of the current beam element is oriented. Actions  1106  and  1108  set mounting point and mounting angle as the start position and the start angle of the first beam element. Action  1108  is followed by action  1114 . 
     In action  1110 , the computer sets the end position (e.g., point  1304  in FIG. 13) of the beam element from the previous iteration (“previous beam element”) as the start position of the current beam element. In action  1112 , the computer sets the finish angle (e.g., θ f  in FIG. 13) of the beam element from the previous beam element as the start angle (e.g., θ s  in FIG. 13) of the current beam element. Actions  1110  and  1112  set the end position and the finish angle of the previous beam element as the start position and the start angle of the current beam element. Action  1112  is followed by action  1114 . 
     In action  1114 , the computer calculates the bending moment at the end of the current beam element. In one implementation, the bending moment is calculated with the following formula: 
     
       
           M   b =−( Y   e   −Y   p ) F   x +( X   e   −X   p ) F   y   
       
     
     where X e  and Y e  are the coordinates of the end position of the current beam without deflection (e.g., point  1303 ), X p  and Y p  are the coordinates of the pivot (i.e., tracking axis  806 ), (X e −X p ) is the moment arm for the X component, (Y e −Y p ) is the moment arm for the Y component, and F x  and F y  are the magnitudes of the X and Y components of force  1216 . 
     X e  and Y e  can be calculated with the following formula: 
     
       
           X   e   =X   s   +L  cos(θ s ) 
       
     
     
       
           Y   e   =Y   s   +L  sin(θ s ) 
       
     
     where L is the beam length, and X s  and Y s  are the coordinates of the start of the current beam element. 
     In action  1116 , the computer calculates the angular deflection (difference between the start and finish angles) of the current beam element from the bending moment. In one implementation, the beam elements are assumed to be so small that the effects of the X and Y components of force  1216  on the angular deflection are negligible. The formula for angular deflection thus becomes:          ∂   θ     =         M   b                   L     EI                     
     where ∂θ is the angular deflection and EI is the bending modulus (beam stiffness). 
     In action  1117 , the computer calculates the finish angle of the current beam element from the starting angle and the angular deflection using the following formula: 
     
       
         θ f =θ s ∂θ. 
       
     
     In action  1118 , the computer calculates the end position of the current beam element. In one implementation, the beam elements are assumed to be so small that the effects of beam deflection on the end position of an individual beam element are negligible. The formula for the beam end position thus becomes: 
     
       
           X   e′   =X   s   +L  cos(θ s ) 
       
     
     
       
           Y   e′   =Y   s   +L  sin(θ s ) 
       
     
     where X e′  and Y e′  are the coordinates of the end position of the current beam element with deflection (e.g., point  1304 ). 
     In action  1120 , the computer decides if the current beam element is the last beam element. If so, action  1120  is followed by action  1122 . Otherwise, action  1120  is followed by the previously described action  1110 . Thus, the computer cycles through method  1100  until it calculates the end position and the finish angle of the last beam element. 
     In action  1122 , the computer determines if the end position and the finish angle of the last beam element are approximately equal to the departure point and the departure angle. The end position and the finish angle are approximately equal to the departure point and the departure angle if they are within a predetermined tolerance. If not, action  1122  is followed by action  1124 . Otherwise, action  1122  is followed by action  1128 . 
     In action  1124 , the computer varies at least one of the beam length and the magnitudes of the X and Y components of force  1216 . Action  1124  is followed by action  1104 , where the computer cycles through method  1100  until it finds values for the beam length and the magnitudes of the X and Y components of force  1216  that produce an end position and a finish angle of the last beam element that are approximately equal to the departure point and the departure angle. 
     In action  1128 , the computer ends method  1100  because it has found a beam length and magnitudes of the X and Y components of force  1216  that place the end position and the finish angle of the last beam element at the departure position and the departure angle. The total length of service loop  802  is the product of the beam length and the total number of beam elements. Service loop  802  does not rotate actuator arm  102  away from its resting position if it conforms to the set mounting point, mounting angle, departure point, departure angle, beam stiffness, and the determined total length. 
     In the implementation using MATLAB™, method  1100  utilizes a function called “fminsearch” to find the minimum difference between the end position and the finish angle of the last beam element and the predetermined departure point and departure angle by varying at least one of the beam length and the magnitudes of the X and Y components of force  1216 . 
     After determining the shape of service loop  802 , a method  1400  (FIG. 14) can be used to calculate moment  1213  (“restoring torque”) exerted by service loop  802  against actuator arm  102  when it rotates away from its resting position. The restoring torque can be used to determine if a rotary driver (e.g., a voice coil) has enough power to rotate actuator arm  102  against service loop  802 . The restoring torque can also be used to select a resting position for actuator arm  102  that results in equal restoring torque when the actuator arm  102  rotates toward the ID or OD of medium  330 . This minimizes the maximum current and maximum motor torque requirement for the tracking motor in the optical drive. 
     Assuming the restoring torque is not zero, then the moment applied by actuator arm  102  to any point on service loop  802  becomes the sum of the moment generated by force  1216  in each beam element and the restoring torque (i.e., moment  1213 ). Thus, the bending moment at the end of the current beam element when actuator arm  102  is rotated away from its resting position becomes: 
     
       
           M   b =−( Y   e   −Y   p ) F   x +( X   e   −X   p ) F   y   +M   r , 
       
     
     where M r  is the restoring torque. 
     In one implementation, the restoring torque is represented as a moment generated by the Y component of force  1212  (which has the same magnitude as Y component of force  1216 ) that is offset from the pivot point (tracking axis  806 ). Thus, the bending moment to any point on service loop  802  becomes: 
     
       
           M   b =−( Y   e   −Y   p ) F   x +( X   e   −X   p )  F   y   +L   offset    F   y   
       
     
     or 
     
       
           M   b =−( Y   e   −Y   p ) F   x +( X   e   −X   p   +L   offset ) F   y , 
       
     
     where L offset  is the X direction offset of the Y component from tracking axis  806 . 
     Method  1400  is the same as method  1100  except: 
     (1) the departure point is moved with actuator arm  102  to the ID or OD of medium  330  (see FIGS.  9 A and  9 B); 
     (2) action  1103  (described below) replaces action  1102 ; 
     (3) action  1114  uses a new formula (described above) for calculating the bending moment; 
     (3) action  1125  (described below) replaces action  1124 ; and 
     (4) action  1126  (described below) is inserted between actions  1122  and  1128  when the end position and the finish angle of the last beam element are approximately equal to the departure point and the departure angle. 
     In action  1103 , the user provides an initial value for the offset of the Y component of force  1216  from tracking axis  806  when actuator arm  102  is located at the ID or OD of medium  330 . The user also provides initial values for the magnitudes of the X and Y components of force  1216 . The user further sets the mounting point, the mounting angle, the number of beam elements, the beam stiffness, and the beam lengths with the values previously provided and determined in method  1100 . The user also sets the departure point and the departure angle when actuator arm  102  is located at the ID or OD of medium  330 . In one implementation, the user sets the rotation angle of actuator arm  102  when it is located at the ID or OD and the computer calculates the corresponding departure point and the departure angle from the rotation angle and the physical dimensions of actuator arm  102 . 
     In action  1125 , the computer varies at least one of Y component offset and the magnitudes of the X and Y components. 
     In action  1126 , the computer calculates the restoring torque experienced by actuator arm  102 . The restoring torque is provided by the following formula: 
     
       
           M   r   =F   y   L   offset . 
       
     
     One implementation of method  1400  as a MATLAB™ computer program is provided in the CD-ROM Appendix. In the MATLAB™ implementation, method  1400  utilizes the previously mentioned “fminsearch” function to find the minimum difference between the end position and the finish angle of the last beam element and the predetermined departure point and departure angle by varying at least one of the Y component offset and the magnitudes of the X and Y components. 
     Although the invention has been described with reference to particular embodiments, the description is only an example of the invention&#39;s application and should not be taken as a limitation. For example, methods  1100  and  1400  can use the departure point as the starting point of the service loop and the mounting point as the ending point of the service loop. Furthermore, although only three of the input parameters are varied by the computer, a greater or lesser number of input parameters can be varied. Input parameters other than the magnitudes of the X and Y forces and the beam length or the offset of the Y force can be varied. In addition, although specific formulas for calculating moments and deflection are provided, other formulas and permutations can be used to calculate moment and deflection. Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention as defined by the following claims. 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 File Name 
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                 BETA_S˜1.M 
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