Abstract:
A plurality of MEMS devices that can be easily configured to impart extended ranges of rotational and/or translational motion. The MEMS devices comprise a micro-electromechanical building block including a bendable member having a first end connectable to a support structure, and a straight rigid member having a first end connected to a second end of the bendable member. In the event the bendable member is in a straight condition, the rigid member extends from the second end of the bendable member toward the support structure. Further, the bendable member has a predetermined length, and the rigid member has a length at least within a range from one half to the full predetermined length of the bendable member to allow a free end of the rigid member to undergo extended rotational and/or translational motion in response to a displacement of the bendable member. The respective MEMS devices can be employed as actuators or sensors in a variety of micro-electromechanical and micro-opto-electromechanical applications.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a 371 of PCT/US01/21641, filed Jul. 10, 2001 which claims benefit of provisional appln 60/217,191 filed Jul. 10, 2000 and a CIP of application Ser. No. 09/700,633 filed Nov. 16, 2000 U.S. Pat. No. 6,657,764 which is a 371 PCT/US00/07075, filed Mar. 17, 2000 which claims benefit of provisional appln 60/124,982 filed Mar. 18, 1999. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     N/A 
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to the field of Micro-ElectroMechanical Systems (MEMS), and more specifically to MEMS devices that can be easily configured to provide extended ranges of rotational and/or translational motion. 
     MEMS devices have been widely employed as actuators or sensors in various micro-electromechanical applications including inkjet printers, read/write heads in computer disk drives, accelerometers, and pressure sensors. More recently, MEMS devices have been employed in optical networking applications including optical cross-connect modules for controlling switching between optical fiber input and output ports. For example, such optical cross-connects typically comprise two or three-dimensional arrays of optical mirrors configured to direct pluralities of beams of light from selected sets of fiber input ports to selected sets of fiber output ports. Further, conventional MEMS devices included in such optical cross-connects are configured to move at least some of the optical mirrors in the array under computer control to bring about a desired switching between the selected sets of fiber input and output ports. 
     MEMS devices employed in today&#39;s optical networking applications are frequently called upon to satisfy demanding performance requirements. For example, such MEMS devices are often required to move relatively large structures (e.g., optical mirrors, prisms, or optical gratings) over relatively large distances with high speed and a high degree of precision. However, conventional MEMS devices used in optical networking applications typically impart only limited ranges of linear or angular displacement. Further, such conventional MEMS devices are typically only capable of causing structures to rotate about a single axis. 
     It would therefore be desirable to have MEMS devices that can be employed as actuators or sensors in micro-electromechanical or micro-opto-electromechanical applications. Such MEMS devices would be easily configured to provide extended ranges of rotational and/or translational motion. It would also be desirable to have a MEMS device that can cause a structure such as an optical mirror to rotate about more than one axis. 
     BRIEF SUMMARY OF THE INVENTION 
     In accordance with the present invention, a plurality of MEMS devices is provided that can be easily configured to impart extended ranges of rotational and/or translational motion. Benefits of the presently disclosed invention are achieved by providing a micro-electromechanical building block, one or more of which can be used to construct a respective MEMS device capable of moving a desired angular and/or linear distance. 
     In a first embodiment, the micro-electromechanical building block includes at least one bendable member having a first end connectable to a support structure, and at least one straight rigid member having a first end connected to a second end of the bendable member. In the event the bendable member is in a straight condition, the rigid member extends from the second end of the bendable member toward the support structure. Further, the bendable member has a predetermined length, and the rigid member has a length within a range from one half to the full predetermined length of the bendable member to allow a free end of the rigid member to undergo extended rotational and/or translational motion in response to a displacement of the bendable member. 
     In a preferred embodiment, the support structure comprises a frame of silicon, the bendable member comprises a length of silicon having regions with depositions providing bender or piezoelectric morph functions when energized with a voltage, and the rigid member comprises a rigid silicon bar. The support structure, the bendable member, and the rigid member are formed from the same silicon wafer by way of a silicon micro-machining fabrication technique. 
     In further embodiments of the present invention, at least one micro-electromechanical building block comprising at least one bendable member connectable to at least one straight rigid member is used to construct respective MEMS devices capable of moving desired angular and/or linear distances. 
     A first MEMS device includes a first bendable member having a first end connectable to a support structure, and a first straight rigid member having a first end connected to a second end of the first bendable member. In the event the first bendable member is in a straight condition, the first rigid member extends toward the support structure. The first MEMS device also includes a second bendable member having a first end connected to a second end of the first rigid member, in which the first and second bendable members are configured to undergo respective displacements in a same direction; and, a second straight rigid member having a first end connected to a second end of the second bendable member. In the event the first and second bendable members are in respective straight conditions, the second rigid member extends toward the support structure. The first and second bendable members have the same predetermined length. Further, the first rigid member has a length equal to the predetermined length of the first and second bendable members, and the second rigid member has a length equal to one half of the length of the first rigid member to allow a free end of the second rigid member to undergo a pure rotation in response to a displacement of at least the first bendable member. 
     A second MEMS device includes a first bendable member having a first end connectable to a support structure, and a straight rigid member having a first end connected to a second end of the first bendable member. In the event the first bendable member is in a straight condition, the rigid member extends toward the support structure. The second MEMS device also includes a second bendable member having a first end connected to a second end of the rigid member. In the event the first and second bendable members are in respective straight conditions, the second bendable member extends away from the support structure. The first and second bendable members have the same predetermined length, and are configured to undergo respective displacements in opposite directions. Further, the rigid member has a length equal to one half of the predetermined length of the first and second bendable members to allow a free end of the second bendable member to undergo a pure translation in response to a displacement of at least the first bendable member. 
     A third MEMS device includes a first bendable member having a first end connectable to a support structure, and a second bendable member having a first end connected to a second end of the first bendable member. In the event the first and second bendable members are in respective straight conditions, the second bendable member extends away from the support structure. The first and second bendable members have the same predetermined length, and are configured to undergo respective displacements in opposite directions to allow a free end of the second bendable member to undergo a pure translation in response to a displacement of at least the first bendable member. 
     A fourth MEMS device includes a first bendable member having a first end connectable to a support structure, and a first straight rigid member having a first end connected to a second end of the first bendable member. In the event the first bendable member is in a straight condition, the first rigid member extends toward the support structure. The fourth MEMS device also includes a second bendable member having a first end connected to a second end of the first rigid member. In the event the first and second bendable members are in respective straight conditions, the second bendable member extends toward the support structure. The fourth MEMS device also includes a second straight rigid member having a first end connected to a second end of the second bendable member. In the event the first and second bendable members are in respective straight conditions, the second rigid member extends away from the support structure. The first and second bendable members have the same predetermined length, and are configured to undergo respective displacements in a same direction. Further, the first and second rigid members have respective lengths equal to one half of the predetermined length of the first and second bendable members to allow a free end of the second rigid member to undergo a pure translation in response to a displacement of at least the first bendable member. 
     By employing at least one micro-electromechanical building block to construct a plurality of MEMS devices, respective MEMS devices capable of moving desired angular and/or linear distances can be easily configured. Further, the respective MEMS devices can be employed as actuators or sensors in a variety of micro-electromechanical and micro-opto-electromechanical applications. 
     Other features, functions, and aspects of the invention will be evident from the Detailed Description of the Invention that follows. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     The invention will be more fully understood with reference to the following Detailed Description of the Invention in conjunction with the drawings of which: 
     FIG. 1 is a schematic diagram depicting a piezoelectric morph device energized with a voltage; 
     FIG. 2 a  is a side view of a first micro-electromechanical building block including the piezoelectric morph device of FIG. 1, in accordance with the present invention; 
     FIG. 2 b  is a top plan view of the first micro-electromechanical building block of FIG. 2 a;    
     FIG. 3 a  is a side view of a second micro-electromechanical building block including the piezoelectric morph device of FIG. 1, in accordance with the present invention; 
     FIG. 3 b  is a top plan view of the second micro-electromechanical building block of FIG. 3 a;    
     FIG. 4 a  is a side view of a first MEMS device including the first and second micro-electromechanical building blocks of FIGS. 2 a  and  3   a , in accordance with the present invention; 
     FIG. 4 b  is a top plan view of the first MEMS device of FIG. 4 a;    
     FIG. 5 a  is a side view of a second MEMS device including the second micro-electromechanical building block of FIG. 3 a , in accordance with the present invention; 
     FIG. 5 b  is a top plan view of the second MEMS device of FIG. 5 a;    
     FIG. 6 a  is a side view of a third MEMS device, in accordance with the present invention; 
     FIG. 6 b  is a top plan view of the third MEMS device of FIG. 6 a;    
     FIG. 7 a  is a side view of a fourth MEMS device including the second micro-electromechanical building block of FIG. 3 a , in accordance with the present invention; 
     FIG. 7 b  is a top plan view of the fourth MEMS device of FIG. 7 a;    
     FIG. 8 is a top plan view of an optical cross-connect module including mirrored configurations of the second MEMS device of FIG. 5 a , in accordance with the present invention; 
     FIG. 9 is a top plan view of a two-morph mirror scanning system, in accordance with the present invention; 
     FIG. 10 is a drawing depicting the operation of the mirror scanning system of FIG. 9; and 
     FIG. 11 is a top plan view of a three-morph mirror scanning system, in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The entire disclosure of U.S. patent application Ser. No. 09/700,633 filed Nov. 16, 2000 is incorporated herein by reference. 
     The entire disclosure of U.S. Provisional Patent Application No. 60/217,191 filed Jul. 10, 2000 is incorporated herein by reference. 
     A plurality of MEMS devices is disclosed that can be easily configured to provide extended ranges of rotational and/or translational motion. The presently disclosed MEMS devices achieve such extended ranges of motion by way of a micro-electromechanical building block, at least one of which can be used to construct a respective MEMS device capable of moving a desired angular and/or linear distance. 
     FIG. 2 a  depicts a side view of a first micro-electromechanical building block  200  according to the present invention. In the illustrated embodiment, the micro-electromechanical building block  200  includes a bendable member  204  having a first end connected to a support structure  202 , and a straight rigid member  206  having a first end connected to a second end of the bendable member  204 . The straight rigid member  206  is connected to the bendable member  204  such that when the bendable member  204  is in a straight condition, the straight rigid member  206  extends from its connection with the bendable member  204  toward the support structure  202 . 
     In a preferred embodiment, the bendable member  204  comprises a piezoelectric bender, which can be made to bend away from a planar position by applying an electric field across at least one piezoelectric layer deposited on a surface thereof. For example, the piezoelectric bender  204  may comprise either a “mono-morph” or a “bimorph” (the term “morph” being used to represent either of other equivalent structures described herein). Further, the micro-electromechanical building block  200  is preferably formed from a silicon wafer by a conventional silicon micro-machining process. Accordingly, the support structure  202  comprises a frame of silicon, the bendable member  204  comprises a length of silicon having regions with depositions providing bender or piezoelectric morph functions when energized by an applied voltage, and the rigid member  206  comprises a rigid silicon bar. 
     It is understood that the bendable member  204  may alternatively comprise a piezo-magnetic bender that can be made to bend away from a planar position by application of a magnetic field across at least one piezo-magnetic layer deposited thereon, or any other type of bender that can be made to bend by inducing a stress gradient (via, e.g., an electric field, a magnetic field, or an application of heat or radiation) along a dimension of the bender. 
     FIG. 1 depicts a schematic diagram of a piezoelectric bender  104  coupled to a voltage source  108 . The piezoelectric bender  104  is representative of the bendable member  204  included in the micro-electromechanical building block  200  (see FIG. 2 a ). Accordingly, when energized by a voltage “V” applied by the voltage source  108 , the piezoelectric bender  104  provides desired bender or piezoelectric morph functions. 
     Specifically, the piezoelectric bender  104  comprises a length of silicon having a first piezoelectric deposition region  104   a  and a second piezoelectric deposition region  104   b . When the voltage V is applied by the voltage source  106 , one of the piezoelectric deposition regions  104   a  or  104   b  expands while the other piezoelectric deposition region contracts, thereby causing the piezoelectric bender  104  to bend by an amount proportional to the applied voltage, V. 
     Those of ordinary skill in the art will appreciate that a piezoelectric bimorph energized by an applied voltage is subject to a plurality of external variables including a tip moment “M”, a tip force “F”, a pressure “p”, and the applied voltage V. It will also be appreciated that canonical conjugates of these four (4) variables are a tip rotation “α”, a tip translation “δ”, a displaced volume “V”, and an electrode charge “Q”, respectively. 
     Each of these external variables M, F, p, and V and their respective conjugates α, δ, V, and Q are depicted in FIG. 1 relative to the piezoelectric bender  104 . The tip rotation α and the tip translation δ are also depicted in FIG. 2 a  relative to the micro-electromechanical building block  200  (see also FIGS. 3 a ,  4   a ,  5   a ,  6   a , and  7   a ). 
     It should further be appreciated that the tip rotation a is proportional to the tip translation δ according to the following equation: 
     
       
         α=2δ/ L,   (1) 
       
     
     in which “L” is the length of the bendable member  204  (see FIG. 2 a ). 
     Accordingly, when the connection between the support structure  202  and the bendable member  204 , as depicted in FIG. 2 a , is conceptually placed at the origin of an x-y coordinate system, the bendable member  204  extends in the x-direction and deflects in the y-direction. Further, the tangent rigid member  206  connected at the tip of the bendable member  204  intersects the x-axis at a distance “L/2” from the origin, and intersects the y-axis at a distance “−δ” from the origin. 
     Both the bendable member  204  and the tangent rigid member  206  are herein defined as standard MEMS elements of the micro-electromechanical building block  200 . Specifically, the bendable member  204  and the rigid member  206  are herein referred to as a bimorph and an “extender”, respectively. Although the extender  206  connected to the bimorph  204  is depicted in FIG. 2 a  as pointing in the positive x-direction, it is understood that the extender  206  may be suitably connected to the bimorph  204  to allow it to point in the negative x-direction. The extender  206  pointing in the positive x-direction is herein referred to as a “forward extender”, and the extender  206  pointing in the negative x-direction is herein referred to as a “reverse extender”. Similarly, the bimorph  204  extending in the positive x-direction is herein referred to as a “forward bimorph”, and the bimorph  204  extending in the negative x-direction is herein referred to as a “reverse bimorph”. 
     Further, although the bimorph  204  is shown in FIG. 2 a  as bending in the positive y-direction, it is understood that the bimorph  204  may be suitably configured to bend in the negative y-direction. The forward bimorph  204  bending in the positive y-direction is herein referred to as a “forward positive bimorph”, and the forward bimorph  204  bending in the negative y-direction is herein referred to as a “forward negative bimorph”. Similarly, the reverse bimorph  204  bending in the positive y-direction is herein referred to as a “reverse positive bimorph”, and the reverse bimorph  204  bending in the negative y-direction is herein referred to as a “reverse negative bimorph”. 
     FIG. 2 b  depicts a top plan view of the micro-electromechanical building block  200 . Specifically, the top plan view shows the supporting structure  202 , the forward positive bimorph  204 , the reverse extender  206 , and a suitable silicon micro-machined connector  207  disposed between the bimorph  204  and the extender  206 . In the illustrated embodiment, the length of the extender  206  is equal to the length L of the bimorph  204 . The extender  206  having a length equal to that of the bimorph  204  to which it is connected is herein referred to as a “full extender”. 
     It is noted that while the free end of the full reverse extender  206  intersects the y-axis at the distance −δ from the origin, the midpoint of the full reverse extender  206  undergoes rotation, only. This is because the midpoint of the full reverse extender  206  is at the equilibrium midpoint of the forward positive bimorph  204 . 
     FIG. 3 a  depicts a side view of a second micro-electromechanical building block  300  according to the present invention. In the illustrated embodiment, the micro-electromechanical building block  300  includes a forward positive bimorph  304  having a first end connected to a support structure  302 , and a reverse extender  309  having a first end connected to a second end of the bimorph  304 . 
     As described above, the midpoint of the full reverse extender undergoes pure rotation because it is at the equilibrium midpoint of the forward positive bimorph to which it is connected. A top plan view of the micro-electromechanical building block  300  comprising the support structure  302 , the forward bimorph  304 , the reverse extender  309 , and a suitable silicon macro-machined connector  307  disposed between the bimorph  304  and the extender  309  (see FIG. 3 b ) shows that the length of the extender  309  is equal to one half the length L of the bimorph  304 . Accordingly, the free end of the reverse extender  309  undergoes pure rotation because it is at the equilibrium midpoint of the forward positive bimorph  304 . 
     Both the forward bimorph  304  and the reverse extender  309  are herein defined as standard MEMS elements of the micro-electromechanical building block  300 . It is noted that the extender  309  having a length equal to one half that of the bimorph  304  to which it is connected is herein referred to as a “half extender”. 
     Although the micro-electromechanical building block  200  includes the full reverse extender  206  (see FIG. 2 a ), and the micro-electromechanical building block  300  includes the half reverse extender  309  (see FIG. 3 a ), it is understood that each of the extenders  206  and  309  may alternatively have a respective length at least within a range from one half to the full length of the bimorph connected thereto to allow the free end of the extender to undergo a desired rotational and/or translational motion. 
     The standard MEMS elements of the micro-electromechanical building blocks  200  and  300  can be connected to each other in various combinations to construct MEMS devices capable of moving desired angular and/or linear distances. 
     FIG. 4 a  depicts a side view of a first MEMS device  400  constructed using a combination of the standard MEMS elements of the micro-electromechanical building blocks  200  and  300  (see FIGS. 2 a  and  3   a ), in accordance with the present invention. Further, FIG. 4 b  depicts a top plan view of this first MEMS device  400 , which is constructed to undergo a pure rotation α at the tip of a half reverse extender  412 . 
     In the illustrated embodiment, the first MEMS device  400  includes a forward positive bimorph  404  having a first end connected to a support structure  402 , a full reverse extender  406  having a first end connected to a second end of the forward positive bimorph  404 , a forward positive bimorph  410  having a first end connected to a second end of the full reverse extender  406 , and the half reverse extender  412  having a first end connected to a second end of the forward positive bimorph  410 . 
     It is noted that the combination of the forward positive bimorph  404  and the full reverse extender  406  conforms to the general configuration of the micro-electromechanical building block  200  (see FIG. 2 a ), and the combination of the forward positive bimorph  410  and the half reverse extender  412  conforms to the general configuration of the micro-electromechanical building block  300  (see FIG. 3 a ). 
     Moreover, the net result of the bending forward positive bimorph  404  and its connection to the full reverse extender  406 , and the bending forward positive bimorph  410  and its connection to the half reverse extender  412  is that the tip of the half reverse extender  412  undergoes a rotation a without translation. 
     FIG. 5 a  depicts a side view of a second MEMS device  500  constructed using the standard MEMS elements of the micro-electromechanical building blocks  200  and  300  (see FIGS. 2 a  and  3   a ), in accordance with the present invention. Further, FIG. 5 b  depicts a top plan view of this second MEMS device  500 , which is constructed to undergo a pure translation δ at the tip of a forward negative bimorph  514 . 
     In the illustrated embodiment, the second MEMS device  500  includes a forward positive bimorph  504  having a first end connected to a support structure  502 , a half reverse extender  512  having a first end connected to a second end of the forward positive bimorph  504 , and the forward negative bimorph  514  having a first end connected to a second end of the half reverse extender  512 . 
     It is noted that the combination of the forward positive bimorph  504  and the half reverse extender  512  conforms to the general configuration of the micro-electromechanical building block  300  (see FIG. 3 a ). 
     Moreover, the net result of the bending forward positive bimorph  504  and its connection to the half reverse extender  512 , and the bending forward negative bimorph  514  is that the tip of the forward negative bimorph  514  undergoes a translation δ without rotation. The construction of this second MEMS device  500  is herein referred to as a “single delta translator”. 
     FIG. 6 a  depicts a side view of a third MEMS device  600  constructed using the standard MEMS elements of the micro-electromechanical building blocks  200  and  300  (see FIGS. 2 a  and  3   a ), in accordance with the present invention. Further, FIG. 6 b  depicts a top plan view of this third MEMS device  600 , which is constructed to undergo an extended range of pure translational motion  2 δ at the tip of a forward negative bimorph  614 . 
     In the illustrated embodiment, the third MEMS device  600  includes a forward positive bimorph  604  having a first end connected to a support structure  602 , and the forward negative bimorph  614  having a first end connected to a second end of the forward positive bimorph  604 . 
     Moreover, the net result of the bending forward positive bimorph  604  and the bending forward negative bimorph  614  is that the tip of the forward negative bimorph  614  undergoes an extended translation 2δ without rotation. The construction of this third MEMS device  600  is herein referred to as a “double delta translator”. 
     FIG. 7 a  depicts a side view of a fourth MEMS device  700  constructed using the standard MEMS elements of the micro-electromechanical building blocks  200  and  300  (see FIGS. 2 a  and  3   a ), in accordance with the present invention. Further, FIG. 7 b  depicts a top plan view of this fourth MEMS device  700 , which is constructed to undergo a pure translation δ at the tip of a half forward extender  716 . 
     In the illustrated embodiment, the fourth MEMS device  700  includes a forward negative bimorph  704  having a first end connected to a support structure  702 , a half reverse extender  712  having a first end connected to a second end of the forward negative bimorph  704 , a reverse negative bimorph  714  having a first end connected to a second end of the half reverse extender  712 , and the half forward extender  716  having a first end connected to a second end of the reverse negative bimorph  714 . 
     Moreover, the net result of the bending forward negative bimorph  704  and its connection to the half reverse extender  712 , and the bending of the reverse negative bimorph  714  and its connection to the half reverse extender  716  is that the tip of the half reverse extender  716  undergoes a translation δ without rotation. The construction of this fourth MEMS device  700  therefore comprises another single delta translator. 
     It is noted that the standard MEMS elements of the micro-electromechanical building blocks  200  and  300  and/or the first, second, third, or fourth MEMS devices  400 ,  500 ,  600 , or  700  may be suitably stacked to form higher order rotators and translators. Further, in order to avoid twisting moments, these constructions can be made symmetrical by mirroring them. For example, a translator may be formed in which a MEMS device and its mirrored counterpart provide a connection to a structure comprising an optical surface (e.g., an optical mirror, a prism, or an optical grating—either transparent or reflective) such that the tip of the last MEMS element of the translator is allowed to undergo a desired translational motion with no twisting moments. 
     FIG. 8 depicts an optical cross-connect module  800  according to the present invention. In the illustrated embodiment, the optical cross-connect module  800  includes a switching unit  802  comprising an optical mirror positioned on a platform  804 , which is connected to three (3) sets of double delta translators  806 ,  808 , and  810  positioned at angles of about 120° from each other. Specifically, the double delta translator  806  is formed by mirroring a stack comprising the second MEMS device  500  connected between two (2) micro-electromechanical building blocks  200 . The double delta translators  808  and  810  are formed in a similar manner. Accordingly, when the double delta translators  806 ,  808 , and  810  are energized with suitable applied voltages, the platform  804  is raised (lowered) to insert (remove) the optical mirror in (from) the path of light beams emitted from optical fiber ports (not shown). 
     It is noted that the raising (lowering) of the platform  804  may alternatively be achieved by employing more than one set of single, double, triple, or higher order translators. 
     FIG. 9 depicts a top plan view of a two-morph mirror scanning system  900  according to the present invention. In the illustrated embodiment, the two-morph mirror scanning system  900  includes a mirrored silicon platform or area  10  supported and etch-released from a silicon frame  12  by respective silicon support arms  14  and  16 . Overlying the arms  14  and  16  are respective morphs  18  and  20  that may be mono-morphs or bimorphs. The morphs  18  and  20  comprise piezoelectric depositions formed during the silicon micro-machining of the device. In their configurations as benders, the morphs  18  and  20  have upper and lower electrical connections  22  and  24  to terminals  26 , each formed as a metalization on the frame  12 . It is noted that the frame  12  is merely shown schematically, and typically would be of greater extent in both directions of the plane of the page. 
     FIG. 10 depicts a diagrammatic illustration of the principle of operation of the two-morph mirror scanning system  900  according to the present invention, in which a mirror  10 ′ is supported on arms  14 ′ and  16 ′ within a frame  12 ′. As the morphs or bimorphs of the arms  14 ′ and  16 ′ are electrically actuated to bend in opposite directions, the mirror  10 ′ can be tilted a considerable distance. By varying and controlling the signals applied to the morphs, the degree of bending and the angle of inclination of the mirror  10 ′ can be precisely set or scanned with knowledge of the exact position of the mirror. For this purpose, the system of the invention is normally operated with a microprocessor or other processor  28  (see FIG.  9 ), which controls the magnitude of the signals applied to terminals  26  with or without interfacing drivers  30  (see FIG.  9 ). 
     It is noted that the respective combinations of the arm  14 ′ and the mirror  10 ′, and the arm  16 ′ and the mirror  10 ′, conform to the general configuration of the micro-electromechanical building block  200  (see FIG. 2 a ). Further, because the midpoint of the mirror  10 ′ is at the respective equilibrium midpoints of the arms  14 ′ and  16 ′, the midpoint of the mirror  10 ′ undergoes rotation without translation. The midpoint of the mirror  10 ′ therefore comprises the axis of rotation of the mirror  10 ′. 
     FIG. 11 depicts a further embodiment of the present invention, in which three “J” shaped arms  1100 , completing nearly a 180° curvature and angled at 120° from each other, are supported from the edge  1102  of a frame. The initial linear portion  1104  of the arms  1100  is plated to function as morphs or benders. A computation system  1106  drives the morphs and accomplishes any coordinate transformations necessary to adjust orthogonal drive signals to the 120° angles. A mirror  1110  is formed in the center, as described above. 
     Stress relief structures  1112  are formed of silicon between the ends of the arms  1100  and the mirror  1108  to accommodate a difference in slope between the sides of the arms  1100  at the juncture with the mirror due to the substantial curving of the arms  1100  at the end and the 120° arm placement. The stress relief structures  1112  comprise a widening of the arms with the centers etched out leaving only outer bands for the attachment over a few degrees of curvature. In a preferred embodiment, the midpoint of the initial linear portion  1104  of each of the three (3) arms  1100  is in line with the stress relief structures  1112  of the remaining two (2) arms  1100 . In this configuration, the arms  1100  can cause the mirror  1108  to move with minimal stress and inertia. 
     Of particular advantage to such a structure is the fact that if the morphs or benders on the arm portions  1104  are electrically driven to bend in the same direction by an identical amount, or nearly so, the mirror  1110  is given a bending moment at its edges where the arms attach. This results in the mirror  1110  being bent slightly in a convex or concave shape, which has usefulness in providing focusing or defocusing effects on light beams reflected thereby. 
     Although “bimorphs” and “extenders” are herein described as distinct standard MEMS elements of the micro-electromechanical building blocks  200  and  300  (see FIGS. 2 a  and  3   a ), it should be understood that a bimorph may be configured to act as a bender and/or an extender. For example, by applying suitable voltages to a bimorph, the bimorph can be transformed from a positive/negative bimorph to an extender and from the extender back to the positive/negative bimorph. 
     Moreover, even though the micro-electromechanical building blocks  200  and  300  (see FIGS. 2 a  and  3   a ) are herein described as including a full reverse extender and a half reverse extender, respectively, it is understood that the building blocks  200  and  300  may alternatively include respective reverse extenders having any desired length, so long as the reverse extenders are disposed internal to the area of the respective bimorphs. Similarly, an optical surface such as the optical surface  10 ′ (see FIG. 10) may have any desired length so long as it is disposed internal to the area of the arm  14 ′ or  16 ′. For example, a bimorph suitably connected at one end to an optical surface conforming to the general configuration of a “quarter reverse extender” may be employed to implement an optical grating. 
     It will further be appreciated by those of ordinary skill in the art that modifications to and variations of the above-described devices and methods may be made without departing from the inventive concepts disclosed herein. Accordingly, the invention should not be viewed as limited except as by the scope and spirit of the appended claims.