PATENT DOCUMENT

Abstract:
Disclosed is a positioner for transmitting movement in up to six degrees-of-freedom to an object on the positioner, the positioner comprising a base plate, a first plate mounted on the base plate by a first mechanical linkage, a first actuator arrangement for moving the first plate, a second plate mounted on the first plate by a second mechanical linkage, a second actuator arrangement for moving the second plate, and a holder attached to the second plate for mounting the object. One of the first and second plates is movable in a plane in up to three degrees-of-freedom, and the other of the first and second plates is movable in up to three degrees-of-freedom that are out of the plane. It is also possible to add an additional plate, including an actuator arrangement for moving the additional plate, mounted by a mechanical linkage between the second plate and the holder.

Full Description:
Field of the Invention  
         [0001]    This invention relates to a mechanism for positioning objects, particularly mirrors, in up to six degrees-of-freedom, namely X-, Y- and Z-translation and rotation about X-, Y- and Z-axes.  
         BACKGROUND OF THE INVENTION  
         [0002]    Known six degrees-of-freedom mechanisms are varied in structure and operation, resulting in different levels of orientational freedom (work volume), positional repeatability, stiffness and coupling. Coupling is related to the extent to which isolation of motion in one of the degrees-of-freedom is possible.  
           [0003]    U.S. Pat. No. 5,028,180 discloses a six degrees-of-freedom motion mechanism that is similar to a Stewart Platform in operation, but is intended for machine tools. Six legs, adjustable in length, connect a platform to a base and can be adjusted to set the platform at a desired orientation.  
           [0004]    U.S. Pat. No. 5,263,382 discloses a mechanism that provides six degrees-of-freedom with only three fixed-length legs attached to the movable platform. The legs are in two sections with a one degree-of-freedom hinge joint at their connection point. Each leg is driven by a pair of motors, by way of a differential drive system. The pitch and yaw of each leg is controlled. By controlling the two degrees-of-freedom of each of the three legs, six degrees-of-freedom motion of the moveable platform is accomplished. This mechanism is complex, particularly the differential drive system.  
           [0005]    U.S. Pat. No. 5,301,566 discloses a hybrid manipulator. Three fixed length limbs are attached to a platform via universal joints. By changing the location of the lower end of each of the three limbs using two degrees-of-freedom parallel drivers, the platform can be positioned in six degrees-of-freedom.  
           [0006]    U.S. Pat. No. 5,333,514 discloses a six degrees-of-freedom parallel manipulator. This manipulator is fully parallel but instead of using linear actuators for the links as in a traditional Stewart Platform, the six arms are in two sections. The first section is mounted to a rotary actuator. By rotating these six base links, the position of the platform can be controlled in six degrees-of-freedom.  
           [0007]    U.S. Pat. No. 5,656,905 discloses a hybrid manipulator for machine tools. Two parallel mechanisms are described in which each is a three degrees-of-freedom mechanism. These two mechanisms can be combined in serial fashion to form a hybrid mechanism or they can be combined in parallel to form a cooperating mechanism. One mechanism is dedicated to translational motion while the other is dedicated to rotational motion.  
           [0008]    U.S. Pat. No. 5,901,936 discloses a fully parallel six degrees-of-freedom motion mechanism. This mechanism is similar to a Stewart Platform. Disclosed is the use of rotary actuators in place of linear actuators for the legs of the manipulator. There are two main embodiments disclosed. In the first embodiment, there are two fixed length links joined by a hinge at their attachment point. The lower link attaches to the base and the upper link attaches to the moving platform. The hinge joint at the connection of the two links is actuated. Combining six copies of this mechanism allows motion in six degrees-of-freedom. In the second embodiment, a universal driver is used at the base. One axis of the universal joint is actuated while the other is passive. The link then attaches to the moving platform.  
           [0009]    U.S. Pat. No. 6,047,610 discloses a hybrid six degrees-of-freedom manipulator. The disclosed device uses two five-bar linkages mounted so that the plane in which they act can rotate. These five-bars are attached to a platform. Coupling the two five-bars together provides five degrees-of-freedom motion. A final motor near the platform provides the last degree-of-freedom. The two serial five-bar linkages, together in parallel arrangement, form the hybrid manipulator.  
         SUMMARY OF THE INVENTION  
         [0010]    The mechanisms in the above known devices are fundamentally different from the mechanism providing motion in six degrees-of-freedom in the apparatus of the present invention.  
           [0011]    In one aspect, the present invention provides a positioner for transmitting movement in up to six degrees-of-freedom to an object on the positioner, the positioner comprising a base plate, a first plate mounted on the base plate by a first mechanical linkage, a first actuator arrangement for moving the first plate, a second plate mounted on the first plate by a second mechanical linkage, a second actuator arrangement for moving the second plate, and a holder attached to the second plate for mounting the object. One of the first and second plates is movable in a plane in up to three degrees-of-freedom, and the other of the first and second plates is movable in up to three degrees-of-freedom that are out of the plane.  
           [0012]    An additional plate, including an actuator arrangement for moving the additional plate, can be mounted by a mechanical linkage between the second plate and the holder and, by this approach, the three degrees-of-freedom systems can be stacked to provide redundantly actuated mechanisms depending on the needs of a given situation. The additional plate can be movable in a plane in up to three degrees-of-freedom if it is desired to provide planar motion, decoupled from non-planar motion, directly to the object in the holder. It is also possible to provide this decoupled motion by arranging the two plates mentioned above with the second plate being movable in a plane in up to three degrees-of-freedom, and the first plate being movable in up to three degrees-of-freedom that are out of the plane in which the second plate can be moved. Such arrangements are suitable when decoupled planar motion of the object is required.  
           [0013]    In a preferred embodiment, the first plate is movable in a plane in up to three degrees-of-freedom, and the second plate is movable in up to three degrees-of-freedom that are out of the plane in which the first plate can be moved.  
           [0014]    Conveniently, the positioner further includes a first bias for biasing the first plate (also referred to herein as “stage one”) against the first actuator arrangement, and a second bias for biasing the second plate (also referred to herein as “stage two”) against the second actuator arrangement. Preferably, the first bias comprises a set of springs (also referred to herein as “actuator preload springs”) anchored to the base plate and to the first plate. More preferably, the first bias comprises a first set of springs anchored to the base plate and to the first plate, for biasing the first edge of the first plate against the first actuator, and a second set of springs anchored to the base plate and to the first plate, for biasing the second edge of the first plate against the second and third actuators. Preferably, the second bias comprises a third set of springs anchored to the second plate and to the first plate.  
           [0015]    It is also possible to use magnetic-based biasing as the first and/or second bias.  
           [0016]    The first actuator arrangement for moving the first plate is suitably a first plurality of actuators mounted on the base plate. Preferably, the first plurality of actuators comprises a first, a second and a third actuator (also referred to herein as “X-, Y 1 - and Y 2 -actuators”, respectively), the first actuator conveniently contacting a first edge of the first plate and the second and third actuators contacting a second edge of the first plate. The first and second edges of the first plate are preferably at substantially right angles to each other (orthogonal). Conveniently, the first, second and third actuators each comprise a micrometer. Motorized micrometers or piezo actuators could also be used.  
           [0017]    The second actuator arrangement is suitably a second plurality of actuators mounted on the first plate. Preferably, the second plurality of actuators comprises a fourth, a fifth and a sixth actuator (also referred to herein as “Z 1 -, Z 2 - and Z 3 -actuators”). More preferably, the fourth, fifth and sixth actuators are spaced apart and extend substantially orthogonally from the first plate and contact a surface of the second plate. Conveniently, the fourth, fifth and sixth actuators each comprise a micrometer assembly that includes a contact pin for contacting the second plate. Motorized micrometers or piezo actuators could also be used.  
           [0018]    Conveniently, the first lockable mechanical linkage comprises a plurality of bolts and a corresponding plurality of nuts, preferably three nut and bolt combinations, wherein the bolts are spaced apart and extend through corresponding clearance holes in the base plate and holes in the first plate. A cam lock system could be used in place of a bolt.  
           [0019]    The second lockable mechanical linkage suitably comprises three rods, each housed in its own passage in the first plate perpendicular to, and intersecting with, the contact pins (also referred to herein as “Z-pins”) of the fourth, fifth and sixth actuators, respectively. Each rod (also referred to herein as “Z-pin lock shaft”) has an indent that partially surrounds a respective contact pin. In addition, each rod has a threaded portion having a nut for tightening to produce frictional engagement of the rod with its respective contact pin. A cam lock system can also be used to produce the frictional engagement.  
           [0020]    The holder conveniently comprises a third plate (also referred to herein as “transition plate”) substantially parallel to the second plate and connected thereto by a third mechanical linkage, and fourth mechanical linkage for connecting the object to the third plate. The holder may alternatively consist of a regular array of threaded holes in the second plate to allow for custom mounting solutions for varying objects.  
           [0021]    The third mechanical linkage suitably comprises a plurality of tooling balls, preferably three, each tooling ball being on a corresponding arm that extends from the third plate. The arms are spaced apart and the balls are sized to pass through corresponding holes in a lock plate into corresponding vee grooves in the second plate. Each hole in the lock plate includes an elongated slot sized to receive a corresponding arm when the lock plate is rotated to a locking position after the tooling balls have been passed through the corresponding holes in the lock plate to lock the third plate to the second plate.  
           [0022]    If the object is a mirror, the fourth mechanical linkage conveniently comprises a plurality of flexures, preferably three, secured to the object in a spaced apart configuration, each flexure including an arm extending from the object and terminating in a locking portion that is substantially orthogonal to the arm. The locking portion is sized to pass through a corresponding hole in the third plate, and each corresponding hole in the third plate includes a slot sized to receive an arm when the object is rotated to a locking position after the locking portions have been passed through the corresponding holes in the third plate. Preferably, the locking portion is bolted to the third plate when each arm is in its corresponding slot.  
           [0023]    The mechanism of the present invention is a hybrid design that provides motion in six degrees-of-freedom by arranging two, distinct, three degrees-of-freedom mechanisms in series. Additional copies of the three degrees-of-freedom parallel mechanisms can be added in series to increase the degree of control of positioning by the system. The division of the degrees-of-freedom allows the mechanism to be split into two parts, each of which is highly symmetric and has a very low profile. Combining the two, three degrees-of-freedom mechanisms together results in a positioner that is very small and is easily adjustable.  
           [0024]    While known parallel mechanisms generally have low work volumes, high mechanical stiffness and complex forward kinematic solutions, the present invention allows high mechanical stiffness to be retained while providing simple kinematics. The positioner of the present invention is useful for positioning mirrors, particularly off-axis conic mirrors, which generally do not require a large work volume.  
           [0025]    Preferably, the object on the positioner is a mirror, such as an off-axis conic mirror. Other objects requiring precision positioning and orientation, including lasers etc., are also suitable.  
           [0026]    The kinematic solution for the positioner of the present invention can be easily found once the forward and inverse solutions for each of the three degrees-of-freedom parallel mechanisms are known. Closed form solutions for each of the three degrees-of-freedom parallel mechanisms exist and are determinable.  
           [0027]    All of the moving components that determine the position of the object are perfectly constrained kinematically. In other words, each moving component is supported at six points in such a way that these six contacts exactly determine the position of the component in space. For a given position of the six contacts, there is exactly one possible position of the component. This makes adjustments extremely repeatable. If the position of each contact is known exactly, then the position of the components will be known exactly.  
           [0028]    The motions in six degrees-of-freedom are separated into two distinct mechanisms. Each of these mechanisms has a low height compared to its width and the footprint of the mechanism is similar in size to the object which is being positioned. However, the overall height of the mechanism is approximately just three times that of the object, if the object is a mirror. Compared to commercially available solutions for providing motion in six degrees-of-freedom, this is very small. This small size is important, as many situations require the overall volume of adjustment mechanisms to be minimized.  
           [0029]    In applications that require very high accuracy, high stiffness is almost always a requirement. As mentioned earlier, parallel mechanisms tend to be very stiff as the payload is supported at a number of points. Combining a number of single degree-of-freedom mechanisms together to form a six degrees-of-freedom mechanism results in a device with low stiffness in comparison to the present invention. This high stiffness allows the mechanism to be moved under changing conditions such as a gravity vector while maintaining the position of the object very accurately. Once adjustment of the object is complete, its position can be locked which significantly increases its stiffness.  
           [0030]    Once the final position of the object is reached in the present invention, the mechanism can be locked to prevent accidental adjustment. While this is not necessary, this is of particular benefit to applications where a one-time alignment will be followed by an operational time of days, weeks or years. The mechanism that is used to lock the adjustments in place is separate from the adjustment mechanisms themselves. This has at least three benefits. Accidental adjustment of the device is near impossible since the locking mechanism will mechanically prevent the actuators from moving the mechanism. The actuators themselves can be removed from the device once the final position is reached. This can allow more accurate and generally more expensive actuators to be used without requiring them to be dedicated to the device. They could be removed from the device after adjustment and used elsewhere, as they are not required to hold the final position of the mechanism. Finally, since the locking mechanism is external to the adjustment mechanism, it can be designed to provide extra stiffness.  
           [0031]    The present invention also allows for the repeatable removal and replacement of the object without requiring re-adjustment of the mechanism. It is possible that once the object is positioned correctly there will never be a desire to re-adjust it. However, there is often a requirement to remove the object from the positioner for servicing or upgrading. The present invention allows the object to be removed from the positioner, then serviced and replaced on the device in exactly the same position from which it was removed. This operation is accomplished using a kinematic clamp.  
           [0032]    The hybrid nature of the mechanism of the present invention allows for simple workspace optimization for any task. The first three degrees-of-freedom parallel mechanism is responsible for planar translation and rotation (in a Right Hand Coordinate system X translation, Y translation and rotation about the Z-axis). The second, three degrees-of-freedom mechanism is responsible for the remaining two rotations and translation along the Z-axis. It is conceivable that there are problems in which large X and Y translations but little rotation about these axes will be required. Optimizing the design to accomplish this is very simple and has no effect on the accuracy or resolution of the system.  
           [0033]    The present invention is also scalable, and can be applied to positioning objects of many sizes. A typical use is for mounting mirrors 100 mm in diameter to 300 mm in diameter. The design, with appropriate considerations made regarding scaling, could be used for mirrors a few centimeters in diameter, or smaller, to meters in diameter. The dimensions of the plates can be adjusted in length, breadth and/or height as required and ultimately the plates may take on any suitable shape that may or may not be plate-like.  
           [0034]    The actuators in the present invention are conveniently located in two closely spaced parallel planes. Preferably, three actuators control Z translation, as well as X and Y rotation, and are all located in a plane parallel to the surface of the first plate. Preferably, three actuators control X and Y translation, as well as Z rotation, and are located in another parallel plane between the base and first plate. This arrangement allows for easy access to the actuators from the back of the device. In a preferred embodiment, the X, Y 1  and Y 2  actuators are stationary, and the Z 1 , Z 2  and Z 3  actuators move with the position dictated by these first three actuators.  
           [0035]    The six degrees-of-freedom in this device are partially decoupled to allow simple and comprehensible adjustment. To perform accurate adjustments of the object in an arbitrary coordinate system, a computer program can be used to calculate necessary actuator adjustments for a particular final position, as all six degrees-of-freedom become coupled. In other words, the design is amenable to implementation in an automatic control system. By implementing sensors to measure the position of the object and motorizing the actuator arrangements, a closed loop control system can be produced. The algorithms for the software control of the six degrees-of-freedom positioner can be implemented in this control system.  
           [0036]    As well as using a computer to calculate the adjustments necessary to position the device, a computer can be used to automate the positioning itself, through communication with motorized actuator arrangements.  
           [0037]    The preferred layout of the actuators does allow for decoupled motions in some cases. Also, it is probable that, at some point during an alignment or adjustment procedure, motions may be required based on trial and error. A typical Stewart Platform, or a variation thereof, precludes this type of adjustment as there is no simple way of knowing which actuator motion, or combination of actuator motions, will accomplish the desired action. The present invention is designed in such a way that trial and error adjustments are easily possible, as moving a particular actuator will have the expected effect within some relatively small error margin. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0038]    Further features and advantages will be evident from the following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings in which:  
         [0039]    [0039]FIG. 1 is a perspective view of an embodiment of a six degrees-of-freedom positioner in which the object to be positioned is a mirror, and shows the coordinate system used to identify the motions imparted by the actuators;  
         [0040]    [0040]FIG. 2 is a perspective view of a structure having two mirrors mounted on two different embodiments of the six degrees-of-freedom positioner of the invention;  
         [0041]    [0041]FIG. 3 is an end view of the first embodiment of the positioner, as seen in FIG. 2, showing the mechanical linkage used to secure the six degrees-of-freedom positioner to a stand, particularly if the positioner and stand are manufactured from different materials;  
         [0042]    [0042]FIG. 4 is an end view of the second embodiment of a positioner, as seen in FIG. 2, showing the mechanical linkage used to secure the six degrees-of-freedom positioner to a stand particularly if the positioner and stand are manufactured from different materials;  
         [0043]    [0043]FIG. 5 is an isometric view of the rear of a mirror, showing mirror flexures used for attaching the mirror to a transition plate;  
         [0044]    [0044]FIG. 6 is a side view of the positioner of FIG. 4;  
         [0045]    [0045]FIG. 7 is an isometric view of the positioner of FIG. 4 with the mirror removed;  
         [0046]    [0046]FIG. 8 is an isometric top view of the base plate of the positioner of FIG. 3;  
         [0047]    [0047]FIG. 9 is an isometric bottom view of the base plate of the positioner of FIG. 3;  
         [0048]    [0048]FIG. 10 is an isometric top view of the populated base plate of the positioner of FIG. 3;  
         [0049]    [0049]FIG. 11 is an isometric bottom view of the populated base plate of the positioner of FIG. 3;  
         [0050]    [0050]FIG. 12 is an isometric top view of stage one of the positioner of FIG. 3;  
         [0051]    [0051]FIG. 13 is an isometric bottom view of stage one of the positioner of FIG. 3;  
         [0052]    [0052]FIG. 14 is a sectional view of stage one of the positioner of FIG. 3;  
         [0053]    [0053]FIG. 15 is the same as FIG. 12, but shows the location of the actuator preload springs;  
         [0054]    [0054]FIG. 16 is an exploded isometric view of the base plate and stage one of the positioner of FIG. 3, showing the stage one locking bolt assemblies;  
         [0055]    [0055]FIG. 17 is and isometric view of a Z-pin actuator assembly;  
         [0056]    [0056]FIG. 18 is an exploded view of the Z-pin actuator assembly of FIG. 17;  
         [0057]    [0057]FIG. 19A is an isometric view of the base plate, stage one and Z-pin actuator assemblies of the positioner of FIG. 3; FIG. 19B shows a Z-pin lock shaft;  
         [0058]    [0058]FIG. 20 is an exploded view of FIG. 19;  
         [0059]    [0059]FIG. 21 is the same as FIG. 19, but also shows the stage two components of the first embodiment in exploded view;  
         [0060]    [0060]FIG. 22 is an isometric top view of stage two of the positioner of FIG. 3;  
         [0061]    [0061]FIG. 23 is an isometric bottom view of stage two of the positioner of FIG. 3;  
         [0062]    [0062]FIG. 24 is a cross-sectional view of a Z-pin contact insert in use, showing a Z-pin held in place with a bolt;  
         [0063]    [0063]FIG. 25 is an isometric view of a lock plate and stage two, in locked position, of the positioner of FIG. 3;  
         [0064]    [0064]FIG. 26 is an isometric view of a lock plate and stage two, in unlocked position, of the positioner of FIG. 3;  
         [0065]    [0065]FIG. 27 is a partial cross-sectional view of FIG. 25, showing the shoulder screw holding the lock plate on stage two;  
         [0066]    [0066]FIG. 28 is an isometric view of the base plate, stage one, stage two, lock plate and transition plate of the positioner of FIG. 3, partially exploded to show tooling balls and flexure bolts, and includes the blade flexures that attach to a mirror;  
         [0067]    [0067]FIG. 29 is an isometric top view of the transition plate of FIG. 28;  
         [0068]    [0068]FIG. 30 is an isometric bottom view of the transition plate of FIG. 28; and  
         [0069]    [0069]FIG. 31 is an isometric view of the mirror safety capture of the positioner of FIG. 3, also showing the blade flexures that attach to a mirror. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0070]    A coordinate system is used in the following discussions of an embodiment of a six degrees-of-freedom positioner. This coordinate system places the XY plane in the plane of the first plate with the Z-axis pointing towards the second plate. The three orthogonal axes simply provide a reference direction for each of the degrees of freedom (FIG. 1).  
         [0071]    There are six micrometers used in the positioner  2  to achieve the required six degrees-of-freedom motion of the mirror  4 . The actuators are named according to the motion that they produce in the defined coordinate system (FIG. 1).  
         [0072]    The two actuators  6  and  8 , located at the lower most portion of the positioner, are known as actuators Y 1  and Y 2 , respectively. These micrometers produce linear motion in the Y-axis as well as rotations about the Z-axis. The actuator in the −X direction is Y 1  and the actuator in the +X direction is Y 2 .  
         [0073]    The actuator that produces linear motion in the X direction is known as the X actuator  10 . The X, Y 1  and Y 2  actuators become coupled for an arbitrary position of the object.  
         [0074]    The three remaining actuators  12 ,  14  and  16  are known collectively as the Z-Pin actuators (or actuator assemblies). The actuators are defined as Z 1 , Z 2  and Z 3 , respectively. The position of each of these actuators is shown in FIG. 1. These actuators produce linear motion in the Z direction as well as rotations about the X- and Y-axes.  
         [0075]    Two distinct positioner embodiments are discussed herein both of which are used to position mirrors. The designs are similar but they handle the mounting of different sized mirrors. The “large positioner” is the first embodiment of the positioner  20 , as found for example in FIGS. 2 and 3. The “small positioner” is the second embodiment of the positioner  22 , as found for example in FIGS. 2 and 4. The large positioner  20  handles mirrors around 300 mm in diameter with masses of up to 10 kg while the small positioner  22  handles mirrors around 150 mm in diameter with masses up to 2 kg.  
         [0076]    There are two interfaces between the six degrees-of-freedom positioners and the surrounding components. These interfaces are strictly mechanical and the first is between a support structure  18  and the first embodiment of a six degrees-of-freedom positioner  20  having a mirror  24 , or the second embodiment of a positioner  22  having a mirror  26  (FIG. 2). The second interface is between a six degrees-of-freedom positioner and the object that it supports.  
         [0077]    The first and second embodiments are attached to the support structure  18  by means of four and three tangential flexures  32  made from the same material as the support structure (Invar 36™ in this case), or other suitable material (FIG. 3 and FIG. 4 respectively). These flexures  32  allow the positioners, which in general are made from a different material (in this case  416  stainless steel) to expand and contract relative to the support structure  18 . The flexures  32  are not directly bolted to the support structure  18 . The flexures are attached to an interface flexure plate  28  and  30 , that allows gross adjustment of the positioner relative to the support structure  18 . This plate is then bolted to the support structure  18 . The flexures  32  are then bolted to the six degrees-of-freedom positioner.  
         [0078]    Each of the mirrors  24  and  26  is attached to its six degrees-of-freedom positioner by three blade flexures  34  attached to the back face of the mirror. These flexures allow the six degrees-of-freedom positioners to expand and contract relative to the mirror  4  without inducing stress in the glass and thus deforming the mirror surface.  
         [0079]    The flexures are spaced 120 degrees apart and are located at 0.645 times the radius of the applicable mirror. This minimizes the root mean square deformation of the mirror surface. The blades of the flexures  34  are parallel to a tangent line drawn at the diameter of the mirror (FIG. 5).  
         [0080]    The flexures  34  are manufactured from a material (Invar  36  in this case) to closely match the coefficient of thermal expansion of the mirrors (Zerodur™ in this case).  
         [0081]    Each flexure  34  is attached to the transition plate  46  using a screw connection. The flexures  34  are in turn attached to the mirror  4  using an adhesive. If the mirror is to be re-coated, an adhesive such as Master Bond™ EP21TCHT-1 is used as it is a low outgassing adhesive and has been successfully used in environments of 10 −9  torr. Also, no organic material is outgassed that could compromise the quality of the mirror coating.  
         [0082]    The six degrees-of-freedom positioner  2  design is separated into four different functional components. Each of these components fulfils a distinct requirement of the positioner. FIG. 6 and FIG. 7 show each part of the positioner and its location relative to the other components. The aforementioned components are:  
         [0083]    Base Plate  36 —The base plate  36  is the foundation of the positioner. The base plate  36  attaches the entire positioner  2  to the system, such as the support structure  18 . The base plate  36  holds the Y 1 , Y 2  and X actuators  6 ,  8  and  10  in place. Additionally, the base plate  36  has a number of other minor functions.  
         [0084]    Stage One  38 —Stage one  38  is located on the base plate  36  by means of three raised pads which provide a semi-kinematic contact surface. Stage one  38  allows the object to be translated along the X and Y axes, as well as rotated about the Z-axis. The Y 1 , Y 2  and X actuators  6 ,  8  and  10  allow these three motions to be achieved. These three degrees-of-freedom are partially decoupled from the three remaining degrees-of-freedom.  
         [0085]    Stage Two  40 —The second stage of the positioner allows the object to be rotated about the X and Y axes and translated along the Z-axis. Stage two is kinematically mounted to Z-pins which are a part of the Z 1 , Z 2  and Z 3  actuators  12 ,  14  and  16 , and provides a kinematic clamping base for the mirror lock mechanism  42 .  
         [0086]    Z-Pin Actuator Assemblies  12 ,  14  and  16 —These three actuator assemblies contain a ramp to change the translation of the actuators in the X-Y plane to a motion in the Z direction. These assemblies house the three Z-pins. This configuration keeps all six actuators parallel to a common plane but allows stage two  40  to be adjusted in the correct orientations. Note that these assemblies move with stage one to partially decouple the three degrees-of-freedom that these assemblies provide from the previous three degrees-of-freedom.  
         [0087]    Mirror Lock  42 —This system is made up of two plates that allow the mirror to be removed and replaced in the same position with extremely high repeatability. The lock plate  44  allows the system to be locked and unlocked, while the transition plate  46  clamps kinematically to stage two  40  and houses flexures  34  that attach to the mirror.  
         [0088]    Mirror Safety Capture  48 —The mirror safety capture  48  ensures that a mirror  4  will not be damaged if a positioner component fails. This system is divided into two sections. The first section acts between the six degrees-of-freedom positioner  2  and the support structure  18 . The second section ensures that the mirror  4  itself can not become separated from the six degrees-of-freedom positioner  2  if the flexures  34  or bonding agent fails. This second sections also includes a removable cover (not shown) to protect the mirror  4  during its removal and installation.  
         [0089]    All of the major components of the six degrees-of-freedom positioners  2  are manufactured from the same material to minimize stress induced deformations from temperature changes (416 stainless steel in this case).  
         [0090]    Base Plate  
         [0091]    The outline of the base plate  36  is approximately circular with radii of 150 mm and 75 mm for the first 24 and second 26 embodiments of the positioners, respectively. These sizes correspond to the size of the mirrors for the first 24 and second 26 embodiments. The base plate  36  is 12 mm and 8 mm thick for the first 24 and second 26 embodiments of the positioners, respectively. Both plates have 1 mm thick raised pads  50  that act as semi-kinematic mounting points.  
         [0092]    The base plate  36  incorporates eight main features that allow the positioner to have the required functionality. The base plate  36  and its features are shown in FIG. 8 and FIG. 9. These main features are:  
         [0093]    Semi-Kinematic Raised Pads  50   
         [0094]    Stage One Lock Clearance Holes  52   
         [0095]    Z-Pin Clearance Slots  54   
         [0096]    Stage One Retaining Spring Holes  56   
         [0097]    Flexure Attachment Insert Feature  58   
         [0098]    Safety Wire Holes  60   
         [0099]    Mass Reduction Pockets  62  (first embodiment only)  
         [0100]    Lock Plate Preload Screw Access Hole  64   
         [0101]    The three raised pads  50  on the surface of the base plate  36  act as semi-kinematic mounting points and contact the back surface of stage one  38 . The actual surface area of the pads is not large but provides ample support. The pads are raised by 1 mm to ensure that stage one  38  will not contact the base plate  36  at other points, however this value keeps the overall positioner height small. The pads are located at the optimal support radii for the mirror  4 . Precision machining is important for semi-kinematic mounts. The three pads should be coplanar within ±3 μm. This ensures that, during the locking of the positioner  2 , stage one  38  will not warp. To ensure smooth movement between stage one  38  and the base plate  36 , solid molybdenum disulphide or other suitable lubricant is used on the pad surfaces.  
         [0102]    The stage one lock-clearance holes  52  pass through the centre of the semi-kinematic pads  50 . These holes  52  allow locking bolts  118  to pass from the rear of the base plate  36  and screw into stage one  38  without limiting the range of motion of stage one  38 .  
         [0103]    The three Z-pin clearance slots  54  allow the Z-pin actuator assemblies  12 ,  14  and  16 , and associated spacer blocks  104 , to move freely with stage one  38  without interfering with the base plate  36 . The clearance slots  54  are slightly larger than necessary for the required motion of stage one  38 .  
         [0104]    There are six retaining spring holes  56  spaced evenly around each semi-kinematic pad at the same radial distance as the pads  50 . The stage one retaining springs  98  preload stage one  38  against the base plate  36  during adjustment of the positioner  2 . These holes  56  have a recessed slot on the rear of the base plate  36 . A dowel pin is placed in this slot to hold the extension spring in place. The holes  56  are to ensure clearance between the springs, the base plate  36  and stage one  38 . The holes  56  are evenly spaced around the pads  50  to minimise the deflection of stage one  38 .  
         [0105]    Around the periphery of the base plate  36  are features  58  that allow the flexure inserts to be attached to the base plate  36 . There are four such features for the first embodiment  20  and three for the second embodiment  22 .  
         [0106]    There are threaded holes  60  near each flexure attachment insert feature  58 . These holes  60  allow stainless steel wire to be attached to the base plate  36 . The wire is attached to a similarly placed hole in the support structure  18 . These wires protect the positioner and object if the flexures  32 , between the support structure  18  and the six degrees-of-freedom positioner  2 , fail.  
         [0107]    The back face of the first embodiment base plate contains three mass reduction pockets  62 . These pockets reduce the mass of the plate by 15% without significantly increasing flexure. These pockets do not pass completely through the base plate  36 .  
         [0108]    In the centre of the base plate  36  there is a through hole  64  that allows the lock plate preload screw to be adjusted once installed.  
         [0109]    Associated Parts  
         [0110]    There are a number of parts that are associated with the base plate that require mention. These components are shown in FIG. 10 and FIG. 11. The components are:  
         [0111]    X and Y Actuator Blocks  66 ,  68   
         [0112]    Actuator Preload Spring Pins  70   
         [0113]    Oversize Washer  72   
         [0114]    Spherical Washer Set  74   
         [0115]    Flexure Inserts  76   
         [0116]    The X and Y actuator blocks  66  and  68  attach to the base plate  36  and serve as mounting points for the Y 1 , Y 2  and X actuators  6 ,  8  and  10  that drive stage one  38 . These blocks position the Y 1  and Y 2  actuators  6  and  8  at one quarter and three quarters of the way along the length of stage one  38 . The X actuator  10  is positioned half way along the length of stage one  38 .  
         [0117]    There are four actuator preload spring pins  70  that are pressed into the base plate  36 . These pins  70  hold the actuator preload springs  100  in place during adjustment of the positioner.  
         [0118]    The oversized washers  72  allow stage one  38  to move through its range of motion and still be secured to the base plate  36 . A bolt  118  passes through the holes  52  in the centre of the pads on stage one  38 . The washer  72  simply allows the bolt  118  to be used in the clearance hole  52 . The washer  72  is sized to ensure that it completely covers the hole  52  for any position of stage one  38 .  
         [0119]    A spherical washer set  74  is placed between the bolt head and the oversized washer  72  on all three lock bolts  118 . The spherical washer sets  74  reduce moments transmitted to stage one  38 .  
         [0120]    The flexure inserts  76  allow the flexures  32  to be attached to the base plate  36 . Inserts  76  are used, instead of a direct connection to the base plate  36 , so that flexures with a height greater than the height of the base plate  36  can be used and properly supported. Large flexure heights are desirable since this stiffens the flexures in planes where no deflection is preferable, but allows the flexures to remain compliant in the radial direction. If inserts were not used the base plate would have to be machined from a thicker blank.  
         [0121]    Stage One  
         [0122]    Stage one  38  rests on the semi-kinematic pads  50  on the base plate  36  and moves in X and Y translation as well as Z rotation. This plate is as small as possible, while still allowing all of the required features to be incorporated. The stage one plates  38  have a thickness of 12 mm and 8 mm in the first and second embodiments, respectively.  
         [0123]    Stage one  38  has nine main features that give it the required functionality. Stage one and its features are shown in FIG. 12, FIG. 13 and FIG. 14. These features are as follows:  
         [0124]    Z-Pin Bushing Holes  78   
         [0125]    Z-Pin Actuator Mounting Holes  80   
         [0126]    Stage One Locking Bolt Holes  82   
         [0127]    Stage One Retaining Spring Holes  84   
         [0128]    Stage Two Retaining Spring Holes  86   
         [0129]    Z-Pin Lock Shaft Holes  88   
         [0130]    Actuator Preload Spring Clearance Slots  90   
         [0131]    Mass Reduction Pockets  92  (first embodiment only)  
         [0132]    Lock Plate Preload Screw Clearance and Access Hole  94   
         [0133]    There are three holes  78  evenly spaced at  120  degrees around stage one  38 . These holes  78  are positioned at the optimum support radius for the mirror. These holes  78  act as bushings and provide a sliding fit for the Z-pins  126 . All three Z-pin actuator assemblies  12 ,  14  and  16  move with stage one  38  and these three holes  78  guide the Z-pins  126  up into contact with stage two  40 .  
         [0134]    Around each of the Z-pin bushings  78  there is a regular array of counterbored holes  80  and two dowel holes  81 . These holes  80  line up with holes on the Z-pin actuator body  122  to allow attachment of the actuator assemblies  12 ,  14  and  16  to stage one  38 . The counterbored holes  80  permit physical attachment of the Z-pin actuator assemblies  12 ,  14  and  16  to stage one  38  whereas the two smaller dowel holes  81  are used to accurately locate the Z-pin actuators  12 ,  14  and  16  under stage one  38 . These dowel holes  81  are drilled after accurate alignment of the actuator assemblies has occurred.  
         [0135]    There are three threaded holes  82  evenly spaced around stage one  38  that allow it to be locked in place. The three stage one locking bolts  118  pass up through the clearance holes  52  in the base plate  36  and thread into these three holes  82 .  
         [0136]    The stage one retaining-spring holes  84  are the counterparts to the retaining-spring holes  56  in the base plate  36 . The diameter of the holes is much larger than the diameter of the springs. This is to allow clearance between the springs and the plates as stage one  38  moves relative to the base plate  36 . There is also a large milled slot on top of each hole  84 . These slots house the dowel pins that hold the extension springs in place. The slots are designed so that the dowel pins and springs can move around as stage one  38  moves relative to the base plate  36 . This ensures that only a net force preloading the two plates together occurs. No net moment or forces acting in the plane of the surface of the plates will occur.  
         [0137]    Surrounding the centre of the plate  38  are six, stage two retaining-spring holes  86 . These holes house the springs  158  that preload stage two  40  against the Z-Pin  126  tips and in turn against the ramped pin  124 . The extension springs are held in place by dowel pins that fit into the slots on the bottom side of the plate (FIG. 13).  
         [0138]    There are three Z-pin lock shaft holes  88 . These three holes are located so that they intersect with the Z-pin bushing holes  78 . These three holes  88  accept shafts  114  that allows movement of a Z-pin  126  in its unlocked position, but secures the pin in place once the positioner has been adjusted. The lock shaft holes  88  are located in such a way that the nuts on the end of the shafts  114  themselves can be accessed and tightened once the positioner has been adjusted.  
         [0139]    On three of the corners of stage one  38  there are slots  90  which allow the actuator preload springs  100  to be attached to stage one  38 . The slots  90  have dowel pins passing through them that allow physical attachment of the spring to the plate. The slots  90  ensure that the springs do not come into contact with stage one  38  during its motion.  
         [0140]    The back face of stage one  38  of the first embodiment contains three mass reduction pockets  92 . These pockets reduce the mass of the plate by 20% without significantly increasing flexure. These pockets do not pass all the way through the plate.  
         [0141]    In the centre of the plate, there is a counterbored hole  94  that allows access to the lock plate preload screw  194  and provides clearance for the head of the screw as it comes near the top surface of stage one  38 .  
         [0142]    Associated Parts  
         [0143]    There are seven components associated with the operation of stage one  38 . These parts are:  
         [0144]    Stage One Micrometer Heads  96   
         [0145]    Stage One Retaining Springs  98   
         [0146]    Actuator Preload Springs  100   
         [0147]    Actuator Interface Pads (not shown)  
         [0148]    Spacer Blocks  104   
         [0149]    Z-Pin Lock Shafts and Nuts  114   
         [0150]    Stage One Lock Bolts  118   
         [0151]    Three actuators  6 ,  8  and  10  control the three degrees-of-freedom of stage one  38 . The X-block  66  and Y- blocks  68 , hold these actuators in position. In the first embodiment  20 , Newport BM17.25 actuators are used, while in the second embodiment  22 , Newport SM-13 actuators are used. Each selected actuator can be directly replaced with a differential micrometer (Newport BD17.25 and Newport DM-13) that will increase the resolution of the stage approximately ten times. Table 1 lists the actuators used for each embodiment as well as the desired travel range and resolution for each degree-of-freedom for each embodiment.  
                                                             TABLE 1                           Stage One Actuators            Positioner   Required X   Required X   Required Y   Required Y   Required Z   Required Z       Published       Possible       Embodi-   Translation   Translation   Translation   Translation   Rotation   Rotation   Selected   Actuator   Actuator   Replacement       ment   Travel   Resolution   Travel   Resolution   Travel   Resolution   Actuator   Resolution   Travel   Actuator               First   ±2 mm   ±5 μm   ±2 mm   ±5 μm   ±5 deg   ±7 asec   Newport   1 μm   25 mm   BD17.25                                   BM17.25       Second   ±2 mm   ±5 μm   ±2 mm   ±5 μm   ±5 deg   ±7 asec   Newport   1 μm   13 mm   DM-13                                   SM-13                  
 
         [0152]    There are six stage one retaining springs  98  (FIG. 21) that preload stage one  38  against the base plate  36  during adjustment of the positioner. Since the positioner is adjusted with the XY plane in a vertical orientation, the springs  98  prevent stage one  38  from separating from the base plate  36 . However, to decrease the frictional forces between stage one  38  and the base plate  36 , these springs are sized to ensure contact only when the positioner  2  is in a vertical position. The springs  98  are not capable of holding stage one  38  and all of the positioner components after it against the base plate  36  if the positioner is turned so that the mirror  4  faces the floor. Due to the orientation of the mount during the adjustment, the springs  98  in the most positive Y position take most of the load. To reduce frictional forces between the plates, these two springs are sized significantly larger to provide the restoring moment required, while the remaining four springs ensure equal normal forces on the two lower semi-kinematic pads. In situations where adjustment is required in another orientation, these springs can be resized accordingly.  
         [0153]    The actuator preload springs  100  are used to preload stage one  38  against the Y 1 , Y 2  and X actuators  6 ,  8  and  10  during adjustment of the positioner  2 . The first embodiment  20  uses six springs and the second embodiment  22  uses four springs. In the first embodiment  20 , only four springs are visible as the other two springs are placed inside the two springs that hold stage one  38  against the X Actuator  10  (FIG. 15). This is done to ensure appropriate applied forces while not exceeding the yield strength of the spring material.  
         [0154]    Actuator interface pads (not shown) reduce the contact stress between the spherical tips of the Y 1 , Y 2  and X actuators  6 ,  8  and  10  and the sides of stage one  38 . These pads change the contact geometry from a point contact to a ring contact. This prevents local plastic deformation at the surfaces and assures smooth movement of stage one  38 . This part is manufactured from drill rod and is oil quenched to increase its hardness.  
         [0155]    There is a spacer block  104  for each Z-pin actuator assembly  12 ,  14  and  16  in both embodiments (FIG. 20). These blocks  104  sit between stage one  38  and the Z-pin actuator bodies  122 . All of the holes  106  are clearance holes. The inner two dowel holes  108  are used to pin the block  104  to a Z-pin actuator assembly  12 ,  14  and  16 . The outer two dowel holes  110  are used to pin a Z-pin actuator assembly  12 ,  14  and  16  and spacer block  104  to stage one  38 . The large central hole  112  fits over the Z-pin  126 .  
         [0156]    There are three lock shafts  114  (FIG. 19B) that are used to lock the Z-pins  126  in place. These shafts allow free movement of the Z-pins  126  during adjustment. However, one end  116  of the shaft is threaded to allow a nut to be threaded on the shaft. Tightening these nuts causes the Z-pin lock shafts  114  to act as a wedge and lock the Z-pins  126  in place. This mechanism prevents movement of the Z-pins  126  perpendicular to stage one  38 .  
         [0157]    The three stage one lock bolts  118  pass through the spherical washer set  74 , oversize washer  72  and the base plate  36  before they screw into a threaded hole  82  in stage one  38  (FIG. 16). These bolts  118  function in two modes. The first mode is when the positioner is being adjusted. The stage one retaining springs  98  are not capable of supporting the entire mass of a mirror and positioner components after the base plate  36 , if the positioner  2  is oriented so that the mirror faces the floor. To prevent mechanical failure of the positioner in case this situation occurs, the stage one locking bolts  118  are loosened ½ a turn from the snug position during adjustment of the positioner. This ensures that complete separation will not occur but still allows the positioner  2  to be adjusted easily. The second mode of operation is when the bolts  118  are used to lock stage one  38  against the base plate  36 .  
         [0158]    Z-Pin Actuator Assemblies  
         [0159]    The Z-pin actuator assemblies  12 ,  14  and  16  control the X rotation, Y rotation and Z translation of stage two  40 . FIG. 17 and FIG. 18 show the assembly alone. FIG. 19 and FIG. 20 show the Z-pin actuator assemblies in relation to the rest of the six degrees-of-freedom positioner discussed thus far. The main parts in these Z-pin actuator assemblies  12 ,  14  and  16  are:  
         [0160]    Micrometer Head  120   
         [0161]    Actuator Body  122   
         [0162]    Ramped Pin  124   
         [0163]    Z-Pin  126   
         [0164]    Z-Pin Guide Nut  128   
         [0165]    Z-Pin Return Spring (not shown)  
         [0166]    Ramped Pin Spring Nut  132   
         [0167]    Ramped Pin Return Spring  134   
         [0168]    Ramped Pin Guide Dowel  136   
         [0169]    Z-Pin Guide Screw  138   
         [0170]    In each Z-pin actuator assembly  12 ,  14  and  16 , the ramped pin  124  multiplies the resolution of the micrometer by the slope of the ramp. For a slope of ⅖, which is used in the first 20 and second 22 embodiments, a 10 micron micrometer motion becomes 4 microns at the tip of the Z-pin  126 . Table 2 indicates required motions and the actuators selected for each positioner. If the actuators selected do not provide sufficient resolution, the micrometers for the second embodiment  22  can be replaced with the one listed in the last column to increase the resolution by a factor of 10. Table 2 lists the actuators used for each embodiment as well as the desired travel range and resolution for each degree-of-freedom for each embodiment.  
                                                             TABLE 2                           Z-Pin Assembly Actuators                Required X   Required X   Required Y   Required Y   Required Z   Required Z       Published       Possible       Embodi-   Rotation   Rotation   Rotation   Rotation   Translation   Translation   Selected   Actuator   Actuator   Replacement       ments   Travel   Resolution   Travel   Resolution   Travel   Resolution   Actuator   Resolution   Travel   Actuator               First   ±2 deg   ±3 asec   ±2 deg   ±3 asec   ±2 mm   ±3 μm   Newport   1 μm   40 mm   NA                                   BM25.40       Second   ±2 deg   ±3 asec   ±2 deg   ±3 asec   ±2 mm   ±3 μm   Newport   1 μm   25 mm   BD17.25                                   BM17.25                  
 
         [0171]    The Z-pin actuator body  122  is made from the same material as the main plates. The body  122  guides the ramped pin  124  using a hole-basis sliding fit to accurately guide the ramped pin  124 . A dowel hole in the bottom of the body  122  houses a guide dowel  136  that passes into a guide groove  125  in the ramped pin  124  to prevent it from rotating. There is also an array of holes on the top of the body  122  that allow location and attachment to stage one  38 . The body  122  also guides the lower section of the Z-pin  126  accurately. A threaded hole in the side of the body  122  intersects the Z-pin bore and houses a Z-pin guide screw  138  that prevents the Z-pin  126  from rotating. Finally, the body has a number of threaded holes that allow special nuts to be inserted which help guide the Z-pin  126  and retain the ramped pin  124 .  
         [0172]    The ramped pin  124  is manufactured from a good bearing material (bronze in this case). This reduces friction around the pin. The ramped pin  124  has a slope of ⅖, which is a compromise between accuracy and size. The pin has a small protrusion on one of its faces to guide the ramped pin return spring  134 . On the opposing face a small conical cut has been made to reduce the contact stress between the micrometer head  120  and the ramped pin  124 . If the micrometer had a flat tip the conical cut would not be present. On the bottom of the pin  124  is a small groove  125  that accepts a dowel pin  136  that prevents rotation of the ramped pin  124  (FIG. 18).  
         [0173]    The Z-pin  126  is made from the same material as the actuator body  122 . This pin  126  contacts the ramped pin  124  and moves perpendicular to the direction of travel of the ramped pin  124 . The Z-pin  126  contacts the ramped pin  124  with a line contact. The tip of the Z-pin  126  is spherical which makes contact with the Z-pin contact insert  152  in stage two  40 . A threaded hole  140  in the tip of the Z-pin  126  is also present which allows a screw to ensure a solid mechanical contact between the tip and stage two  40  (FIG. 24). The pin also has a vee-shaped groove  142  that is in contact with the Z-pin guide screw  138  to prevent rotation. The first embodiment  20  has a Z-pin diameter of 12 mm while the second embodiment  22  Z-pin has a diameter of 6 mm. These diameters minimize the bending of the Z-pins  126  due to gravitational loading from the mirrors to approximately 1 micron in each case. The contact stress is also significant between the Z-pins  126  and the Z-pin contact inserts  152 . Therefore, the Z-pins  126  and Z-pin contact inserts  152  are hardened and ground. The tolerances between each Z-pin  126  and its bushing  78  in stage one  38  are very close. This is to reduce the amount of lateral movement that occurs when the Z-pin lock shafts  114  are tightened against the Z-pins  126 . The Z-pins  126  and bushings  78  are sized as a hole-basis sliding fit. The positioners  22  and  20  also have three Z-pins of different lengths. This allows the mirror to be oriented at some initial arbitrary tip/tilt with respect to the base plate  36 . This is done to ease the mounting of the base plate  36  by not requiring it to be planar parallel to the mirror  4 .  
         [0174]    The Z-pin guide nut  128  is used to aid in the accurate guiding of the Z-pin  126 .  
         [0175]    A compression spring (not shown) can be used between the Z-pin  126  and the Z-pin guide nut  128 . This spring provides extra restoring force to ensure that the Z-pin  126  remains in contact with the ramped pin  124 .  
         [0176]    The ramped pin spring nut  132  is installed in the body  122  and holds the ramped pin return spring  134  in place during operation of the positioner  2 .  
         [0177]    The ramped pin return spring  134  ensures that the ramped pin  124  tracks well with the movement of the micrometer head  120 . This spring is sized so that the force generated by the compression spring in its extended position is greater than the frictional force between the ramped pin  124  and the Z-pin  126 . The frictional force between the two pins is due to the masses of the positioner components, the object being positioned, and the force generated by the stage two retaining springs  158  and the Z-pin return springs (not shown). The Z-pin return springs assist the stage two retaining springs  158  in ensuring that the Z-pin  126  remains in contact with the ramped pin  124 .  
         [0178]    The ramped pin guide dowel  136  is present to ensure that the ramped pin  124  does not rotate in its bore in the actuator body  122 . This dowel  136  is press fit into the actuator body  122 .  
         [0179]    Each actuator body  122  has a threaded hole that allows a set screw  138  to be passed though to intersect the Z-pin  126 . A cone point set screw  138  is used and runs into the vee-shaped groove  142  in the Z-pin  126  to prevent it from rotating and damaging the surface finish of the ramped pin  124 .  
         [0180]    Each actuator body  122  is attached to stage one  38  by Z-pin actuator mounting bolts  144 .  
         [0181]    Stage Two  
         [0182]    Stage two  40  rests on the tips of the three Z-pins  126  and moves in X and Y rotation as well as Z translation (FIG. 21). Differential motions of the Z-pins  126  provide X and Y rotation and equal movements of the Z-pins provide translation in the Z direction.  
         [0183]    Stage two  40  is manufactured from the same material as the base plate  36 . As with stage one  38 , the radial distances at which the Z-pins contact the plate govern the dimensions of stage two. Large chamfers on the corner of stage two  40  reduce its mass. These plates are subject to large point loads and must be very stiff to ensure adequate flexural performance of the positioner.  
         [0184]    Stage two  40  has six main features shown in FIGS. 21, 22 and  23 . These features are:  
         [0185]    Tooling Ball Contact Insert Holes  146   
         [0186]    Z-Pin Contact Insert Holes  150   
         [0187]    Shoulder Screw Hole  154   
         [0188]    Stage Two Retaining Spring Holes  156   
         [0189]    Stage One Clearance Chamfer  160   
         [0190]    Mass Reduction Pockets  162  (first embodiment only)  
         [0191]    The tooling ball contact insert holes  146  house, and provide attachment for, tooling ball contact inserts  148 . The Z-pin contact insert holes  150  house, and provide attachment for, Z-pin contact inserts  152 .  
         [0192]    In the centre of stage two  40  there is a counterbored hole  154 . The through hole section of this feature supports the shoulder screw  194  that screws into the lock plate  44 . The larger diameter counterbore allows a stack of Belleville spring washers  196  to be placed between the head of the shoulder screw  194  and the bottom of stage two  40 .  
         [0193]    Surrounding the centre counterbore hole  154  are six stage two retaining-spring holes  156 . These holes house six springs  158  that preload stage two  40  towards stage one  38 . These holes use a similar pin system to retain the springs as the stage one retaining springs  98 .  
         [0194]    Around the perimeter of stage two  40  there is a chamfer  160  on the bottom surface that prevents stage two  40  from contacting stage one  38  at the extremes of its motion.  
         [0195]    In the first embodiment  20 , there are a number of mass reduction pockets  162  in stage two  40 . These reduce the mass of the plate by 18% without significantly increasing the flexure of the plate.  
         [0196]    Associated Parts  
         [0197]    There are five components associated with the operation of stage two  40 . These parts are:  
         [0198]    Tooling Ball Contact Inserts  148   
         [0199]    Z-Pin Contact Inserts  152   
         [0200]    Stage Two Retaining Springs  158   
         [0201]    Stage Two Spherical Washers  164   
         [0202]    Stage Two Lock Belleville Spring Washers  166   
         [0203]    The tooling ball contact inserts  148  are manufactured from a hardenable grade of stainless steel. Each insert contains a triangular groove  168  passing through the centre of the insert (FIG. 21). Since these inserts are subjected to high contact stress they are hardened to prevent plastic deformation in the contact area from occurring. The contact surfaces are also ground to ensure smooth contact. These parts are manufactured as inserts rather than being incorporated into stage two  40  directly. This allows surface hardening and grinding operations, as mentioned above, to be carried out. The three vee-shaped grooves  168  in these inserts  148 , in conjunction with the tooling balls  178  themselves, define a kinematic clamp between stage two  40  and the transition plate  46 .  
         [0204]    The Z-pin contact inserts  152  are present for the same reasons as the tooling ball contact inserts  148 . These inserts contain a large diameter counterbore  170  to allow space for a spherical washer set  164  and a smaller through hole  172  to allow a bolt  174  to be screwed into the Z-pin  126  (FIG. 21). Each Z-pin contact insert  152  also includes a groove  176  for contacting the tip of the Z-pin  126 . The three vee-shaped grooves  176  in these inserts  152 , in conjunction with the spherical tips of the Z-pins  126 , define a kinematic clamp. Therefore, for an arbitrary position for each Z-pin  126  tip, there is exactly one orientation of stage two  40 .  
         [0205]    A spherical washer set  164  is positioned in the counterbore of each Z-pin contact insert  152 . Stage two  40  does not remain perpendicular to the Z-pins  126  and so these spherical washers  164  are required to provide a way to secure the bolt  174  through stage two  40  into each Z-pin  126 . These washers  164  allow stage two  40  to be bolted into place in any orientation while having the bolts  174  pass properly into the Z-pin  126  tips (FIG. 24).  
         [0206]    On top of each of the spherical washer sets  164 , there is a stack of Belleville spring washers  166  in series. These washers, when compressed, ensure that stage two  40  will always stay in contact with the tips of the Z-pins  126 . The spring washers are sized so that they load stage two  40  against the Z-pin  126  tips with two times the weight of the positioner components from stage two out to, and including, the object to be positioned.  
         [0207]    The six stage two retaining springs  158  are used to ensure that, during adjustment of the positioner  2 , the Z-pins  126  tracks well with the motion of the ramped pin  124  in each Z-pin actuator assembly  12 ,  14  and  16 . These springs are sized to overcome the moments from the cantilevered plates and object and, as mentioned, to supply a suitable force between the Z-pins  126  and the ramped pin  124 . Due to the arrangement of the springs and the adjustment positions, the springs in the most positive Y direction are largest, as they are most able to counteract the moments from the plates and object. In the least extended state of the springs, which occurs when stage two  40  is at its most negative Z translation and at some maximum tip and tilt, the springs must still be capable of loading the Z-pins  126  against the ramped pins  124  with a suitable force. In situations where adjustment of the positioner  2  is required in another orientation these springs can be resized accordingly.  
         [0208]    Lock Plate  
         [0209]    The lock plate  44  is the final moving part of the six degrees-of-freedom positioner. While the lock plate  44  does not allow adjustment of the positioner in any degrees-of-freedom, it is an important part of the positioner  2  if the object to be positioned is a mirror. One feature of the positioner  2  is that it allows a mirror  4  to be removed and replaced with a high degree of repeatability to accommodate mirror re-coating. The lock plate  44  is one half of the mechanism that allows this to be possible. The function of the lock plate  44  is to either hold tooling balls  178 , which are attached to the transition plate  46 , securely in their vee-shaped grooves  168 , or to allow the tooling balls  178 , and thus the transition plate  46 , to be released from the rest of the positioner  2 . Moving from the locked position to the unlocked position can be accomplished simply by rotating the lock plate  44 . FIG. 25 shows the lock plate  44  oriented in a position that locks the tooling balls  178  in place. FIG. 26 shows the lock plate  44  in the unlocked position.  
         [0210]    The lock plate  44  is manufactured from the same material as the base plate  36  and consists of three symmetric spokes that each contain the same features for locking of the tooling balls  178 . The radius of the plate, and thus the length of each spoke from the centre of the plate, is governed by the position of the tooling balls  178  while allowing physical access to the spokes. Each spoke protrudes from the side of the positioner  2  so that the lock plate  44  can be turned by hand.  
         [0211]    The lock plate  44  has six main features. The lock plate  44 , with labeled features, is shown, for example, in FIGS. 25 and 26. The six features are as follows:  
         [0212]    Tooling Ball Release Hole  180   
         [0213]    Contact Groove  182   
         [0214]    Tooling Ball Lock Groove (not shown)  
         [0215]    Shoulder Screw Threaded Hole  186   
         [0216]    Clearance Slot  188   
         [0217]    Lock Bolt Hole  190   
         [0218]    In each of the spokes there is a tooling ball release hole  180 . These clearance holes allow the tooling balls  178  to pass through the lock plate  44 .  
         [0219]    Proceeding clockwise from the tooling ball release hole  180  is the contact groove  182  (FIG. 27) which approximates a helix with a triangular cross section. As the lock plate  44  is rotated counter-clockwise from the tooling ball release holes  180 , the contact groove  182  causes the lock plate  44  to rise approximately 1 mm which in turn causes the spring washers  196  to be compressed. Towards the end of the contact groove  182  a small lip (not shown) is present that prevents accidental rotation of the lock plate  44  once it is in its locked position. When this lip is in contact with the tooling balls  178 , the maximum force between the contact grooves  182  and the tooling balls  178  occurs. Once the lock plate  44  has been rotated counter-clockwise past the safety lips, the tooling balls  178  snap into their locking grooves (not shown). In the locked orientation of the lock plate  44 , a force equal to two times the mass of the applicable mirror and positioner components that the lock plate  44  must retain is applied to the tooling balls  178 . The lock grooves (not shown) ensure that the tooling balls  178  remain in contact with the tooling ball inserts  148  in stage two  40 , without imposing significant kinematic constraints on the system.  
         [0220]    A threaded hole  186  is present in the centre of the lock plate  44  for the shoulder screw  194  to thread into.  
         [0221]    There are three clearance slots  188  in the lock plate  44  that provide clearance for the heads of the screws  174  that secure stage two  40  to the Z-pins  126 .  
         [0222]    There is a threaded hole  190  in the side of one blade of the lock plate  44 . This hole passes through into a tooling ball release hole  180 . Once the lock plate  44  is moved to its locked position, a screw is threaded into this hole to prevent the lock plate  44  from becoming unlocked.  
         [0223]    Associated Parts  
         [0224]    There are three components associated with the operation of the lock plate  44 . They are:  
         [0225]    Shoulder Screw  194   
         [0226]    Lock Plate Belleville Spring Washers  196   
         [0227]    Lock Bolt (not shown)  
         [0228]    A stack of Belleville spring washers  196  are used to apply a force to the tooling balls  178  through the lock plate  44  (FIG. 27). These spring washers are positioned between the head of the shoulder screw  194  and the underside of stage two  40 . When the shoulder screw  194  is tightened, it causes a force to be applied to the lock plate  44  in the negative Z direction. It is this force that holds the tooling balls  178  in place. These springs washers  196  are sized so that in the locked position of the lock plate  44 , the springs load the tooling balls  178  against the tooling ball contact inserts  148  in stage two  40  with two times the weight of the transition plate  46  and mirror  4 .  
         [0229]    The shoulder screw  194  is used to locate and load the lock plate  44 . The stack of spring washers  196  is placed on the body of the screw. Tightening or loosening this screw determines the forces that are applied to the tooling balls  178  in the locked and unlocked position.  
         [0230]    The lock bolt (not shown) is used to prevent accidental unlocking of the lock plate  44 . The bolt passes through the clearance hole  180  and into the contact groove  182  but does not actually come into contact with the tooling ball  178 . The length of the bolt prevents the lock plate  44  from rotating past the safety lip.  
         [0231]    Transition Plate  
         [0232]    The transition plate  46  is the final plate in the six degrees-of-freedom positioner. This plate is called the transition plate because it is the transition between the actual positioner mechanisms and the object to be positioned. This plate is permanently attached to the mirror  4  by three tangential blade flexures  34 . Due to the design of the system, this plate and anything attached to it, would be placed in a coating chamber along with the mirror when coating is required. Therefore, it is necessary to ensure that the transition plate  46  and any components attached to it are vacuum compatible. FIG. 28 shows the position of the transition plate  46  relative to the rest of the positioner as well as the components associated with the transition plate  46 .  
         [0233]    The transition plate  46  is manufactured from the same material as the base plate  36 .  
         [0234]    The transition plate  46  has five main features that provide the required functionality. The transition plate  46  and its features are shown in FIG. 29 and FIG. 30. These features are:  
         [0235]    Vented Tooling Ball Holes  200   
         [0236]    Vented Flexure Bolt Holes  202   
         [0237]    Flexure Insertion Hole  204   
         [0238]    Flexure Attachment and Clearance Slot  206   
         [0239]    Mirror Capture Ring Bracket Holes  208   
         [0240]    Mass Reduction Pockets  210  (first embodiment only)  
         [0241]    There are three vented tooling ball holes  200  located in the transition plate  46 . The shanks of the tooling balls  178  are pressed into these holes thus necessitating a tight interference fit. There are also smaller holes drilled through the top of the plate into the tooling ball holes  200 . This vent hole prevents air from being trapped and forming a virtual leak when the assembly is in a vacuum.  
         [0242]    The flexures  34  are bolted to the bottom side of the transition plate  46  through bolt holes  202  to reduce the overall height of the system. Three flexure-insertion holes  204  are located in such a manner that the flexures  34  can easily be inserted and moved to their final positions.  
         [0243]    There are three slots  206  located in the transition plate  46  that allow the flexures  34  to bend during operation of the positioner. These slots  206  are centred at the optimal support radius of the mirror being mounted to the six degrees-of-freedom positioner. There is also a recess  212  and threaded bolt holes  202  on the underside of the transition plate  46  that allow for attachment of the flexure  34 .  
         [0244]    On each side of the transition plate  46  there is a threaded hole  208 . These holes allow the mirror capture ring brackets  216  to be attached to the transition plate  46 .  
         [0245]    There are three mass reduction pockets  210  in the back of the transition plate  46 . These pockets reduce the mass of the plate by 30% without significantly increasing the flexure of the plate. These pockets do not pass all the way through the plate.  
         [0246]    Associated Parts  
         [0247]    There are two components associated with the operation of the transition plate  46 . These parts are:  
         [0248]    Tooling Balls  178   
         [0249]    Flexures  34   
         [0250]    There are three tooling balls  178  that are pressed into the transition plate  46 . These tooling balls  178  pass through the lock plate  44  and establish a kinematic clamp to stage two  40 . The tooling balls  178  are made from a hardened stainless steel with a solid welded shank.  
         [0251]    The flexures  34  that attach the mirrors  4  to the transition plate  46  are manufactured from a material to closely match the coefficient of thermal expansion of the mirror (in this case Invar  36 ).  
         [0252]    Mirror Safety Capture  
         [0253]    The mirror safety capture  48  is composed of two sections. The first section ensures that the six degrees-of-freedom positioner does become separated from the support structure  18 . The second section ensures that the mirror  4  does not become separated from the six degrees-of-freedom positioner. Separation could occur because of flexure failure or a failure of the adhesive between the flexures  34  and mirror  4 . The main part of the mirror safety capture  48  is a ring  214  that prevents the mirror from moving by more than one millimetre (see FIG. 31).  
         [0254]    The mirror capture ring  214  is manufactured from an engineering thermoplastic such as Delrin™. Delrin™ is used to reduce possible damage to the mirrors in the event of a component failure as a metal ring may cause the mirror edges to chip.  
         [0255]    There are three features on the mirror capture ring  214  that give the part its functionality. FIG. 31 shows these features.  
         [0256]    “Inverted L” Cross Section  
         [0257]    Mirror Capture Ring Bracket Bolt Holes  218   
         [0258]    Mirror Safety Cover Bolt Holes  220   
         [0259]    Temporary Mirror Holding Holes  222   
         [0260]    The mirror capture ring  214  has an “Inverted L” cross section. This cross section allows the ring to capture the mirror securely.  
         [0261]    There are four mirror capture ring bracket bolt holes  218  spaced around the mirror capture ring  214 . These holes allow mirror capture ring brackets  216  to be attached to the mirror capture ring  214 .  
         [0262]    There are four threaded holes  220 , for a mirror safety cover (not shown), spaced around the mirror capture ring  214 . These holes allow a mirror safety cover to be attached to the mirror capture ring  214 .  
         [0263]    Around the circumference of the mirror capture ring  214  are eight threaded holes  222 . Nylon™ screws are used in these holes to grip the mirrors  4  and position them accurately on the flexures  34  during initial alignment before they are bonded to the flexures  34 .  
         [0264]    Associated Parts  
         [0265]    There is one component associated with the mirror capture ring  214 . This part is:  
         [0266]    Mirror Capture Ring Bracket  216   
         [0267]    The mirror capture ring brackets  216  are different for each positioner. In each case, these components are manufactured from Delrin™. The brackets hold the mirror capture ring  214  in the correct position relative to the appropriate mirror. On the top of each bracket is a small feature (not shown) that engages with a complementary slot  226  on the bottom side of the capture ring (FIG. 31). These features ensure that the capture ring  214  can be repeatably placed on the brackets  216 .  
         [0268]    Many modifications and variations are possible and would be apparent to a person skilled in the art in light of the above teachings. It is therefore to be understood that the invention can be practiced otherwise than as specifically described herein and still will be within the spirit and scope of the appended claims.