Fine positioning device and displacement controller therefor

Abstract: A fine positioning device is formed of a central rigid portion (15), a first set of outwardly-extending portions (16a,16b) extending symmetrically along a first axis from the central rigid portion (15), a second set of outwardly-extending portions (17a,17b) extending symmetrically from the central rigid portion (15) along a second axis which is perpendicular to the first axis, a first set of parallel flexible-beam displacement mechanisms (16F xa ,16F xb ) provided symmet­ rically to each other with the first set of outwardly-­ extending portions (16a,16b) respectively to produce translational displacements along the second axis, and a second set of parallel flexible-beam displacement mechanisms (17F ya ,17F yb ) provided symmetrically to each other with the second set of outwardly-extending portions (17a,17b) respectively to produce transla­ tional displacements along the first axis. A displace­ ment controller for the fine positioning device is also disclosed.

Description: This invention relates to a fine positioning device suitable for use in an apparatus which requires fine adjustment on the order of micrometers, such as semiconductor fabrication apparatus or electron microscope. Description of the Prior Art: In various fields of technology, there has recently been a strong demand for devices which enable fine adjustment of displacements on the µm order. As a typical technical field, may be mentioned semiconductor fabrication apparatus employed in the fabrication processes of LSI (large-scale integrated circuits) and super large-scale integrated circuits, such as mask aligners, electron-beam drawing machines and the like. In these apparatus, it is necessary to achieve fine positioning of the µm order. The degree of integration increases and products of higher performance can be fabricated, as the positioning accuracy is improved. Such fine positioning is required not only for the above-described semiconductor fabrication apparatus but also for a variety of high-magnification optical apparatus, led by electron microscopes, and the like. Improved accuracy contributes significantly to the development of advanced technology such as biotechnology, space development, etc. As such fine positioning devices, a variety of devices have heretofore been proposed, for example, as shown in a Japanese magazine, "Kikai Sekkei (Machine Designing)", 27(1) , 32-36, January 1983. Of such fine positioning devices, those making use of parallel springs and fine motion actuators are considered to be superb in that inter alia , they do not require cumbersome displacement reducing mechanisms and their structures are simple. Accordingly, a fine positioning device of the above sort will hereinafter be described with reference to Figure 1. Figure 1 is a side view of a conventional fine positioning device, in which there are illustrated a support table 1, planar parallel springs 2a,2b fixed in parallel to each other on the support table 1, and a fine motion table 3 supported on the parallel spring 2a,2b and having a high degree of rigidity. Designated at numeral 4 is a fine motion actuator mounted between the support table 1 and fine motion table 3. The fine motion actuator 4 makes use of a piezoelectric element, electromagnetic solenoid or the like, which is energized to apply a force to the fine motion table 3 along the x-axis of the coordinate system depicted in the figure. The parallel springs 2a,2b, reflecting their structure, have low rigidity in the direction of the x-axis but high rigidity in the direction of the z-axis and in the direction of the y-axis (namely, in the direction perpendicular to the drawing sheet). When the fine motion actuator 4 is energized, the fine motion table 3 thus undergoes a displacement practically along the x-axis only and no substantial displacements take place in the other directions. Figure 2 is a perspective view of another conventional fine positioning device which is readily conceivable from the devices disclosed by way of example in the above-mentioned magazine. In the figure, there are shown a support plate 6, a pair of planar parallel springs 7a,7b fixed in parallel to each other on the support table 6, a middle table 8 fixed on the parallel springs 7a,7b and having a high degree of rigidity, another pair of parallel springs 9a,9b fixed on the middle table 8 and extending in parallel to each other in a direction perpendicular to the parallel spring 7a,7b, and a fine motion table 10 fixed on the parallel spring 9a,9b and having a high degree of rigidity. When a coordinate system is established as shown in the figure, the parallel spring 7a,7b are arranged along the x-axis, while the parallel springs 9a,9b are disposed along the y-axis. This structure corresponds basically to a structure obtained by stacking two structures, each of the same type as the one-axis (displaceable along the x-axis only) structure depicted in Figure 1, one over the other. An arrow F x indicates a force to be applied along the x-axis to the fine motion table 10, while an arrow F y designates a force to be applied along the y-axis to the middle table 8. Unillustrated actuators which can apply the forces F x ,F y are provided respectively between the support table 6 and fine motion table 10 and between the support table 6 and the middle table 8. When the force F x is applied to the fine motion table 10, the parallel springs 9a,9b are deformed. Since the parallel springs 7a,7b have high rigidity against the force F x applied along the x-axis, the fine motion table 10 is allowed to undergo a displacement practically along the x-axis only. When the force F y is exerted to the middle table 8 on the other hand, the parallel springs 7a,7b are deformed and by way of the parallel springs 9a,9b, the fine motion table 10 is displaced practically along the y-axis only. When both forces F x ,F y are applied at the same time, the parallel springs 7a,7b,9a,9b are simultaneously deformed. Correspondingly, the fine motion table 10 is displaced two-dimensionally. As described above, the device shown in Figure 2 can perform positioning along two axes whereas the device illustrated in Figure 1 is a one-axis positioning device. In each of the devices shown respectively in Figures 1 and 2, the fine motion table 10 is displaced linearly along the specific axis. On the other hand, Japanese Patent Publication No. 50433/1982 discloses a fine positioning device in which a fine motion table is caused to undergo a fine angular displacement about a specific axis. This fine positioning device will next be described with reference to Figure 3. Figure 3 is a partially cut-away perspective view of a conventional fine positioning device which makes use of fine angular displacements. In the figure, numeral 11 indicates a fixed central portion in the form of a cylindrical column and numerals 11a,11b,11c designate vertical slots formed with an equal interval, along the length of the fixed central portion, in the circumferential wall of the fixed central portion 11. There are also depicted a ring-shaped stage 12 provided movably about the fixed central portion 11 and U-like metal members 12a₁-12a₃, 12b₁-12b₃,12c₁-12c₃ secured fixedly on the stage 12 in opposition to the vertical slots 11a,11b,11c respectively. Designated at numeral 13 are bimorph cells mounted between the individual vertical slots 11a,11b, 11c and their corresponding U-like metal members 12a₁-12c₃, while numeral 13A indicates beads fixed on the bimorph cells 13 at locations where the bimorph cells 13 engage their corresponding U-like metal members 12a₁-12c₃. The fixed central portion 11, stage 12 and individual U-like metal members 12a₁-12c₃ are all rigid. Here, the above-mentioned bimorph cells 13 are described in brief with reference to Figure 4. Figure 4 is a perspective view of one of the bimorph cells 12a₁-12c₃. In the figure, there are shown piezoelectric elements 13a,13b and a common electrode 13c provided between the piezoelectric elements 13a,13b. The piezoelectric elements 13a,13b are rigidly cemented together with the common electrode 13c interposed therebetween. Designated at numerals 13d,13e are surface electrodes applied fixedly to the piezoelectric elements 13a,13b respectively. In the above stacked or double-layered structure, when a voltage of such a polarity that the piezoelectric element 13a is caused to contract is applied between the surface electrode 13d and common electrode 13c and at the same time, another voltage of such a polarity that the piezoelectric element 13b is caused to expand is applied between the surface electrode 13e and common electrode 13c, the piezoelectric elements 13a,13b are respectively caused to contract and expand in the directions shown by arrows. As a result, the bimorph cell 13 is deformed as a whole as shown in the figure. Owing to this property, the bimorph cell 13 can provide a greater degree of displacement compared with a single piezoelectric element. In the device shown in Figure 3, the bimorph cells 13 which have the above-described property are fixed at one ends thereof in their corresponding vertical slots 11a,11b,11c but the other ends of the bimorph cells 13 remain as free ends and are kept via their respective beads 13A in contact with the corresponding U-like metal members 12a₁-12c₃. Let's now assume that suitable voltages are applied respectively to the bimorph cells 13 so as to cause them to undergo such deformations as shown in Figure 4. Corresponding to the deformations of the bimorph cells 13, the stage 12 undergoes an angular displacement about the fixed central portion 11. If a fine motion table is fixedly mounted on the stage 12, it is possible to have the fine motion table to undergo the angular displacement. In the above-described conventional device, the U-like metal members 12a₁-12c₃ and their corresponding bimorph cells 13 are kept in mutual contact. Owing to this structural feature, the bimorph cells are mounted while being allowed to undergo free deformations. This structural feature can thus avoid the imminent restraint (interference) of displacements which takes place if the bimorph cells 13 should be fixed to the stage 12. The fine positioning devices depicted in Figures 1 and 2 may be used only for one-dimensional and two-dimensional positioning respectively. They can produce neither displacement along the z-axis nor angular displacement about the x-, y- or z-axis. Turning to the fine positioning device shown in Figure 3, it can produce neither displacement along the x-, y- or z-axis nor angular displacement about any one of the other two axes. From these conventional fine positioning devices, it may only be feasible to contemplate a 3-axis fine positioning device, which can produce displacements along both x-axis and y-axis and an angular displacement about the z-axis, by combining the device of Figure 2 and that of Figure 3 together. It is believed to be extremely difficult to construct a 4-axis or larger multi-axis fine positioning device on the basis of such conventional devices. The closest prior art results from document EP-A-0 195 479 falling within the terms of Article 54(3). With the foregoing in view, the present invention has as its principal objects the solution of the problems of the above-described prior art and at the same time the provision of a fine positioning device which can produce with a simple and small structure displacements along and/or about at least two axes out of displacements along x-, y- and z-axes and those about x-, y- and z-axes. In order to achieve the above objects, the present invention provides in a first aspect thereof a fine positioning device comprising: a central rigid portion; a first set of outwardly-extending portions extending symmetrically along a first axis from the central rigid portion; a second set of outwardly-extending portions extending symmetrically from the central rigid portion along a second axis which is perpendicular to the first axis; a first set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the first set of outwardly-extending portions respectively to produce translational displacements along the second axis; and a second set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the second set of outwardly-extending portions respectively to produce translational displacements along the first axis. The above fine positioning device can obtain translational displacements along each of two axes which are perpendicular to each other. In a second aspect of this invention, there is also provided a fine positioning device comprising: a rigid support member; a first set of radial flexible-beam displacement mechanisms provided symmetrically to each other on the support member to produce angular displacements about a first axis; a second set of radial flexible-beam displacement mechanisms provided symmetrically to each other on the support member to produce angular displacements about a second axis which is perpendicular to the first axis; and a third set of radial flexible-beam displacement mechanisms connected to either one of the sets of radial flexible-beam displacement mechanisms to produce angular displacements about a third axis which is perpendicular to both first and second axes. The above fine positioning device can obtain angular displacements about each of three axes which are perpendicular to one another. In a third aspect of this invention, there is also provided a fine positioning device comprising: a first block comprising a central rigid portion, a first set of outwardly-extending portions extending symmetrically along a first axis from the central rigid portion and equipped respectively with first parallel flexible-beam displacement mechanisms to produce in the first set of outwardly-extending portions translational displacements along a second axis which is perpendicular to the first axis, and a second set of outwardly-extending portions extending symmetrically along the second axis from the central rigid portion and equipped respectively with second parallel flexible-beam displacement mechanisms to produce in the second set of outwardly-extending portions translational displacements along the first axis; a second block comprising a central rigid portion and a set of outwardly-extending portions extending symmetrically along the second axis from the central rigid portion, said outwardly-extending portions being equipped respectively with parallel flexible-beam displacement mechanisms adapted to produce translational displacement along a third axis, which is perpendicular to both first and second axes, and connected to the second set of outwardly-extending portions respectively; and a third block comprising a rigid ring, a set of first radial flexible-beam displacement mechanisms provided on the rigid ring and adapted to produce angular displacements about the first axis, a set of second radial flexible-beam displacement mechanisms provided on the rigid ring and adapted to produce angular displacements about the second axis, and a set of outwardly-extending portions extending symmetrically from a central rigid portion, which is connected to the central rigid portion of the second block, and equipped respectively with third radial flexible-beam displacement mechanisms for producing angular displacements about the third axis. The above fine positioning device can obtain both translational and angular displacements along and about each of three axes which are perpendicular to one another. In a fourth aspect of this invention, there is also provided a fine positioning device comprising: a central rigid portion; a first set of outwardly-extending portions extending symmetrically along a first axis from the central rigid portion; a second set of outwardly-extending portions extending symmetrically from the central rigid portion along a second axis which is perpendicular to the first axis; a set of radial flexible-beam displacement mechanisms provided symmetrically to each other with the first set of outwardly-extending portions respectively and adapted to produce angular displacements about a third axis which is perpendicular to both first and second axes, and a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the first set of outwardly-extending portions respectively and adapted to produce translational displacements along the second axis; and a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the second set of outwardly-extending portions and adapted to produce translational displacements along the first axis. The above fine positioning device can obtain translational displacements along each of two axes extending perpendicularly to each other and angular displacements about a further axis extending at right angles to the two axes. In a fifth embodiment of this invention, there are also provided a fine positioning device comprising: a central rigid portion; a first set of outwardly-extending portions extending symmetrically along a first axis from the central rigid portion; a second set of outwardly-extending portions extending symmetrically from the central rigid portion along a second axis which is perpendicular to the first axis; a set of radial flexible-beam displacement mechanisms provided symmetrically to each other with the first set of outwardly-extending portions respectively and adapted to produce angular displacements about a third axis which is perpendicular to both first and second axes, and a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the first set of outwardly-extending portions respectively and adapted to produce translational displacements along the second axis; a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the second set of outwardly-extending portions and adapted to produce translational displacements along the first axis; and a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the second set of outwardly-extending portions and adapted to produce translational displacements along the third axis. The above fine positioning device can obtain translational displacements along each of three axes extending perpendicularly to one another and angular displacements about one of these three axes. In a sixth aspect of this invention, there is also provided a fine positioning device comprising: a rigid support plate; radial flexible-beam displacement mechanisms provided on the support plate and adapted to produce angular displacements about a first axis; and radial flexible-beam displacement mechanisms provided on the support plate and adapted to produce angular displacements about a second axis which is perpendicular to the first axis. The above fine positioning device can obtain angular displacements about each of two axes which are perpendicular to each other. In a seventh aspect of this invention, there is also provided a fine positioning device comprising: a central rigid portion; a first set of outwardly-extending portions extending symmetrically along a first axis from the central rigid portion; a second set of outwardly-extending portions extending symmetrically from the central rigid portion along a second axis which is perpendicular to the first axis; a set of radial flexible-beam displacement mechanisms provided symmetrically to each other with the first set of outwardly-extending portions respectively and adapted to produce angular displacements about a third axis which is perpendicular to both first and second axes, and a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the first set of outwardly-extending portions respectively and adapted to produce translational displacements along the second axis; a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the second set of outwardly-extending portions and adapted to produce translational displacements along the first axis, and a set of parallel flexible-beam displacement mechanisms provided symmetrically to each other with the second set of outwardly-extending portions and adapted to produce translational displacements along the third axis; a rigid support plate; radial flexible-beam displacement mechanisms provided on the support plate and adapted to produce angular displacements about the fist axis and radial flexible-beam displacement mechanisms provided on the support plate and adapted to produce angular displacements about the second axis; and connecting portions connecting rigid portions of one set of radial flexible-beam displacement mechanisms, out of both radial flexible beam displacement mechanisms provided on the support plate, to one ends of one set of outwardly-extending portions out of the first and second sets of outwardly-extending portions. The above fine positioning device can obtain translational displacements along each of three axes extending perpendicularly to one another and angular displacements about each of the three axes. As described above, the fine positioning device of this invention is constructed by providing one or more parallel flexible-beam displacement mechanisms and/or radial flexible beam displacement mechanisms in a rigid member. The fine positioning device hence has a simple and small overall structure. Each parallel flexible-beam displacement mechanism or radial flexible-beam displacement mechanism can be provided with a displacement controller. Alternatively, a displacement controller can be provided for the entire fine positioning device. It is therefore possible to obtain a displacement of high accuracy. The above and other objects, features and advantages of this invention will become apparent from the following description and the appended claims, taken in conjunction with the accompanying drawings, in which: Figures 1, 2 and 3 are side view, perspective view and partly cut-away perspective view of conventional fine positioning devices respectively; Figure 4 is a perspective view of one of the bimorph cells employed in the device depicted in Figure 3; Figures 5 is an exploded perspective view of a fine positioning device according to a first embodiment of this invention; Figures 6A and 6B are side views of a symmetrical parallel flexible-beam displacement mechanism; Figure 7 is an exploded perspective view of a fine positioning device according to a second embodiment of this invention; Figure 8A and 8B are side views of an asymmetrical radial flexible-beam displacement mechanism; Figure 9A and 9B are side views of a symmetrical radial flexible-beam displacement mechanism; Figure 10 is an exploded perspective view of a fine positioning device according to a third embodiment of this invention; Figure 11 is an exploded perspective view of a fine positioning device according to a fourth embodiment of this invention; Figure 12 is an exploded perspective view of a fine positioning device according to a fifth embodiment of this invention; Figure 5 is an exploded perspective view of a fine positioning device according to the first embodiment of this invention, in which there are shown coordinate axes x, y and z which are perpendicular to one another, a central rigid portion 15, an outwardly-extending portion 16a extending out along the y-axis from the central rigid portion 15, another outwardly-extending portion 16a extending out along the y-axis from the central rigid portion 15, another outwardly-extending portion 16b extending out from the central rigid portion 15 in a direction opposite to the outwardly-extending portion 16a, a further outwardly-extending portion 17a extending out along the x-axis from the central rigid portion 15, and a still further outwardly-extending portion 17b extending out from the central rigid portion 15 in a direction opposite to the outwardly-extending portion 17a. There are also depicted fixed portions 18a,18b provided at lower end parts of the outwardly-extending portions 16a,16b, fine motion table connecting portions 19a,19b provided at upper end parts of the outwardly-extending portions 17a,17b, and a fine motion table 20. The outwardly-extending portions 16a,16b,17a, 17b, fixed portions 18a,18b and fine motion table connecting portions 19a,19b are all formed of the same material as the central rigid portion 15 and are worked or machined out together with the central rigid portion 15 from a single block. Designated at numerals 16F xa ,16F xb are parallel flexible-beam displacement mechanisms formed in the outwardly-expanding portions 16a,16b respectively. The parallel flexible-beam displacement mechanisms 16F xa , 16F xb are formed symmetrically to each other relative to the central rigid portion 15. The parallel flexible-beam displacement mechanisms 16F xa ,16F xb cooperate to produce translational displacements along the x-axis. Designated at numerals 17F ya ,17F yb are parallel flexible-beam displacement mechanisms formed in the outwardly-expanding portions 17a,17b respectively. The parallel flexible-beam displacement mechanisms 17F ya , 17F yb are formed symmetrically to each other relative to the central rigid portion 15. The parallel flexible-beam displacement mechanisms 17F ya ,17F yb cooperate to produce translational displacements along the y-axis. The structure of the parallel flexible-beam displacement mechanism will be described subsequently. The parallel flexible-beam displacement mechanisms 16F xa ,16F xb ,17F ya ,17F yb are formed by formed predetermined through-holes at desired locations in the respective outwardly-extending portions 16a,16b,17a, 17b. Letter S indicates strain gauges provided with each parallel flexible-beam displacement mechanism. The structure of the above parallel flexible-beam displacement mechanisms will next be described with reference to drawings. Figures 6A and 6B are side views of a symmetrical parallel flexible-beam displacement mechanism. In each of these drawings, numerals 21a,21b,21c indicate rigid portions while numerals 24a₁,24a₂ designate parallel flexible beams connected in parallel to each other between the rigid portions 21c,21a. The parallel flexible beams 24a₁,24a₂ are formed by a through hole 22a formed through the rigid portion. Designated at numerals 24b₁,24b₂ designate parallel flexible beams connected in parallel to each other between the rigid portions 21b,21c. The parallel flexible beams 24a₁,24a₂ are formed by a through hole 22b formed through the rigid portion. Numerals 26a, 26b indicate piezoelectric actuators, which are fit between tongues extending from the rigid portions into the respective through-holes 22a,22b. A parallel flexible-beam displacement mechanism 29a is constructed by the elements located on the left hand relative to the center line of the rigid portion 21c, while another parallel flexible-beam displacement mechanism 29b is by the elements located on the right hand relative to the center line of the rigid portion 21c. Similar to Figure 5, Letter S indicates strain gauges provided at suitable locations on each parallel flexible beam. Let's now establish coordinate axes as shown in the drawings (the y-axis extends in a direction perpendicular to the drawing sheet). Voltages are now applied simultaneously to the piezoelectric actuators 26a,26b respectively so as to generate forces f of the same magnitude along the z-axis. Let's now investigate a displacement to be produced in one of the parallel flexible-beam displacement mechanisms, for example, in the parallel flexible-beam displacement mechanism 29a. Upon application of the voltage to the piezoelectric actuator 26a, the rigid portion 21 is pressed by the force f along the z-axis. The parallel flexible-beam 24a₁,24a₂ thus undergo a bending deformation like the parallel springs 2a,2b depicted in Figure 1, so that the rigid portion 21c is displaced along the z-axis as illustrated in Figure 6B. If the other parallel flexible-beam displacement 29b were not provided, a lateral displacement (a displacement along the x-axis) should take place at the same time in the rigid portion 21c albeit extremely small. A discussion will next be made of a displacement which could occur in the parallel flexible-beam displacement mechanism 29b if the associated parallel flexible-beam displacement mechanism 29a were not provided. Since the parallel flexible-beam displacement mechanism 29b is constructed plane-symmetrically with the parallel flexible-beam displacement mechanism 29a relative to a plane (standard plane) which extends along the y-axis through the center of the rigid portion 21c, the rigid portion 21c also undergoes the above-mentioned lateral displacement in unison with a displacement along the z-axis upon application of the force f which is plane-symmetrical, relative to the standard plane, with the force f applied to the parallel flexible-beam displacement mechanism 29a. Relative to the standard plane, the magnitude and direction of the lateral displacement are plane-symmetrical with those of the lateral displacement of the parallel flexible-beam displacement mechanism 29a. Regarding the above-described lateral displacements, the lateral displacement occurred in the parallel flexible-beam displacement mechanism 29a is a combination of a displacement occurred in the leftward direction along the x-axis as viewed in the drawing and an angular displacement occurred counterclockwise about the y-axis as viewed in the same drawing, while the lateral displacement occurred in the parallel flexible-beam displacement mechanism 29b is a combination of a displacement occurred in the rightward direction along the x-axis as viewed in the drawing and an angular displacement occurred clockwise about the y-axis as viewed in the same drawing. Further, the magnitudes of the displacements along the x-axis are equal to each other and those of the angular displacements about the y-axis are also equal to each other. The lateral displacements occurred respectively in the parallel flexible-beam displacement mechanisms 29a,28b are canceled each other. As a result, a slight increase in internal stress is alone caused to occur in each of the parallel flexible beams 24a₁,24a₂,24b₁,24b₂ due to a lengthwise elongation thereof by the application of the force f and the rigid portion 21c undergoes a displacement (principal displacement) ε along the z-axis only. As soon as the voltages applied to the piezoelectric actuators 26a,26b are removed, the parallel flexible beams 24a₁,24a₂,24b₁,24b₂ returns to their respective state before their deformation so that the parallel flexible-beam displacement mechanisms 29a,29b return to their respective state shown in Figure 6A and the displacement ε is reduced to 0. Accurate positioning can be performed by detecting actual displacements by the respective strain gauges S in the course of the above-described operation and then effecting a feedback control based on the displacements. The operation of the embodiment shown in Figure 5 will next be described. When an identical voltage is applied to each of the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 16F xa ,16F xb , their parallel flexible beams 24a₁,24a₂, 24b₁,24b₂ are deformed respectively along the x-axis of Figure 5 in proportion to the applied voltages as shown in Figure 6B so that they undergo translational displacements. Since these parallel flexible-beam displacement mechanisms 16F xa ,16F xb are unitary with the central rigid portion 15, the parallel flexible-beam displacement mechanisms 17F ya ,17F yb and the fine motion table 20 fixed on the fixed portions 19a,19b, their translational displacements along the x-axis are transmitted to the fine motion table 20 as they are. The fine motion table 20 thus undergoes a translational displacement to the same degree along the x-axis. When an identical voltage is applied to each of the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 17F ya ,17F yb in the same manner, the fine motion table 20 undergoes a translational displacement along the y-axis. In addition, a combined translational displacement can be obtained when these respective parallel flexible-beam mechanisms are actuated at the same time. Owing to the above-described structure, the fine positioning device of the first embodiment can avoid lateral displacements and can obtain translational displacements along two axes in spite of its extremely simple and small construction. Figure 7 is an exploded perspective view of the fine positioning device according to the second embodiment of this invention. In the drawing, x, y and z indicate coordinate axes respectively. Designated at numeral 35 is a square ring made of a rigid material. Numerals 36M ya and 36M yb indicate respectively radial flexible-beam displacement mechanisms arranged symmetrically on the ring 35. Each of the radial flexible-beam displacement mechanisms 36M ya ,36M yb produces angular displacements about the y-axis. Numerals 36M xa and 36M xb indicate respectively radial flexible-beam displacement mechanisms arranged symmetrically on the ring 35. They individually produces angular displacements about the x-axis. The structure of each of the radial flexible-beam displacement mechanisms 36M ya ,36M yb ,36M xa ,36M xb will be described subsequently. Numerals 37a,37b indicate one set of rigid portions forming the radial flexible-beam displacement mechanisms 36M ya ,36M yb respectively (the other rigid portion being the ring 35), while numerals 38a,38b indicate one set of rigid portions forming the radial flexible-beam displacement mechanisms 36M xa ,36M xb respectively (the other rigid portion being also the ring 35). Designated at numerals 38a′ and 38b′ are attachment portions provided on the upper surfaces of end portions 38a,38b respectively. Designated at numeral 40 is a central rigid portion, numeral 41a indicates an outwardly-extending portion extending out along the y-axis from the central rigid portion 40, and numeral 41b designates another outwardly-extending portion extending out from the central rigid portion 40 in a direction opposite to the former outwardly-extending portion 41a. The outwardly-extending portion 41a and the rigid portion 37a of the radial flexible displacement mechanisms 36M ya are connected to each other, whereas the outwardly-extending portion 41b and the rigid portion 37b of the radial flexible displacement mechanisms 36M yb are connected to each other. Numerals 41M za ,41M zb indicate radial flexible-beam displacement mechanisms formed in the outwardly-extending portions 41a,41b respectively. They are arranged symmetrically to each other relative to the central rigid portion 40. These radial flexible-beam displacement mechanisms 41M za ,41M zb cooperate to produce angular displacements about the z-axis. These radial flexible-beam displacement mechanisms 41M za , 41M zb and the aforementioned radial flexible-beam displacement mechanisms 36M xa ,36M xb ,36M ya ,36M yb are constructed by forming desired through-holes at predetermined locations. The structure of the radial flexible-beam displacement mechanisms 41M za ,41M zb will also be described subsequently. The ring 35, the rigid portions 37a,37b,38a,38b, the individual radial displacement flexible-beam mechanisms formed between the ring and the rigid portions 37a,37b,38a,38b, the central rigid portion 40, and the outwardly-extending portions 41a,41b are all formed as an integral unit from a single piece of high-rigidity material. Numeral 43 indicates a fine motion table mounted on attachment portions 38a′38b′ of the rigid portions 38a,38b. An object to be subjected to fine positioning is fixedly mounted on the fine motion table 43. The manner of attachment between the fine motion table 43 and attachment portions 38a′38b′ is indicated at one location only by a two-dot chain line in the drawing. Incidentally, it is not absolutely necessary to limit the shape of the fine motion table 43 to a rectangular shape as shown in the drawing. It may be formed into any shape facilitating the fixed mounting of an object such as a substantially square shape in which the y-axis dimension of the fine motion table has been increased further. Numeral 44 indicates a mount made of a rigid material. The mount 44 is formed of a recessed portion 44c, land portions 44a,44b provided on both sides of the recessed portion 44c, and attachment portions 44d,44e extending out from lower end portions of the respective land portions 44a,44b. The central rigid portion 40 is fit and fixed in the recessed portion 44c. The manner of this fixed fitting is indicated at one location only by a two-dot chain line in the drawing. The attachment portions 44d,44e are fixed on the fixing portions (not shown). With the central rigid portion 40 fixed on the recessed portion 44c, a major portion of the mount 44 is received within a space surrounded by the ring 35. Thus, the radial flexible-beam displacement mechanisms 36M xa ,36M xb , 36M ya ,36M yb are suspended together with the ring 35 from the outwardly-extending portions 41a,41b. In the drawing, letter S indicates strain gauges provided with each of the radial flexible-beam displacement mechanisms. The structure of each radial flexible-beam displacement mechanism is now explained with reference to Figures 8A and 8B, which are side views of the radial flexible-beam displacement mechanism respectively. In the drawings, numerals 45a,45b indicate rigid portions located on left-hand and right-hand sides respectively. Designated at numerals 46,46′ are planar radial flexible beams formed between the rigid portions 45a,45b as integral members with the rigid portions 45a,45b and arranged radially about a fixed point O as a center. Numeral 47 indicates a through-hole bored to form the radial flexible beams 46,46′ and rigid portions 45a,45b as an integral unit. Numeral 48a indicates a tongue projecting into the through-hole 47 from the rigid portion 45a while numeral 48b designates another tongue projecting into the through-hole 47 from the rigid portion 45b. These tongues 48a,48b are overlapped with each other in the vertical direction as viewed in the drawing, with an interval left therebetween. Designated at numeral 49 is a piezoelectric actuator fixed between the tongue 48a and tongue 48b. When a circle passing through the piezoelectric actuator 49 is drawn about the point O, the piezoelectric actuator 49 generates a force f (which can be considered as a torque relative to the point O) in a direction tangent to the circle so that a bending deformation is caused to occur in each of the radial flexible beams. The magnitude of such a force is controlled by a voltage to be applied to the piezoelectric actuator 49. Numeral 50 indicates a rigid structure on which the rigid portion 45a is supported. Letter S indicates strain gauges cemented to the respective radial flexible beams at desired locations. These strain gauges S are provided to detect the degrees of displacements of the radial flexible beams. In the above structure, a radial flexible-beam displacement mechanism 52 is constructed by the rigid portions 45a,45b, radial flexible beams 46,46′, tongues 48a,48b and piezoelectric actuator 49. A line which extends through the point O and is perpendicular to the drawing sheet will hereinafter be considered as a standard axis showing the position and the direction of arrangement of the radial flexible-beam displacement mechanism 52. The operation of the above radial flexible-beam displacement mechanism 52 will next be described with reference to Figure 8B. Figure 8B is a side view of the radial flexible-beam displacement mechanism 52, which is illustrated in Figure 8A, after its deformation. Let's now apply a voltage to the piezoelectric actuator 49 to generate the force f in the direction of the above-mentioned tangent line. The tongue 48b is then pushed upwardly along the tangent line by the force generated in the piezoelectric actuator 49. The rigid portion 45b is in a state connected to the rigid portion 45a by way of the radial flexible beams 46,46′. As a result of application of the above force, portions of the flexible beams 46,46′ at which portions the flexible beams 46,46′ are connected to the rigid portion 45a remain respectively on straight lines L₁,L₂ extending out radially from the point O but portions of the flexible beams 46,46′ at which portions the flexible beams 46,46′ are connected to the rigid portion 45b undergo small displacements so that the latter portions are displaced onto straight lines L 1′ ,L 2′ (the straight lines L 1′ ,L 2′ also extend out radially from the point O) offset slightly from the corresponding straight lines L₁,L₂. As a consequence, the rigid portion 45b is caused to turn over a small angle δ clockwise as viewed in the drawing. Since the degree of this angular displacement δ is determined by the flexural rigidity of the radial flexible beams 46,46′, the angular displacement δ can be controlled with the same accuracy as the force f provided that the force f is controlled precisely. After elimination of the voltage applied to the piezoelectric actuator 49, the individual radial flexible beams 46,46′ are allowed to return their respective states before their deformations so that the radial flexible-beam displacement mechanism 52 returns to the state depicted in Figure 8A and the angular displacement δ is reduced to 0. An accurate angular displacement can be produced in the above operation if a feedback control is effected based on values detected by the strain gauges S. From the above description of the radial flexible-beam displacement mechanism, it has now been understood that the standard axis of each of the radial flexible-beam displacement mechanisms 36M ya ,36M yb shown in Figure 7 is the y-axis while the standard axis of each of the radial flexible-beam displacement mechanisms 36M xa ,36M xb is the x-axis. It has also been appreciated that the ring 35 depicted in Figure 7 corresponds to the rigid portion 45b while the rigid portions 37a,37b,38a,38b correspond to the rigid portion 45a. Further, the respective standard axes y,x of the radial flexible-beam displacement mechanisms 36M ya ,36M yb ,36M xa ,36M xb shown in Figure 7 may be set to extend on the surface of the fine motion table 43 provided that the opening angle ϑ between their associated radial flexible beams 46,46′ is chosen suitably. The radial flexible-beam displacement mechanisms 41M za ,41M zb shown in Figure 7 share the rigid portion 45b. Two rigid portions, each of which is of the same type as the rigid portion 40, are provided on both sides of the common rigid portion 45b, whereby a symmetrical radial flexible-beam displacement mechanism is formed. In this construction, the rigid portion 45b is fixed in contrast to the structure depicted in Figure 8A. The symmetrical radial flexible-beam displacement mechanism will next be described. Figures 9A and 9B are side views of the symmetrical radial flexible-beam displacement mechanism, in which numerals 55a,55b,55c indicate rigid portions while numerals 58a₁, 58a₂, 58b₁ and 58b₂ designate radial flexible beams. The radial flexible beams 58a₁, 58a₂, 58b₁ and 58b₂ extend radially along their corresponding two-dot chain lines L₁,L₂ relative to an axis O which extends through the center of the rigid portion 55c and is perpendicular to the drawing sheet. The radial flexible beams 58a₁, 58a₂, 58b₁ and 58b₂ therefore connect the corresponding adjacent rigid portions. The radial flexible beams 58a₁,58a₂ are formed by boring a through-hole 56a, while the radial flexible beams 58b₁,58b₂ are formed by boring a through-hole 56b. Designated at numerals 60a,60b are piezoelectric actuators, which are mounted between their corresponding tongues extending into the through-holes 56a,56b from the corresponding rigid portions. A radial flexible-beam displacement mechanism 63a is constructed by the elements on the left-hand side of the axis O, while a radial flexible-beam displacement mechanism 63b is constructed by the elements on the right-hand side of the axis O. Letter S indicate strain gauges cemented on the radial flexible beams at desired locations. The strain gauges S are provided to detect the degrees of deformations of the radial flexible beams. Let's now apply predetermined voltages respectively to the piezoelectric actuators 60a,60b at the same time to generate forces f of the same magnitude in directions tangent to a circle drawn about the central axis O as a center. The left-hand tongue of the rigid portion 55c is then pushed upwardly along the tangent line by the force generated in the piezoelectric actuator 60a. On the other hand, the right-hand tongue of the rigid portion 55c is pushed downwardly along the tangent line by the force generated in the piezoelectric actuator 60b. The rigid portion 55c is in a state connected to the rigid portions 55a,55b by way of the radial flexible beams 58a₁,58a₂,58b₁,58b₂. As a result of application of the above forces, portions of the flexible beams 58a₁,58a₂,58b₁,58b₂ at which portions the flexible beams are connected to their corresponding rigid portion 55a,55b as shown in Figure 9B remain respectively on straight lines L₁,L₂ extending out radially from the point O but portions of the flexible beams at which portions the flexible beams are connected to the rigid portion 55c undergo small displacements so that the latter portions are displaced onto straight lines L 1′ ,L 2′ (which are also straight lines extending radially from the point O) offset slightly from the corresponding straight lines L₁,L₂. As a consequence, the rigid portion 55c is caused to turn over a small angle δ clockwise as viewed in the drawing. Since the degree of this angular displacement δ is determined by the flexural rigidity of the radial flexible beams 58a₁,58a₂,58b₁,58b₂, the angular displacement δ can be controlled with the same accuracy as the forces f provided that the forces f are controlled precisely. After elimination of the voltages applied respectively to the piezoelectric actuator 60a,60b, the individual radial flexible beams 58a₁,58a₂,58b₁,58b₂, are allowed to return their respective states before their deformations so that the radial flexible-beam displacement mechanism returns to the state depicted in Figure 9A and the angular displacement δ is reduced to 0. Similar to the parallel and radial flexible-beam displacement mechanisms described above, the strain gauges S are employed to achieve accurate fine positioning. The operation of the fine positioning device shown in Figure 7 is now described. When voltages are applied respectively to the piezoelectric actuators of the radial flexible-beam displacement mechanisms 36M ya , 36M yb , the planer flexible beams 46,46′ are deformed in proportion to the voltages as depicted in Figure 8B. Since the rigid portion 37a is in a state fixed via the central rigid portion 40 and radial flexible-beam displacement mechanisms 41M za ,41M zb , the radial flexible-beam displacement mechanisms 36M ya ,36M yb produce angular displacements about the y-axis so that the fine motion table 43 undergoes an angular displacement about the y-axis. When voltages are applied respectively to the piezoelectric actuators of the radial flexible-beam displacement mechanisms 36M xa ,36M xb on the other hand, the radial flexible beams are deformed in proportion to the voltages so that angular displacements are produced about the x-axis. Since the ring 35 is in a state fixed via the radial flexible-beam displacement mechanisms 36M ya ,36M yb ,41M za ,41M zb , these angular displacements are transmitted to the rigid portions 38a,38b and the fine motion table 43 undergoes an angular displacement about the x-axis. When voltages are applied respectively to the piezoelectric actuators of the radial flexible-beam displacement mechanisms 41M za ,41M zb on the other hand, the radial flexible beams are deformed in proportion to the voltages so that angular displace ments are produced about the z-axis. These angular displacements are then transmitted to the fine motion table 43 by way of the rigid portions 37a,37b, radial flexible-beam displacement mechanisms 36M ya ,36M yb , ring 35, radial flexible-beam displacement mechanisms 36M xa ,36M xb and rigid portions 38a,38b, whereby the fine motion table 43 undergoes an angular displacement about the z-axis. Further, when desired two or more of the radial flexible-beam displacement mechanisms 36M ya ,36M yb , radial flexible-beam displacement mechanisms 36M xa , 36M xb and radial flexible-beam displacement mechanisms 41M za ,41M zb are chosen and driven simultaneously, the fine motion table 43 undergoes an angular displacement which is a combination of angular displacements of the desired two or more radial flexible-beam displacement mechanisms. In the above description of the second embodiment of this invention, the crossing point of the x-axis, y-axis and z-axis is located on the surface of the fine motion table. It is however not essential for the crossing point to assume a position on the surface of the fine motion table. The location of the crossing point can therefore be selected at any location as desired. Owing to the above-described structure, the fine positioning device of the second embodiment can obtain angular displacements about three axes in spite of its simple structure. Since the y-axis and x-axis which are standard axes of each radial flexible-beam displacement mechanism are positioned on the fine motion table, the turning center of each angular displacement is also located on the fine motion table so that the angular displacement can be achieved accurately. Figure 10 is an exploded perspective view of a fine positioning device according to the third embodiment of this invention. This embodiment is a combination of the fine positioning device according to the first embodiment, the fine positioning device according to the second embodiment and a further fine positioning device capable of producing translational displacements along two axes, thereby constructing a 6-axis fine positioning device (translational displacements along the x-, y- and z-axes and angular displacements about the x-, y- and z-axes). In the drawing, letter B₁ indicates a block constituting the same fine positioning device as that shown in Figure 5, while letter B₃ designates another block constituting the same fine positioning device as that depicted in Figure 7. Among elements forming these blocks B₁,B₃, those similar to their corresponding parts in Figures 5 and 7 are identified by like reference numerals and letters and their description is omitted herein. A block B₂ is a block constructed of a fine positioning device having the same external shape as the mount 44 shown in Figure 7. In the drawing, there are shown a central rigid portion 65 made of a material having high rigidity, an outwardly-extending portion 66a extending out from the central rigid portion 65 along the x-axis, and another outwardly-extending portion 66b extending out from the central rigid portion 65 in a direction opposite to the outwardly-extending portion 66a. Designated at numerals 67a,67b are connecting portions extending out respectively from lower edge portions of the outwardly-extending portions 66a,66b. The connecting portions 67a,67b are connected to connecting portions 19a,19b of the block B₁. This connection is indicated by two-dot chain lines. The central rigid portion 65, outwardly-extending portions 66a,66b and connecting portions 67a,67b are worked out as an integral unit from a single block. Designated at numerals 66F za ,66F zb are parallel flexible-beam displacement mechanisms constructed in the outwardly-extending portions 66a,66b respectively. The parallel flexible-beam displacement mechanisms 66F za ,66F zb are arranged symmetrically to each other relative to the central rigid portion 65. These parallel flexible-beam displacement mechanisms 66F za , 66F zb cooperate with each other to produce translational displacements along the z-axis. The parallel flexible-beam displacement mechanisms 66F za ,66F zb are formed by boring predetermined through-holes in the corresponding outwardly-extending portions 66a,66b at desired locations respectively. The block B₂ is connected to the central rigid portion 40 of the block B₃. Namely, the central rigid portion 40 of the block B₃ is superposed on the central rigid portion 65 of the block B₂ and the block B₂ and block B₃ are then connected to each other by a suitable means (one of connecting routes is indicated by a double-dot chain line in the drawing). In this state, a major part of the block B₂ is received within the space of the block B₃. Hence, the radial flexible-beam displacement mechanisms 36M xa ,36M xb ,36M ya ,36M yb are suspended together with the ring 35 from the outwardly-extending portions 41a,41b. The fine motion table 43 is connected to the rigid portions not connected to the outwardly-extending portions 41a,41b in the block B₃, namely, to the connecting portions 38a′,38b′ of the rigid portions 38a,38b (one of these connecting routes is indicated by a double-dot chain line in the drawing). Incidentally, it is not absolutely necessary to limit the shape of the fine motion table 43 to a rectangular shape as shown in the drawing. It may be formed into any shape facilitating the fixed mounting of an object, such as a substantially square shape in which the y-axis dimension of the fine motion table has been increased further. In the above-described structure, the turning axes of the respective radial flexible-beam displacement mechanisms 36M xa ,36M xb ,36M ya ,36M yb ,41M za ,41M zb can be designed to cross perpendicularly at one point on the surface of the fine motion table 43 by choosing the opening angles of the respective flexible beams suitably. The operation of the fine positioning device of the third embodiment of this invention shown in Figure 10 will next be described. Let's now assume that voltages are applied respectively to the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 16F xa ,16F xb . Their parallel flexible beams are deformed respectively along the x-axis of Figure 10 in proportion to the applied voltages as shown in Figure 6B so that they undergo translational displacements. These translational displacements are then transmitted to the fine motion table 43 fixed on the rigid portions 38a,38b by way of the parallel flexible-beam displacement mechanisms 17F ya ,17F yb , 66F za ,66F zb , central rigid portions 65,40, radial flexible-beam displacement mechanisms 41M za ,41M zb , rigid portions 37a,37b, radial flexible-beam displacement mechanisms 36M ya ,36M yb , ring 35, and radial flexible-beam displacement mechanisms 36M xa ,36M xb , so that the fine displacement table 43 undergoes a translational displacement along the x-axis. Similarly, when voltages are applied respectively to the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 17F ya ,17F yb , the fine motion table 43 undergoes a translational displacement along the y-axis. When voltages are applied respectively to the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 66F za ,66F zb , the fine motion table 43 undergoes a translational displacement along the z-axis. On the other hand, when voltages are applied respectively to the piezoelectric actuators of the radial flexible-beam displacement mechanisms 36M ya , 36M yb , the fine motion table 43 undergoes an angular displacement about the y-axis in proportion to the voltages applied. When voltages are applied respectively to the piezoelectric actuators of the radial flexible-beam displacement mechanisms 36M xa ,36M xb , the fine motion table 43 undergoes a radial displacement about the x-axis. When voltages are applied respectively to the piezoelectric actuators of the radial flexible-beam displacement mechanisms 41M za ,41M zb , the fine motion table 43 undergoes an angular displacement about the z-axis. Both translational and angular displacements with respect to one axis have been described. The fine motion table 43 can however be displaced as desired by choosing desired plural displacement mechanisms from the above-described parallel flexible-beam displacement mechanisms and radial flexible-beam displacement mechanisms and then applying desired voltages to the thus-chosen displacement mechanisms. In addition, the degree of each displacement can be controlled accurately by using strain gauges S. In the above description of the third embodiment, the end portions of the outwardly-extending portions extending out along the y-axis in the block B₁ are fixed while its connecting portions are provided at the end portions of the outwardly-extending portions extending out along the x-axis. Needless to say, it is apparent that an opposite arrangement is feasible, namely, the end portions of the outwardly-extending portions extending out along the x-axis may be fixed and the block B₂ may be connected to the end portions of the outwardly-extending portions extending out along the y-axis. Each of the turning axes is not absolutely required to assume a position on the surface of the fine motion table. The position of each turning axis can be chosen as desired. Owing to the above-described structure, the fine positioning device according to the third embodiment can obtain translational displacements along three axes and angular displacements about three axes in spite of its simple and small structure. Since all the turning axes cross perpendicularly at one point on the surface of the fine motion table, the turning center of angular displacements is located on the fine motion table so that accurate angular displacement can be effected. Figure 11 is an exploded perspective view of the fine positioning device according to the fourth embodiment of this invention. This embodiment has a structure which is obtained by adding to the first embodiment a radial flexible-beam displacement mechanism capable of producing angular displacements about two axes and a parallel flexible-beam displacement mechanism capable of producing translational displacements along two axes. In the drawings, x, y and z indicate respectively coordinate axes which are perpendicular to one another. There are also shown a central rigid portion 70, an outwardly-extending portion 71a extending out along the y-axis from the central rigid portion 70, an outwardly-extending portion 71b extending out from the central rigid portion 70 in a direction opposite to the outwardly-extending portion 71a, an outwardly-extending portion 72a extending out along the x-axis from the central rigid portion 70, and an outwardly-extending portion 72b extending out from the central rigid portion 70 in a direction opposite to the outwardly-extending portion 72a. Numerals 73a,73b designate fixing portions provided at lower edge portions of the outwardly-extending portions 71a,71b respectively. Designated at numerals 74a,74b are fine motion table connecting portions provided on upper end portions of the outwardly-extending portions 72a,72b respectively. Numeral 75 indicates a fine motion table. The outwardly-extending portions 71a,71b,72a,72b, fixing portions 73a,73b and fine motion table connecting portions 74a,74b are all formed of the same material as the central rigid portion 70. They are worked out together with the central rigid portion 70 from a single piece of block. Designated at numeral 71M za ,71M zb are respectively radial flexible-beam displacement mechanisms, which are constructed in the outwardly-extending portions 71a,71b respectively. The radial flexible-beam displacement mechanisms are constructed symmetrically to each other with respect to the central rigid portion 70 and cooperate with each other to produce angular displacements about an axis extending in the direction of the z-axis. Numerals 71F xa ,71F xb indicate respectively parallel flexible-beam displacement mechanisms provided outside the respective radial flexible-beam displacement mechanisms 71M za ,71M zb in the outwardly-extending portions 71a,71b. The parallel flexible-beam displacement mechanisms 71F xa , 71F xb are constructed symmetrically to each other relative to the central rigid portion 70 and cooperate with each other to produce translational displacements along the x-axis. Designated at numeral 72F ya ,72F yb are respectively parallel flexible-beam displacement mechanisms, which are constructed in the outwardly-extending portions 72a,72b respectively. The parallel flexible-beam displacement mechanisms are constructed symmetrically to each other with respect to the central rigid portion 70 and cooperate with each other to produce translational displacements along the y-axis. Numerals 72F za ,72F zb indicate respectively parallel flexible-beam displacement mechanisms provided outside the respective parallel flexible-beam displacement mechanisms 72F ya ,72F yb in the outwardly-extending portions 72a,72b. The parallel flexible-beam displacement mechanisms 72F za ,72F zb are constructed symmetrically to each other relative to the central rigid portion 70 and cooperate with each other to produce translational displacements along the z-axis. The portions where the parallel flexible-beam displacement mechanisms 72F za , 72F zb are constructed are formed in such a way that their upper end portions are taller than the other portions. The radial flexible-beam displacement mechanisms 71M za ,71M zb and parallel flexible-beam displacement mechanisms 71F xa ,71F xb ,72F ya ,72F yb ,72F za ,72F zb are constructed by boring predetermined through-holes in the respective outwardly-extending portions 71a,71b,72a,72b at desired locations. The operation of the fine positioning device of the fourth embodiment of this invention shown in Figure 10 will next be described. Let's now assume that equal voltages are applied respectively to the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 71F xa ,71F xb . Their parallel flexible beams are deformed respectively along the x-axis of Figure 11 in proportion to the applied voltages as shown in Figure 6B so that they undergo translational displacements. These translational displacements along the x-axis are then transmitted, as they are, to the fine motion table 75 and the fine motion table 75 undergoes a translational displacement to the same degree along the x-axis, since these parallel flexible-beam displacement mechanisms 71F xa ,71F xb are integral with the radial flexible-beam displacement mechanisms 71M za , 71M zb , central rigid portion 70, parallel flexible-beam displacement mechanisms 72F ya ,72F yb ,72F za ,72F zb , and the fine motion table 75 fixed on the fixing portions 74a,74b. On the other hand, when equal voltages are applied respectively to the piezoelectric actuators of the radial flexible-beam displacement mechanisms 71M za ,71M zb , their radial flexible beams are deformed about the z-axis of Figure 11 to undergo angular displacements as shown in Figure 9B. These angular displacements are transmitted to the fine motion table 75 by way of the central rigid portion 70, parallel flexible-beam displacement mechanisms 72F ya ,72F yb ,72F za , 72F zb , and fixing portions 74a,74b, so that the fine motion table 75 undergoes an angular displacement about the same axis. Similarly, when an identical voltage is applied to each of the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 72F ya , 72F yb , the fine motion table 75 undergoes a translational displacement along the y-axis. When an identical voltage is applied to each of the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 72F za ,72F zb , the fine motion table 75 undergoes a translational displacement along the z-axis. When two or more sets of these flexible-beam displacement mechanisms are driven at the same time, a combined translational displacement or a combined displacement of both translational and angular displacements can be obtained. In the above description of the fourth embodiment, parallel flexible-beam displacement mechanisms are provided to produce translational displacements along the z-axis. The parallel flexible-beam displacement mechanism may be removed depending on the application field. In the above description of the fourth embodiment, the end portions of the outwardly-extending portions extending out along the y-axis are fixed and the fine motion table is provided on the end portions of the outwardly-extending portions extending out along the x-axis. Needless to say, it is apparent that an opposite arrangement is feasible, namely, the end portions of the outwardly-extending portions extending out along the x-axis may be fixed and the fine motion table may be provided on the end portions of the outwardly-extending portions extending out along the y-axis. Further, the portions on which the fine motion table is fixed is constructed taller than the other portions. These portions may however be formed at the same height as the other portions and legs may instead be provided on the side of the fine motion table. Owing to the above-described structure, the fine positioning device according to the fourth embodiment of this invention can obtain translational displacements along two or three axes and angular displacements about one axis in spite of its extremely simple and small structure. Figure 12 is an exploded perspective view of the fine positioning device according to the fifth embodiment of this invention. This embodiment has a structure equivalent to a structure which is obtained by omitting from the second embodiment the radial flexible-beam displacement mechanisms capable of producing angular displacements about the z-axis. In the drawings, x, y and z indicate respectively coordinate axes. Numerals 78M ya ,78M yb indicate respectively radial flexible-beam displacement mechanisms provided symmetrically to each other on a support plate 77. Each of the radial flexible-beam displacement mechanisms 78M ya ,78M yb produces angular displacements about the y-axis. Designated at numerals 78M xa ,78M xb are radial flexible-beam displacement mechanisms arranged symmetrically on the support plate 77. Each of the radial flexible-beam displacement mechanisms 78M xa ,78M xb produces angular displacements about the x-axis. Designated at numerals 79a,79b are one set of rigid portions constructing the radial flexible-beam displacement mechanisms 78M ya , 78M yb (the other rigid portion being the support plate 77), while numerals 80a,80b indicate one set of rigid portions constructing the radial flexible-beam displacement mechanisms 78M xa , 78M xb (the other rigid portion being also the support plate 77). Numerals 81a,81b indicate L-shaped fixing portions connected fixedly to the rigid portions 80a,80b, while numeral 82 indicates a fine motion table fixed on the rigid portions 79a,79b. An object to be subjected to fine positioning is mounted fixedly on the fine motion table 82. The standard axes of the respective radial flexible-beam displacement mechanisms can be designed to extend on the surface of the fine motion table 82 by choosing the opening angles ϑ of their respective radial flexible beams. When an identical voltage is applied to each of the piezoelectric actuators of the radial flexible-beam displacement mechanisms 78M ya ,78M yb , their radial flexible beams are deformed as shown in Figure 8B. Since the support plate 77 is in a state fixed by way of fixing legs 81a,81b and radial flexible-beam displacement mechanisms 78M xa ,78M xb , the radial flexible-beam displacement mechanisms 78M ya ,78M yb produce angular displacements about the y-axis so that the fine motion table 82 undergoes an angular displacement about the y-axis. When an identical voltage is applied to each of the piezoelectric actuators of the radial flexible-beam displacement mechanisms 78M xa ,78M xb on the other hand, their radial flexible beams are deformed to produce angular displacements about the x-axis. These angular displacements are transmitted to the fine motion table 82 via the support plate 77, radial flexible-beam displacement mechanism 78M ya ,78M yb , whereby the fine motion table 82 undergoes an angular displacement about the x-axis. When the radial flexible-beam displacement mechanisms 78M ya ,78M yb and radial flexible-beam displacement mechanisms 78M xa ,78M xb are driven concurrently, the fine motion table 82 undergoes an angular displacement which is a combination of the angular displacements of the respective radial flexible-beam displacement mechanisms. In the fifth embodiment described above, two radial flexible-beam displacement mechanisms are provided symmetrically with respect to each axis. They are however not necessarily limited to the above arrangement. One of the two sets of radial flexible-beam displacement mechanisms may be replaced by a single radial flexible-beam displacement mechanism provided centrally. If the single radial flexible-beam displacement mechanism provided centrally is not the radial flexible-beam displacement mechanism that is fixed at its fixing portions, its rigid portion serves as the fine motion table. Further, it is not essential for the y-axis and x-axis that they are present on the surface of the fine motion table. The positions of the y-axis and x-axis can be chosen as desired. Owing to the structure described above, the fine positioning device of the fifth embodiment can obtain angular displacements about two axes in spite of its simple structure. Figure 13 is an exploded perspective view of the fine positioning device according to the sixth embodiment of this invention. The fine positioning device of the sixth embodiment has a structure equivalent to a combination of the fine positioning device of the fourth embodiment and that of the fifth embodiment. Elements either identical or equivalent to their corresponding elements shown in Figures 11 and 12 are identified by like reference numerals and letters and their description is omitted herein. The connecting portions 74a,74b of the outwardly-extending portions 72a,72b and the L-shaped connecting portions 81a,81b are connected as indicated by two-dot chain lines in the drawing. As a result, the support plate 77, the radial flexible-beam displacement mechanisms 78M xa ,78M xb ,78M ya ,78M yb supported on the support plate 77 and the fine motion table 82 are in a state suspended over the central rigid portion 70 from the connecting portions 74a,74b,81a,81b. By suitably choosing the opening angles of the respective flexible beams of the respective radial flexible-beam displacement mechanisms 78M xa , 78M xb , 78M ya ,78M yb ,71M za ,71M zb in the above state, their turning axes are designed to cross perpendicularly at a single point on the surface of the fine motion table 82. The operation of the fine positioning device according to the sixth embodiment will next be described. When an identical voltage is applied to each of the piezoelectric actuators of the parallel flexible-beam displacement mechanisms 71F xa ,71F xb , their parallel flexible beams are deformed along the x-axis of Figure 13 as shown in Figure 6B in proportion to the voltages applied, so that they produce translational displacements. These translational displacements are then transmitted to the fine motion table 82 fixed on the rigid portions 79a,79b, by way of the radial flexible-beam displacement mechanisms 71M za , 71M zb , central rigid portion 70, parallel flexible-beam displacement mechanisms 72F ya ,72F yb ,72F za ,72F zb , connecting portions 74a,74b,81a,81b, radial flexible-beam displacement mechanisms 78M xa ,78M xb , support plate 77, and radial flexible-beam displacement mechanisms 78M ya ,78M yb , so that the fine motion table 82 undergoes a translational displacement to a corresponding degree along the x-axis. When an identical voltage is applied to each of the piezoelectric actuators of the radial flexible-beam displacement mechanisms 71M za ,71M zb , their radial flexible beams are deformed about the z-axis of Figure 13 as shown in Figure 9B in proportion to the voltages applied, so that the flexible beams undergo an angular displacement. These angular displacements are transmitted to the fine motion table 82 by way of the central rigid portion 70, parallel flexible-beam displacement mechanisms 72F ya ,72F yb ,72F za ,72F zb , connecting portions 74a,74b,81a,81b, radial flexible-beam displacement mechanisms 78M xa ,78M xb , support plate 77, and radial flexible-beam displacement mechanisms 78M ya ,78M yb , so that the fine motion table 82 undergoes an angular displacement about the z-axis. Similarly, when an identical voltage is applied to each of the actuators of the parallel flexible-beam displacement mechanisms 72F ya ,72F yb respectively, the fine motion table 82 undergoes a translational displacement along the y-axis. When an identical voltage is applied to each of the actuators of the parallel flexible-beam displacement mechanisms 72F za ,72F zb on the other hand, the fine motion table 82 undergoes a translational displacement along the z-axis. When an identical voltage is applied to each of the piezoelectric actuators of the radial flexible-beam displacement mechanisms 78M ya ,78M yb respectively, angular displacements are produced about the y-axis so that the fine motion table 82 undergoes an angular displacement about the y-axis. When an identical voltage is applied to each of the piezoelectric actuators of the radial flexible-beam displacement mechanisms 78M xa ,78M xb on the other hand, the fine motion table 82 undergoes an angular displacement about the x-axis. Both translational and angular displacements about a single axis have been described above. It is however possible to displace the fine motion table 82 as desired by choosing plural displacement mechanisms out of the respective parallel flexible-beam displacement mechanisms and radial flexible-beam displacement mechanisms and applying desired voltages thereto. In the above description of the sixth embodiment, the end portions of the outwardly-extending portions extending out along the y-axis are fixed and the connecting portions are provided at the end portions of the outwardly-extending portions extending out along the x-axis. Needless to say, it is apparent that an opposite arrangement is feasible, namely, the end portions of the outwardly-extending portions extending out along the x-axis may be fixed and the connecting portions may be provided on the leg portions of the outwardly-extending portions extending out along the y-axis. In the sixth embodiment described above, two radial flexible-beam displacement mechanisms are provided symmetrically on the support plate with respect to each axis. They are however not necessarily limited to the above arrangement. One of the two sets of radial flexible-beam displacement mechanisms may be replaced by a single radial flexible-beam displacement mechanism provided centrally. If the single radial flexible-beam displacement mechanism provided centrally is not the radial flexible-beam displacement mechanism that is fixed at its fixing portions, its rigid portion serves as the fine motion table. Further, it is not essential for each turning axis to reside on the surface of the fine motion table. The positions of the turning axes can be chosen as desired. Owing to the structure described above, the fine positioning device of the sixth embodiment can obtain translational displacements along three axes and angular displacements about three axes in spite of its extremely simple and small structure. Since all the turning axes cross perpendicularly at one point on the surface of the fine motion table, the turning center of each angular displacement is also located on the fine motion table so that an accurate angular displacement can be effected. The structures of several fine positioning devices making use of one or more parallel flexible-beam displacement mechanisms and/or radial flexible-beam displacement mechanisms have been described by way of example. These fine positioning devices can each produce a desired displacement with relatively high accuracy by applying a predetermined voltage to each of their piezoelectric actuators.

Claims: A fine positioning device comprising: a rigid support portion (81a, 81b; 40, 41a, 41b); a rigid support plate (77, 35); a first radial flexible-beam displacement mechanism (78M xa ; 36M ya ) adapted to produce angular displacements about a first axis (x; y) and provided between the support plate (77, 35) and the rigid support portion (81a, 81b; 40, 41a, 41b); a fine motion table (82, 43); a second radial flexible-beam displacement mechanism (78M ya ; 36M xa ) adapted to produce angular displacements about a second axis (y; x) and provided between the fine motion table (82, 43) and the support plate (77, 35); the first and second axes (x, y) extending on the surface of the fine motion table (82, 43), two first radial flexible-beam displacement mechanisms (78M xa , 78M xb ; 36M ya , 36M yb ) with coinciding first axes (x; y) and placed one at either side of the second axis (y; x), and two second radial flexible-beam displacement mechanisms (78M ya , 78M yb ; 36M xa , 36M xb ) with coinciding second axes (y; x) and placed one at either side of the first axis (x; y), said two first and two second radial flexible-beam displacement mechanisms being arranged at the same side of the rigid support plate (77; 35) and the rigid support portion (81a, 81b; 40, 41a, 41b) at least partly extending between the rigid support plate (77; 35) and the fine motion table (82, 43). (Figs 12, 7, 10, 13) A fine positioning device according to claim 1, characterized by two third radial flexible-beam displacement mechanisms (41M za , 41M zb ) adapted to produce angular displacements about a common third axis (z) and provided in the rigid support portion between two rigid lateral parts (41a, 41b) and a central rigid part (40), said third axis (z) of said two third radial displacement mechanisms (41M za , 41M zb ) extending through the intersection point of said first and second axes (x, y) extending on the surface of the fine motion table (82, 43). (Fig. 7, 10) A fine positioning device according to claim 2, characterized by a first block (B₁) comprising a central rigid portion (15), a first set of outwardly-extending portions (16a, 16b) extending symmetrically along the first axis (y) and equipped respectively with two first parallel flexible-beam displacement mechanisms (16F xa , 16F xb ) to produce in the first set of outwardly-extending portions (16a, 16b) translational displacements along the second axis (x), and a second set of outwardly-extending portions (17a, 17b) extending symmetrically along the second axis (x) and equipped respectively with two second parallel flexible-beam displacement mechanisms (17F ya , 17F yb ) to produce in the second set of outwardly-extending portions (17a, 17b) translational displacements along the first axis (y); a second block (B₂) comprising a central rigid portion (65), a third set of outwardly-extending portions (66a, 66b) extending symmetrically along the second axis (x) and equipped respectively with two third parallel flexible-beam displacement mechanisms (66F za , 66F zb ) to produce in the third set of outwardly-extending portions (66a, 66b) translational displacements along the third axis (z), the second set of outwardly-extending portions (17a, 17b) of first block (B₁) being attached to the third set of outwardly-extending portions (66a, 66b) of the second block (B₂), and the central rigid portion (65) of the second block (B₂) being attached to the central rigid part (40) of the rigid support portion (40, 41a, 41b). (Fig. 10) A fine positioning device according to claim 1, characterized by a central rigid portion (70); a first set of outwardly-extending portions (71a, 71b) extending symmetrically along the second axis (y); a second set of outwardly-extending portions (72a, 72b) extending symmetrically along the first axis (x); a first set of two parallel flexible-beam displacement mechanisms (71F xa , 71F xb ) provided symmetrically to each other with the first set of outwardly-extending portions (71a, 71b) respectively and adapted to produce translational displacements along the first axis (x); a second set of two parallel flexible-beam displacement mechanisms (72F ya , 72F yb ) provided symmetrically to each other with the second set of outwardly-extending portions (72a, 72b) and adapted to produce translational displacements along the second axis (y), and a third set of two parallel flexible-beam displacement mechanisms (72F za , 72F zb ) provided symmetrically to each other with the second set of outwardly-extending portions (72a, 72b) and adapted to produce translational displacements along the third axis (z), the second set of outwardly-extending portions (72a, 72b) being attached to the rigid support portion (81a, 81b). (Fig. 13) A fine positioning device according to any one of claims 1 - 4, characterized by an actuator (26a, 26b; 49; 60a, 60b), especially a piezoelectric actuator is present for applying a moment or a force to introduce a bending deformation in a flexible beam displacement mechanism. A fine positioning device according to claim 5, characterized in that the actuator (26a, 26b; 49; 60a, 60b) is a piezoelectric actuator

Inventors: HOSHINO YOSHIHIRO, MURAYAMA KEN, NAGASAWA KIYOSHI, OGATA KOJIRO, ONO KOZO, HOSHINO, YOSHIHIRO, MURAYAMA, KEN, NAGASAWA, KIYOSHI, OGATA, KOJIRO, ONO, KOZO
Applicants: HITACHI CONSTRUCTION MACHINERY, HITACHI CONSTRUCTION MACHINERY CO., LTD.
Application year: 1987
Main classification: B23Q1
IPC codes: G01B5, G05D3, G05B19, B23Q15, H01L41, H01L21, B23Q1, G01B7