Abstract:
A capacitive strain gage assembly ( 10 ) for measuring strain in a component ( 40 ) includes a housing ( 12 ) attachable to the component ( 40 ) at a first location ( 42 ). The strain gage assembly ( 10 ) includes a first target sensor ( 24,26 ) and second target sensor ( 28,30 ) disposed in the housing ( 12 ). The strain gage assembly ( 10 ) also includes a sensor member ( 14 ) attachable to the component ( 40 ) at a second location ( 44 ) in movable relation to the housing ( 12 ). The sensor member ( 14 ) includes a sensor element ( 32 ) operable to transmit capacitive signals to the first and second target sensors ( 24,26,28,30 ). The sensor element ( 32 ) is disposed between the first and second target sensors ( 24,26,28,30 ). The strain gage assembly ( 10 ) may also be constructed using generally buckle resistant flexible materials for nonplanar strain measurement applications.

Description:
TECHNICAL FIELD OF INVENTION 
     This invention relates in general to the field of strain gages and, more particularly, to a capacitive strain gage and method. 
     BACKGROUND OF THE INVENTION 
     A strain gage is a device used to measure surface strains in structural materials. One type of strain gage used to measure surface strain is a foil type resistance strain gage. Another type of strain gage used to measure surface strain is a capacitive strain gage. A capacitive strain gage generally utilizes capacitors with capacitive plates or elements which are moveable relative to each other as a function of applied strain. As force is applied to the structural material, relative movement of the capacitor elements causes the capacitance to change. The change in capacitance is measured by detecting a change in an applied electrical signal. 
     Capacitive strain gages, however, generally measure strain in a selected axial or lateral direction. For example, as force is applied to the structural material, movement of the capacitor elements in the selected direction causes a change in capacitance. However, movement of the capacitor elements in a direction other than the selected direction may cause changes in capacitance not associated with applied strain, thereby causing erroneous strain measurements. 
     Additionally, nonplanar displacement of the structural material may result in erroneous strain measurements or strain gage failure. For example, using a strain gage generally requires securely affixing or bonding the strain gage to the structural material. As forces are applied to the structural material, nonplanar surface displacement of the structural material may cause the strain gage to disbond from the structural material resulting in a loss of strain measurement data. 
     Usage of strain gages is also generally limited to structural materials having a high modulus of elasticity. For example, foil type resistance strain gages are generally encapsulated in a polyimide resin and attached to a phenolic-type backing material. The backing material is then securely affixed to the structural material using high strength adhesives. The polyimide resin, backing material, and adhesive generally require large forces to elongate the polyimide resin, backing material and adhesive. Thus, conventional strain gages cannot accurately measure strain in low modulus of elasticity materials because the low modulus of elasticity material will elongate prior to elongation of the strain gage. 
     Further, nonplanar displacement of the structural material may cause erroneous strain measurements. For example, changes in distance between the capacitor elements of a capacitive strain gage in a direction other than the selected measurement direction may result in a change in capacitance unassociated with strain. Therefore, nonplanar displacement of the structural material may result in erroneous strain measurements. 
     SUMMARY OF THE INVENTION 
     Accordingly, a need has arisen for an improved capacitive strain gage and method that provide greater ease and flexibility of use. The present invention provides a capacitive strain gage and method that addresses shortcomings of prior capacitive strain gages. 
     According to one embodiment of the present invention, a capacitive strain gage assembly comprises a housing attachable to the component at a first location. A plurality of target members are disposed within the housing. Each target member includes a first target sensor and a second target sensor. A length of the second target sensor is greater than a length of the first target sensor. The strain gage assembly also comprises a sensor member attachable to the component at a second location in moveable relation to the housing. The sensor member is disposed between the target members adjacent the first target sensor of each target member. The sensor member includes a sensor element operable to transmit capacitive signals to the first and second target sensors of each target member. 
     According to another embodiment of the present invention, a method for fabricating a capacitive strain gage for measuring strain in a component comprises providing a housing attachable to a first location of the component. The method also includes securing a plurality of target members in the housing, each of the target members having a first target sensor and a second target sensor. The length of the second target sensor is greater than the length of the first target sensor of each target member. The method further includes disposing a sensor member attachable to a second location of the component in moveable relation to the housing adjacent the first target sensor of each target member. The sensor member includes a sensor element operable to transmit capacitive signals to the first and second target sensors of each target member. 
     Embodiments of the present invention provide several technical advantages. For example, one embodiment of the present invention provides a capacitive strain gage assembly that provides greater accuracy than prior capacitive strain gage assemblies by compensating for nonplanar displacement of the structural material. In the same embodiment, the present invention provides increased accuracy of strain measurements for nonplanar structural materials. 
     Other technical advantages are readily apparent to one skilled in the art from the following figures, descriptions, and claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following descriptions taken in connection with the accompanying drawings in which: 
     FIG. 1 illustrates an enlarged isometric view of a capacitive strain gage assembly constructed in accordance with the teachings of the present invention; 
     FIG. 2A illustrates an enlarged section view of the capacitive strain gage assembly shown in FIG. 1 taken along the line  2 — 2  of FIG. 1; 
     FIG. 2B illustrates the capacitive strain gage assembly shown in FIG. 2A used in a nonplanar application; 
     FIG. 3 illustrates an enlarged section view of the capacitive strain gage assembly shown in FIG. 1 taken along the line  3 — 3  of FIG. 1; 
     FIG. 4 is a schematic drawing in elevation for illustrating capacitive properties of one embodiment of the present invention in connection with Appendix A; 
     FIG. 5 is a schematic drawing in elevation for illustrating capacitive properties of an alternate embodiment of the present invention in connection with Appendix B; and 
     FIG. 6 is a schematic drawing for illustrating capacitive properties of an alternate embodiment of the present invention in connection with Appendix C. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the present invention and its advantages are best understood by referring to FIGS. 1-3 of the drawings, like numerals being use for like and corresponding parts of the various drawings. 
     FIG. 1 illustrates an enlarged isometric view of one embodiment of a capacitive strain gage assembly  10  constructed in accordance with teachings of the present invention. Strain gage assembly  10  includes a housing  12  and a sensor member  14 . Housing  12  includes a pad  16  for attaching a lead of a capacitive displacement readout device (not explicitly shown). Sensor member  14  also includes a pad  18  for attaching a lead from the capacitive displacement readout device. As will be described in greater detail in conjunction with FIG. 2A, strain gage assembly  10  is used to measure strain from the displacement of sensor member  14  relative to housing  12 . 
     Housing  12  of strain gage assembly  10  is constructed using generally nonconductive materials. Housing  12  may also be constructed using generally flexible materials that provide flexibility and resist buckling. For example, housing  12  may be constructed using fiberglass circuit board material. However, other suitable materials may be used to construct housing  12 . As will be described in greater detail in conjunction with FIG. 2B, constructing housing  12  using generally flexible materials allows strain gage assembly  10  to accurately measure strain in nonplanar applications. 
     Sensor member  14  of strain gage assembly  10  is also constructed using generally nonconductive materials. Sensor member  14  may also be constructed using generally flexible materials that provide flexibility and resist buckling. For example, sensor member  14  may be constructed using fiberglass circuit board materials; however, other suitable materials may be used for constructing sensor member  14 . As will be described in greater detail in conjunction with FIG. 2B, constructing sensor member  14  using generally flexible materials allows strain gage assembly  10  to accurately measure strain in nonplanar applications. 
     FIG. 2A is an enlarged section view of strain gage assembly  10  shown in FIG. 1 taken along the line  2 — 2  of FIG.  1 . In the illustrated embodiment, sensor member  14  of stain gage assembly  10  is disposed between a target member  20  and a target member  22 . Target members  20  and  22  are constructed using generally nonconductive materials. Target members  20  and  22  may also be constructed using generally flexible materials that provide flexibility and resist buckling. For example, target members  20  and  22  may be constructed using fiberglass circuit board materials. However, other suitable materials may be used to construct target members  20  and  22 . As will be described in greater detail in conjunction with FIG. 2B, constructing target members  20  and  22  from generally flexible materials allows strain gage assembly  10  to accurately measure strain in nonplanar applications. 
     In the illustrated embodiment, target members  20  and  22  are disposed adjacent to and in contact with sensor member  14 . However, target members  20  and  22  may also be disposed adjacent sensor member  14  having a predetermined clearance distance to sensor member  14  (not explicitly shown). For example, disposing target members  20  and  22  a predetermined clearance distance from sensor member  14  would eliminate frictional forces between sensor member  14  and target members  20  and  22 , thereby allowing easier movement of sensor member  14  relative to housing  12  and increased sensitivity of strain gage assembly  10  to surface strains. 
     Target member  20  of strain gage assembly  10  includes target sensors  24  and  26 . Target member  22  of strain gage assembly  10  includes target sensors  28  and  30 . In the illustrated embodiment, target sensors  24 ,  26 ,  28  and  30  are disposed on surfaces of target members  22  and  24 , respectively. However, target sensors  24 ,  26 ,  28  and  30  may be disposed at other suitable locations and orientations of target members  22  and  24 , respectively. As illustrated in FIG. 2A, target sensors  24 ,  26 ,  28 , and  30  are electrically coupled together along a rearward area of housing  12 . Additionally, target sensors  24 ,  26 ,  28 , and  30  are electrically coupled to pad  16  for connecting to the capacitive displacement readout device. 
     Target sensors  24 ,  26 ,  28 , and  30  are constructed using generally conductive materials, such as copper; however, other suitable conductive materials may be used for constructing target sensors  24 ,  26 ,  28 , and  30 . Additionally, in the illustrated embodiment, target members  20  and  22  and target sensors  24 ,  26 ,  28  and  30  are constructed having a generally flat and rectangular configuration. However, target members  20  and  22  and target sensors  24 ,  26 ,  28  and  30  may be constructed having other suitable shapes and configurations. 
     As illustrated in FIG. 2A, target sensor  24  is disposed between target sensor  26  and sensor member  14 . Additionally, target sensor  28  is disposed between target sensor  30  and sensor member  14 . Target sensor  26  of target member  20  is constructed having a length greater than a length of target sensor  24 . Therefore, target sensor  26  is constructed having a greater cross sectional area than target sensor  24 . Additionally, target sensor  30  of target member  22  is constructed having a length greater than target sensor  28 . Therefore, target sensor  30  is constructed having a greater cross sectional area than target sensor  28 . As will be described in greater detail below, the difference in cross sectional areas between target sensors  24  and  26  and between target sensors  28  and  30  provides increased sensitivity of strain gage assembly  10 . 
     Sensor member  14  of strain gage assembly  10  also includes a sensor element  32  for transmitting capacitive signals to target sensors  24 ,  26 ,  28 , and  30 . In the illustrated embodiment, sensor element  32  is disposed at a mid-plane of sensor member  14 . For example, sensor member  14  may be constructed having sensor element  32  centrally disposed between flexible fiberglass circuit board materials. However, sensor element  32  may be disposed at other suitable locations and orientations of sensor member  14  provided sensor element  32  does not contact target sensors  24  and  28 . As will be described in greater detail in conjunction with FIG. 2B, constructing sensor member  14  from flexible materials allows strain gage assembly  10  to measure strain in nonplanar applications. 
     Sensor element  32  of sensor member  14  is constructed using generally conductive materials such as copper; however, sensor element  32  may be constructed using other suitable conductive materials. Sensor member  14  also includes a sensor lead  34  for electrically coupling sensor element  32  to pad  18 . As described above, pad  18  provides an attachment location for the capacitive displacement readout device. 
     In the embodiment illustrated in FIG. 2A, strain gage assembly  10  also includes a pressure element  36 . Pressure element  36  provides a generally light force to target member  20  for maintaining contact between target members  20  and  22  and sensor member  14  and allowing movement of sensor member  14  relative to target members  20  and  22 . In the embodiment illustrated in FIG. 2, pressure element  36  is constructed using a foam material; however, pressure element  36  may be constructed using other suitable materials. 
     As illustrated in FIG. 2A, sensor member  14  is disposed between target members  20  and  22  and extends through an opening  38  of housing  12 . In operation, housing  12  is attached to a component  40  at attachment location  42 . Housing  12  may be attached to component  14  using low melting point adhesives or double-sided tape; however, other suitable materials and methods may be used to attach housing  12  to component  40  at attachment location  42 . 
     Sensor member  14  is attached to component  40  at attachment location  44 . A support  46  may be used to couple sensor member  14  to component  40  at attachment location  44 . However, sensor member  14  may be constructed so that support  46  is an integral extension of sensor member  14 . In the embodiment illustrated in FIG. 2, support  46  is also secured to sensor member  14  at attachment location  48 . Support  46  may be secured to sensor member  14  and component  40  using low melting point adhesives or double-sided tape; however, other suitable materials or methods may be used to attach support  46  to sensor member  14  and component  40 . 
     The operation of strain gage assembly  10  will now be briefly described. Capacitance is generally a function of a distance between two capacitive elements and an overlapping cross sectional area between the two capacitive elements. For example, capacitance may be generally defined by the following equation:              C   =       ∈   A     d             (   1   )                                
     where C is the capacitance between capacitive elements, ε is the dielectric constant of the material used to construct the capacitive elements, A is the amount of cross sectional area overlap of the capacitive elements, and d is the distance between the capacitive elements. Thus, capacitance is inversely proportional to the distance between the capacitive elements and directly proportional to the amount of cross sectional area overlap between the two capacitive elements. 
     Referring to FIG. 2A, as forces are applied to component  40  causing strain and surface displacement of component  40 , surface displacement of component  40  between attachment location  42  and attachment location  44  causes sensor member  14  to move or translate between target members  20  and  22 . For example, surface displacement of component  40  may cause the distance between attachment location  42  and attachment location  44  to increase, thereby causing sensor member  14  to translate in a forward displacement direction away from the rearward area of housing  12 . As sensor member  14  translates in the forward displacement direction, the amount of cross sectional area overlap between sensor element  32  and target sensors  24 ,  26 ,  28  and  30  changes. However, the distance between sensor element  32  and target sensors  24 ,  26 ,  28  and  30  remains generally constant. Thus, the movement of sensor member relative to target members  20  and  22  causes a change in capacitance. 
     For ease of illustration, the change in capacitance of strain gage assembly  10  due to the movement of sensor member  14  relative to target members  20  and  22  will be described by illustrating the change in capacitance relative to sensor member  14  and only target member  20 . For example, the capacitance between sensor member  14  and target member  20  may be generally defined by the following equation:                C   1     =         ∈     A   1         d   1       +       ∈     A   2         d   2                 (   2   )                                
     where C 1  is the total capacitance between sensor element  32  and target sensors  24  and  26 , ε is the dielectric constant of the material used to construct sensor element  32  and target sensors  24  and  26 , A 1  is the cross sectional area overlap between sensor element  32  and target sensor  24 , d 1  is the distance between sensor element  32  and target sensor  24 , A 2  is the cross sectional area overlap between sensor element  32  and target sensor  26 , and d 2  is the distance between sensor element  32  and target sensor  26 . For ease of illustration, the materials used to construct sensor element  32  and target sensors  24  and  26  for this example have the same dielectric constant ε; however, other suitable materials having different dielectric constants may be used to construct sensor element  32  and target sensors  24  and  26 . 
     As sensor member  14  translates in a forward displacement direction relative to target member  20 , the value of A 1  decreases and the value of A 2  increases. However, the values of d 1  and d 2  remain generally constant because the distances between sensor element  32  and target sensors  24  and  26  remain generally constant. Therefore, the capacitance between sensor element  32  and target sensors  24  and  26 , defined generally as C 1 , changes due to movement of sensor member  14  relative to target member  20 . The change in capacitance between sensor element  32  and target sensors  24  and  26  due to movement of sensor element  32  relative to target sensors  24  and  26  is described more fully below in connection with FIG.  4  and Appendix A. 
     Accordingly, the total capacitance of strain gage assembly  10  may be generally defined by the following equation: 
     
       
           C   total   =C   1   +C   2   (3)  
       
     
     where C total  is the total capacitance of strain gage assembly  10 , C 1  is the capacitance between sensor element  32  and target sensors  24  and  26 , and C 2  is the capacitance between sensor element  32  and target sensors  28  and  30 . As previously described, target sensors  24 ,  26 ,  28  and  30  are electrically coupled together along the rearward area of housing  12 . Thus, strain gage assembly  10  measures strain using a plurality of capacitive elements coupled in parallel. Therefore, strain gage assembly  10  provides greater accuracy and sensitivity than prior capacitive strain gages. 
     Additionally, the capacitive sensitivity of strain gage assembly  10  may be increased by constructing sensor element  32  having a length greater than or equal to the length of target sensors  26  and  30 . For example, referring to FIG.  2 A and equation (2), as sensor element  32  translates in a forward displacement direction, the values of A 1  and A 2  would both decrease, thereby causing a capacitance change associated with both target sensor  24  and target sensor  26 . This example is described more fully below in connection with FIG.  5  and Appendix B. 
     Additionally, sensor element  32  and target sensors  24 ,  26 ,  28  and  30  may be constructed having various shapes to increase or decrease changes in capacitance due to displacement of sensor element  32  resulting from varying cross sectional area overlap between sensor element  32  and target sensors  24 ,  26 ,  28  and  30 . For example, sensor element  32  may be constructed having a generally triangular cross sectional area. This example is described more fully below in connection with FIG.  6  and Appendix C. 
     Strain gage assembly  10  also provides greater accuracy than prior capacitive strain gage assemblies by compensating for nonplanar displacement of sensor member  14  relative to target members  20  and  22 . For example, as described above, capacitance is generally a function of the distance between capacitive elements. Thus, as the distance between capacitive elements changes, the capacitance changes inversely between the capacitive elements. Therefore, nonplanar displacement of sensor member  14  relative to target members  20  and  22  may cause capacitive changes unassociated with surface displacement of component  40  in a planar displacement direction. 
     Strain gage assembly  10 , however, provides greater accuracy than prior capacitive strain gages by compensating for nonplanar displacement of sensor member  14  relative to target members  20  and  22  by using a plurality capacitive elements. Referring to FIG. 2A, for example, strain gage assembly  10  includes target member  20  disposed above sensor member  14  and target member  22  disposed below sensor member  14 . If sensor member  14  moves toward target member  20  due to nonplanar displacement of sensor member  14 , sensor member  14  would move away from target member  22  a corresponding amount. Thus, the change in distances between sensor element  32  and target sensors  24  and  26  would be compensated by a corresponding change in distances between sensor element  32  and target sensors  28  and  30 . Therefore, capacitance changes due to nonplanar displacement of sensor member  14  are substantially reduced. Thus, strain gage assembly  10  provides greater accuracy than prior capacitive strain gages by compensating for nonplanar displacement of component  40 . 
     Additionally, strain gage assembly  10  provides greater flexibility than prior strain gages by allowing strain to be measured in components having a low modulus of elasticity. For example, strain gage assembly  10  may be secured to a low modulus of elasticity component  40  at attachment location  42  and attachment location  44 . Generally small forces applied to the low modulus of elasticity component  40  will cause surface displacement of component  40  between attachment location  42  and attachment location  44 , thereby causing movement of sensor member  14  relative to target members  20  and  22 . Thus, generally small forces applied to the low modulus of elasticity component  40  result in measurable capacitance changes. Therefore, strain gage assembly  10  provides greater flexibility than prior strain gages by allowing strain to be measured in low modulus of elasticity components  40 . 
     FIG. 2B illustrates strain gage assembly  10  shown in FIG. 2A used in a nonplanar application. For example, strain gage assembly  10  provides greater accuracy and flexibility than prior capacitive strain gages by allowing strain to be measured in nonplanar components  40 . For example, as previously described, housing  12 , sensor member  14 , and target members  20  and  22  may be constructed using generally flexible materials that resist buckling, such as flexible fiberglass or kapton circuit board material. The flexible characteristics of housing  12 , sensor member  14 , and target members  20  and  22  allow strain gage assembly  10  to be secured to nonplanar components  40 . 
     Additionally, forces applied to component  40  resulting in nonplanar displacement of component  40  may be accurately measured using strain gage assembly  10 . For example, as previously described, housing  12 , sensor member  14 , and target members  20  and  22  may be constructed using generally flexible materials allowing strain gage assembly  10  to accommodate nonplanar displacement of component  40 . Thus, strain gage assembly  10  provides greater accuracy and flexibility than prior strain gage assemblies by accommodating nonplanar components  40  and nonplanar displacements of components  40 . 
     FIG. 3 is an enlarged section view of strain gage assembly  10  shown in FIG. 1 taken along the line  3 — 3  of FIG.  1 . In the embodiment illustrated in FIG. 3, strain gage assembly  10  also includes an alignment element  50  for providing controlled directional displacement of sensor member  30  relative to target members  20  and  22 . For example, alignment element  50  may be used to maintain longitudinal displacement of sensor member  14  relative to target members  20  and  22 . In the embodiment illustrated in FIG. 3, alignment element  50  includes an alignment key  52  disposed on sensor member  14  and an alignment grove  54  disposed in target member  22 . Alignment key  52  cooperates with alignment grove  54  to restrain movement of sensor member  14  to a desired translation direction. Thus, strain gage assembly  10  provides greater accuracy than prior capacitive strain gage assemblies by restraining movement of sensor member  14  relative to target members  20  and  22  to minimize capacitance changes unassociated with strain measurements in a desired direction. 
     Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions, and alterations can be made therein without departing from the spirit and scope of the present invention as defined by the appended claims. 
     APPENDIX A 
     FIG. 4 is a schematic drawing in elevation illustrating one example of a positional relationship of sensor element  32  and target sensors  24  and  26  of the present invention. Prior to forward displacement of sensor element  32  relative to target sensors  24  and  26 , the cross sectional area overlap between sensor element  32  and target sensors  24  and  26  may be generally defined by the following equations: 
     
       
           wL   1   =A   1   (4)  
       
     
     
       
           w ( L−L   1 )= A   2   (5)  
       
     
     where A 1  is the value of cross sectional area overlap between sensor element  32  and target sensor  24 , A 2  is the value of cross sectional area overlap between sensor element  32  and target sensor  26 , L represents the length of sensor element  32 , L 1  represents the length of target sensor  24 , and w represents the width of sensor element  32  and target sensors  24  and  26 . In the illustrated example, the sensor element  32  and target sensors  24  and  26  are constructed having substantially equal widths, represented by the value w. However, sensor element  32  and target sensors  24  and  26  may be constructed having different widths. 
     From equations (1), (4) and (5), the capacitance between sensor element  32  and target sensors  24  and  26  prior to forward displacement of sensor element  32  may be generally expressed by the following equation:                C   1     =         ∈     A   1         d   1       +       ∈     A   2         d   2                 (   6   )                                
     where C 1  represents the capacitance between sensor element  32  and target sensors  24  and  26 , d 1  represents the distance between sensor element  32  and target sensor  24 , d 2  represents the distance between sensor element  32  and target sensor  26 , and ε represents the dielectric constant of the material used to construct sensor element  32  and target sensors  24  and  26 . In the illustrated example, sensor element  32  and target sensors  24  and  26  are constructed from material having substantially equal values of dielectric constant, represented by ε. However, sensor element  32  and target sensors  24  and  26  may be constructed from material having different values of dielectric constant. 
     From equations (4), (5) and (6), the capacitance between sensor element  32  and target sensors  24  and  26  may also be represented by the following equation:                C   1     =     ∈     w        (         L   1       d   1       +       L   -     L   1         d   2         )                 (   7   )                                
     As sensor element  32  translates in a forward displacement direction relative to target sensors  24  and  26 , the cross sectional area overlap between sensor element  32  and target sensors  24  and  26  may be generally represented by the following equations: 
     
       
           A′   1   =w ( L   1   −Δx )  (8)  
       
     
     
       
           A′   2   =w ( L−L   1   +Δx )  (9)  
       
     
     where Δx represents the amount of forward displacement of sensor element 32, A′ 1  represents the cross sectional area overlap between sensor element  32  and target sensor  24  after forward displacement of sensor element 32, and A′ 2  represents the cross sectional area overlap between sensor element  32  and target sensor  26  after forward displacement of sensor element  32 . 
     Based on the above equations, the capacitance between sensor element  32  and target sensors  24  and  26  after forward displacement of sensor element  32  may be generally expressed by the following equations:                C   1   ′     =     ∈     w        (           L   1     -     Δ                 x         d   1       +       L   -     L   1     +     Δ                 x         d   2         )                 (   10   )                 C   1   ′     =     ∈       w        (         L   1       d   1       +       L   -     L   1         d   2         )       -     ∈     wΔ                   x        (       1     d   1       -     1     d   2         )                   (   11   )                 C   1   ′     =         C   1     -     ∈       w        (       1     d   1       -     1     d   2         )          Δ                 x               (   12   )                                
     where C′ 1  represents the value of capacitance between sensor element  32  and target sensors  24  and  26  after forward displacement of sensor element  32  by an amount equal to the value Δx. 
     Further, the change in capacitance between sensor element  32  and target sensors  24  and  26  resulting from forward displacement of sensor element  32  may be generally expressed as a function of the forward displacement of sensor element  32  by the following equation:                  Δ                 C       Δ                 x       =     -     ∈     w        (       1     d   1       -     1     d   2         )                   (   13   )                                
     where ΔC is the change in capacitance between sensor element  32  and target sensors  24  and  26  resulting from forward displacement of sensor element  32  by an amount equal to the value to Δx. 
     APPENDIX B 
     FIG. 5 is a schematic drawing in elevation illustrating one example of a positional relationship of sensor element  32  and target sensors  24  and  26  of the present invention. In this example, sensor element  32  is constructed having a length substantially equal to the length of target sensor  26 . Prior to forward displacement of sensor element  32  relative to target sensors  24  and  26 , the cross-sectional area overlap between sensor element  32  and target sensors  24  and  26  may be generally defined by the following equations: 
     
       
           A   1   =wL   1   (14)  
       
     
     
       
           A   2   =w ( L   2−L   1 )  (15)  
       
     
     where A 1  is the value of cross-sectional area overlap between sensor element  32  and target sensor  24 , A 2  is the value of cross-sectional area overlap between sensor element  32  and target sensor  26 , L 1  represents the length of target sensor  24 , L 2  represents the length of target sensor  26 , and w represents the width of sensor element  32  and target sensors  24  and  26 . In the illustrated example, sensor element  32  and target sensors  24  and  26  are constructed having substantially equal widths, represented by the value w. However, sensor element  32  and target sensors  24  and  26  may be constructed having different widths. 
     From equations (1), (14) and (15), the capacitance between sensor element  32  and target sensors  24  and  26  prior to forward displacement of sensor element  32  may be generally expressed by the following equation:                C   1     =           ∈     A   1         d   1       +       ∈     A   2         d   2         =     ∈     w        (         L   1       d   1       +         L   2     -     L   1         d   2         )                   (   16   )                                
     where C 1  represents the capacitance between sensor element  32  and target sensors  24  and  26 , d 1  represents the distance between sensor element  32  and target sensor  24 , d 2  represents the distance between sensor element  32  and target sensor  26 , and ε represents the dielectric constant of the material used to construct sensor element  32  and target sensors  24  and  26 . In the illustrated example, sensor element  32  and target sensors  24  and  26  are constructed from material having substantially equal values of dielectric constant, represented by ε. However, sensor element  32  and target sensors  24  and  26  may be constructed from material having different values of dielectric constant. 
     As sensor element  32  translates in a forward displacement direction relative to target sensors  24  and  26 , the cross-sectional area overlap between sensor element  32  and target sensors  24  and  26  may be generally represented by the following equations: 
     
       
           A′   1   =w ( L   1   −Δx )  (17)  
       
     
     
       
           A′   2   =w ( L   2   −L   1 )  (18)  
       
     
     where Δx represents the amount of forward displacement of sensor element  32 , A′ 1  represents the cross-sectional area overlap between sensor element  32  and target sensor  24  after forward displacement of sensor element  32 , and A′ 2  represents the cross-sectional area overlap between sensor element  32  and target sensor  26  after forward displacement of sensor element  32 . 
     Based on the above equations, the capacitance between sensor element  32  and target sensors  24  and  26  after forward displacement of sensor element  32  may be generally expressed by the following equations:                C   1   ′     =     ∈     w        (           L   1     -     Δ                 x         d   1       +         L   2     -     L   1         d   2         )                 (   19   )                                              C   1   ′     =     ∈       w        (         L   1       d   1       +         L   2     -     L   1         d   2         )       -     (       ∈     wΔ                 x         d   1       )                 (   20   )                 C   1   ′     =       C   1     -       ∈     wΔ                 x         d   1                 (   21   )                                 
     where C′ 1  represents the value of capacitance between sensor element  32  and target sensors  24  and  26  after forward displacement of sensor element  32  by an amount equal to the value Δx. 
     Further, the change in capacitance between sensor element  32  and target sensors  24  and  26  resulting from forward displacement of sensor element  32  may be generally expressed as a function of the forward displacement of sensor element  32  by the following equation:                  Δ                 C       Δ                 x       =       -     ∈   w         d   1               (   22   )                                
     where ΔC is the change in capacitance between sensor element  32  and target sensors  24  and  26  resulting from forward displacement of sensor element  32  by an amount equal to the value Δx. Referring to the above equation and equation (13) of Appendix A, the magnitude of the change in capacitance between sensor element  32  and target sensors  24  and  26  resulting from forward displacement of sensor element  32  an amount equal to the value of Δx for the above illustrated example is greater than the example illustrated in Appendix A by the following amount:                ∈   w       d   2             (   23   )                                
     Thus, the capacitive sensitivity of strain gage assembly  10  may be increased by constructing sensor element  32  having a length greater than or equal to the length of target sensors  26  and  30 . 
     APPENDIX C 
     FIG. 6 is a schematic drawing illustrating capacitive properties between a triangular shaped wedge  56  having an angle of 2θ and a rectangular shaped strip  58  having a length L and a width W defined by the points ABCD. The projected area between the rectangular strip  58  and triangular wedge  56  comprises a trapezoid defined by the points JBDM. The area of this trapezoid is the area of a rectangular strip of sides H and L, defined by the points JKLM, and the area of two right triangles of base L and altitude y, defined by the points JBK and MDL, where y may be generally defined by the following equation: 
     
       
           y=L  tan Θ  (24)  
       
     
     Thus, the projected area between the rectangular strip  58  and the triangular wedge  56  may be generally expressed by the following equations:              A   =       HL   +     2        (     1   2     )          (   L   )          (     L                 tan                 Θ     )         =     HL   +       L   2        tan                 Θ                 (   25   )                                
     
       
           A=L ( H+y )  (26)  
       
     
     where A is the projected area between the rectangular strip  58  and the triangular wedge  56 . 
     If the triangular wedge  56  is translated to the right relative to the rectangular strip  58 , the resulting projected area between the triangular wedge  56  and the rectangular strip  58  comprises a trapezoid defined by the points STUV. The area of this trapezoid is the area of a rectangular strip, defined by the points SNPV, and the area of two right triangles, defined by the points STN and VPU. The areas of triangles STN and VPU are equal to the areas of triangles JBK and MDL discussed above. Thus, the projected area between triangular wedge  56  and rectangular strip  58  after rightward displacement of triangular wedge  56  may generally be expressed by the following equations: 
     
       
           E=H− 2 Δy   (27)  
       
     
     
       
         Δ y=Δx  tan Θ  (28)  
       
     
     
       
           A′=L ( H− 2 Δy )+ Ly   (29)  
       
     
     
       
           A′=L ( H+y )−2 LΔy   (30)  
       
     
     
       
           A′=A− 2 LΔx  tan Θ  (31)  
       
     
     where Δx is the amount of rightward displacement of the triangular wedge  56  relative to the rectangular strip  58 , A′ is the projected area between the triangular wedge and the rectangular strip after rightward displacement of this triangular wedge  56 , and E is the width of the rectangular strip defined by the points SNPV. 
     Referring to FIG. 4 where target sensor  24  is constructed having a length of L 1  and target sensor  26  is constructed having a length of L 2 , and where sensor element  32  is constructed having a generally triangular cross section as described above, the capacitance between the triangular-shaped sensor element  32  and target sensors  24  and  26  may be generally expressed by the following equations:                C   1     =         ∈     A   1         d   1       +       ∈     A   2         d   2                 (   32   )                                
     
       
           A   1   =L   1 ( H+L   1  tan Θ)  (33)  
       
     
       A   2   =L   2 ( H+L   1  tan Θ+ L   2  tan Θ)  (34) 
     where C 1  is the capacitance between the triangular-shaped sensor element  32  and target sensors  24  and  26 , A 1  is the amount of cross sectional area overlap between the triangular-shaped sensor element  32  and target sensor  24 , A 2  is the amount of cross sectional area overlap between the triangular-shaped sensor element  32  and target sensor  26 , and ε represents the dielectric constant of the material used to construct the triangular-shaped sensor element and target sensors  24  and  26 . 
     As the triangular-shaped sensor element  32  translates in a forward displacement direction relative to target sensors  24  and  26 , the cross sectional area overlap between the triangular-shaped sensor element  32  and target sensors  24  and  26  may be generally represented by the following equations: 
     
       
           A′   1   =A   1 −2 L   1   Δx  tan Θ  (35)  
       
     
     
       
           A′   2   =A   2 −2 L   2   Δx  tan Θ  (36)  
       
     
     where Δx represents the amount of forward displacement of the triangular-shaped sensor element  32 , A′ 1  represents the cross sectional area overlap between the triangular-shaped sensor element  32  and target sensor  24  after forward displacement of the triangular-shaped sensor element  32 , and A′ 2  represents the cross sectional area overlap between the triangular-shaped sensor element  32  and target sensor  26  after forward displacement of the triangular-shaped sensor element  32 . 
     Using the above equations, the capacitance between the triangular-shaped sensor element  32  and target sensors  24  and  26  after forward displacement of the triangular-shaped sensor element  32  may be generally expressed by the following equations:                C   1   ′     =         ∈     A   1         d   1       -       ∈     2        L   1        Δ                 x                 tan                 Θ         d   1       +       ∈     A   2         d   2       -       ∈     2        L   2        Δ                 x                 tan                 Θ         d   2                 (   37   )                 C   1   ′     =         C   1     -     ∈     Δ                 x                 tan                   Θ        (         L   1       d   1       +       L   2       d   2         )                   (   38   )                                
     where C′ 1  represents the value of capacitance between the triangular-shaped sensor element  32  and target sensor  24  and  26  after forward displacement of the triangular-shaped sensor element  32  by an amount equal to the value Δx. 
     The change in capacitance resulting from forward displacement of the triangular-shaped sensor element  32  may also be generally defined by the following equations as a function of the forward displacement:                  Δ                 C       Δ                 x       =     -     ∈     tan                   Θ        (         L   1       d   1       +       L   2       d   2         )                     (   39   )                                
     where ΔC is the change in capacitance between the triangular-shaped sensor element  32  and target sensors  24  and  26  resulting from forward displacement of the triangular-shaped sensor element  32  by an amount equal to the value of Δx. As illustrated in equation (39), the change in capacitance to target sensor  26  adds to the total capacitance instead of subtracting from the total capacitance. Thus, sensor element  32  and target sensors  24 ,  26 ,  28  and  30  may be constructed having various shapes to increase or decrease changes in capacitance due to displacement of sensor element  32 .