Abstract:
A biaxial driver includes an induction coil that is moveable in two dimensions and a linearly oriented magnet. A payload platform for holding a tool or workpiece is attached to the moveable coil. The inventive driver provides motion parallel to an axis of the magnet, even while the coil is moved transversely or obliquely to the axis of the coil, and permits the degree of coil extension to be varied while the biaxial driver is operated. Because the magnet is held stationary during movement of the payload platform, there is no inertia from the stationary magnet to overcome. A result, the payload platform can be moved from one position to another in less time, the payload platform can carry a more massive payload than previous positioning drivers and the invention requires less energy consumption.

Description:
[0001]     This application claims the benefit of and right of priority from U.S. Provisional Patent Application Ser. No. 60/413,224, filed Sep. 24, 2002, which is hereby incorporated by reference.  
         [0002]     The invention relates generally to planar motors and, more specifically, to a biaxial driver for driving a movable platform used to transfer or position a tool or workpiece. 
     
    
     FIELD OF THE INVENTION  
     Background of the Invention  
       [0003]     Previously known devices for positioning a platform along a single axis are often termed “linear drivers” and include various mechanisms capable of producing linear motion, such as a piston, a rotating screw thread and threaded collar or a mechanical linkage, among others. For example, the linear driver may be actuated by a linear electric motor including a stationary magnet and a movable coil or a movable magnet and a stationary coil. The movable coil or movable magnet travels in a line, and is said to have one degree of freedom, because it is movable along a single axis (hereinafter referred to as “the first axis”). The movable coil or movable magnet is supported by a bearing that glides on a stationary guide rail, which defines the first axis. A platform for mounting a tool or workpiece is usually attached to the movable coil or movable magnet and/or the bearing. An example of a linear electric motor is described in U.S. Pat. No. 5,998,890, issued to Sedgewick et al., which is hereby incorporated by reference.  
         [0004]     Previously known devices for positioning a platform along two crossing or intersecting axes are termed “biaxial” or “planar drivers.” The biaxial driver may be, for example, a checkerboard magnet array and coil arrangement, as described in U.S. Pat. No. 6,097,114, issued to Hazelton, which is hereby incorporated by reference. As another example, the biaxial driver may include two moving coil linear electric motors, each as described above, joined head-to-tail so that the platform of the first motor supports the magnet of the second motor. The second motor positions a second platform along a second axis (hereinafter referred to as “the second axis”), which is often arranged perpendicularly to the first axis. This head-to-tail concept can also be applied to three linear motors in a multi-axial driver for positioning a platform according to any three dimensional, Cartesian coordinates in a specified volume.  
         [0005]     While the head-to-tail multiaxis linear motor driver with movable coils is known, it requires that the second motor magnet move in tandem with first motor platform and coil. Because the magnets are often the most massive components of the biaxial driver, the inertia of the second motor magnet significantly impedes movement of the first motor coil and platform. Although more powerful motors and more sensitive controllers can alleviate this problem to some extent, the additional inertia due to moving the second motor magnet tends to make the head-to-tail biaxial driver operate in a relatively inefficient manner. Also, the inertia of the second motor magnet exerts dynamic forces on the first motor bearing that require the first motor bearing construction to be more complex and expensive than would otherwise be necessary.  
         [0006]     A need exists for a new biaxial driver that does not require a checkerboard magnet array, or a second magnet that must be moved each time a payload platform is moved along the first axis. Desirably, a new biaxial driver could be utilized with a combination of one or more linear drivers and one or more nonlinear drivers.  
       SUMMARY OF THE INVENTION  
       [0007]     The invention is a biaxial driver including a magnet assembly for producing a magnetic field arranged along a longitudinal axis and a coil assembly. When the coil assembly is under the influence of the magnetic field, and when the coil is electrically energized, the coil has two degrees of freedom. The coil assembly interacts with the magnetic field to produce a motive force generally parallel to the longitudinal axis. The biaxial driver also includes a cross driver for moving the coil assembly or the magnet assembly along an axis that crosses the longitudinal axis. Under the influence of the motive force and the cross driver, the coil assembly or the magnet assembly can be maneuvered throughout a planar area, rather than being confined to a single axis.  
         [0008]     In some embodiments of the invention, the cross driver is a linear driver for moving the coil assembly or the magnet assembly along the crossing axis. These two axes define a plane in which the second coil assembly or the magnet assembly, and an associated payload platform, can be accurately and reproducibly positioned. The linear driver may be, for example, a linear electric motor including a magnet assembly that remains at rest.  
         [0009]     In other embodiments of the invention, the cross driver is a nonlinear driver such as, for example, a pair of pivoting links, a cam surface and follower, or a tongue and guide groove. These embodiments can be used for, among other things, directing a glue nozzle over an irregular path or area.  
         [0010]     The invention provides a motive force parallel to the longitudinal axis of a magnet. The coil assembly sustains the motive force while the coil assembly extends to various distances from the longitudinal axis. The coil assembly is shaped and proportioned to facilitate moving the coil assembly along another axis that crosses or intersects the longitudinal axis during operation.  
         [0011]     Additionally, the invention positions a platform in two dimensions. The driver includes a payload platform stationary magnet assembly, which would previously have contributed to the inertia of payload platform movement. With less inertia, the payload platform can be moved from one position to another in less time than prior platform positioning drivers. A further benefit is greater energy efficiency due to lower power consumption. Also, the payload platform can carry a more massive payload than before, for a given coil assembly and magnet assembly. The invention can be applied to two- and three-axis positioning drivers. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]      FIG. 1  is a perspective view of a linear driver of the prior art;  
         [0013]      FIG. 2  is a perspective view of a biaxial driver of the prior art;  
         [0014]      FIG. 3  is a perspective view of a biaxial driver of the present invention including a linear electric motor;  
         [0015]      FIG. 4  is a perspective view of a biaxial driver of the present invention including a piston and cylinder;  
         [0016]      FIG. 5  is a perspective view of a biaxial driver of the present invention including a mechanical linkage;  
         [0017]      FIG. 6  is an elevation view of a biaxial driver of the present invention including a pair of pivoting links;  
         [0018]      FIG. 7  is a cross-sectional view taken along line D-D of  FIG. 6 , showing a coil assembly of the present invention extended in an intermediate position with respect to a magnet assembly;  
         [0019]      FIG. 8  is a cross-sectional view showing the coil assembly of  FIG. 6  minimally extended with respect to the magnet assembly;  
         [0020]      FIG. 9  is a cross-sectional view showing the coil assembly of  FIG. 6  greatly extended with respect to the magnet assembly;  
         [0021]      FIG. 10  is a cross-sectional view taken along line E-E of  FIG. 9 , showing the arrangement of nonoverlapping, polyphasic coil loops in the energizable portion of the coil assembly;  
         [0022]      FIG. 11  is an elevation view of a biaxial driver of the present invention including a cam and a follower;  
         [0023]      FIG. 12  is an elevation view of a biaxial driver of the present invention including a serpentine groove and a tongue;  
         [0024]      FIG. 13  is a perspective view of a coil and moving magnet assembly of the present invention;  
         [0025]      FIG. 14  is a cross-sectional view taken along line F-F of  FIG. 13 ; and  
         [0026]      FIG. 15  is a cross-sectional view of the coil assembly and the magnet assembly of  FIG. 1 . 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0027]     A representative single-axis linear driver of the prior art, designated driver  1 , is depicted in  FIG. 1 . Stationary base  10  is rigidly attached to stationary platform  11 . Sensor  12  is fixed to the platform  11  for determining the relative position for an encoder (not shown) to provide feedback for a positioning controller (not shown). Pad  14  secures stationary, channel-shaped magnet  15  to base  10 . Coil  16  moves only along a single axis (hereinafter referred to as “the first axis”) along axis A. Bearing  17 , which rides on guide rail  13  (shown in  FIG. 1 ), supports coil  16 . First platform  21  is fixed to bearing  17  and coil  16 . The encoder (not shown) that cooperates with sensor  12  is mounted on platform  21 . Platform  21  may be used, for example, to transfer or position a tool or workpiece along the first axis. A tool or workpiece mounted on platform  21  can be moved along the first axis for interaction with another workpiece or tool (such as in an assembly line) by moving platform  21  under the power of the coil and magnet, according to well-known principles.  
         [0028]     A representative two-axis, head-to-tail driver of the prior art, designated driver  2 , is depicted in  FIG. 2 . Driver  2  includes all of the elements described above with regard to driver  1 . Additionally, driver  2  includes sensor  22 , guide rail  23  and magnet  25 , all attached to platform  21 . When platform  21  translates along the first axis in response to movement by coil  16 , sensor  22 , guide rail  23  and magnet  25  translate along the first axis as well. Driver  2  also includes coil  26 , which is attached to bearing  27  and payload platform  28 . Bearing  27  glides along guide rail  23  in response to any movement of coil  26  along the second axis parallel to axis B. Significantly, platform  28  and coil  26  remain at a fixed distance from magnet  25 . Accordingly, driver  2  can position platform  28  along the first axis and the second axis. Platform  28  is said to have two degrees of freedom.  
         [0029]     The head-to-tail multiaxis linear motor driver requires moving magnet  25  in tandem with platform  21  and coil  16 . Because magnet  25  is usually one of the most massive components of driver  2 , its presence adds a significant amount of inertia to coil  16  movement. Each time payload  28  is accelerated and decelerated in either direction along the first axis, the inertia of magnet  25  must be overcome. Although more powerful motors and more sensitive controllers can alleviate this problem to some extent, the additional inertia due to moving magnet  25  tends to make driver  2  operate in a relatively inefficient manner. The inertia and weight of magnet  25  exert dynamic forces on bearing  17 , requiring that bearing  17  be more complex and expensive than would otherwise be necessary.  
         [0030]     A preferred embodiment of the inventive biaxial driver is driver  100 , depicted in  FIG. 3 . Components depicted in  FIG. 3  that have the same two final digits as components depicted in  FIGS. 1 and 2  correspond to those components and to the same descriptions of those components (i.e., component  10  of  FIG. 1  is the same as component  110  of  FIG. 3 , component  11  of  FIG. 1  is the same as component  111  of  FIG. 3 , etc).  
         [0031]     Driver  100  includes a stationary base  110  that provides mechanical support for the other components of driver  100 . Stationary base  110  is rigidly attached to stationary platform  111 . Guide rail  113  is secured to base  110 , for supporting bearing  117  and moveable platform  121 .  
         [0032]     Sensor  112  is fixed to the platform  111  for determining its position relative to that of an encoder (not shown). For example, the sensor  112  may include a read head member that determines the position of platform  121  relative to platform  111  and provides feedback for a positioning controller (not shown). Preferably, the encoder (not shown) is an optical scale attached to the underside of platform  121 . The positioning controller (not shown) receives a target position as input, compares the present position of payload platform  128  as indicated by sensor  112 , and sends electrical power to coil assembly  116  and/or coil assembly  126  as necessary to move payload platform  128  to the target position.  
         [0033]     Pad  114  secures stationary, channel-shaped magnet assembly  115  to base  10 . The longitudinal axis of magnet assembly  115  defines the first axis of driver  100  for movement parallel to axis A in  FIG. 3 . Another pad  130  secures stationary, channel-shaped magnet assembly, 125  to base  10 . The longitudinal axis of magnet assembly  125  defines the second axis of driver  100  for movement parallel to axis B in  FIG. 3 . As can be inferred from  FIG. 3 , the first and second axes are perpendicular to each other when the depicted embodiment is viewed in two dimensions from above but are generally not co-planar. In contrast, axes A and B are generally coplanar and cross or intersect each other. The invention can be practiced successfully when axes A and B intersect at any angle other than 0 or 180 degrees, preferably at an interior angle of about 1 to about 90 degrees.  
         [0034]     A first linear motor includes coil assembly  116  and magnet assembly  115 , as depicted in cross-section in  FIG. 15 . Magnet assembly  125  includes a yoke supporting two magnet rows  156 ,  158 , which are constituted by permanent magnets arranged with alternating polarity. The yoke is generally U-shaped and forms floor  150  between the magnet rows  156 ,  158 . Coil assembly  126  is inserted between magnet rows  156 ,  158  with an air gap  152  between coil assembly  126  and floor  150 . The vertical length of energizing portion  165  is indicated by length L 2  in  FIG. 15 . The length of magnet rows  156 ,  158  is indicated by length L 3 . Coil assembly  116  moves forward and back parallel to axis A under the influence of magnet assembly  115 . For example, a coil assembly and a magnet assembly suitable for use in the present invention are commercially available from Anorad Corporation of Shirley, N.Y. as part no. LEB-S-6-S-NC-TE-C and part no. LEB-S-750, respectively.  
         [0035]     Referring again to  FIG. 3 , bearing  117 , which rides on guide rail  113 , supports coil assembly  116 . First platform  121  is fixed to bearing  117  and coil assembly  116  so that as coil assembly  116  moves parallel to axis A, so does first platform  121 . The encoder (not shown) that cooperates with sensor  121  is mounted on the underside of platform  121 . Platform  121  may be used, for example, to transfer or position a tool or workpiece along axis A.  
         [0036]     Driver  100  also includes sensor  122 , guide rail  123  and magnet assembly  125 , all attached to platform  121 . When platform  121  translates along axis A in response to movement by coil assembly  116 , sensor  122  and guide rail  123  translate along the first axis as well. Magnet assembly  125  is mounted rigidly to base  110  and does not translate.  
         [0037]     A second linear motor includes coil assembly  126  and magnet assembly  125 . Coil assembly  126  moves forward and back parallel to axis B under the influence of magnet assembly  125 . Additionally, coil assembly  126  moves forward and back parallel to axis A under the influence of coil assembly  116  and magnet assembly  115 . The ability of coil assembly  126  to move in two axes eliminates any need for movement of magnet assembly  125  relative to base  110 , at least over a significant range of distances. Desirably, coil assembly  126  moves forward and back up to about 10 millimeters along axis A using conventional, commercially available linear motor coil assemblies and magnet assemblies. This amount of extension and retraction is sufficient for many commercially important positioning applications. As will be discussed below, coil assemblies and magnet assemblies can be adapted to provide greater ranges of movement along axis A.  
         [0038]     Coil assembly  126  is attached to bearing  127  and payload platform  128 . Bearing  127  and payload platform  128  glide along guide rail  123  in response to movement of coil assembly  126  along axis B. An encoder (not shown) that cooperates with sensor  122  is mounted on the underside of payload platform  128 . Guide rail  123  and payload platform  128  move along the first axis A in response to movement of coil assembly  116  along the first axis. Accordingly, driver  100  can position payload platform  128  over significant ranges of distance along the first axis and the second axis and within the plane defined by axes A and B. By controlling the timing and the amount of power that the positioning controller (not shown) sends to coil assembly  116  and coil assembly  126 , respectively, payload platform  128  can be made to trace any two-dimensional pattern imaginable within the biaxial travel limits of coil assembly  126 .  
         [0039]     The intensity of the magnetic field in which coil assembly  126  operates decreases as coil assembly  126  moves away from magnet assembly  125 . Accordingly, magnet assembly  125  should be suitable for providing a magnetic field intensity that is sufficient to operate coil assembly  126  at the greatest operational distance contemplated for a particular application, without requiring an excessive flow of electrical current that would tend to overheat coil assembly  126 .  
         [0040]     The invention can be practiced utilizing various types of linear drivers such as, for example, a hydraulic piston, a gas-powered piston, or a mechanical linkage as a driver for axis B, rather than the first linear motor as shown in  FIG. 3 . For example, driver  200  depicted in  FIG. 4  includes a double action pneumatic cylinder and piston  215  to drive rod  216  forward and back along the first axis. Block  219  attaches rod  216  to platform  221 . With the exception of components  215 ,  216  and  219 , components depicted in  FIG. 4  that have the same two final digits as components depicted in  FIG. 3  correspond to those components and their descriptions. The cylinder, piston and rod assembly produces a motion for platforms  221  and  228  parallel to axis A, as the first linear motor did.  
         [0041]     As another example, driver  300  depicted in  FIG. 5  includes a mechanical linkage  315  actuated by movement in the direction of second axis B to drive rod  316  forward and back along axis A. This produces motion for the platforms  321  and  328  parallel to axis A, as the first linear motor did. With the exception of components  315 ,  316  and  319 , components depicted in  FIG. 5  that have the same two final digits as components depicted in  FIG. 3  correspond to those components and their descriptions.  
         [0042]     In another embodiment, the invention is biaxial driver  500  comprising magnet assembly  525  and coil assembly  526 , as depicted in  FIG. 6 . With the exception of components  514 ,  515 ,  516  and  519 , components depicted in  FIG. 6  that have the same two final digits as components depicted in  FIG. 3  correspond to those components and their descriptions. Magnet assembly  525  includes a row of permanent magnets (not shown) fixed to base  510  and arranged with alternating polarity to produce a magnetic field oriented along a longitudinal axis, illustrated by line C in  FIG. 6 . Coil assembly  526  is shaped and sized to operate throughout a range of distance from the longitudinal axis of the magnet and to produce, when electrically energized, a motive force parallel to axis B of  FIG. 6 . As can be seen from  FIG. 6 , axes B and C are parallel to each other in this embodiment.  
         [0043]     Two pivoting links  515  are each pivotally connected to magnet assembly  525  and cross-bar  519  by lower pivot points  514  and upper pivot points  516 , respectively. Because cross-bar  519  is fixed to coil assembly  526 , links  515  guide coil assembly  526  and platform  528  as they move under the influence of the motive force. Coil assembly  526  moves along an arcuate path, indicated by arrow G, when electrically energized because pivot links  515  move between the horizontal and vertical positions. Of course, the movement of coil assembly  526  is a vector quantity that can be expressed as the sum of motion along two perpendicular axes, such as axis A and axis B. Tool or workpiece  540 , which is fixed to coil assembly  526  via platform  528 , can be precisely and accurately positioned along the arcuate path indicated by arrow G.  
         [0044]     In other embodiments of the invention, various nonlinear drivers are employed to guide coil assembly  526  as it moves under the influence of magnet assembly  525 . For example, the nonlinear driver may be a cam and a follower, generally as depicted in  FIG. 11 . As another example, the nonlinear driver may be a guide and a tongue, generally as depicted in  FIG. 12 .  
         [0045]     Details of magnet assembly  525  and coil assembly  526  are presented in  FIG. 7 . Magnet assembly  525  includes magnet support yoke  542  and two sheets or rows of magnets  556 ,  558 . Yoke  542  is attached to base  510  and includes two opposed side plates  544 ,  546  and end  548 , the side plates and the end cooperating to define a cavity between them. The cavity extends from floor  550  to shoulder  554 , which are both surfaces of yoke  554 . Magnet rows  556 ,  558  adjoin side plates  544 ,  546 , respectively and each magnet row includes a plurality of permanent magnets arranged with alternating polarity so that magnetic poles of opposite polarity face each other across the cavity.  
         [0046]     Coil assembly  526  includes moving coil  560 , which is divided into energizable portion  565 , mounting portion  564 , and bracket portion  566 . Energizable portion  565  includes copper conductors  563  molded inside electrically insulating resin binder  562 . Sides  570 ,  572  of energizable portion  565  are generally flat, approximately parallel to each other and spaced to fit loosely within the cavity. Air gap  552  is a variable distance measured from floor  550  to energizable portion  565 , when it is inserted into the cavity. As depicted in  FIG. 7 , coil assembly  526  is in an intermediate position with respect to floor  550 . By volume, energizable portion  565  is predominantly electrically conductive material, preferably at least  70  percent conductive material, and more preferably about at least  90  percent conductive material. For the present purposes, “electrically conductive material” means material that is at least as electrically conductive as wrought iron.  
         [0047]     Mounting portion  564  is primarily a structural member, contains little or no electrically conductive material and is substantially nonconductive. Mounting portion  564  generates little or no motive force when exposed to the magnetic field of magnet assembly  525 . Preferably, mounting portion  564  is composed predominantly of electrically insulating material, also termed dielectric material, more preferably at least 70 percent by volume electrically insulating material. Preferably, mounting portion  564  includes essentially no electrically conductive coil loops, such as coil loops  561  (best seen in  FIG. 10 ). For the present purposes, “essentially no electrically conductive coil loops” means so few coil loops that any motive force generated by them is too small to change the essential operation of an associated coil assembly, such as coil assembly  525 .  
         [0048]     Mounting portion  564  is attached to energizable portion  565 , and has a thickness appropriate for insertion into the cavity. Preferably, the thickness of mounting portion  564  is about equal to or less than the thickness of energizable portion  565 . The length of mounting portion  564 , which is illustrated as L 1  in  FIG. 8 , is preferably at least about one-quarter of the length of energizable portion  565 ; more preferably, at least about one-half; and, most preferably, about equal to or greater than the length of energizable portion  565 , which is illustrated as L 2  in  FIG. 8 .  
         [0049]     Bracket portion  566  is attached to mounting portion  564  primarily for the purpose of providing a surface for attaching other components, such as a tool, workpiece or platform, and is often made of the same material as, and integral with, mounting portion  564 . Depending on the nature of the tool, workpiece or platform to be moved by coil assembly  526 , bracket portion  566  may be unnecessary in some applications.  
         [0050]      FIG. 8  depicts coil assembly  526  in a minimally extended position, with respect to floor  550 . This position occurs, for example, when pivot links  515  (best seen in  FIG. 6 ) are at their closest approach to horizontal. Coil assembly  526  may be below the longitudinal axis C of the magnetic field at this point. However, because conductors  563  are still between magnet rows  556 ,  558 , coil assembly  526  continues to generate a satisfactory amount of motive force parallel to the longitudinal axis C and exhibits no indications of overheating. The length of magnet rows  556 ,  558  is indicated by L 3  in  FIG. 8 .  
         [0051]     Coil assembly  526  is greatly extended from floor  550 , as depicted in  FIG. 9 . This extension may occur, for example, when links  515  are vertical. When coil assembly  536  moves away from floor  550  during operation, it continues to generate sufficient motive force without overheating. As can be seen in  FIG. 9 , air gap  552  is significantly increased, as compared to  FIG. 8 , while conductors  563  remain between magnet rows  556 ,  558 .  
         [0052]      FIG. 10  depicts a cross-section taken along B-B of  FIG. 9 , illustrating that conductors  563  include six nonoverlapping, polyphasic coil loops  561 . The size and placement of coil loops  561  determine the dimensions of energizable portion  565 . Coil loops  561  are configured in three sets, each set being appropriate for energizing by one phase of a three-phase,  240  volt electrical current. The, width of each of coil loops  561  is calculated to cooperate with the size and arrangement of permanent magnets in magnet rows  556 ,  568  so that at least one coil loop  561  of each set is always generating motive force while the electrical current is on. U.S. Pat. No. 6,348,746 B1, issued to Fujisawa et al., describes field magnets and polyphasic armature coils and is hereby incorporated by reference.  
         [0053]     Additionally, the relative size and number of permanent magnets and coil loops  561  is calculated using widely known principles so that the desired amount of motive force is generated by coil assembly  526  without overheating at various positions of extension and retraction of coil assembly  526  with respect to floor  550 . The invention is not limited to operation with energizable portion  565  entirely between magnet rows  556 ,  568 . It is contemplated that the permanent magnets and energizable portion  565  may be sized and constructed so that energizable portion  565  may be operated at least partially above or below magnet rows  556 ,  568 .  
         [0054]     In still another embodiment, the invention includes biaxial driver  600  comprising magnet assembly  625  and coil assembly  626 , as depicted in  FIG. 11 . With the exception of components  614  and  615 , components depicted in  FIG. 6  that have the same two final digits as components depicted in  FIG. 3  correspond to those components and their descriptions. Magnet assembly  625  includes a row of permanent magnets (not shown) fixed to base  610  and arranged with alternating polarity to produce a magnetic field oriented along a longitudinal axis, illustrated as axis C. Coil assembly  626  is shaped and sized to operate throughout a range of distance from axis C and to produce, when electrically energized, a motive force parallel to axis B. As can be seen from  FIG. 11 , axes B and C are parallel to each other in this embodiment.  
         [0055]     Cam  614  is rigidly attached to base  610  and, consequently, is fixed with respect to magnet assembly  625 . Follower  615  is attached to coil assembly  626 . The force of gravity holds follower  615  against surface  619  of cam  614  as coil assembly  626  is propelled along axis B by the motive force. Coil assembly  626  moves along axis A under the influence of follower  615  as it follows the surface of cam  614 . Accordingly, the actual path of coil assembly  626  and platform  628  is described by curve H, which parallels surface  619  of cam  614 . Guide rail  613  glides along bearing  617 . Guide rail  623  glides along bearing  627 . The bearings  617 ,  627  are located in bearing block  618 . Tool or workpiece  640 , which is fixed to coil assembly  626  via platform  628 , can be precisely and accurately positioned along the arcuate path indicated by arrow H.  
         [0056]     In yet another embodiment, the invention includes biaxial driver  700  comprising magnet assembly  725  and coil assembly  726 , as depicted in  FIG. 12 . With the exception of components  714  and  715 , components depicted in  FIG. 6  that have the same two final digits as components depicted in  FIG. 3  correspond to those components and their descriptions. Coil assembly  726  is shaped and sized to operate throughout a range of distance from axis C of the magnet and to produce, when electrically energized, a motive force parallel to axis B. As can be seen from  FIG. 12 , axis B is parallel to axis C, which is the longitudinal axis of magnet assembly  625 .  
         [0057]     Serpentine groove or track  714  is formed in block  720 , which is rigidly attached to base  710  and, consequently, is fixed with respect to magnet assembly  725 . Tongue  715  is attached to coil assembly  726  and inserted into groove  714 . The position of tongue  715  with respect to axis A is limited by groove  714 . As coil assembly  726  is propelled along axis B by the motive force, coil assembly  726  moves along axis A under the influence of tongue  715  as it tracks the inner surface  719  of groove  714 . Accordingly, the actual path of coil assembly  726  and platform  728  is described by curve I, which parallels groove  714 . The bearings  717 ,  727  are located in bearing block  718  to support the guide rail  713 ,  23 , respectively.  
         [0058]     While the invention has been described above by reference to a stationary magnet and a moveable coil, the invention may also be practiced with a stationary linear coil and moving magnet, as depicted in  FIG. 13 . Coil and extensible magnet assembly  800  includes a coil support yoke  810  for supporting conductors  820 , which have a plurality of electrically energizable coil loops  821 - 829 . When energized, conductors  820  produce an electromagnetic field along longitudinal axis G. Although coil loops  821 - 829  are depicted in  FIG. 11  as overlapping one another, nonoverlapping coils may also be successfully employed in conductors  820 , provided that the electrical current is commutated in accordance with well-known principles.  
         [0059]     Continuing with  FIG. 13 , assembly  800  also includes extensible magnet assembly  830  having at least one row of magnets  840  arranged side-by-side in alternating polarity to produce a magnetic field in the longitudinal axis. Specifically, magnets  842  having north poles facing upwardly alternate with magnets  844  having south poles facing upwardly to produce magnetic flux that varies sinusoidally as a function of distance in the longitudinal axis. U.S. Pat. No. 4,051,398, issued to Kondo, describes rectangular and U-shaped coils for driving a movable magnet member and is hereby incorporated by reference.  
         [0060]      FIG. 14  is a cross-sectional view taken along C-C in  FIG. 13 , which shows electromagnetic field region  850  concentrated between conductors  820 . Magnet assembly  830  is inserted between conductors  820  so that magnet rows  840  reside in electromagnetic field region  850 . Variable air gap  890  is located between magnet rows  840  and yoke  810 .  
         [0061]     Mounting portion  860  is primarily a mechanical support member and is substantially nonmagnetic. Preferably, mounting portion  860  includes essentially no magnets. As can be seen in  FIG. 14 , mounting portion  860  is attached to magnet rows  840  and has a length that is illustrated as L 4 . Bracket portion  870  is attached to mounting portion  860 .  
         [0062]     To operate assembly  800 , conductors  820  are energized with electrical current by a commutator in accordance with well known principles to produce an electromagnetic field along longitudinal axis G. The electromagnetic field interacts with magnetic field produced by magnet rows  840 , generating a motive force generally parallel to longitudinal axis G. Because the length of electromagnetic field region  850 , which is illustrated as L 6  in  FIG. 14 , is greater than the length of magnet rows  840 , which is illustrated as L 5  in  FIG. 14 , magnet assembly  830  can be extended away from or retracted toward longitudinal axis G over a significant range of distance without excessive heat or unacceptable loss of motive force.  
         [0063]     It is also contemplated that the invention can produce movement along three axes by, for example, utilizing an extensible coil and one or two linear electric motors. With three motors, the first axis magnet assembly may be fixed relative to the second axis magnet assembly so that the second axis coil assembly (which includes an extensible coil) operates in an extended position relative to the second magnet assembly.  
         [0064]     Alternatively, the second axis magnet assembly may be fixed relative to the third axis magnet assembly so that the third axis coil assembly (which includes an extensible coil) operates in an extended position relative to the third magnet assembly. Those who study this application will find that it suggests other arrangements, which are also intended to be within the scope of the invention. The figures and descriptions set forth above are intended to be exemplary only and not to limit the scope of the appended claims.