Title of Invention: Expandable surgical reaming tool Abstract: An expanding reamer for reaming or cutting a concave surface, for example, for reaming an acetabulum in preparation for implanting a prosthetic component during a hip arthroplasty. A rotating shaft cooperates with a surgical drill or other power source at one end and rotates a reamer head at the other end, and an actuation system expands one or more blades on the reamer head. The reamer head comprises one or more cutting blades, which act as segments of a cutting sphere, wherein the blades are expandable in directions non-parallel to the plane of the respective blades in order to enlarge the cutting sphere. Upon rotation of the reamer head, the blade(s) form a portion of an effective cutting sphere that is preferably greater-than-180-degrees; this allows greater flexibility in placement of the shaft of the reamer relative to the surface being reamed, for example, relative to the center of axis of the acetabulum. In one embodiment, two parallel blades move out away from each other and away from the rotational axis of the device, staying parallel to each other to become, in effect, more distanced, but still parallel, segments of a larger cutting sphere. In another embodiment, two blades start generally parallel to each other and to the rotational axis of the device, but pivot out from each other in directions generally perpendicular to their respective blade planes, again becoming more distanced, but not parallel, segments of a larger cutting sphere. Detailed Description: This application claims priority of U.S. application Ser. No. 11/137,123, filed May 24, 2005, and also claims priority of and incorporates by this reference U.S. application Ser. No. 60/749,968, filed Dec. 15, 2005. BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates generally to a reaming device and, more particularly, to an expandable reaming device that may be used for reaming an acetabulum in preparation for implanting a prosthetic component, such as an acetabular cup or socket during a hip arthroplasty. 2. Related Art The hip joint is a ball-and-socket joint formed by the articulation of the rounded, convex surface of the head of the femur with the cuplike acetabulum on the pelvis. In a healthy hip joint, the head of the femur and the acetabulum are lined by surface cartilage; the entire joint is surrounded by a capsule which has a thin lining of synovial cells that produce a thin layer of lubrication film called synovial fluid. The synovial fluid, together with the cartilage, acts as a shock absorber and allows the joint to move. If the surface cartilage is badly damaged, or if the joint surfaces are not aligned properly, then the cartilage will wear out, and as a result, the bone under the cartilage layer is exposed. The exposed bone starts to rub against each other and the process of osteoarthritis is established. Osteoarthritis is the result of mechanical wear and tear on a joint, in this case, the hip joint. The main indication is a loss of surface cartilage due to the bone rubbing on bone. The formation of bone spurs, called osteophytes and cysts around the joint is another indication of osteoarthritis. The body tries to relieve the pain from the rubbing of the bone by increasing the amount of fluid in the joint. In an arthritic hip, the cartilage lining is thinner than normal or completely absent; the capsule of the arthritic hip is swollen; the joint space is narrowed and irregular in outline; and/or excessive osteophytes can build up around the edges of the joint. The combination of these factors cause pain and will eventually result in the loss of motion of the hip. Hip arthroplasty is a surgery performed to replace all or part of a joint, deteriorated from osteoarthritis, with an artificial device in order to restore joint movement. There are different types of hip arthroplasty. If a hemi-arthroplasty is performed, either the femoral head or the acetabulum is replaced with a prosthetic device. In a total hip arthroplasty, both the femoral head and the acetabulum are replaced with prosthetic devices. Hip arthroplasty involves reforming the patient's natural acetabulum, so that a proper bearing surface for the ball of a femur is established in order to support the normal motion of the leg. The acetabulum needs to be reshaped so that it can properly receive a metallic or plastic artificial socket; typically osteophytes and other deteriorated and diseased bone are removed from within and around the acetabulum using a bone chisel, until healthy bone becomes visible. Typically, a reamer is used to accomplish this reshaping of the acetabulum, and reamer heads of increasingly larger size are required as bone is cut away and the socket is enlarged. Each time a larger reamer head is needed, the reaming system must be removed from the patient's acetabulum, the reamer head is removed from the drive shaft of the surgical drill, and the next larger reamer head is attached. This sequence may be repeated several times until the acetabulum is completely prepared to receive an acetabular prosthetic implant. The process of replacing reamer heads multiple times during a surgery is time consuming, inefficient, inconvenient, and may also lead to surgical errors in that the angle of acetabular penetration may not be accurately preserved during each reamer head substitution. Standard hip arthroplasty is typically performed using a posterolateral or anterolateral approach, with an incision of 25-30 cm in length (see FIG. 1A). The approach provides substantial exposure, and complete and continuous observation, of the hip. With this large incision, it is unlikely that the reamer will be off axis. However, this exposure comes at the expense of trauma to the muscle and tendons and of considerable postoperative pain, requiring inpatient stay and delay of postoperative physical therapy. Recently, minimally invasive (MIS) hip arthroplasty has been used as an alternative. MIS hip arthroplasty approaches include single-incision and 2-incision techniques, wherein each incision measures about 10 cm in length (see FIG. 1B). With the MIS techniques, a decrease in muscle and tendon trauma is achieved at the expense of not having complete and continuous observation of the hip. With a small incision, it is more difficult to place the acetabular reamer in direct alignment with the axis of the acetabulum. If the smaller incision is not exactly aligned with the acetabulum (see FIG. 2A), the reamer will be off axis relative to the axis of the acetabulum. If the reamer is off axis and the head of the reamer has hemispherical or less cutting capability (“180 degrees or less head”), it will be unable to cut a perfect hemisphere in the acetabular space (see FIG. 2B). A portion P of the acetabular space will be improperly reamed, or, more likely, not jamesbrown@example.com. Therefore, the inventor believes that there is still a need for an acetabular reamer that is expandable to eliminate the need for multiple reamers and a reamer head that is greater than 180 degrees to allow the surgeon to cut a perfect hemisphere even when the reamer is off axis. Issued patents relating to expandable acetabular reaming devices include the following: Fishbein (U.S. Pat. No. 3,702,611) discloses an expanding reamer including a head with a convex end adapted to seat in a previously-prepared concavity in the central part of the acetabulum; the head pivotally mounts a set of expansive blades and is telescopically mounted on the end of a rotary drive shaft. Temeles (U.S. Pat. No. 6,283,971) discloses an expandable acetabular reaming system having a plurality of blades that project or retract through a reamer head according to a desired reamer head size. The degree projection or retraction of the reaming blades is manually controlled by user actuation of an air bladder. SUMMARY OF THE INVENTION The present invention relates to an expandable reaming device for reaming, cutting, or drilling, which has one or more moveable blades for increasing the effective diameter of the reamer head. The expandable device may be adapted for reaming an acetabulum in preparation for implanting a prosthetic component, such as an acetabular cup or socket, during a hip arthroplasty. The preferred reaming device comprises blades or blade portions that, individually or together, provide a greater-than-180-degree cutting edge(s), so that, upon rotation of the reamer head, the device may ream a hemisphere in a surface even if the rotational axis of the device is not parallel to the axis of the concave surface being reamed/cut. During a hip arthroplasty, this offers greater flexibility in placement of the shaft of the reaming device relative to the center of axis of the acetabulum, and, hence, is advantageous for MIS hip arthroplasty Preferred embodiments of the invention comprise at least one generally plate-shaped cutting blade that acts as a segment of a sphere, wherein the reamer head is expandable to a greater cutting diameter by said segment being moved in a direction that is non-parallel to the plane of the segment. Thus, said segment becomes a segment of a sphere with a greater diameter, and, hence, reams to a larger diameter, preferably a larger hemisphere or greater-than-hemisphere. Preferably, said at least one blade is positioned so that its plane is generally parallel to the rotational axis of the reaming device, so that, upon rotation around the central axis, the blade cuts a sphere/partial sphere. Moving the cutting blade out in a direction exactly or substantially perpendicular to its plane makes the blade serve, without enlarging the diameter of the blade, as a segment of a larger sphere, and, hence, upon further rotation around the rotational axis of the device, it reams/cuts a larger sphere/partial sphere. Thus, instead of pivoting or tipping a blade out in a plane parallel to its own blade plane, as in several of the reaming heads of the prior art, the invented blade moves in a direction non-parallel, and preferably generally perpendicularly, to its own plane and reams/cuts a perfect or nearly perfect sphere or partial sphere. “Generally perpendicularly” may range from exactly perpendicularly to substantially perpendicularly, wherein the major vector of movement of the blade from its starting/contracted position is in a direction perpendicular to the blade plane. Included in substantially perpendicularly is a blade that starts generally parallel to the rotational axis and pivots out and down at its top in a direction perpendicular to the blade plane. Many embodiments of the reaming device comprise a drill bit on a rotating shaft for cooperating with a surgical drill or other power unit, a plurality of blades connected directly or indirectly to the rotating shaft, and a gearing system or other actuation system adapted to expand the moveable blades. In one preferred embodiment, the moveable, “expanding blade(s)” comprise two parallel blades that remain parallel to each other and to the rotational axis throughout expansion, the blades each being greater than 180 degrees in circumference and each generally forming a segment of a sphere. As the expanding blades move outward, perpendicularly to their respective blade planes, the effective diameter of the reaming head increases and the reaming head may ream/cut increasingly larger-diameter partial spheres. The expanding blades are preferably raised as they are moved outward, to maintain the effective reaming/cutting shape of the reaming head very close to a perfect partial sphere. The two expanding blades may be located on either side of, and parallel to, a central blade passing through the axis of rotation of the device. A transverse blade is preferably positioned perpendicular to the expanding blades and the central blade, and centered so that it also passes through the axis of rotation of the device. The central blade and/or the transverse blade may also be used for reaming/cutting, especially reaming/cutting of the bottom region of the concave surface being formed, and especially after the moveable blades have been expanded outward. The preferred expanding blades move out along the transverse blade, guided by ramps in or on the transverse blade that raise the blades at the same time they are expanding. In an alternative embodiment, two expanding blades start, when the reamer head is contracted, generally parallel to the rotational axis of the device, and then expand by pivoting out and down generally perpendicularly to their respective blade planes. Thus, the two blades, at the start of reaming, are generally parallel, and are pivoted generally outward during expansion to become non-parallel to each other and non-parallel to the rotational axis. The blades preferably are each greater than 180 degrees in circumference and each generally form a segment of a sphere. As the expanding blades move outward, the effective diameter of the reaming head increases and the reaming head may ream/cut increasingly larger-diameter partial spheres. The expanding blades maintain the effective reaming/cutting shape of the reaming head very close to a perfect partial sphere throughout expansion. In the pivoting blade embodiment, a transverse blade(s) is(are) preferably positioned perpendicularly to the expanding blades, and centered to pass through the axis of rotation of the device. The transverse blade(s) may serve as support guides for the moveable/expandable blades, and may also contribute a reaming/cutting edge(s). For example, when the reamer head is fully-contracted, a substantial portion of the transverse blade edge preferably will be positioned where it will ream/cut, thereby supplementing the action of the moveable blade cutting edges. After expansion, as the transverse blade preferably does not expand, the transverse blade will typically cut only a small portion of the bottom region of the concave surface being formed, while the expandable blades will cut the majority of the concave surface being formed. BRIEF DESCRIPTION OF THE DRAWINGS In the following drawings, gear teeth and threads are not drawn, but are understood when parts are described by the terms “gear”, “teeth”, “threads,” “threaded,” “toothed surfaces,” or “threaded surfaces.” FIG. 1A is a front/anterior view of the standard incision made during a total hip arthroplasty. FIG. 1B is a front/anterior view of the new incision made during a minimally invasive total hip arthroplasty. FIG. 2A is a schematic illustrating the standard acetabular reamer when the reamer is aligned with the axis of the acetabulum. FIG. 2B is a schematic illustrating the standard acetabular reamer when the reamer is not aligned with the axis of the acetabulum. FIG. 3 is a perspective view of one embodiment of the invented reaming device. FIG. 4A is a front view of the embodiment shown in FIG. 3, with the rear view being the same due to the preferred symmetry of the device. FIG. 4B is a right side view of the embodiment shown in FIGS. 3-4A, with the left view being the same due to the preferred symmetry of the device. FIG. 4C is a top view of the embodiment of FIG. 4A, used to show the direction of cross-sectional views for FIGS. 5A and 5B. FIG. 5A is a right side cross-sectional view of the embodiment shown in FIGS. 3-4B, viewed along the line 5A-5A in FIGS. 4A and 4C. FIG. 5B is a rear cross-sectional view of the embodiment shown in FIGS. 3-5A, viewed along the line 5B-5B in FIGS. 4B and 4C. FIG. 6 is an enlarged version of the right side cross-sectional view of FIG. 5A. FIG. 7 is a partial exploded view of the embodiment shown in FIGS. 3-6B, featuring the planetary transmission system used for adjusting the moveable blades. FIG. 8A is a bottom view of the bottom plate of the embodiment shown in FIGS. 3-7. FIG. 8B is a side view of the bottom plate of the embodiment shown in FIGS. 3-8A. FIG. 8C is a top view of the bottom plate of the embodiment shown in FIGS. 3-8B. FIG. 9 is a side view of the central rod of the embodiment shown in FIGS. 3-8C. FIG. 10A is a side view of the head of the reamer of the embodiment shown in FIGS. 3-9. FIG. 10B is a cross-sectional view of the head of the reamer of FIGS. 3-9, viewed along the line 10B-10B in FIG. 10A. FIG. 10C is a cross-sectional view of the head of the reamer of FIGS. 3-9, viewed along the line 10C-10C in FIG. 10A. FIG. 10D is a cross-sectional top view of the head of the reamer of FIGS. 3-9, viewed along the line 10D-10D in FIG. 10A. FIG. 11A is an exploded view of the head of the reamer of the embodiment shown in FIGS. 3-10D. FIG. 11B is a front exploded view of the head of FIG. 11A. FIG. 12A is a front view of the worm of the embodiment shown in FIGS. 3-11B, wherein the worm is drawn without its teeth and threads. FIG. 12B is an end view of a worm gear of the embodiment shown in FIGS. 3-12A, wherein the worm gear is drawn without its teeth. FIG. 13A is a front view of the central blade and guide blade combination of the embodiment shown in FIGS. 3-13A. FIG. 13B is a cross-sectional view of the central blade of the embodiment shown in FIGS. 3-12B, viewed along the line 13B-13B in FIG. 13A. FIG. 14 is a top view of the central blade and guide blade of the FIG. 13A. FIG. 15A is a first side view of the gear plate of the embodiment shown in FIGS. 3-14. FIG. 15B is a top view of the gear plate of FIG. 15A. FIG. 15C is a second (opposing) side view of the gear plate of FIGS. 15A and B. FIG. 15D is an end view of the gear plate of FIGS. 15A-C. FIGS. 16A-16E are front views of the reamer head of the embodiment shown in FIGS. 3-15D, as the cutting blades are expanding (from 16A to 16E). FIG. 17A is a schematic top cross-sectional view of a fully-contracted reamer head, showing in dashed lines the effective cutting diameter of the head. FIG. 17B is a schematic top cross-sectional view of the reamer head of FIG. 17A (same size and same diameter blades) in a fully-expanded condition, again showing in dashed lines the larger effective cutting diameter of the head. FIG. 18A is a schematic illustrating a generalized embodiment of the invented acetabular reamer during use when the reamer is aligned with the axis of the acetabulum. FIG. 18B is a schematic illustrating a generalized embodiment of the invented acetabular reamer during use when the reamer is not aligned with the axis of the acetabulum. FIG. 19 is a front perspective view of an alternative embodiment of the invented reamer, with the reamer head contracted. FIG. 20 is a front perspective view of the embodiment of FIG. 19, with the reamer head expanded. FIG. 21 is a right perspective view of the embodiment of FIGS. 19 and 20, with reamer head expanded. FIG. 22 is a top perspective view of the embodiment of FIGS. 19-21, with reamer head expanded. FIG. 23 is a bottom perspective view of the embodiment of FIGS. 19-22, with reamer head expanded. FIG. 24A is a front view of the shaft unit of the embodiment of FIGS. 19-23, which comprises a rotational shaft for connection to a power unit, and a transverse blade connected to the lower end of the rotational shaft. FIG. 24B is a cross sectional view of the transverse blade of FIG. 24A, viewed along the line 24B-24B in FIG. 24A. FIG. 24C is a right side view of the shaft unit of FIGS. 24A and B. FIG. 24D is a cross-sectional view of the transverse blade of FIGS. 24A-C, viewed along the line 24D-24D in Figure FIG. 24C. FIG. 24E is a top view of the shaft unit of FIGS. 24A-D. FIG. 25A is a view of an expanding blade of the reamer of FIGS. 19-23. FIG. 25B is a side edge view of the blade of FIG. 25A. FIG. 25C is a top edge view of the blade of FIGS. 25A and B. FIG. 25D is a cross-sectional view of the blade of FIGS. 25A-25C, viewed along the line 25D-25D in FIG. 25B. FIG. 26A is a front view of a pivot arm of the embodiment of FIGS. 19-23. FIG. 26B is a side view of the pivot arm of FIG. 26A. FIG. 26C is a bottom view of the pivot arm of FIGS. 26A and B. FIG. 27A is a schematic side cross-sectional view of a fully-contracted reamer head of the type of FIGS. 19-26C, showing the effective cutting diameter/sphere of the head in dashed lines. FIG. 27B is a schematic side cross-sectional view of the reamer head of FIG. 27B (same size/diameter blades) in a fully-expanded condition, again showing in dashed lines the larger effective cutting diameter/sphere of the head. FIG. 28A is a schematic illustrating a generalized embodiment of the invented acetabular reamer of FIGS. 19-27B when the reamer is aligned with the axis of the acetabulum. FIG. 28B is a schematic illustrating the generalized embodiment of the invented acetabular reamer of FIGS. 19-27B when the reamer is not aligned with the axis of the acetabulum. FIGS. 29A and B illustrate a spherical cap and a spherical segment, respectively, which are representations according to conventional geometry terminology. Many embodiments of the expandable blades used in embodiments of the invention may therefore be called thin segments, which, upon rotation, from a cutting sphere or a cutting sphere with a spherical cap removed (due to space being allocated for the rotational system/shaft). FIGS. 30A and 30B illustrate what may be called herein the “plane” of a cutting segment. DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to the figures, there are shown several, but not the only, embodiments of the invented expandable reaming device. While the preferred embodiments are especially-well adapted for reaming an acetabulum in hip arthroplasty, the preferred or other embodiments may be useful for other reaming, cutting, and drilling applications, both in the human body, animals, and/or other applications including non-surgical applications. Therefore, the terms “reaming,” “cutting,” and “reaming device” are not intended to limit the invented device to a particular medical procedure. FIGS. 1A and B, and 2A and B illustrate prior art surgical techniques for hip arthroplasty. FIGS. 3-15C illustrate one embodiment of the invented reaming device and pieces-parts thereof. FIGS. 16A-E, and 17A and B schematically illustrate the preferred expansion structure and methods of the embodiment of FIGS. 3-15C, and FIGS. 18A and 18B schematically illustrate an embodiment such as that is FIGS. 3-15C in use reaming the acetabulum. FIGS. 19-26C illustrate an alternative embodiment, which has additional benefits because of its simplicity of manufacture and use, and FIGS. 27A and 27B schematically illustrate expansion of the embodiment of FIGS. 19-26C. FIGS. 28A and 28B schematically illustrate an embodiment such as that is FIGS. 19-26C in use reaming the acetabulum. FIGS. 29A and 29B illustrate the geometry of a spherical cap and spherical segment, and FIGS. 30A and 30B (and also FIGS. 27A and 27B) illustrate what may be called herein the “plane” of the cutting segment, or “blade plane.” In general, the preferred reaming device may be described as an elongated tool having a reamer head at one end and a bit or other connection or handle for receiving power at the opposing second end. The reaming device has expandable blades that may be actuated from at or near the second end of the device so that the surgeon may do so while the reamer head is inside the patient. The expansion actuation may be done by a gear system that transmits rotation of a knob or other control member near the second end of the device to rotation of an elongated member that is preferably coaxial with the central axis of the device and that extends down to the reamer head. In the embodiment of FIGS. 3-15C, said elongated member operates a worm gear assembly in or near the reamer head that transmits rotation of the elongated member to rotation of at least one worm at 90 degrees to the central axis of the device. This rotation, at 90 degrees to the central axis of the device, can be used to move the expandable blades in and out in a direction transverse to the central axis. Preferably, multiple cutting blades are provided, wherein at least one has a cutting edge extending greater than 180 degrees, or wherein said multiple cutting blades have a group of (multiple) cutting edges that together total greater than 180 degrees. Said cutting edge is, or said group of cutting edges totals, preferably 200-270 degrees, or more preferably 220-250 degrees. Alternatively, a combination of two or more blades may have cutting edges that, when the reamer head is rotated 360 degrees, together are capable of cutting greater than a hemisphere, preferably 200-270 degrees, or more preferably 220-250 degrees. This way, no matter what the orientation of the reamer head in the acetabulum, the reamer head can cut approximately a hemisphere to receive the hemispherical prosthetic socket. See FIGS. 18A and 18B. The expansion of the reamer head is done with preferred structure and methods that provide extremely accurate reaming of various hemispherical diameters. At least one of the preferred moveable cutting blades serves as a segment of the “cutting sphere” (more precisely, a segment of a sphere with a spherical cap removed). See FIGS. 29A and B. When the segment is moved outward in a direction that is non-parallel to its plane, the segment becomes a segment of a larger sphere, and, hence, “expands” the sphere, or, in other words, “expands” the effective size of the sphere created by rotating the reamer head. In many embodiments of the invention, the cutting blades may be said to move transversely or generally transversely relative to the axis of rotation of the reaming head and/or transversely or generally transversely (perpendicularly or generally perpendicularly) to its own plane, wherein “its own plane” is illustrated in FIGS. 27 A and B and 30A and B as the central plane through the typically plate-like segment/blade. While the blades need not be perfectly plate-shaped or have perfectly planar front or back surfaces, and the blades may have various thicknesses, the blades will tend to be generally plate-like and, hence, be describable as having a “central plane” or “blade plane.” Upon moving in a direction non-parallel to its plane, the same segment (and hence, the same blade) becomes a segment of a larger cutting sphere. Therefore, by moving at least one “cutting segment” outward, the effective spherical diameter of the rotating reamer head increases so that the diameter of the reamed surface also increases. In the embodiment of FIGS. 3-15C, two of these blades acting as “cutting segments” are provided, parallel to each other and moveable outward on opposite sides of the head. The preferred segments each have a leading cutting edge(s) that total greater than 180 degrees on a single radius (being portions of a circumference). This provides a set of two greater-than-180-degree blade cutting edges, following the same rotational path, but on opposite sides of the head, for providing a balanced head and for increasing the total length of cutting edge. The circular edge of each of the segments is mainly for reaming the “sides” S of the acetabulum (FIGS. 18A and B), especially as the segments are moved out from the central axis of the reamer head, because, in effect, they rotate around the central axis of the head a distance from the axis. The circular edge of an additional blade extending parallel to and through the central axis is used for cutting the “bottom” B of the acetabulum in FIGS. 18A and B, that is, the curved bottom surface of the acetabulum (starting from the center axis of the head and extending out a distance generally equal to said distance of the cutting segments from the axis). In the preferred reamer head of FIGS. 3-15C, two blades are provided that extend parallel to and through the axis of rotation and that are preferably perpendicular to each other. One or both of these blades, or portions of one or both of these blades may be sharpened or otherwise shaped for cutting/reaming the bottom B. One or both of these blades should have edges or portions or their edges that together or individually, upon a revolution of the reamer head, ream the bottom B in the area from the central axis of the tool to the radial location of the cutting segments. One or both may have a portion that, instead of cutting, mainly moves bone material out of the way after it has been cut from the acetabulum by the other blades. See FIGS. 18A and 18B, illustrating the “sides” S portions and “bottom” B portion of the acetabulum, wherein these portions change depending on the orientation of the device in the acetabulum. Also, these portions will change as the reamer head is expanded (not shown in FIGS. 18A and B). The portion of the acetabulum being reamed by the blade(s) extending through the central axis will increase, while the portion being reamed by the cutting segments will decrease. The cutting segment structure and method of expanding the reamer head may be better understood by viewing FIGS. 16A-E, which show progressive stages of expansion of blades such as those in FIGS. 3-15C, and FIGS. 17A and B, in which the expansion is exaggerated, compared to that normally desired in a surgical reaming device, for the sake of clarity. In FIGS. 17A and B, the moveable blades are called-out as 25′ and 35′, the central blade is called-out as 30′, and the transverse blade is called-out as 20′. Alternatively, blades may move, in other ways and in direction(s) that are non-parallel to their planes. For example, blades may move perpendicularly or generally perpendicularly to their respective planes by pivoting in directions that are not parallel to their respective planes. Also, alternative actuation systems may be used for expanding the blades. One such embodiment illustrating pivoting blades and an alternative actuation system is illustrated in FIGS. 19-26C, with its operation illustrated schematically in FIGS. 27A, B, and 28A and B. For example, a member on the outside of the rotating shaft system may force at least one pivot arm down to expand at least one expandable blade. In the embodiment of FIGS. 19-26C, preferably a first and second of said pivot arms are linked to the sleeve member at their upper ends, and are linked to first and second expandable blades, respectively, at their lower ends. Upon pushing the sleeve down to push the upper ends of the pivot arms down parallel to the rotational axis of the reamer, the pivot arms expand and the expandable blades expand. In reverse, pulling upwards on the sleeve will raise the upper ends of the pivot arms, contract the lower ends of the pivot arms and contract the expandable blades. Each blade is generally a plate having a blade plane, and each blade has a pivot axle parallel to its plane and near its bottom edge. As previously discussed herein, the blades need not be perfectly plate-shaped or have perfectly planar front or back surfaces, and the blades may have various thicknesses, but the blades will tend to be generally plate-like and, hence, be describable as having a “central plane” or “blade plane.” Each blade pivots on its pivot axle so that the blade above the pivot axle swings outward away from the rotational axis of the reamer and the blade below the pivot axle swings inward toward the rotational axis. See FIGS. 27A and B for schematic representations. Because the pivot axles are so near the bottom edges of their respective blades and near the bottom of the reamer, the blades may be described as expanding by pivoting substantially outward in a direction perpendicular to their planes. Preferably, the pivot axles are located on the blade in the range of ¼-⅙ (and more preferably about ⅕) of the way up the blade from the blade bottom edge, so that from ¾ to ⅚ of the blade pivots outward away from the rotational axis and only ¼-⅙ of the blade pivots inward toward the rotational axis. Thus, it may be said that a substantial portion of the blade pivots outwards away from the rotational axis. Said at least one (and preferably two) expandable blade(s) has(have) a cutting edge extending greater than 180 degrees, or a group of cutting edges that together total greater than 180 degrees. Said cutting edge is, or said group of cutting edges totals, preferably 200-325 degrees, or more preferably 250-330 degrees, so that, when the blades are pivoted outwards and their top edges are, in effect lowered, most of the top edges are still capable of reaming and greater than a hemisphere may be reamed. Alternatively, a combination of two or more blades may have cutting edges that, when the reamer head is rotated 360 degrees, together are capable of cutting greater than a hemisphere, preferably 200-325 degrees, or more preferably 250-330 degrees. This way, no matter what the orientation of the reamer head in the acetabulum, the reamer head can cut approximately a hemisphere to receive the hemispherical prosthetic socket. See FIGS. 28A and 28B. As in the case of the description of the embodiment of FIGS. 3-17B, when the phrase “no matter what the orientation of the reamer head in the acetabulum” is used, it is understood that this refers to the orientations that would typically result from hip arthroplasty, including those resulting from both standard “large incision” arthroplasty and “small incision” MIS arthroplasty. The expansion of the reamer head of FIGS. 19-26C is done with preferred structure and methods that provide extremely accurate reaming of various hemispherical diameters. At least one, and preferably two, of the preferred moveable cutting blades serves as a segment of the “cutting sphere” (more precisely, a segment of a sphere with a spherical cap removed). When the segment is moved outward by pivoting out transversely to the plane of the segment/blade, that same segment, in effect, becomes a segment of a larger cutting sphere. Therefore, as discussed above, moving at least one “cutting segment” outward, the effective spherical diameter of the rotating reamer head increases so that the diameter of the reamed surface also increases, and a larger cutting sphere is created that is extremely accurate. In the embodiment of FIGS. 19-26C, two of these blades acting as “cutting segments” are provided, at first generally parallel to each other (when completely contracted), and moveable outward on opposite sides of the head, by pivoting away from each other at their top ends. The preferred segments each have a leading cutting edge that totals greater than 180 degrees on a single radius (being a portion/portions of a circumference). This provides a set of two greater-than-180-degree cutting edges, following the same rotational path, but on opposite sides of the head, for providing a balanced head and for increasing the total length of cutting edge. The circular edge of each of the segments is mainly for reaming the “sides” S of the acetabulum (See FIGS. 28A and B), because they rotate around the central axis of the head a distance from the axis. The circular edge of an additional blade extending parallel to and through the central axis is also used for cutting/reaming. The preferred reamer head of FIGS. 19-26c is made so that the transverse blade diameter is the diameter of the sphere of which the two expandable blades are segments when in the fully-contracted condition. Therefore, when the head is fully-contracted, the transverse blade and also the expandable blades are all cutting/reaming. Then, as the head is expanded, the expandable blades “take over” as they define the diameter of the cutting sphere, rather than the transverse blade. Even when the head is expanding/expanded, however, a portion of the transverse blade will continue to cut/ream and, hence define a portion of the concave surface being formed by the device, that is, the “bottom” B of the acetabulum. See FIGS. 27A, 27B, 28A, and 28B. With this embodiment, bottom B is a very small curved bottom surface portion of the acetabulum, as it is cut by the transverse blade portion that is between the rotational axis and the portions of the cutting segment bottom edges that are on the “cutting sphere surface” and so are positioned properly to ream. Because the bottom edges of the cutting segments are so close to the central axis in this embodiment, whether contracted or expanded, said distance is very short. Therefore, the reaming sphere “surface” is created by a very small portion of the rotating transverse blade edge and the majority of the rotating cutting segment edges, and, hence, is nearly a perfect sphere. Of note here is that the bottom edges of the cutting segments move closer to the center axis as the blades are expanded, and so, while the bottom extremity of the blades moves slightly in and up relative to the central axis, the portions of the blade that are on the cutting sphere and, therefore, are reaming, are still just above the bottom extremity and are close to the central axis. See FIGS. 27A and B, and FIGS. 28A and B. The cutting segment structure and method of expanding the reamer head of FIGS. 19-26C may be better understood by viewing FIGS. 27A and 27B, which show the fully contracted condition and an expanded condition of blades such as those in FIGS. 19-26C. In FIG. 27A, 6 centimeter diameter blades B create an approximately 6.2 centimeter diameter cutting sphere C upon rotation of the blades. In FIG. 27B, the same 6 centimeter diameter blades are expanded by pivoting, forming approximately a 7.3 centimeter diameter cutting sphere C. The cutting spheres C are shown in FIGS. 27A and 27B as two dimensional, for ease of illustration, but it is understood that the cutting spheres are formed by rotation of the reaming head and, hence, are three dimensional (spheres rather than circles). Blade planes BP, rotational axis RA, sphere center SC, and the bottom portion of the transverse blade BT are also shown in FIGS. 27A and 27B. Referring specifically to FIGS. 3-15C: As shown in FIG. 3, the preferred embodiment of the invented expandable reamer 100 comprises a rotating shaft 5; a drill bit 10 on one end of the rotating shaft 5 for cooperating with a surgical drill; an expansion control rod 15 inside said rotating shaft 5; a reamer head 150 comprising three cutting blades 25, 30, 35 and a transverse guide blade 20 operationally connected to the rotating shaft 5; a knob 40 for actuating a gearing system and the expansion control rod 15 to expand radially at least one and preferably two of the cutting blades to be the “cutting segments” described above. Preferably, a portion of the rotating shaft 5, with the expansion control rod 15 inside the shaft, is contained within a handle sleeve 1 that floats freely on the outside of the main shaft 5 for being grasped by the surgeon. As shown in FIGS. 5A, 5B, 6, and 7 to best advantage, the drill bit 10 is rigidly connected to the rotating shaft 5, and the rotating shaft is preferably rigidly connected to the central cutting blade 30, wherein “connected” may imply a direct connection, or an indirect connection including intermediate or intervening connectors. For example, as illustrated in FIGS. 5A, 5B, 6, and 7, the drill bit 10 is rigidly connected to tubular shaft portion 5′, which is rigidly connected to top plate 45. Top plate 45, as is further discussed later in this Description, is rigidly connected to bottom plate 42 (for example, by screws), which is rigidly connected to the main shaft 5. Thus, drill bit 10, tubular shaft portion 5′, top plate 45, bottom plate 42, and main shaft 5 collectively may be called the rotational shaft system of this embodiment. Main shaft 5 is rigidly connected to the guide blade 20, which is preferably fixed to and perpendicular to the central blade 30, and the expandable blades 25, 35 ride on worms mounted in the central blade 30 and are guided by sloped channels 22, 24 in the guide blade 20. In operation, a power unit (may be a conventional, hand-held, surgical reaming power unit, for example, not shown) connected to the drill bit 10 serves to rotate the entire reaming device 100, including the expansion actuation system (knob 40, planetary gear system 41, control 15, and worm gear system) but with the exception of the floating sleeve 1. The sleeve 1 is gripped in the surgeon's hand for stabilizing and guiding the reaming device 100 but does not interfere with rotation of the device 100. Typically, the surgeon will grasp the power unit in one hand and the sleeve 1 in the over. Rotating the bit 10 rotates the shaft 5, which rotates the entire reamer head 150, with power being transmitted from the power unit to the reaming head via the rotational shaft system (drill bit 10, tubular shaft portion 5′, top plate 45, bottom plate 42, and main shaft 5). When expansion is desired, rotation is stopped, and the expansion actuation is operated relative to the rotational shaft system to expand the blades, all without removing the reaming head from the patient. With one hand on the power unit, the surgeon may rotate the knob 40 with his other hand to actuate blade expansion. The surgeon may then return to reaming by returning his non-power-unit-grasping hand to the sleeve for guiding and stabilizing the reaming device 100. As illustrated to best advantage in FIGS. 4A and 4B, each of the three parallel cutting blades 25, 30, 35 has an outer circumference curving on its respective single radius and is greater than 180 degrees (preferably 200-270 degrees, and more preferably 220-250 degrees), so that, when the reamer head is rotated, the cutting blades 25, 30, 35 are capable of cutting/reaming a portion of a sphere 200 that is 180 degrees or greater than 180 degrees. More precisely, in the preferred application, the sphere portion 200 is capable of cutting/reaming a hemisphere in the acetabulum even when off-axis relative to the acetabulum. As discussed above, knob 40 may be rotated relative to the rotational shaft system in order to actuate the gearing system that expands cutting blades 25, 35. Knob 40 is typically operated only when the user has stopped rotation of the shaft 5 and the reamer head 150. The knob 40 is preferably manually operated, whereby, as shown in FIGS. 5A, 5B, 6 and 7, turning knob 40 relative to the rotational shaft system serves to rotate the planetary gear system housed in the interior space of the knob, which in turn rotates the control rod 15, which in turn operates the gearing system in the reaming head, as further detailed below. As shown in FIGS. 5A, 5B, 6 and 7, a top plate 45, planetary gear system 41, and an indicator disk system are housed within knob 40, with bottom portions of the planet gears rotationally supported in bottom plate 42 (see FIGS. 7, 8A-8C). As shown in FIG. 7, the planetary gear system 41 comprises a system of spur gears in which the toothed inner surface 146 of an outer gear ring 46 turns three inner planet gears 47, 48, and 49, which in turn drive a central sun gear 50. The outer perimeter of the gear ring 46 is rigidly attached to the bottom of the knob 40, and the sun gear 50 is rigidly connected to the expansion control rod 15 (see FIGS. 7 and 9). The three planet gears 47, 48, and 49 each comprise a bottom portion 47′, 48′, and 49′, toothed portion 147, 148, and 149 for meshing with the toothed inner surface 146 of the ring 46 and the toothed outer surface 150 of the sun gear, a sleeve portion 47″, 48″, and 49″, and a top portion 47′″, 48′″, and 49′″. In the preferred embodiment, the gear ring 46, the toothed portion 147, 148, and 149 and the sleeve portion 47″, 48″, and 49″, and the sun gear 50 are contained between the bottom plate 42 and top plate 45. Preferably, the bottom plate 42 and top plate 45 each contain six apertures: three apertures 43 for the planet gears 47, 48, 49 and three apertures 44 for screws to hold the bottom plate 42 and top plate 45 together. The bottom portions 47′, 48′, and 49′ of the planet gears insert into the apertures 43 in the bottom plate 42, the top portions 47′″, 48′″, and 49′″ extend up through the apertures in the top plate 45 and through planet gear apertures 43 in the indicator disk 52. The two plates 42 and 45 are held together by screws (not shown) which insert into the screw apertures in the top and bottom plates 45, 42. The two plates 42 and 45 are separated by the sleeve portions 47″, 48″, and 49″ on the planet gears to allow room for the gear ring 46 and planet gears 47, 48, 49 to rotate. In the preferred embodiment, one of the planet gears 49 is threaded on its top portion 49′″. The indicator disk 52 threadably engages the top portion 49′″ while the other two planet gears 47 and 48 merely pass through the apertures 43 in the indicator disk without engaging the disk 52. The knob 40 comprises one or more viewing windows 54 for viewing the indicator disc 52. As the knob 40 is turned, the gear ring 46 also turns, in turn rotating the planet gears 47, 48, and 49, which rotate the sun gear 50, which rotates the rod 15, in turn expanding the two outer cutting blades 25 and 35 via a worm gear system such as will be discussed below. As the planet gears 47, 48, and 49 are rotating, the preferred indicator disk 52 rides up and down on the threaded planet gear top end 49′″, with how far it moves indicating how far the blades 25, 35 have expanded. There may be indicia on the knob 40 surface outside the viewing window(s) 54 to allow the surgeon to know exactly how far out the blades 25 and 35 have moved. Further, the indicating disk may be a color, such as red or another easily-visible color, to aid in seeing the indicator disk 52 through the viewing window 54. Additionally, the knob 40 may be fitted with traction bumps 56 to aid in gripping and turning the knob 40. The expansion control rod or “center rod” 15 preferably extends down from the sun gear 50 through the shaft 5 and is coaxial and fixed with the center of a worm gear 60 (see FIGS. 5, 6A-6B, 10A-D, and 11A). Preferably, the worm gear 60 is right hand threaded to mesh with two center toothed portions 62, 64 on two cooperating worms 63, 65. The two center portions 62, 64 of the worms 63, 65 are rotatably mounted in, or otherwise extending through, the central blade 30. Preferably, worm 63 has left hand threads on one of its ends 63′ and right hand threads 63″ on the other of its ends (FIGS. 10D and 11A). The threads on the two ends of worm 65 are oriented to be opposite those of worm 63, so that end 65′ of worm 65 has right hand threads, and end 65″ of worm 65 has left hand threads. FIGS. 13A-13B and FIG. 14 illustrate the relationship between the guide blade 20 and the central blade 30. The central blade 30 and the guide blade 20 are perpendicular to one another, as shown in FIG. 14. One or both of them may have sharp edges, so that they are adapted to aid in cutting, and one or both cut/ream bottom B of the acetabulum, as shown in FIGS. 18A and 18B. One or both of blades 20, 30 is/are useful in moving debris (i.e. cut bone or other material) out of the way. Preferably, the radius of curvature for both the guide blade 20 and central blade 30 is designed to be the radius of the smallest hemisphere that is to be cut in the acetabulum; in this case the smallest radius of curvature is 45 mm, however other sizes may be used. As shown in FIGS. 11B and 13B, the guide blade 20 comprises channels 22, 24, which, for the preferred head 150 that expands from a diameter of 45 to 53 mm, are at a 21 degree slope, that is, at an angle 21 degrees from a plane that is perpendicular to the axis of rotation. As shown in FIGS. 11A and 11 B, two gear plates 66, 68 threadably engage over the ends of the worms 63, 65. The gear plates 66, 68 comprise threaded cylinders 67, 69 for receiving the ends of the worms 63, 65. Preferably, the gear plates 66, 68 comprise two slightly flared edges 70, 71 for being inserted into a mortise 72, 73 (see FIG. 11A) on the cutting blades 25, 35 similar to the connection used in a dovetail joint. Other slidable connection means
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