Patent Publication Number: US-6991957-B2

Title: Micro-machined electromechanical system (MEMS) accelerometer device having arcuately shaped flexures

Description:
This application is a divisional of application Ser. No. 10/223,947, filed Aug. 20, 2002, now U.S. Pat. No. 6,897,538, issued May 24, 2005, which claims the benefit of U.S. Provisional 60/313,777, filed on Aug. 20, 2001. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to micro-machined electromechanical sensor (MEMS) devices and methods for manufacturing the same, and in particular to suspension devices and methods for mounting rotational masses in MEMS devices. 
     BACKGROUND OF THE INVENTION 
     Many micro-machined electromechanical sensor (MEMS) devices and methods for manufacturing the same are generally well-known. See, for example, U.S. Pat. No. 6,642,067, M ETHOD OF  T RIMMING  M ICRO -M ACHINED  E LECTROMECHANICAL  S ENSORS  (MEMS) D EVICES , issued Nov. 4, 2003, to Paul W. Dwyer, which is assigned to the assignee of the present application and the complete disclosure of which is incorporated herein by reference, that describes a MEMS acceleration sensor and method for manufacturing the same. In another example, U.S. Pat. No. 6,428,713, MEMS S ENSOR  S TRUCTURE AND  M ICROFABRICATION  P ROCESS  T HEREFORE , issued to Christenson, et al. on Aug. 6, 2002, which is incorporated herein by reference, describes a capacitive acceleration sensor formed in a semiconductor layer as a MEMS device. Other known MEMS devices include, for example, micro-mechanical filters, pressure sensors, gyroscopes, resonators, actuators, and rate sensors, as described in U.S. Pat. No. 6,428,713. 
     MEMS accelerometer devices generally measure acceleration forces applied to a body by being mounted directly onto a surface of the accelerated body. One common type of MEMS accelerometer is the capacitive accelerometer. As disclosed in U.S. Pat. No. 4,435,737, L OW  C OST  C APACITIVE  A CCELEROMETER , issued to Colton on Mar. 6, 1984, which is incorporated herein by reference, capacitive accelerometers are generally well known in the art. In a closed-loop capacitive accelerometer, the acceleration sensor is a proof mass suspended by flexures or hinges for rotation relative to an outer frame portion. The acceleration sensor is bonded between glass plates with the proof mass forming a differential capacitor with the glass plates. 
     The proof mass rotates about the flexures according to the principle of Newton&#39;s law: F=ma, when subjected to acceleration along the input or “sensitive” axis which is normal to the plane of the proof mass. An electrical drive and sense circuit measures applied acceleration force as a function of the displacement of the proof mass and the resulting differential capacitance. 
     Accelerometers of the type that are based on a rotating mass often need to be firmly constrained relative to the in-plane axes while being permitted movement in the third input axis. In devices having a rotating mass, the position of the axis of rotation also needs to be constrained. Recently, the proof mass and flexures have been fabricated in an active epitaxial or layer grown on a silicon substrate. The proof mass and flexures are structured using Reactive Ion Etching (RIE) or Deep Reactive Ion Etching (DRIE), which permits etching of very narrow slots between nearly vertical walls. DRIE permits the width, length, and thickness of the flexures to be closely controlled so that desirable bending characteristics are obtained. The flexures define a linear axis of rotation or “hinge” axis about which the proof mass moves in response to an applied force, such as the acceleration of the accelerated body, for example, a vehicle, aircraft or other accelerated body having the accelerometer mounted thereon. Traditionally, the flexures are substantially rectangularly shaped with a substantially constant cross-sectional area. The substantially rectangular shape gives the flexures greater in-plane stiffness along the major axis, i.e., the accelerometer hinge axis, and substantially less in-plane stiffness along its minor axis. 
     Prior art micromachined accelerometers have effectively used the substantially rectangular flexures for pliantly suspending a rotating or translating proof mass. However, the flexures of some prior art devices, such as those fabricated using RIE or DRIE, are essentially two-dimensional designs that do not permit changes in material thickness that can be used to control flexure stiffness. The rectangular flexures operate as a beam having a constant area moment of inertia, I, which is defined as the integral of the area of the cross-section times the square of the distance of the incremental area from the neutral axis. See, e.g., Shigley, M ECHANICAL  E NGINEERING  D ESIGN , 3 rd  edition, page 45, which is incorporated herein by reference. The rectangular flexures bend along their entire lengths, similarly to a beam of constant cross-section that is supported at both ends. The rectangular flexures therefore lack a well-defined hinge axis. 
     SUMMARY OF THE INVENTION 
     The present invention overcomes limitations of the prior art for providing proof mass suspension in a force sensor, which is critical to isolating the accelerometer mechanism from in-plane force inputs during operation while responding to out-of-plane force inputs. 
     The arcuate suspension apparatus of the invention is stiffer when loaded in the plane of the arcuate shape than out-of-plane. The arcuate suspension apparatus transfers in-plane loads along the included arch, which causes the arcuate suspension apparatus to be strong and rigid in opposing in-plane loads, and flexes or bends when subjected to out-of-plane loads, which causes the arcuate suspension apparatus to be flexibly compliant when loaded out-of-plane. 
     According to one aspect of the invention, the arcuate suspension apparatus includes a first substantially arcuately shaped flexure having a cross-section that is relatively substantially extended in the plane of the arcuate shape, the first flexure having a first end structured for connection to a support structure and a second end structured for connection to a movable structure to be suspended from the support structure; and a second substantially flexure that is arcuately shaped similarly to the first flexure and having a cross-section that is relatively substantially extended in the plane of the arcuate shape and having a first end structured for connection to the support structure and a second end structured for connection to the movable structure, the arcuate shape of the second flexure being aligned with the arcuate shape of the first flexure and with the first flexure forming a hinge having an axis of rotation that extends through the first and second flexures. The arcuate shape of the first and second flexures are aligned either facing oppositely from one another, or facing toward one another. 
     According to another aspect of the invention, the invention includes a structure to be suspended and a support structure spaced away from the structure to be suspended. The first ends of the first and second flexures are connected to the support structure, and the second ends of the first and second flexures are connected to the structure to be suspended. 
     According to another aspect of the invention, the structure to be suspended is an accelerometer sensor mechanism structured using micro-machined electromechanical sensor (MEMS) techniques in an epitaxial growth of semiconductor material on a silicon substrate. 
     According to still other aspects of the invention, methods for suspending an acceleration apparatus are provided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same becomes better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein: 
         FIG. 1  is a side view of a basic single proof mass differential capacitance accelerometer, including drive and sense electronics; 
         FIG. 2  is a plan view of an accelerometer mechanism die having the apparatus and method of the invention embodied therein as a pair of semicircular flexures; 
         FIG. 3  is a cross-section taken through one of the pair of semicircular flexures illustrated in  FIG. 2 , which illustrates that the major axis of the substantially rectangular cross-section is substantially longer than the minor axis; 
         FIG. 4  illustrates an enhanced tendency for the major axis of the pair of semicircular flexures to increase as a function of increasing distance from an axis of rotation; 
         FIG. 5  illustrates that the arcuate shaped suspension apparatus can be formed in any rounded shape; 
         FIG. 6  illustrates the arcuate shaped suspension apparatus of the invention embodied in another accelerometer as two pair of flexures pliantly suspending a proof mass from a support structure embodied as an inner sensor plate in a “teeter-totter” arrangement; 
         FIG. 7  illustrates the arcuate shaped suspension apparatus of the intention alternately embodied in a configuration that employs corner arches to selectively stabilize an interior mass; and 
         FIG. 8  illustrates the arcuate shaped suspension apparatus of the intention alternately embodied in another configuration that employs two pair of side arches to selectively stabilize an interior mass. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENT 
     In the Figures, like numerals indicate like elements. 
     The present invention is an apparatus and method for suspending a relatively movable structure of an acceleration sensor, i.e., a proof mass, from a support structure, i.e., an inner sensor frame. The suspension apparatus of the invention includes at least first and second arcuately shaped flexures each having similar cross-sections that are relatively substantially extended in a plane in which the arcuate shape lies. The first and second arcuately shaped flexures each have a first end structured for connection to the support structure and a second end structured for connection to the movable structure that is to be suspended from the support structure. The first and second flexures both lie in the same plane and are aligned with their respective outer arcuate shapes facing oppositely each from the other and forming a hinge having an axis of rotation in the plane of the first and second arcuate shapes that extends linearly through respective portions of the first and second flexure that are aligned substantially cross-wise to the axis of rotation. 
       FIG. 1  is not to scale but clearly illustrates the apparatus and method of the invention embodied by example and without limitation in a suspension structure for pliantly suspending a single cantilevered proof mass in a micro-machined electromechanical sensor (MEMS) accelerometer  10 . For clarity, the top and bottom cover plates are shown spaced apart from the sensor mechanism  12 . The sensor mechanism  12  is structured in an epitaxial growth or “active” semiconductor layer grown on a silicon substrate (not shown). Structuring of the sensor mechanism  12  includes structuring a cantilevered proof mass  14  operable as a rotating or “moveable” electrode. Opposing cover plates  16  are formed in glass wafers and provided with fixed surface electrodes  18 . The sensor mechanism  12  is bonded, for example, by electrostatic bonding, to one of the two cover plates  16  with the fixed electrode  18  aligned with one planar surface of the proof mass  14 . The silicon substrate is removed, leaving the sensor mechanism  12 , including the second surface of the proof mass  14 , exposed. Using electrostatic bonding, the second of the two cover plates  16  is bonded to the sensor mechanism  12  opposite the first cover plate  16  and having its fixed electrode  18  aligned with the proof mass  14 . The proof mass  14  thus operates as a moveable electrode between the two fixed electrodes  18  on either side. An electrical drive and sense circuit  20  measures differential capacitance between the proof mass  14  and each of the opposing fixed electrodes  18  as a function of the displacement of the proof mass  14  resulting from an acceleration force applied along an input axis I, and outputs a resulting acceleration signal. 
     The sensor mechanism  12  is structured having one or more pairs of flexures, indicated generally at  22 , that are structured according to the invention for pliantly suspending the proof mass  14  from an inner sensor frame or plate  24  for movement of the proof mass  14  along the input axis I normal to the proof mass  14 . Each pair of flexures  22  defines a linear hinge axis H about which the proof mass  14  moves in response to an applied force, such as the acceleration of the accelerated body having the accelerometer  10  mounted thereon. As illustrated in  FIG. 1 , the flexures  22  are identical in thickness to the remainder of the sensor mechanism  12 , because they are similarly formed in the epitaxial growth or active layer grown on the silicon substrate and are similarly structured using one of the RIE or DRIE processes that do not permit changes in material thickness. The flexures  22  therefore are structured according to the invention using an arcuate shape, shown in  FIG. 2 , that is used to control flexure stiffness and to accurately position the hinge axis H. 
       FIG. 2  illustrates the apparatus and method of the invention embodied by example and without limitation in a suspension structure for pliantly suspending a proof mass in another single proof mass micro-machined electromechanical sensor (MEMS) accelerometer  100 , commonly referred to as a Tee design. The invention is similarly practicable as a suspension structure for pliantly suspending a proof mass in another pendulous mass accelerometer such as one of the different accelerometer designs illustrated in each of U.S. Pat. No. 5,287,744, A CCELEROMETER WITH  F LEXURE  I SOLATION , issued to Norling, et al. on Feb. 22, 1994; U.S. Pat. No. 4,944,184, A SYMMETRIC  F LEXURE FOR  P ENDULOUS  A CCELEROMETER , issued to Blake, et al. on Jul. 31, 1990; and U.S. Pat. No. 6,282,959, C OMPENSATION OF  S ECOND -O RDER  N ON -L INEARITY IN  S ENSORS  E MPLOYING  D OUBLE -E NDED T   UNING  F ORKS , issued to Blake, et al. on Sep. 4, 2001, which are all incorporated herein by reference. 
     The accelerometer  100  in  FIG. 2  is formed, as described above, in an epitaxial or “active” layer  102  of semiconductor material grown on a silicon substrate (not shown). The accelerometer  100  includes an acceleration sensor mechanism  110  having one or more pairs of flexures  112  structured according to the invention for pliantly suspending a proof mass  114  from an inner sensor frame or plate  116  for movement of the proof mass  114  along an input axis I 2  normal to the proof mass  114 . Each of the two pairs of flexures  112  define coincident linear hinge axes H 2  about which the proof mass  114  moves in response to an applied force, such as the acceleration of the accelerated body having the accelerometer  100  mounted thereon. The proof mass  114  is thus operable as a rotatable or “moveable” electrode. As described above, top and bottom cover plates (not shown) are structured with opposing fixed electrodes and are bonded to opposite sides of the sensor mechanism  100  to form capacitive force sensors in combination with the moveable electrode  114 . 
     The sensitive acceleration sensor mechanism  110  is supported by mechanical coupling of the accelerometer sensor frame  116  to a pair of cover plates  16 , as shown in  FIG. 1 , one of which in turn is typically connected to a ceramic or metal mounting plate (not shown). The sensor frame  116  may be suspended from a second outer or external frame portion  124  by flexures  126  formed by overlapping slots  128  and  130  through the layer  102 . The sensor frame  116  is thus able to move relative to the outer frame  124 , as described above and in U.S. Pat. No. 5,948,981, Vibrating Beam Accelerometer, issued to Woodruff on Sep. 7, 1999, and assigned to the Assignee of the present application, which is incorporated herein by reference. Such isolation minimizes the distortion of the sensor frame  116 , and thereby decreases the effects of external stresses and strains on the sensor mechanism. 
     The flexures  112  are structured in the epitaxial semiconductor layer  102  using one of the RIE or DRIE processes. The flexures  112  are arcuately shaped having first and second curved or rounded arch members  112   a  and  112   b  that lie in the plane of the epitaxial semiconductor layer  102  each of the flexures  112   a ,  112   b  are formed with first and second ends, the first ends are structured for connection to the support structure, i.e., the sensor frame  116 , and the second ends are structured for connection to the movable structure, i.e., the proof mass  114 . The arcuate shape of the first and second flexures  112   a ,  112   b  are aligned with one another, but the arcuate shape of each flexure faces oppositely each from the arcuate shape of the other flexure, as illustrated in  FIG. 2 . 
     The first and second flexures  112   a ,  12   b  together form a hinge having an axis of rotation H 2  in the plane of the first and second arcuate shapes that extends linearly through the first and second flexures. In cross-section, the first and second flexures  112   a ,  12   b  are substantially rectangularly shaped, each having its major axis lying in a plane that is substantially parallel with the plane of the epitaxial semiconductor layer  102  and the axis of rotation H 2 , and its minor axis lying substantially cross-wise to the plane of the epitaxial layer  102  or through it thickness. Thus, as illustrated in  FIG. 3 , the cross-section of the flexures  112   a ,  12   b  is substantially extended in the plane of the arcuate shape relative to the cross-section taken cross-wise to the plane of the arcuate shape. 
       FIG. 3  shows a cross-section taken through the first flexure  112   a  along the hinge axis H 2 , which illustrates that the major axis X of the substantially rectangular cross-section is substantially longer than its minor axis Y that is aligned along the hinge axis H 2 . The arcuate shape of each of the flexures  112   a ,  12   b  includes a respective portion, shown in  FIG. 3 , that is aligned substantially cross-wise to the axis of rotation H 2 . The axis of rotation H 2 , i.e., the hinge axis, extends through these respective cross-wise portions of the flexures  112   a ,  112   b.    
     One drawback to the prior art rectangular-style flexures is that they are essentially two-dimensional designs that do not permit changes in material thickness that can be used to control flexure stiffness. This inability to control flexure stiffness by varying material thickness is avoided by the feature of the arcuate flexure geometry of the present invention that provides a cross-section having a major axis that can be varied by changing the relative inside and outside radii, r and R, respectively, of the arcuate forms. For example, when the inside and outside radii are concentric, increasing the difference between the inside and outside radii increases the major axis X of the rectangular cross-section relative to the minor axis Y, while decreasing the difference decreases the major axis relative to the minor axis. The arcuate beam geometry of the present invention thus provides a distinct advantage over the rectangular-style flexures of the prior art. 
     Furthermore, when the flexures  112   a ,  112   b  are formed with concentric inner and outer radii r and R, respectively, the curvature of the flexures  112   a ,  12   b  causes the length of the major axis X of the cross-section to increase to a length X 1  along the direction of the axis of rotation H 2  as the a function of increasing distance from the axis of rotation, while the length of the minor axis Y remains substantially constant. In other words, the width of the flexures  112   a ,  112   b  is a minimum at the axis of rotation H 2 , and the flexures  112   a ,  112   b  become wider in cross-section as cross-sections are taken further from the axis of rotation H 2 . At the same time the thickness of the epitaxial semiconductor layer  102  remains substantially constant, so that the length of the minor axis Y does not change. 
       FIG. 4  illustrates that this tendency for the major axis X to increase as a function of increasing distance from the axis of rotation is enhanced by increasing the outer radius R and positioning its centerline offset at a distance from the centerline of the inner radius r along the axis of rotation H 2  in the concave direction of the arcuate shape. Thus, the inner and outer radii r, R are in closest proximity where the cross-section intersects the axis of rotation H 2 , and the distance X between the inner and outer radii increases rapidly to X 2  as distance from the axis of rotation increases. 
     The arcuate shaped suspension apparatus of the present invention is stiffer when loaded in-plane, i.e., in the plane containing the arcuate shape, than when loaded out-of-plane, i.e., along the accelerometer input axis I. The arcuate shape and relatively wide in-plane cross-section of the suspension apparatus provide a high modulus of rigidity in the plane of the arcuate shape, and the flat, planar shape and relatively thin out-of-plane cross-section cause it to have a very low out-of-plane modulus of rigidity. The suspension apparatus thus transfers in-plane loads along the arch of the wide, arcuate shape of the suspension apparatus causing it to be strong and stiff. In contrast, the suspension apparatus flexes or bends when subjected to out-of-plane loads, which causes it to be very flexible. This flexing or bending feature allows sensitivity to acceleration applied along input axis I, while the suspension apparatus remains rigid in the plane of the arcuate shape. The arcuate shaped suspension apparatus is thus useful as a flexure in micromachined accelerometers that are designed to be sensitive to out-of-plane force or acceleration inputs. The arcuate shaped suspension apparatus of the present invention is particularly useful in controlling rotating masses in structures where depth of structure is limited, such as structures formed using RIE and DRIE processing. 
       FIG. 5  illustrates that, while the arcuate shaped suspension apparatus of the invention is embodied in  FIG. 2  as two flexures  112  each formed of pairs of semi-circular flexures  112   a ,  112   b  that combine form substantially circular flexures  112 , the individual flexure members  112   a ,  112   b  of the arcuate shaped suspension apparatus of the invention do not need to be semi-circular flexure members, nor do the pairs of the individual flexure members  112   a ,  112   b  need to form completely circular flexures  112 . Rather, the arcuate shaped suspension apparatus can be formed in any curved or rounded shape. The completely circular arcuate shaped suspension apparatus functions well as a hinge axis because the individual semi-circular flexure members  112   a ,  112   b  flex or bend at a predictable place, i.e., across the center at hinge axis H 3 , in response to a force or acceleration applied along the input axis I 2 , while remaining rigid in the two in-plane axes. In the exemplary embodiment of the arcuate shaped suspension apparatus of the invention illustrated in  FIG. 5 , two individual semi-circular flexure members  112   c ,  112   d  lie with their respective outer arcuate shapes facing toward each other and are interconnected at the peaks of their respective arches in an “X” configuration that exhibits many of the characteristics of a circular suspension apparatus. 
       FIGS. 6A and 6B  illustrate the arcuate shaped suspension apparatus of the invention embodied in other accelerometers  200   a  and  200   b , respectively, as two pair of flexures  212  pliantly suspending an epitaxial semiconductor proof mass  214  from a support structure embodied as an inner sensor plate  216  in a “teeter-totter” arrangement between fixed electrodes (not shown) for measuring forces applied to the proof mass  214 . 
     Each of the flexures includes first and second arcuately shaped flexure members  212   a ,  212   b  each having a first end structured for connection to the inner sensor plate  216  and a second end structured for connection to the movable proof mass  214  that is to be suspended from the inner sensor plate  216 . The first and second flexure members  212   a ,  212   b  both lie in the same plane and are aligned, as illustrated in  FIG. 6A , with their respective outer arcuate shapes facing oppositely each from the other and forming a hinge having an axis of rotation or hinge axis H 4  in the plane of the first and second arcuate shapes that extends linearly through respective portions of the first and second flexure that are aligned substantially cross-wise to the axis of rotation. 
     Alternatively, as illustrated in  FIG. 6B , the flexure members  212   a ,  212   b  of each pair of flexures  212  are aligned with their respective outer arcuate shapes facing toward each other and similarly forming a hinge having an axis of rotation or hinge axis H 4  in the plane of the first and second arcuate shapes that extends linearly through respective portions of the first and second flexure that are aligned substantially cross-wise to the axis of rotation. 
     In  FIGS. 6A and 6B  the arcuate shaped suspension apparatus of the invention are embodied in a pair of quarter-round flexure members  212   a ,  212   b  of substantially identical shape each being aligned with the interior of their respective arcuate shape facing one toward the other. As illustrated by example and without limitation in  FIGS. 6A ,  6 B, each of the flexure members  212   a ,  212   b  of the two flexures  212  may be structured with their inner and outer radii being substantially concentric, as shown in  FIG. 3 , and each of the two different pairs of flexure members  212   a ,  212   b  may share substantially the same center point which also lies on the hinge axis H 4 . The two flexures  212  formed of quarter-round flexure members  212   a ,  212   b  result in a suspension apparatus that is much stiffer in the rotational axis than that formed of two pair of semicircular flexure members  112   a ,  112   b , as illustrated in  FIG. 2 , while providing the in-plane rigidity that is desirable in force/displacement sensors. 
       FIG. 7  illustrates the arcuate shaped suspension apparatus of the invention alternately embodied by example and without limitation in a configuration that employs corner arches to selectively stabilize an interior mass. The arcuate shaped suspension apparatus of the intention is, for example, embodied in a capacitive accelerometer  300  as four flexures  312  pliantly suspending an interior proof mass  314  from a support structure embodied as an outer sensor frame or plate  316  in a “trampoline” arrangement for measuring forces applied to the epitaxial proof mass  314 . The capacitive accelerometer  300  illustrated in  FIG. 7  is constructed in an epitaxial semiconductor layer using conventional microcircuit techniques as described herein and includes a pair of glass plates  318  (bottom plate shown) having opposed parallel planar faces. The plates  318  are spaced from one another and each has a metal layer electrode  320  of predetermined configuration deposited on one surface to form a capacitor plate. The interior epitaxial semiconductor layer proof mass  314  suspended from the outer sensor frame  316  is positioned between the metal layer electrodes  320  to form a common capacitor plate which moves in response to an applied force or acceleration. The outer sensor frame  316  is attached to the opposed faces of the top and bottom glass plates  318  with the interior proof mass  314  suspended therebetween by the four flexible flexures  312  forming two pairs of capacitor plates with the metal layer electrodes  320  on the opposed top and bottom glass plates  318 . Movement of the interior semiconductor proof mass  314  in response to an applied force or acceleration changes the spacing between the interior semiconductor proof mass  314  and the metal layer electrodes  320 , thereby causing a change in capacitance which is indicative of the applied force or acceleration. 
     The metal layer electrodes  320  and the interior semiconductor proof mass  314  suspended therebetween are coupled to electrical circuits capable of measuring the capacitance between the plates formed by the respective metal layer electrodes  320  and the interior semiconductor proof mass  314 . Such electrical circuits are generally well known in the art. By example and without limitation, one of such an electrical circuit is disclosed in U.S. Pat. No. 4,077,132, D IGITAL  L EVEL  I NDICATOR , issued to Erickson on Mar. 7, 1978, which is incorporated herein by reference. 
     Each of the flexures  312  suspending the interior proof mass  314  includes first and second arcuately shaped flexure members  312   a ,  312   b  each having a first end structured for connection to the outer sensor frame  316  and a second end structured for connection to the movable proof mass  314  that is to be suspended from the outer sensor frame  316 . The first and second flexure members  312   a ,  312   b  both lie in the same plane and are aligned with their respective outer arcuate shapes facing each toward the other, in contrast to the first and second arcuately shaped flexure members previously illustrated. Each of the different pairs of first and second flexure members  312   a ,  312   b  are spaced apart along one edge of the interior proof mass  314  in a gap formed between it and the outer sensor frame  316 . The flexure members  312   a ,  312   b  form a hinge having an axis of rotation or hinge axis H 5  in the plane of the first and second arcuate shapes and that extends linearly through respective portions of the first and second flexure that are aligned substantially cross-wise to the axis of rotation. 
     In  FIG. 7  the arcuate shaped suspension apparatus of the invention are embodied in a pair of quarter-round flexure members  312   a ,  312   b  of substantially identical shape each being aligned with the interior of their respective arcuate shape facing outwardly, i.e., facing away one another. As illustrated by example and without limitation in  FIG. 7 , each of the flexure members  312   a ,  312   b  of the four flexures  312  may be structured with their inner and outer radii being substantially concentric, as shown in  FIG. 3 , with their respective centerlines lying on the hinge axis H 5 . The four flexures  312  formed of approximately quarter-round flexure members  312   a ,  312   b  result in a suspension apparatus that permits the interior proof mass  314  to move up and down in a “trampoline” manner relative to the outer sensor frame or plate  316  along an input axis I 3  normal to the plane of the sensor  300 , while providing the in-plane rigidity that is desirable in force/displacement sensors. 
       FIG. 8  illustrates the arcuate shaped suspension apparatus of the intention alternately embodied by another example and still without limitation in a configuration that employs two pair of side arches to selectively stabilize an interior mass. The arcuate shaped suspension apparatus of the intention is, for example, embodied in another capacitive accelerometer  400  as two flexures  412  pliantly suspending an interior proof mass  414  from a support structure embodied as an outer sensor frame or plate  416  in another “trampoline” arrangement for measuring forces applied to the proof mass  414  similar to the configuration illustrated in  FIG. 7 . 
     Each of the side flexures  412  suspending the interior proof mass  414  includes first and second arcuately shaped flexure members  412   a ,  412   b  each having a first end structured for connection to the outer sensor frame  416  and a second end structured for connection to the movable proof mass  414  that is to be suspended from the outer sensor frame  416 . The first and second flexure members  412   a ,  412   b  both lie in the same plane and, in contrast to the embodiment illustrated in  FIG. 7 , are aligned with their respective inner arcuate shapes facing each toward the other similarly to the first and second arcuately shaped flexure members  112   a ,  112   b  illustrated in  FIG. 2 . Each of the different pairs of first and second flexure members  412   a ,  412   b  are spaced apart along one edge of the interior proof mass  414  in a gap formed between it and the outer sensor frame  416 . The flexure members  412   a ,  412   b  form a hinge having an axis of rotation or hinge axis H 6  in the plane of the first and second arcuate shapes that extends linearly through respective portions of the first and second flexure that are aligned substantially cross-wise to the axis of rotation. 
     In  FIG. 8  the arcuate shaped suspension apparatus of the invention are embodied in a pair of quarter-round flexure members  412   a ,  412   b  of substantially identical shape each being aligned with the interior of their respective arcuate shape facing inwardly, i.e., facing toward one another. As illustrated by example and without limitation in  FIG. 8 , each of the flexure members  412   a ,  412   b  of the two flexures  412  may be structured with their inner and outer radii being substantially concentric, as shown in  FIG. 3 , with their respective centerlines being coincident and lying on the hinge axis H 6 . The two flexures  412  formed of quarter-round flexure members  412   a ,  412   b  result in a suspension apparatus that permits the interior proof mass  414  to move up and down in a “trampoline” manner along an input axis I 4  normal to the plane of the sensor  400  relative to the outer sensor frame or plate  416 , while providing the in-plane rigidity that is desirable in force/displacement sensors. 
       FIG. 8  also illustrates the arcuate shaped suspension apparatus of the invention embodied in an optional configuration wherein a single pair of half-round flexure members  412   a ,  412   b  of substantially identical shape extend between opposing inner walls in a space  418  within the outer sensor frame  416  and share a common centerline. Accordingly, pair of half-round flexure members  412   a ,  412   b  form a circularly shaped suspension apparatus  412  with the interior proof mass  414  suspended on top. 
     While the preferred embodiment of the invention has been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention.