Patent Publication Number: US-2016245711-A1

Title: Load Transducer and Force Measurement Assembly Using the Same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation-in-part of U.S. Nonprovisional patent application Ser. No. 14/158,809, entitled “Low Profile Load Transducer”, filed on Jan. 18, 2014, and further claims the benefit of U.S. Provisional Patent Application No. 61/887,357, entitled “Low Profile Load Transducer”, filed on Oct. 5, 2013, the disclosure of each of which is hereby incorporated by reference as if set forth in their entirety herein. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not Applicable. 
    
    
     NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT 
     Not Applicable. 
     INCORPORATION BY REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISK 
     Not Applicable. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The field of the invention relates to multi-component load transducers utilizing multiple strain gage load channels for precise measurement of forces and moments and, more particularly, to beam-style load cells requiring an overall small size, high capacity, and yet high sensitivity. 
     2. Background and Related Art 
     The use of strain gages in load transducers to measure forces and moments is a known art. A transducer can incorporate one or more load channels. Each load channel measures one of the load components, and is comprised of one or more strain gages mounted to one or more elastic elements that deform under the applied load. An appropriate circuitry relates the resistance change in each set of gages to the applied force or moment. Strain gages have many industrial, medical, and electrical applications due to their small size, low production cost, flexibility in installation and use, and high precision. 
     A typical low profile, small, multi-component load transducer only functions correctly when the axial (i.e. vertical) force acts relatively central to the transducer. Specifications of such transducers indicate a maximum allowable offset for the force being approximately half the diameter of the transducer. Technical specifications of transducers are given as the allowable force and moment ratings, where the moment rating is obtained by multiplying the maximum allowable force with the maximum allowable offset of the force. 
     Transducers can be used to measure forces and moments in linkages such as those found in a robotic arm, where the links are connected by joints, and the magnitude and offset of the forces transmitted by these joints are used to control the linkage. In such applications, it is desirable to have a transducer which has significantly higher moment capacity than those available in the market. Accordingly, there is a need for an improved multi-component, low profile load transducer with high moment capacity. 
     When conventional load transducers are utilized in conjunction with force plates, unique load transducers must be designed and fabricated for force plates having a particular footprint size. Consequently, in order to fit force plates with varying footprint sizes, many different custom load transducers are required. These custom load transducers significantly increase the material costs associated with the fabrication of a force plate. Also, conventional load transducers often span the full length or width of the force plate component to which they are mounted, thereby resulting in elongate load transducers that utilize an excessive amount of stock material. 
     Therefore, what is needed is a load transducer that is capable of being interchangeably used with a myriad of different force plate sizes so that load transducers that are specifically tailored for a particular force plate size are unnecessary. Moreover, there is a need for a universal load transducer that is compact and uses less stock material than conventional load transducers, thereby resulting in lower material costs. Furthermore, there is a need for a force measurement assembly that utilizes the compact and universal load transducer thereon so as to result in a more lightweight and portable force measurement assembly. 
     BRIEF SUMMARY OF EMBODIMENTS OF THE INVENTION 
     Accordingly, the present invention is directed to a load transducer and a force measurement assembly using the same that substantially obviates one or more problems resulting from the limitations and deficiencies of the related art. 
     In accordance with one or more embodiments of the present invention, there is provided a load transducer that includes a plurality of beam portions connected to one another in succession, the plurality of beam portions being arranged in a circumscribing pattern whereby a central one of the plurality of beam portions is at least partially circumscribed by one or more outer ones of the plurality of beam portions; and at least one load cell disposed on one of the plurality of beam portions, the at least one load cell configured to measure at least one force or moment component of a load applied to the load transducer. 
     In a further embodiment of the present invention, the at least one load cell comprises a strain gage configured to measure the at least one force or moment component of the load applied to the load transducer. 
     In yet a further embodiment, the plurality of beam portions are each part of a transducer frame, the transducer frame being compact and of one-piece construction. 
     In still a further embodiment, the circumscribing pattern in which the plurality of beam portions are arranged is generally G-shaped. 
     In yet a further embodiment, the circumscribing pattern in which the plurality of beam portions are arranged is generally spiral-shaped. 
     In still a further embodiment, the at least one load cell comprises at least three load cells, each of the at least three load cells being disposed on a respective one of the plurality of beam portions, a first of the at least three load cells configured to be sensitive to a vertical force component, a second of the at least three load cells configured to be sensitive to a first shear force component, a third of the at least three load cells configured to be sensitive to a second shear force component, the first shear force component being generally perpendicular to the second shear force component, and each of the first and second shear force components being generally perpendicular to the vertical force component. 
     In yet a further embodiment, the plurality of beam portions comprises at least two pairs of beam portions that are disposed generally parallel to one another. 
     In still a further embodiment, each of the at least two pairs of beam portions comprises two beam portions that are laterally spaced apart from one another by a gap. 
     In yet a further embodiment, one or more of the plurality of beam portions comprises a first top surface that is disposed at a first elevation relative to a bottom surface of the load transducer and a second top surface that is disposed at a second elevation relative to the bottom surface of the load transducer, the second elevation being greater than the first elevation; and wherein a recessed area created by the difference in elevation between the second elevation and the first elevation is used to accommodate one or more electrical components of the at least one load cell. 
     In accordance with one or more other embodiments of the present invention, there is provided a load transducer that includes a plurality of beam portions connected to one another in succession, the plurality of beam portions being arranged in a looped configuration whereby a central one of the plurality of beam portions emanates from a generally central location within a footprint of the load transducer and outer ones of the plurality of beam portions are wrapped around the central one of the plurality of beam portions; and a plurality of load cells, each of the load cells being disposed on a respective one of the plurality of beam portions, the plurality of load cells configured to measure one or more force components or one or more moment components, or both one or more force components and one or more moment components. 
     In a further embodiment of the present invention, the looped configuration in which the plurality of beam portions are arranged is generally G-shaped. 
     In yet a further embodiment, the looped configuration in which the plurality of beam portions are arranged is generally spiral-shaped. 
     In still a further embodiment, the plurality of load cells comprises at least three load cells, each of the at least three load cells being disposed on a respective one of the plurality of beam portions, a first of the at least three load cells configured to be sensitive to a vertical force component, a second of the at least three load cells configured to be sensitive to a first shear force component, a third of the at least three load cells configured to be sensitive to a second shear force component, the first shear force component being generally perpendicular to the second shear force component, and each of the first and second shear force components being generally perpendicular to the vertical force component. 
     In yet a further embodiment, one or more of the plurality of beam portions comprises a mounting aperture disposed near a respective end thereof for accommodating a fastener. 
     In still a further embodiment, one or more of the plurality of beam portions comprises an aperture disposed therein and a strain gage disposed on an outer surface thereof, the outer surface of the one or more of the plurality of beam portions on which the strain gage is disposed being generally opposite to an inner surface of the aperture. 
     In yet a further embodiment, one or more of the plurality of beam portions comprises a first top surface that is disposed at a first elevation relative to a bottom surface of the load transducer and a second top surface that is disposed at a second elevation relative to the bottom surface of the load transducer, the second elevation being greater than the first elevation; and wherein a recessed area created by the difference in elevation between the second elevation and the first elevation is used to accommodate one or more electrical components of the at least one load cell. 
     In accordance with yet one or more other embodiments of the present invention, there is provided a force measurement assembly that includes at least one plate component having a measurement surface for receiving a portion of a body of a subject; and a plurality of load transducers. Each of the plurality of load transducers includes a plurality of beam portions connected to one another in succession, the plurality of beam portions being arranged in a circumscribing pattern whereby a central one of the plurality of beam portions is at least partially circumscribed by one or more outer ones of the plurality of beam portions; and at least one load cell disposed on one of the plurality of beam portions, the at least one load cell configured to measure at least one force or moment component of a load applied to the load transducer. In these one or more other embodiments, one or more of the plurality of load transducers is disposed proximate to a respective corner of the at least one plate component. 
     In a further embodiment of the present invention, none of the plurality of load transducers extend substantially an entire length or width of the at least one plate component. 
     In yet a further embodiment, at least one of the plurality of load transducers comprises a first top surface that is disposed at a first elevation relative to a bottom surface of the load transducer and a second top surface that is disposed at a second elevation relative to the bottom surface of the load transducer, the second elevation being greater than the first elevation; and wherein a recessed area created by the difference in elevation between the second elevation and the first elevation is used to accommodate one or more electrical components of the at least one load cell of the load transducer. 
     From the foregoing disclosure and the following more detailed description of various preferred embodiments it will be apparent to those skilled in the art that the present invention provides a significant advance in the technology and art of load transducers. Particularly significant in this regard is the potential the invention affords for providing a low profile load transducer with high moment capacity. Additional features and advantages of various preferred embodiments will be better understood in view of the detailed description provided below. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The invention will now be described, by way of example, with reference to the accompanying drawings, in which: 
         FIG. 1  is a perspective view of a low profile load transducer, according to a first embodiment of the invention; 
         FIG. 2  is a first side view of the low profile load transducer of  FIG. 1 , according to the first embodiment of the invention; 
         FIG. 3  is a second side view of the low profile load transducer of  FIG. 1 , according to the first embodiment of the invention; 
         FIG. 4  is a top view of the low profile load transducer of  FIG. 1 , according to the first embodiment of the invention; 
         FIG. 5  is a block diagram illustrating data manipulation operations carried out by the load transducer data processing system, according to an embodiment of the invention; 
         FIG. 6  is a perspective view of a low profile load transducer, according to a second embodiment of the invention; 
         FIG. 7  is a first side view of the low profile load transducer of  FIG. 6 , according to the second embodiment of the invention; 
         FIG. 8  is a second side view of the low profile load transducer of  FIG. 6 , according to the second embodiment of the invention; 
         FIG. 9  is a top view of the low profile load transducer of  FIG. 6 , according to the second embodiment of the invention; 
         FIG. 10  is a perspective view of a low profile load transducer, according to a third embodiment of the invention; 
         FIG. 11  is a first side view of the low profile load transducer of  FIG. 10 , according to the third embodiment of the invention; 
         FIG. 12  is a second side view of the low profile load transducer of  FIG. 10 , according to the third embodiment of the invention; 
         FIG. 13  is a top view of the low profile load transducer of  FIG. 10 , according to the third embodiment of the invention; 
         FIG. 14  is a bottom view of the low profile load transducer of  FIG. 10 , according to the third embodiment of the invention; 
         FIG. 15  is a perspective view of a low profile load transducer, according to a fourth embodiment of the invention; 
         FIG. 16  is a first side view of the low profile load transducer of  FIG. 15 , according to the fourth embodiment of the invention; 
         FIG. 17  is a second side view of the low profile load transducer of  FIG. 15 , according to the fourth embodiment of the invention; 
         FIG. 18  is a top view of the low profile load transducer of  FIG. 15 , according to the fourth embodiment of the invention; 
         FIG. 19  is a perspective view of a low profile load transducer, according to a fifth embodiment of the invention; 
         FIG. 20  is a perspective view of a low profile load transducer, according to a sixth embodiment of the invention; 
         FIG. 21  is a perspective view of a low profile load transducer, according to a seventh embodiment of the invention; 
         FIG. 22  is a perspective view of a low profile load transducer, according to an eighth embodiment of the invention; 
         FIG. 23  is a perspective view of a low profile load transducer, according to a ninth embodiment of the invention; 
         FIG. 24  is a perspective view of a low profile load transducer, according to a tenth embodiment of the invention; 
         FIG. 25  is a perspective view of an exemplary mounting arrangement for the low profile load transducer illustrated in  FIGS. 15-18 ; 
         FIG. 26  is a top perspective view of a load transducer, according to an eleventh embodiment of the invention; 
         FIG. 27  is a first side view of the load transducer of  FIG. 26 , according to the eleventh embodiment of the invention; 
         FIG. 28  is a second side view of the load transducer of  FIG. 26 , according to the eleventh embodiment of the invention; 
         FIG. 29  is a bottom perspective view of the load transducer of  FIG. 26 , according to the eleventh embodiment of the invention; 
         FIG. 30  is a top perspective view of a load transducer, according to a twelfth embodiment of the invention; 
         FIG. 31  is a first side view of the load transducer of  FIG. 30 , according to the twelfth embodiment of the invention; 
         FIG. 32  is a second side view of the load transducer of  FIG. 30 , according to the twelfth embodiment of the invention; 
         FIG. 33  is a bottom perspective view of the load transducer of  FIG. 30 , according to the twelfth embodiment of the invention; 
         FIG. 34  is a perspective view of a force measurement system that utilizes the load transducer of  FIG. 30 , according to an embodiment of the invention; 
         FIG. 35  is a bottom, assembled perspective view of the force measurement assembly of the force measurement system of  FIG. 34 ; 
         FIG. 36  is a bottom, partially exploded perspective view of the force measurement assembly of the force measurement system of  FIG. 34 ; 
         FIG. 37  is a block diagram of constituent components of the force measurement system of  FIG. 34 ; and 
         FIG. 38  is a block diagram illustrating data manipulation operations carried out by the force measurement system of  FIG. 34 . 
     
    
    
     It should be understood that the appended drawings are not necessarily to scale, presenting a somewhat simplified representation of various preferred features illustrative of the basic principles of the invention. The specific design features of the load transducers as disclosed herein, including, for example, specific dimensions, orientations, locations, and shapes of the various components, will be determined in part by the particular intended application and use environment. Certain features of the illustrated embodiments have been enlarged or distorted relative to others to facilitate visualization and clear understanding. In particular, thin features may be thickened, for example, for clarity or illustration. All references to direction and position, unless otherwise indicated, refer to the orientation of the load transducers illustrated in the drawings. In general, up or upward generally refers to an upward direction within the plane of the paper in  FIG. 1  and down or downward generally refers to a downward direction within the plane of the paper in  FIG. 1 . 
     DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION 
     It will be apparent to those skilled in the art, that is, to those who have knowledge or experience in this area of technology, that many uses and design variations are possible for the improved load transducers disclosed herein. The following detailed discussion of various alternative and preferred embodiments will illustrate the general principles of the invention. Other embodiments suitable for other applications will be apparent to those skilled in the art given the benefit of this disclosure. 
     Referring now to the drawings,  FIGS. 1-4  illustrate a load transducer  10  according to a first exemplary embodiment of the present invention. This load transducer  10  is designed to have a low profile, small size, trivial weight, high sensitivity, and easy manufacturability. The load transducer  10  generally includes a one-piece compact transducer frame  12  having a central body portion  14  and a plurality of beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  extending outwardly from the central body portion  14 . As best illustrated in the perspective view of  FIG. 1 , each of the beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  comprises a respective load cell or transducer element for measuring forces and/or moments. For example, the load cells of beams  16 ,  18 ,  24 ,  26  are configured to respectively measure the forces F 1 , F 2 , F 3 , F 4  with force vector components F 1   x , F 1   y , F 1   z , F 2   x , F 2   y , F 2   z , F 3   x , F 3   y , F 3   z , F 4   x , F 4   y , F 4   z . In addition to forces, the output of the load cells can also be used to determine moments and the point of application of a force (i.e., its center of pressure). Referring again to  FIG. 1 , it can be seen that the illustrated load transducer  10  comprises eight single or multi-axis load cells that are mounted to a common structure or body portion  14 . 
     The illustrated transducer frame  12  is shown in  FIGS. 1-4 . The illustrated transducer frame  12  includes the central body portion  14  and a plurality of beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  extending outwardly therefrom. In the illustrated embodiment, the transducer frame  12  is milled as one solid and continuous piece of a single material. That is, the transducer frame  12  is of unitary or one-piece construction with the body portion  14  and the beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  integrally formed together. The transducer frame  12  is preferably machined in one piece from aluminum, titanium, steel, or any other suitable material that meets strength and weight requirements. Alternatively, the beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  can be formed separately and attached to the body portion  14  in any suitable manner. 
     With reference to  FIG. 1 , it can be seen that the illustrated central body portion  14  is generally in the form of rectangular prism (i.e., a square prism) with substantially planar top, bottom, and side surfaces. In  FIG. 1 , it can be seen that the body portion  14  comprises a first pair of opposed sides  14   a,    14   c  and a second pair of opposed sides  14   b,    14   d.  The side  14   a  is disposed generally parallel to the side  14   c,  while the side  14   b  is disposed generally parallel to the side  14   d.  Each of the sides  14   a,    14   b,    14   c,    14   d  is disposed generally perpendicular to the planar top and bottom surfaces. Also, each of the first pair of opposed sides  14   a,    14   c  is disposed generally perpendicular to each of the second pair of opposed sides  14   b,    14   d.  While not explicitly shown in  FIGS. 1-4 , the central body portion  14  may comprise one or more apertures disposed therethrough for accommodating fasteners (e.g., screws) that attach electronics or circuitry to the body portion  14 . In addition to fasteners, it is noted that any other suitable means for attachment of the electronics or circuitry can alternatively be utilized (e.g., suitable adhesives, etc.). While the illustrated body portion  14  is generally in the form of a square prism, it is to be understood that the body portion  14  can alternatively have other suitable shapes. 
     As shown in  FIGS. 1-4 , the illustrated beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  are each attached to one of the sides  14   a,    14   b,    14   c,    14   d  of the body portion  14 , and extend generally horizontally outward therefrom. In particular, beams  16 ,  18  extend generally horizontally outward from side  14   a  of the body portion  14 , beams  20 ,  22  extend generally horizontally outward from side  14   b  of the body portion  14 , beams  24 ,  26  extend generally horizontally outward from side  14   c  of the body portion  14 , and beams  28 ,  30  extend generally horizontally outward from side  14   d  of the body portion  14 . In addition, each of the illustrated beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  extend substantially parallel to the top and bottom surfaces of the body portion  14 . Each of the illustrated beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  has a cantilevered end relative to the body portion  14  that allows for deflection of the ends of the beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  in the vertical direction. 
     With particular reference to  FIGS. 1 and 4 , it can be seen that the beams  16 ,  18  extending from side  14   a  are substantially parallel to one another, and laterally spaced apart from one another by a gap. Opposed beams  24 ,  26 , which extend from side  14   c,  also are substantially parallel to one another, and laterally spaced apart from one another by a gap. Beam  16  extends in a longitudinal direction that is generally co-linear with, but opposite to the extending direction of beam  26  (i.e., both beams  16  and  26  are aligned along central longitudinal axis LA 1 ). Similarly, beam  18  extends in a longitudinal direction that is generally co-linear with, but opposite to the extending direction of beam  24  (i.e., both beams  18  and  24  are aligned along central longitudinal axis LA 2 ). The beams  20 ,  22  extending from side  14   b  are substantially parallel to one another, and laterally spaced apart from one another by a gap. Opposed beams  28 ,  30 , which extend from side  14   d,  also are substantially parallel to one another, and laterally spaced apart from one another by a gap. Beam  20  extends in a longitudinal direction that is generally co-linear with, but opposite to the extending direction of beam  30  (i.e., both beams  20  and  30  are aligned along central longitudinal axis LA 3 ). Similarly, beam  22  extends in a longitudinal direction that is generally co-linear with, but opposite to the extending direction of beam  28  (i.e., both beams  22  and  28  are aligned along central longitudinal axis LA 4 ). The illustrated beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  are provided with generally vertically extending apertures  32  near their ends for accommodating fasteners that are used to secure the load transducer  10  to additional structures. Although, it is noted that any other suitable means for attachment of the load transducer  10  can alternatively be utilized (e.g., a suitable adhesive for attaching metallic components to one another). 
     The main body portions of illustrated beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  have a rectangular-shaped cross section to form generally planar, opposed top and bottom surfaces, and generally planar, opposed side surfaces for attachment of load cell components as described hereinafter. The illustrated beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  have generally cylindrical end portions, which include the fastener apertures  32 . As best shown in  FIG. 1 , the illustrated top planar surfaces of the beam main body portions of beams  16 ,  18 ,  24 ,  26  are recessed below the top surfaces of the beam cylindrical end portions to protect the load cell components from engagement with the structure to which the load transducer  10  is attached, while the illustrated bottom planar surfaces of the beam main body portions of beams  20 ,  22 ,  28 ,  30  are recessed above the bottom surfaces of the beam cylindrical end portions to protect the load cell components from engagement with the structure to which the load transducer  10  is attached. In other words, as shown in  FIG. 1 , the cylindrical end portions of beams  16 ,  18 ,  24 ,  26  are provided with a top standoff portion (i.e., a cylindrical portion protruding from the top of each beam having the aperture  32 ), while the cylindrical end portions of beams  20 ,  22 ,  28 ,  30  are provided with a bottom standoff portion (i.e., a cylindrical portion protruding from the bottom of each beam having the aperture  32 ). While not explicitly shown in the figures, beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  may also include apertures disposed therethrough for increasing the deflectability of the beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  as desired (e.g., the apertures could be disposed below, or adjacent to each of the strain gages  34 ,  36 ,  38 ). In order to accommodate these apertures, the length of each beam  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  could be extended so that multiple strain gages  34 ,  36  on a common beam could be spaced apart from one another along a length of the beam (i.e., each strain gage  34 ,  36  would occupy a dedicated, respective segment of the beam). It is noted that these apertures can be of any suitable size and shape as needed and also can be eliminated if desired. It is further noted that the beams  16 ,  18 ,  20 ,  22 ,  24 ,  26 ,  28 ,  30  can alternatively have other cross-sectional shapes depending on whether it is desired to have planar surfaces at the top and/or bottom or left and/or right sides for the load cell components but the illustrated rectangular shape is particularly desirable because the same frame can be used for multiple configurations of the transducer load cells. 
     The illustrated one-piece frame  12  has a low profile or is compact. The terms “low profile” and “compact” are used in this specification and the claims to mean that the height is substantially smaller than the footprint dimensions so that the load transducer  10  can be utilized in a mechanical joint without significant changes to the mechanical joint. The illustrated one piece frame  12  has a height H that is about 20% its footprint width W 1  or W 2  (see  FIGS. 2, 3, 7 , and  8 ). As a result, the load transducer  10  has a low profile or is compact and has a height H that is about 20% its footprint width W 1  or W 2 . The term “load cell” is used in the specification and claims to mean a load sensing element of the load transducer that is capable of sensing one or more load components of the applied load. 
     As best shown in  FIG. 1 , the illustrated load cells are located on beams  16 ,  18 ,  20 ,  24 ,  26 , and  30 . In the illustrated embodiment, beams  22 ,  28  do not contain any load cells, but, in other embodiments, may contain load cells with strain gages  38  similar to beams  20 ,  30 . Beams  16 ,  26  also may contain strain gages  36 , similar to beams  18 ,  24 , in other embodiments. In a preferred embodiment, each load cell comprises one or more strain gages  34 ,  36 ,  38 . Specifically, in the illustrated embodiment, beams  16 ,  18 ,  24 ,  26  each comprise a strain gage  34  disposed on the top surface thereof that is sensitive to the vertical force component (i.e., a F Z  strain gage). Opposed beams  18 ,  24  also each comprise a strain gage  36  disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). Opposed beams  20 ,  30  each comprise a strain gage  38  disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). All eight (8) of the strain gages  34 ,  36 ,  38  are measuring a difference in the bending moments in the beams. If the applied shears to each of the two parallel beams  18 ,  24  or  20 ,  30  are equal (which is most likely the case), this is an optimal number of strain gages for a six-component load transducer (i.e., for a load transducer that is capable of measuring the three (3) force components F X , F Y , F Z  and the three (3) moment components M X , M Y , M Z ). Shear web gages can also be used in lieu of one or more of the illustrated strain gages  34 ,  36 ,  38 . Also, in other preferred embodiments alternate load and/or moment sensors may be utilized as required or desired as long as they do not interfere with the advantages of the design as a whole. For example, piezoelectric gages or Hall-effect sensors are possible alternatives to the strain gages  34 ,  36 ,  38 . 
     As best shown in  FIG. 1 , the illustrated load cells are configured as bending beam load cells. The illustrated strain gages  34 ,  36 ,  38  are mounted to either top or side surfaces of the beams  16 ,  18 ,  20 ,  24 ,  26 ,  30  between their attachment locations to the body portion  14  and the cylindrical end portions thereof. Alternatively, the strain gages  34  can be mounted to the bottom surfaces of the beams  16 ,  18 ,  24 ,  26  between their attachment locations to the body portion  14  and the cylindrical end portions thereof, while the strain gages  36 ,  38  can be mounted to the opposite side surfaces of the beams  18 ,  20 ,  24 ,  30  between their attachment locations to the body portion  14  and the cylindrical end portions thereof. That is, the strain gages  34 ,  36 ,  38  are mounted to surfaces generally normal to the direction of applied vertical and/or shear forces (i.e., F X , F Y , F Z ). It is also noted that alternatively, the strain gages  34  can be mounted at both the top surface and the bottom surface of the beams  16 ,  18 ,  24 ,  26 , and/or the strain gages  36 ,  38  can be mounted at both opposed side surfaces of the beams  18 ,  20 ,  24 ,  30 . These strain gages  34 ,  36 ,  38  measure force either by bending moment or difference of bending moments at two cross sections. As force is applied to the ends of the beams (e.g., forces F 1 , F 2 , F 3 , F 4  with force vector components F 1   x , F 1   y , F 1   z , F 2   x , F 2   y , F 2   z , F 3   x , F 3   y , F 3   z , F 4   x , F 4   y , F 4   z , applied to the ends of respective beams  16 ,  18 ,  24 ,  26 ), the beams  16 ,  18 ,  20 ,  24 ,  26 ,  30  with strain gages attached thereto bend. This bending either stretches or compresses the strain gages  34 ,  36 ,  38 , in turn changing the resistances of the electrical currents passing therethrough. The amount of change in the electrical voltage or current is proportional to the magnitude of the applied force (e.g., forces F 1 , F 2 , F 3 , F 4  with force vector components F 1   x , F 1   y , F 1   z , F 2   x , F 2   y , F 2   z , F 3   x , F 3   y , F 3   z , F 4   x , F 4   y , F 4   z , applied to the ends of respective beams  16 ,  18 ,  24 ,  26 ). 
     Alternatively, the load cells can be configured as shear-web load cells. In this configuration, the strain gages are mounted to either one of the lateral side surfaces of the beams between their attachment locations to the body portion  14  and the cylindrical end portions thereof. It is noted that alternatively, the strain gages can be mounted at both of the lateral side surfaces of the beams. Mounted in these positions, the strain gages directly measure shear as force is applied to the end of the beam. 
     As best shown in  FIG. 1 , the load transducer  10  measures applied forces (e.g., forces F 1 , F 2 , F 3 , F 4  with force vector components F 1   x , F 1   y , F 1   z , F 2   x , F 2   y , F 2   x , F 3   x , F 3   y , F 3   z , F 4   x , F 4   y , F 4   z , applied to the ends of respective beams  16 ,  18 ,  24 ,  26 ) at each of the load cells. The sum of the forces is the force being applied to any assembly attached to the top of the load transducer  10 . The load cells of the beams  16 ,  26  measure the force being applied to one lateral side of the load transducer  10 ; whereas, load cells of the beams  18 ,  24  measure the force being applied to the other lateral side of the load transducer  10 . The various moments are determined by subtracting the sum total of the forces acting on one pair of load cells from the sum total acting upon the opposite pair. For example, subtracting the sum total of the forces acting on load cell of beam  16  and load cell of beam  18  from the sum total of the forces acting on load cell of beam  24  and load cell of beam  26 , subtracting the sum total of load cells of beams  18 ,  24  from the sum total of load cells of beams  16 ,  26 . 
     The sensory information from the strain gages  34 ,  36 ,  38  is transmitted to a microprocessor which could then be used to control the assembly to which the load transducer is a part of such as a robotic assembly. As best shown in  FIG. 1 , the planar central body portion  14  of the transducer frame  12  provides an area where associated electronics and/or circuitry can be mounted. Alternatively, the electronics and/or circuitry can be mounted at any other suitable location.  FIG. 5  schematically illustrates exemplary electronic components that can be included in the load transducer data processing system. The strain gages  34 ,  36 ,  38  of load transducer  10  may be electrically connected to a signal amplifier/converter  40 , which in turn, is electrically connected to a computer  42  (i.e., a data acquisition and processing device or a data processing device with a microprocessor). The components  10 ,  40 ,  42  of the system may be connected either by wiring, or wirelessly to one another. 
       FIG. 5  graphically illustrates the acquisition and processing of the load data carried out by the exemplary load transducer data processing system. Initially, as shown in  FIG. 5 , external forces F 1 -F 4  and/or moments are applied to the load transducer  10 . When the electrical resistance of each strain gage  34 ,  36 ,  38  is altered by the application of the applied forces and/or moments, the change in the electrical resistance of the strain gages brings about a consequential change in the output voltage of the strain gage bridge circuit (e.g., a Wheatstone bridge circuit). Thus, in one embodiment, the eight (8) strain gages  34 ,  36 ,  38  output a total of eight (8) analog output voltages (signals). In some embodiments, the eight (8) analog output voltages from the eight (8) strain gages  34 ,  36 ,  38  are then transmitted to a preamplifier board (not shown) for preconditioning. The preamplifier board is used to increase the magnitudes of the analog voltage signals, and preferably, to convert the analog voltage signals into digital voltage signals as well. After which, the load transducer  10  transmits the output signals S TO1 -S TO8  to a main signal amplifier/converter  40 . Depending on whether the preamplifier board also includes an analog-to-digital (A/D) converter, the output signals S TO1 -S TO8  could be either in the form of analog signals or digital signals. The main signal amplifier/converter  40  further magnifies the transducer output signals S TO1 -S TO8 , and if the signals S TO1 -S TO8  are of the analog-type (for a case where the preamplifier board did not include an analog-to-digital (A/D) converter), it may also convert the analog signals to digital signals. Then, the signal amplifier/converter  40  transmits either the digital or analog signals S ACO1 -S ACO8  to the data acquisition/data processing device  42  (computer  42 ) so that the forces and/or moments that are being applied to the load transducer  10  can be transformed into output load values OL. The computer or data acquisition/data processing device  42  may further comprise an analog-to-digital (A/D) converter if the signals S ACO1 -S ACO8  are in the form of analog signals. In such a case, the analog-to-digital converter will convert the analog signals into digital signals for processing by the microprocessor of the computer  42 . 
     When the computer or data acquisition/data processing device  42  receives the voltage signals S ACO1 -S ACO8 , it initially transforms the signals into output forces and/or moments by multiplying the voltage signals S ACO1 -S ACO8  by a calibration matrix. After which, the force components F X , F Y , F Z  and the moment components M X , M Y , M Z  applied to the load transducer  10  are determined by the computer or data acquisition/data processing device  42 . Also, the center of pressure (i.e., the x and y coordinates of the point of application of the force applied to the load transducer  10 ) can be determined by the computer or data acquisition/data processing device  42 . 
       FIGS. 6-9  illustrate a load transducer  10 ′ according to a second exemplary embodiment of the present invention. With reference to these figures, it can be seen that, in some respects, the second exemplary embodiment is similar to that of the first embodiment. Moreover, some parts are common to both such embodiments. For the sake of brevity, the parts that the second embodiment of the load transducer has in common with the first embodiment will only be briefly mentioned, if at all, because these components have already been explained in detail above. Furthermore, in the interest of clarity, these components will be denoted using the same reference characters that were used in the first embodiment. 
     Initially, referring to the perspective view of  FIG. 6 , it can be seen that, like the first exemplary embodiment, the transducer frame  12 ′ of the second embodiment includes a central body portion  14  and a plurality of beams  16 ,  18 ,  20 ′,  24 ′,  28 ,  30  extending outwardly therefrom. Although, unlike the first exemplary embodiment of the load transducer, the side  14   b  of the body portion  14  of the load transducer  10 ′ contains only a single beam  20 ′ extending therefrom, rather two beams  20 ,  22  (see  FIG. 1 ). Similarly, unlike the load transducer  10  of the first embodiment, the side  14   c  of the body portion  14  of the load transducer  10 ′ contains only a single beam  24 ′ extending therefrom, rather two beams  24 ,  26  (refer to  FIG. 1 ). Also, unlike the load transducer  10  of the first embodiment, the load transducer  10 ′ includes only three strain gages  34  that are sensitive to the vertical force component (i.e., three F Z  strain gages), rather than four strain gages. 
     In particular, in the second embodiment, beams  16 ,  18 ,  24 ′ each comprise a strain gage  34  disposed on the top surface thereof that is sensitive to the vertical force component (i.e., a F Z  strain gage). Beams  18 ,  24 ′ also each comprise a strain gage  36  disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage), while beams  20 ′,  30  each comprise a strain gage  38  disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). The load transducer  10 ′ of the second embodiment is capable of measuring the three force components (F X , F Y , F Z ) and the three moment components (M X , M Y , M Z ) with a minimum of six beams  16 ,  18 ,  20 ′,  24 ′,  28 ,  30  (i.e., three input beams and three output beams) and a minimum of seven strain gages  34 ,  36 ,  38 . 
     Now, with reference to the top view illustrated in  FIG. 9 , it can be seen that the central longitudinal axis LA 5  of the beam  20 ′, which extends from side  14   b  of the body portion  14 , is generally equally spaced apart from the central longitudinal axis LA 3  and LA 4  (i.e., the central longitudinal axis LA 5  of the beam  20 ′ is generally centered between the central longitudinal axis LA 3  of beam  30  and the central longitudinal axis LA 4  of beam  28 ). Similarly, as shown in  FIG. 9 , the longitudinal axis LA 6  of the beam  24 ′, which extends from side  14   c  of the body portion  14 , is generally equally spaced apart from the central longitudinal axis LA 1  and LA 2  (i.e., the central longitudinal axis LA 6  of the beam  24 ′ is generally centered between the central longitudinal axis LA 1  of beam  16  and the central longitudinal axis LA 2  of beam  18 ). The other features of the load transducer  10 ′ are similar to that of the load transducer  10 , and thus, need not be reiterated herein. 
       FIGS. 10-14  illustrate a load transducer  100  according to a third exemplary embodiment of the present invention. Referring initially to the perspective view of  FIG. 10 , it can be seen that the load transducer  100  generally includes a one-piece compact transducer frame  112  having a central body portion  114  and a plurality of generally U-shaped transducer beams  116 ,  118 ,  120 ,  122  extending outwardly from the central body portion  114 . As best illustrated in  FIG. 10 , each of the beams  116 ,  118 ,  120 ,  122  comprises a plurality of load cells or transducer elements for measuring forces and/or moments. 
     With reference again to  FIG. 10 , it can be seen that the illustrated central body portion  114  is generally in the form of square band-shaped element with a central opening  102  disposed therethrough. In  FIG. 10 , it can be seen that the body portion  114  comprises a first pair of opposed sides  114   a,    114   c  and a second pair of opposed sides  114   b,    114   d.  The side  114   a  is disposed generally parallel to the side  114   c,  while the side  114   b  is disposed generally parallel to the side  114   d.  Each of the sides  114   a,    114   b,    114   c,    114   d  is disposed generally perpendicular to the planar top and bottom surfaces of the body portion  114 . Also, each of the first pair of opposed sides  114   a,    114   c  is disposed generally perpendicular to each of the second pair of opposed sides  114   b,    114   d.  In addition, as shown in  FIG. 10 , each of the opposed sides  114   a,    114   c  comprises a beam connecting portion  128  extending outward therefrom. In the illustrated embodiment, it can be seen that each of the beam connecting portions  128  comprises a plurality of apertures  130  (e.g., two apertures  130 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  100  to another object, such as a robotic arm, etc. Also, as depicted in the side views of  FIGS. 11 and 12  and the bottom view of  FIG. 14 , the bottom surface of the central body portion  114  comprises a raised portion or standoff portion  126  for elevating the transducer beams  116 ,  118 ,  120 ,  122  above the object (e.g., robotic arm) to which the load transducer  100  is attached so that forces and/or moments are capable of being accurately measured by the load transducer  100 . In one or more embodiments, the structural components to which the load transducer  100  is mounted are connected only to the top standoff portions  124  and the bottom standoff  126  so as to ensure that the total load applied to the load transducer  100  is transmitted through the transducer beams  116 ,  118 ,  120 ,  122 . 
     As shown in  FIGS. 10-14 , the illustrated generally U-shaped transducer beams  116 ,  118 ,  120 ,  122  are each attached to one of the sides  114   a,    114   b,    114   c,    114   d  of the body portion  114  via a connecting portion  128 , and extend generally horizontally outward therefrom. In particular, beams  116 ,  118  extend generally horizontally outward from opposed sides of the beam connecting portion  128  attached to side  114   a  of the body portion  114 , while the beams  120 ,  122  extend generally horizontally outward from opposed sides of the beam connecting portion  128  attached to side  114   c  of the body portion  114 . As best shown in  FIG. 10 , the top and bottom surfaces of each of the illustrated beams  116 ,  118 ,  120 ,  122  are disposed substantially co-planar with the top and bottom surfaces of the body portion  114 . Each of the illustrated beams  116 ,  118 ,  120 ,  122  has a U-shaped cantilevered end relative to the body portion  114  that allows for deflection of the ends of the beams in multiple directions. 
     With particular reference to  FIGS. 10, 13, and 14 , it can be seen that each of the generally U-shaped beams  116 ,  118 ,  120 ,  122  comprises a plurality of segmental beam portions, wherein each of the successive beam portions are disposed substantially perpendicular to the immediately preceding beam portion. For example, as shown in  FIG. 10 , the first generally U-shaped transducer beam  116  comprises a first beam portion  116   a  extending from a first side of the beam connecting portion  128 , a second beam portion  116   b  connected to the first beam portion  116   a  and disposed substantially perpendicular thereto, a third beam portion  116   c  connected to the second beam portion  116   b  and disposed substantially perpendicular thereto, and a fourth beam portion  116   d  connected to the third beam portion  116   c  and disposed substantially perpendicular thereto. Similarly, the second generally U-shaped transducer beam  118  comprises a first beam portion  118   a  extending from a second side of the beam connecting portion  128  (which is generally opposite to the first side of the beam connecting portion  128  from which the first beam portion  116   a  extends), a second beam portion  118   b  connected to the first beam portion  118   a  and disposed substantially perpendicular thereto, a third beam portion  118   c  connected to the second beam portion  118   b  and disposed substantially perpendicular thereto, and a fourth beam portion  118   d  connected to the third beam portion  118   c  and disposed substantially perpendicular thereto. With reference to  FIGS. 10, 13, and 14 , it can be seen that the generally U-shaped transducer beams  120 ,  122  are generally minor images of the generally U-shaped transducer beams  116 ,  118 , and thus, have the same structure as the generally U-shaped transducer beams  116 ,  118 . Referring again to  FIGS. 10, 13, and 14 , it can be seen that the fourth beam portion of each of the generally U-shaped transducer beams  116 ,  118 ,  120 ,  122  comprises a raised portion or standoff portion  124  with mounting apertures  132  (e.g., two apertures  132 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  100  to another object, such as a robotic arm, etc. In addition, as shown in  FIGS. 10 and 13 , each generally U-shaped transducer beam  116 ,  118 ,  120 ,  122  comprises a central beam gap  106 , which is bounded by the second, third, and fourth beam portions. Also, it can be seen that the first and second beam portions of each transducer beam  116 ,  118 ,  120 ,  122  are separated from the opposing sides of the central body portion  114  by an L-shaped gap  104 . That is, the sides of the central body portion  114 , which face the sides of the first and second beam portions in an opposing relationship, are separated from the sides of the first and second beam portions by the L-shaped gap  104 . 
     As best shown in the perspective view of  FIG. 10 , the illustrated load cells are located on the transducer beams  116 ,  118 ,  120 ,  122 . In the illustrated embodiment, each load cell comprises a plurality of strain gages  134 ,  136 ,  138 . Specifically, in the illustrated embodiment, each of the first portions (e.g.,  116   a,    118   a ) of the transducer beams  116 ,  118 ,  120 ,  122  comprise a strain gage  134  disposed on the top surface thereof that is sensitive to the vertical force component (i.e., a F Z  strain gage). The first portions (e.g.,  116   a,    118   a ) of the transducer beams  116 ,  118 ,  120 ,  122  also each comprise a strain gage  138  disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F Y  strain gage). Also, in the illustrated embodiment, each of the fourth portions (e.g.,  116   d,    118   d ) of the transducer beams  116 ,  118 ,  120 ,  122  comprise a strain gage  136  disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F X  strain gage). 
     As best shown in  FIG. 10 , the illustrated load cells are configured as bending beam load cells. The illustrated strain gages  134 ,  136 ,  138  are mounted to either top or side surfaces of the beams  116 ,  118 ,  120 ,  122  between their attachment locations to the beam connecting portions  128  and the raised end portions  124  thereof. Alternatively, the strain gages  134  can be mounted to the bottom surfaces of the first beam portions (e.g.,  116   a,    118   a ) of the transducer beams  116 ,  118 ,  120 ,  122 , while the strain gages  138  can be mounted to the opposite side surfaces of the first beam portions (e.g.,  116   a,    118   a ) of the transducer beams  116 ,  118 ,  120 ,  122 . Similarly, the strain gages  136  can be mounted to the opposite side surfaces of the fourth beam portions (e.g.,  116   d,    118   d ) of the transducer beams  116 ,  118 ,  120 ,  122 . In general, the strain gages  134 ,  136 ,  138  are mounted to surfaces generally normal to the direction of applied vertical and/or shear forces (i.e., F X , F Y , F Z ). It is also noted that alternatively, the strain gages  134  can be mounted at both the top surface and the bottom surface of the first beam portions of the beams  116 ,  118 ,  120 ,  122 , the strain gages  138  can be mounted at both opposed side surfaces of first beam portions of the beams  116 ,  118 ,  120 ,  122 , and/or the strain gages  136  can be mounted at both opposed side surfaces of the beams  116 ,  118 ,  120 ,  122 . These strain gages  134 ,  136 ,  138  measure force either by bending moment or difference of bending moments at two cross sections. As force is applied to the ends of the beams, the beams  116 ,  118 ,  120 ,  122  bend. This bending either stretches or compresses the strain gages  134 ,  136 ,  138 , which in turn changes the resistance of the electrical current passing therethrough. The amount of change in the electrical voltage or current is proportional to the magnitude of the applied force, as applied to the ends of respective beams  116 ,  118 ,  120 ,  122 . 
     Next, referring to  FIGS. 15-18 , a load transducer  200  according to a fourth exemplary embodiment of the present invention will be described. Referring initially to the perspective view of  FIG. 15 , it can be seen that the load transducer  200  generally includes a one-piece compact transducer frame  204  that is generally in the form of square band-shaped element with a central opening  202  disposed therethrough. As best illustrated in  FIGS. 15 and 18 , the square band-shaped transducer frame  204  comprises a first transducer beam side portion  206 , a second transducer beam side portion  208 , a third transducer beam side portion  210 , and a fourth transducer beam side portion  212 . Also, as shown in  FIG. 15 , the transducer beam side portions  206 ,  208 ,  210 ,  212  comprise a plurality of load cells or transducer elements for measuring forces and/or moments. The transducer frame  204  of the load transducer  200  is similar to the other transducers (e.g., transducers  300 ,  400 ) that will be described hereinafter, except that the central body portion of these transducers (e.g.,  300 ,  400 ) has been removed in the load transducer  200 . 
     As shown in  FIGS. 15-18 , the illustrated transducer beam side portions  206 ,  208 ,  210 ,  212  of the transducer frame  204  are arranged in a generally square configuration. In particular, with reference to  FIGS. 15 and 18 , the first transducer beam side portion  206  is connected to the second transducer beam side portion  208  on one of its longitudinal ends, and the fourth transducer beam side portion  212  on the other one of its longitudinal ends, and the first transducer beam side portion  206  is disposed generally perpendicular to each of the second and fourth transducer beam side portions  208 ,  212 . The second transducer beam side portion  208  is connected to the first transducer beam side portion  206  on one of its longitudinal ends, and the third transducer beam side portion  210  on the other one of its longitudinal ends, and the second transducer beam side portion  208  is disposed generally perpendicular to each of the first and third transducer beam side portions  206 ,  210 . The third transducer beam side portion  210  is connected to the second transducer beam side portion  208  on one of its longitudinal ends, and the fourth transducer beam side portion  212  on the other one of its longitudinal ends, and the third transducer beam side portion  210  is disposed generally perpendicular to each of the second and fourth transducer beam side portions  208 ,  212 . The fourth transducer beam side portion  212  is connected to the third transducer beam side portion  210  on one of its longitudinal ends, and the first transducer beam side portion  206  on the other one of its longitudinal ends, and the fourth transducer beam side portion  212  is disposed generally perpendicular to each of the first and third transducer beam side portions  206 ,  210 . Referring to  FIGS. 15, 17, and 18 , it can be seen that the top surface of the second transducer beam side portion  208  and the top surface of the fourth transducer beam side portion  212  each comprises a central raised portion or standoff portion  214  with spaced apart mounting apertures  218  (e.g., two spaced apart apertures  218 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  200  to another object, such as a robotic arm, etc. Similarly, with reference to  FIGS. 15 and 16 , it can be seen that the bottom surface of the first transducer beam side portion  206  and the bottom surface of the third transducer beam side portion  210  each comprises a central raised portion or standoff portion  216  with spaced apart mounting apertures  218  (e.g., two spaced apart apertures  218 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  200  to another object, such as a robotic arm, etc. 
     As best shown in the perspective view of  FIG. 15 , the illustrated load cells are located on the transducer beam side portions  206 ,  208 ,  210 ,  212 . In the illustrated embodiment, each load cell comprises one or more strain gages  220 ,  222 ,  224 . Specifically, in the illustrated embodiment, the first transducer beam side portion  206  and the third transducer beam side portion  210  each comprise a plurality of spaced apart strain gages  220  (e.g., two spaced apart strain gages  220 ) disposed on the top surface thereof that is sensitive to the vertical force component (i.e., a F Z  strain gage). The second transducer beam side portion  208  and the fourth transducer beam side portion  212  also each comprise a plurality of spaced apart strain gages  222  (e.g., two spaced apart strain gages  222 ) disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). Also, in the illustrated embodiment, the first transducer beam side portion  206  and the third transducer beam side portion  210  also each comprise a plurality of spaced apart strain gages  224  (e.g., two spaced apart strain gages  224 ) disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). 
     As best shown in  FIG. 15 , the illustrated load cells are configured as bending beam load cells. The illustrated strain gages  220 ,  222 ,  224  are mounted to either top or side surfaces of the transducer beam side portions  206 ,  208 ,  210 ,  212  between the opposed longitudinal ends thereof. Alternatively, the strain gages  220  can be mounted to the bottom surfaces of the first and third transducer beam side portions  206 ,  210 , while the strain gages  222  can be mounted to the opposite side surfaces of the second and fourth transducer beam side portions  208 ,  212 . Similarly, the strain gages  224  can be mounted to the opposite side surfaces of the first and third transducer beam side portions  206 ,  210 . In general, the strain gages  220 ,  222 ,  224  are mounted to surfaces generally normal to the direction of applied vertical and/or shear forces (i.e., F X , F Y , F Z ). It is also noted that alternatively, the strain gages  220  can be mounted at both the top surface and the bottom surface of the first and third transducer beam side portions  206 ,  210 , the strain gages  222  can be mounted at both opposed side surfaces of second and fourth transducer beam side portions  208 ,  212 , and/or the strain gages  224  can be mounted at both opposed side surfaces of the first and third transducer beam side portions  206 ,  210 . These strain gages  220 ,  222 ,  224  measure force either by bending moment or difference of bending moments at two cross sections. As force is applied to the beams, the beams  206 ,  208 ,  210 ,  212  bend. This bending either stretches or compresses the strain gages  220 ,  222 ,  224 , which in turn changes the resistance of the electrical current passing therethrough. The amount of change in the electrical voltage or current is proportional to the magnitude of the applied force, as transferred through the end portions of respective beams  206 ,  208 ,  210 ,  212 . 
     An exemplary mounting arrangement for the load transducer  200  is illustrated in  FIG. 25 . As depicted in the perspective view of  FIG. 25 , the load transducer  200  is mounted between a top plate member  226  and a bottom plate member  228 . Specifically, in this mounting arrangement, the bottom surface  226   a  of the top plate member  226  abuts the top surfaces of the standoff portions  214  on the second and fourth transducer beam side portions  208 ,  212 , while the top surface  228   a  of the bottom plate member  228  abuts the bottom surfaces of the standoff portions  216  on the first and third transducer beam side portions  206 ,  210 . As such, in this mounting arrangement, an upper gap  230  is formed between the top surfaces of the load transducer  200  and the bottom surface  226   a  of the top plate member  226  by the two spaced apart top standoff portions  214 . Similarly, a lower gap  232  is formed between the bottom surfaces of the load transducer  200  and the top surface  228   a  of the bottom plate member  228  by the two spaced apart bottom standoff portions  216 . Thus, as result of the mounting arrangement illustrated in  FIG. 25 , the entire load exerted on the load transducer  200  by the top and bottom plate members  226 ,  228  is transferred through the corner portions of the transducer frame  204 , which are instrumented with the strain gages  220 ,  222 ,  224  and are spaced apart from the top and bottom plate members  226 ,  228  by the standoff portions  214 ,  216 . 
     While the exemplary mounting arrangement is illustrated in  FIG. 25  using the load transducer  200 , it is to be understood that each of the other load transducers  10 ,  10 ′,  100 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800  described herein are mounted in generally the same manner to adjoining structures (e.g., plate members  226 ,  228  or components of a robotic arm). That is, the standoff portions described on the load transducers  10 ,  10 ′,  100 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800  perform the same functions as those described in conjunction with the load transducer  200  above. In particular, the adjoining structures to which the transducers are mounted are only connected to the top standoff portions and the bottom standoff portions of each load transducer  10 ,  10 ′,  100 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800  so as to ensure that the total loads applied to the load transducers  10 ,  10 ′,  100 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800  are transmitted through the instrumented portions of the transducer beams of the transducers. 
       FIG. 19  illustrates a load transducer  300  according to a fifth exemplary embodiment of the present invention. With reference to this figure, it can be seen that, in some respects, the fifth exemplary embodiment is similar to that of the fourth embodiment. Moreover, some parts are common to both such embodiments. For the sake of brevity, the parts that the fifth embodiment of the load transducer has in common with the fourth embodiment will only be briefly mentioned because these components have already been explained in detail above. 
     Initially, referring to the perspective view of  FIG. 19 , it can be seen that, unlike the fourth exemplary embodiment of the load transducer, the load transducer  300  comprises a central body portion  302 . Also, unlike the load transducer  200  of the fourth embodiment, the second and fourth transducer beam side portions  308 ,  312  have side projecting portions  326  extending from the inner sides thereof towards the central body portion  302 . As shown in  FIG. 19 , the load transducer  300  generally includes a one-piece compact transducer frame  304  with a central body portion  302  and a plurality of transducer beam side portions  306 ,  308 ,  310 ,  312 . 
     With reference again to  FIG. 19 , it can be seen that the illustrated central body portion  302  is generally in the form of rectangular band-shaped element with a central opening  303  disposed therethrough. In  FIG. 19 , it can be seen that the body portion  302  comprises a first pair of opposed side portions  302   a,    302   c  and a second pair of opposed side portions  302   b,    302   d.  The side portion  302   a  is disposed generally parallel to the side portion  302   c,  while the side portion  302   b  is disposed generally parallel to the side portion  302   d.  Each of the side surfaces of the side portions  302   a,    302   b,    302   c,    302   d  is disposed generally perpendicular to the planar top and bottom surfaces thereof. Also, each of the first pair of opposed side portions  302   a,    302   c  is disposed generally perpendicular to each of the second pair of opposed sides portions  302   b,    302   d.  In addition, as shown in  FIG. 19 , each of the opposed side portions  302   a,    302   c  forms a middle portion of the first and third transducer beam side portions  306 ,  310 . In the illustrated embodiment, it can be seen that each of the opposed side portions  302   a,    302   c  comprises a plurality of apertures  318  (e.g., two apertures  318 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  300  to another object, such as a robotic arm, etc. Also, as depicted in the  FIG. 19 , the central body portion  302  comprises a raised top portion or top standoff portion  314  for spacing the transducer beam side portions  306 ,  308 ,  310 ,  312  apart from the object (e.g., robotic arm) to which the load transducer  300  is attached so that forces and/or moments are capable of being accurately measured by the load transducer  300 . 
     As shown in  FIG. 19 , the illustrated transducer beam side portions  306 ,  308 ,  310 ,  312  of the transducer frame  304  are arranged in a generally square configuration. In particular, with reference to  FIG. 19 , the first transducer beam side portion  306  is connected to the second transducer beam side portion  308  on one of its longitudinal ends, and the fourth transducer beam side portion  312  on the other one of its longitudinal ends, and the first transducer beam side portion  306  is disposed generally perpendicular to each of the second and fourth transducer beam side portions  308 ,  312 . The second transducer beam side portion  308  is connected to the first transducer beam side portion  306  on one of its longitudinal ends, and the third transducer beam side portion  310  on the other one of its longitudinal ends, and the second transducer beam side portion  308  is disposed generally perpendicular to each of the first and third transducer beam side portions  306 ,  310 . The third transducer beam side portion  310  is connected to the second transducer beam side portion  308  on one of its longitudinal ends, and the fourth transducer beam side portion  312  on the other one of its longitudinal ends, and the third transducer beam side portion  310  is disposed generally perpendicular to each of the second and fourth transducer beam side portions  308 ,  312 . The fourth transducer beam side portion  312  is connected to the third transducer beam side portion  310  on one of its longitudinal ends, and the first transducer beam side portion  306  on the other one of its longitudinal ends, and the fourth transducer beam side portion  312  is disposed generally perpendicular to each of the first and third transducer beam side portions  306 ,  310 . Referring to  FIG. 19 , it can be seen that the bottom surface of the second transducer beam side portion  308  and the bottom surface of the fourth transducer beam side portion  312  each comprises a central standoff portion  316 , which is connected to the side projecting portion  326  on each of the transducer beam side portions  308 ,  312 . The side projecting portions  326  each comprise spaced apart mounting apertures  328  (e.g., two spaced apart apertures  328 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  300  to another object, such as a robotic arm, etc. 
     As best shown in the perspective view of  FIG. 19 , the illustrated load cells are located on the transducer beam side portions  306 ,  308 ,  310 ,  312 . In the illustrated embodiment, each load cell comprises one or more strain gages  320 ,  322 ,  324 . Specifically, in the illustrated embodiment, the second transducer beam side portion  308  and the fourth transducer beam side portion  312  each comprise a plurality of spaced apart strain gages  320  (e.g., two spaced apart strain gages  320 ) disposed on the top surface thereof that is sensitive to the vertical force component (i.e., a F Z  strain gage). The second transducer beam side portion  308  and fourth transducer beam side portion  312  also each comprise a plurality of spaced apart strain gages  322  (e.g., two spaced apart strain gages  322 ) disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). Also, in the illustrated embodiment, the first transducer beam side portion  306  and the third transducer beam side portion  310  also each comprise a plurality of spaced apart strain gages  324  (e.g., two spaced apart strain gages  324 ) disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). 
       FIG. 20  illustrates a load transducer  400  according to a sixth exemplary embodiment of the present invention. With reference to this figure, it can be seen that, in some respects, the sixth exemplary embodiment is similar to that of the fifth embodiment. Moreover, some parts are common to both such embodiments. For the sake of brevity, the parts that the sixth embodiment of the load transducer has in common with the fifth embodiment will only be briefly mentioned because these components have already been explained in detail above. 
     Initially, referring to the perspective view of  FIG. 20 , it can be seen that, unlike the fifth exemplary embodiment of the load transducer, all four sides of the central body portion  402  of the load transducer  400  are spaced apart from the transducer beam side portions  406 ,  408 ,  410 ,  412 . In particular, the central body portion  402  is spaced apart from the transducer beam side portions  406 ,  408 ,  410 ,  412  by the two C-shaped gaps  426 . Also, unlike the load transducer  300  of the fifth embodiment, the first and third transducer beam side portions  406 ,  410  of the load transducer  400  are connected to the central body portion  402  by the beam connecting portions  417 . Although, like the load transducer  300 , the load transducer  400  generally includes a one-piece compact transducer frame  404  with a central body portion  402  and a plurality of transducer beam side portions  406 ,  408 ,  410 ,  412 . 
     With reference again to  FIG. 20 , it can be seen that the illustrated central body portion  402  is generally in the form of rectangular band-shaped element with a central opening  403  disposed therethrough. In  FIG. 20 , it can be seen that the body portion  402  comprises a first pair of opposed side portions  402   a,    402   c  and a second pair of opposed side portions  402   b,    402   d.  The side portion  402   a  is disposed generally parallel to the side portion  402   c,  while the side portion  402   b  is disposed generally parallel to the side portion  402   d.  Each of the side surfaces of the side portions  402   a,    402   b,    402   c,    402   d  is disposed generally perpendicular to the planar top and bottom surfaces thereof. Also, each of the first pair of opposed side portions  402   a,    402   c  is disposed generally perpendicular to each of the second pair of opposed sides portions  402   b,    402   d.  In addition, as shown in  FIG. 20 , each of the opposed side portions  402   a,    402   c  is connected to the first and third transducer beam side portions  406 ,  410  by beam connecting portions  417 . In the illustrated embodiment, it can be seen that each of the beam connecting portions  417  comprises a plurality of apertures  418  (e.g., two apertures  418 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  400  to another object, such as a robotic arm, etc. 
     As shown in  FIG. 20 , the illustrated transducer beam side portions  406 ,  408 ,  410 ,  412  of the transducer frame  404  are arranged in a generally square configuration. In particular, with reference to  FIG. 20 , the first transducer beam side portion  406  is connected to the second transducer beam side portion  408  on one of its longitudinal ends, and the fourth transducer beam side portion  412  on the other one of its longitudinal ends, and the first transducer beam side portion  406  is disposed generally perpendicular to each of the second and fourth transducer beam side portions  408 ,  412 . The second transducer beam side portion  408  is connected to the first transducer beam side portion  406  on one of its longitudinal ends, and the third transducer beam side portion  410  on the other one of its longitudinal ends, and the second transducer beam side portion  408  is disposed generally perpendicular to each of the first and third transducer beam side portions  406 ,  410 . The third transducer beam side portion  410  is connected to the second transducer beam side portion  408  on one of its longitudinal ends, and the fourth transducer beam side portion  412  on the other one of its longitudinal ends, and the third transducer beam side portion  410  is disposed generally perpendicular to each of the second and fourth transducer beam side portions  408 ,  412 . The fourth transducer beam side portion  412  is connected to the third transducer beam side portion  410  on one of its longitudinal ends, and the first transducer beam side portion  406  on the other one of its longitudinal ends, and the fourth transducer beam side portion  412  is disposed generally perpendicular to each of the first and third transducer beam side portions  406 ,  410 . Referring to  FIG. 20 , it can be seen that the top surface of the second transducer beam side portion  408  and the top surface of the fourth transducer beam side portion  412  each comprises a central raised portion or standoff portion  414  with spaced apart mounting apertures  428  (e.g., two spaced apart apertures  428 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  400  to another object, such as a robotic arm, etc. Similarly, with reference to  FIG. 20 , it can be seen that the bottom surface of the first transducer beam side portion  406  and the bottom surface of the third transducer beam side portion  410  each comprises a central raised portion or standoff portion  416 . 
     As best shown in the perspective view of  FIG. 20 , the illustrated load cells are located on the transducer beam side portions  406 ,  408 ,  410 ,  412 . In the illustrated embodiment, each load cell comprises one or more strain gages  420 ,  422 ,  424 . Specifically, in the illustrated embodiment, the first transducer beam side portion  406  and the third transducer beam side portion  410  each comprise a plurality of spaced apart strain gages  420  (e.g., two spaced apart strain gages  420 ) disposed on the top surface thereof that is sensitive to the vertical force component (i.e., a F Z  strain gage). The second transducer beam side portion  408  and fourth transducer beam side portion  412  also each comprise a plurality of spaced apart strain gages  422  (e.g., two spaced apart strain gages  422 ) disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). Also, in the illustrated embodiment, the first transducer beam side portion  406  and the third transducer beam side portion  410  also each comprise a plurality of spaced apart strain gages  424  (e.g., two spaced apart strain gages  424 ) disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). 
       FIG. 21  illustrates a load transducer  500  according to a seventh exemplary embodiment of the present invention. With reference to this figure, it can be seen that, in some respects, the seventh exemplary embodiment is similar to that of the fifth embodiment. Moreover, some parts are common to both such embodiments. For the sake of brevity, the parts that the seventh embodiment of the load transducer has in common with the fifth embodiment will only be briefly mentioned because these components have already been explained in detail above. 
     Initially, referring to the perspective view of  FIG. 21 , it can be seen that, like the fifth embodiment described above, the load transducer  500  generally includes a one-piece compact transducer frame  504  with a central body portion  502  and a plurality of transducer beam side portions  506 ,  508 ,  510 ,  512 ,  514 ,  516 . Although, the central body portion  502  of the load transducer  500  is considerably wider than the central body portion  302  of the load transducer  300 . 
     With reference again to  FIG. 21 , it can be seen that the illustrated central body portion  502  is generally in the form of square band-shaped element with a central opening  530  disposed therethrough. In  FIG. 21 , it can be seen that the body portion  502  comprises a first pair of opposed side portions  502   a,    502   c  and a second pair of opposed side portions  502   b,    502   d.  The side portion  502   a  is disposed generally parallel to the side portion  502   c,  while the side portion  502   b  is disposed generally parallel to the side portion  502   d.  Each of the side surfaces of the side portions  502   a,    502   b,    502   c,    502   d  is disposed generally perpendicular to the planar top and bottom surfaces thereof. Also, each of the first pair of opposed side portions  502   a,    502   c  is disposed generally perpendicular to each of the second pair of opposed sides portions  502   b,    502   d.  In addition, as shown in  FIG. 21 , each of the opposed side portions  502   a,    502   c  is disposed between a respective pair of transducer beam side portions  506 ,  508  and  512 ,  514 . In the illustrated embodiment, it can be seen that each of the opposed side portions  502   a,    502   c  comprises a plurality of apertures  532  (e.g., two apertures  532 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  500  to another object, such as a robotic arm, etc. Also, as depicted in the  FIG. 21 , the central body portion  502  comprises a raised bottom portion or bottom standoff portion  520  for spacing the transducer beam side portions  506 ,  508 ,  510 ,  512 ,  514 ,  516  apart from the object (e.g., robotic arm) to which the load transducer  500  is attached so that forces and/or moments are capable of being accurately measured by the load transducer  500 . 
     As shown in  FIG. 21 , the first set of illustrated transducer beam side portions  506 ,  514 ,  516  of the transducer frame  504  are arranged in a generally C-shaped configuration on a first side of the central body portion  502 . A first side aperture  534  is formed between the side portion  502   d  of the central body portion  502  and the first set of transducer beam side portions  506 ,  514 ,  516 . Referring again to  FIG. 21 , it can be seen that the first transducer beam side portion  506  is connected to the sixth transducer beam side portion  516  on one of its longitudinal ends, and the side portion  502   d  of the central body portion  502  on the other one of its longitudinal ends, and the first transducer beam side portion  506  is disposed generally perpendicular to the side portion  502   d  of the central body portion  502  and to sixth transducer beam side portion  516 . Similarly, the fifth transducer beam side portion  514  is connected to the sixth transducer beam side portion  516  on one of its longitudinal ends, and the side portion  502   d  of the central body portion  502  on the other one of its longitudinal ends, and the fifth transducer beam side portion  514  is disposed generally perpendicular to the side portion  502   d  of the central body portion  502  and to sixth transducer beam side portion  516 . The sixth transducer beam side portion  516  is connected to the first transducer beam side portion  506  on one of its longitudinal ends, and the fifth transducer beam side portion  514  on the other one of its longitudinal ends, and the sixth transducer beam side portion  516  is disposed generally perpendicular to each of the first and fifth transducer beam side portions  506 ,  514 . Turning again to  FIG. 21 , it can be seen that the second set of transducer beam side portions  508 ,  510 ,  512  of the transducer frame  504  is arranged in a generally C-shaped configuration on a second side of the central body portion  502 , which is opposite to the first side of the central body portion  502 . A second side aperture  534  is formed between the side portion  502   b  of the central body portion  502  and the second set of transducer beam side portions  508 ,  510 ,  512 . In  FIG. 21 , it can be seen that the second transducer beam side portion  508  is connected to the third transducer beam side portion  510  on one of its longitudinal ends, and the side portion  502   b  of the central body portion  502  on the other one of its longitudinal ends, and the second transducer beam side portion  508  is disposed generally perpendicular to the side portion  502   b  of the central body portion  502  and to third transducer beam side portion  510 . Similarly, the fourth transducer beam side portion  512  is connected to the third transducer beam side portion  510  on one of its longitudinal ends, and the side portion  502   b  of the central body portion  502  on the other one of its longitudinal ends, and the fourth transducer beam side portion  512  is disposed generally perpendicular to the side portion  502   b  of the central body portion  502  and to third transducer beam side portion  510 . The third transducer beam side portion  510  is connected to the second transducer beam side portion  508  on one of its longitudinal ends, and the fourth transducer beam side portion  512  on the other one of its longitudinal ends, and the third transducer beam side portion  510  is disposed generally perpendicular to each of the second and fourth transducer beam side portions  508 ,  512 . Also, as shown in  FIG. 21 , it can be seen that the top surface of the third transducer beam side portion  510  and the top surface of the sixth transducer beam side portion  516  each comprises a central standoff portion  518 . The central standoff portions  518  each comprise spaced apart mounting apertures  522  (e.g., two spaced apart apertures  522 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  500  to another object, such as a robotic arm, etc. 
     As best shown in the perspective view of  FIG. 21 , the illustrated load cells are located on the transducer beam side portions  506 ,  508 ,  510 ,  512 ,  514 ,  516 . In the illustrated embodiment, each load cell comprises one or more strain gages  524 ,  526 ,  528 . Specifically, in the illustrated embodiment, the first transducer beam side portion  506 , the second transducer beam side portion  508 , the fourth transducer beam side portion  512 , and the fifth transducer beam side portion  514  each comprise a strain gage  524  disposed on the top surface thereof that is sensitive to the vertical force component (i.e., a F Z  strain gage). The third transducer beam side portion  510  and the sixth transducer beam side portion  516  also each comprise a plurality of spaced apart strain gages  526  (e.g., two spaced apart strain gages  526 ) disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). Also, in the illustrated embodiment, the first transducer beam side portion  506 , the second transducer beam side portion  508 , the fourth transducer beam side portion  512 , and the fifth transducer beam side portion  514  each comprises a strain gage  528  disposed on an outer side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). 
       FIG. 22  illustrates a load transducer  600  according to an eighth exemplary embodiment of the present invention. With reference to this figure, it can be seen that, in some respects, the eighth exemplary embodiment is similar to that of the preceding embodiments. Moreover, some parts are common to all of the embodiments. For the sake of brevity, the parts that the eighth embodiment of the load transducer has in common with the preceding embodiments will only be briefly mentioned because these components have already been explained in detail above. 
     Initially, referring to the perspective view of  FIG. 22 , it can be seen that, like the preceding embodiments described above, the load transducer  600  generally includes a one-piece compact transducer frame  604  with a central body portion  602  and a plurality of transducer beams  606 ,  608 ,  610 ,  612 ,  614 ,  616  connected thereto. Although, the transducer beams  606 ,  608 ,  610 ,  612 ,  614 ,  616  are arranged in a different configuration than that which was described for the preceding embodiments. 
     With reference again to  FIG. 22 , it can be seen that the illustrated central body portion  602  is generally in the form of square band-shaped element with a central opening  630  disposed therethrough. In  FIG. 22 , it can be seen that the body portion  602  comprises a first pair of opposed side portions  602   a,    602   c  and a second pair of opposed side portions  602   b,    602   d.  The side portion  602   a  is disposed generally parallel to the side portion  602   c,  while the side portion  602   b  is disposed generally parallel to the side portion  602   d.  Each of the side surfaces of the side portions  602   a,    602   b,    602   c,    602   d  is disposed generally perpendicular to the planar top and bottom surfaces thereof. Also, each of the first pair of opposed side portions  602   a,    602   c  is disposed generally perpendicular to each of the second pair of opposed sides portions  602   b,    602   d.  In addition, as shown in  FIG. 22 , each of the opposed side portions  602   b,    602   d  is connected to a respective set of transducer beams  606 ,  608 ,  610  and  612 ,  614 ,  616 . In the illustrated embodiment, it can be seen that each of the opposed side portions  602   a,    602   c  comprises a plurality of apertures  632  (e.g., two apertures  632 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  600  to another object, such as a robotic arm, etc. 
     As shown in  FIG. 22 , the first set of illustrated transducer beams  606 ,  608 ,  610  of the transducer frame  604  is arranged in a generally T-shaped configuration on a first side of the central body portion  602 . A first side aperture  634  is formed between the side portion  602   d  of the central body portion  602  and the first set of transducer beam side portions  606 ,  608 ,  610 . Referring again to  FIG. 22 , it can be seen that the first transducer beam  606  is connected to the side portion  602   d  of the central body portion  602  by means of two spaced apart connecting transducer beams  608 ,  610 . Specifically, the second transducer beam  608  is connected to an inner side of the first transducer beam  606  on one of its longitudinal ends, and the side portion  602   d  of the central body portion  602  on the other one of its longitudinal ends, and the second transducer beam  608  is disposed generally perpendicular to the side portion  602   d  of the central body portion  602  and to first transducer beam  606 . Similarly, the third transducer beam  610  is connected to the inner side of the first transducer beam  606  on one of its longitudinal ends, and the side portion  602   d  of the central body portion  602  on the other one of its longitudinal ends, and the third transducer beam  610  is disposed generally perpendicular to the side portion  602   d  of the central body portion  602  and to first transducer beam  606 . Turning again to  FIG. 22 , it can be seen that the second set of transducer beams  612 ,  614 ,  616  of the transducer frame  604  is arranged in a generally T-shaped configuration on a second side of the central body portion  602 , which is opposite to the first side of the central body portion  602 . A second side aperture  634  is formed between the side portion  602   b  of the central body portion  602  and the second set of transducer beam side portions  612 ,  614 ,  616 . In  FIG. 22 , similar to the first transducer beam  606 , it can be seen that the fourth transducer beam  612  is connected to the side portion  602   b  of the central body portion  602  by means of two spaced apart connecting transducer beams  614 ,  616 . Specifically, the fifth transducer beam  614  is connected to an inner side of the fourth transducer beam  612  on one of its longitudinal ends, and the side portion  602   b  of the central body portion  602  on the other one of its longitudinal ends, and the fifth transducer beam  614  is disposed generally perpendicular to the side portion  602   b  of the central body portion  602  and to fourth transducer beam  612 . Similarly, the sixth transducer beam  616  is connected to the inner side of the fourth transducer beam  612  on one of its longitudinal ends, and the side portion  602   b  of the central body portion  602  on the other one of its longitudinal ends, and the sixth transducer beam  616  is disposed generally perpendicular to the side portion  602   b  of the central body portion  602  and to fourth transducer beam  612 . Also, as shown in  FIG. 22 , it can be seen that the bottom surface of the first transducer beam  606  and the bottom surface of the fourth transducer beam  612  each comprises a central standoff portion  620 . In addition, it can be seen that the opposed longitudinal ends of the first transducer beam  606  and the fourth transducer beam  612  are each provided with raised standoff portions  618 . Each raised standoff portion  618  is provided with a mounting aperture  622  disposed therethrough for accommodating a respective fastener (e.g., a screw) that attaches the load transducer  600  to another object, such as a robotic arm, etc. 
     As best shown in the perspective view of  FIG. 22 , the illustrated load cells are located on the transducer beams  606 ,  608 ,  610 ,  612 ,  614 ,  616 . In the illustrated embodiment, each load cell comprises one or more strain gages  624 ,  626 ,  628 . Specifically, in the illustrated embodiment, the first transducer beam  606  and the fourth transducer beam  612  each comprise a pair of spaced apart strain gages  624  disposed on the top surfaces thereof that are sensitive to the vertical force component (i.e., F Z  strain gages). In  FIG. 22 , it can be seen that each of the strain gages  624  is disposed near the raised standoff portions  618  at the opposed ends of the beams  606 ,  612 . Also, in the illustrated embodiment, the second transducer beam  608 , the third transducer beam  610 , the fifth transducer beam  614 , and the sixth transducer beam  616  each comprise a strain gage  626  disposed on an outer side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). The first transducer beam  606  and the fourth transducer beam  612  also each comprise a plurality of spaced apart strain gages  628  (e.g., two spaced apart strain gages  628 ) disposed on an outer side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). 
       FIG. 23  illustrates a load transducer  700  according to a ninth exemplary embodiment of the present invention. With reference to this figure, it can be seen that, in some respects, the ninth exemplary embodiment is similar to that of the eighth embodiment. Moreover, some parts are common to all of the embodiments. For the sake of brevity, the parts that the ninth embodiment of the load transducer has in common with the eighth embodiment will only be briefly mentioned because these components have already been explained in detail above. 
     Initially, referring to the perspective view of  FIG. 23 , it can be seen that, like the eighth embodiment described above, the load transducer  700  generally includes a one-piece compact transducer frame  704  with a central body portion  702  and a plurality of transducer beams  706 ,  708 ,  710 ,  712 ,  714 ,  716  connected thereto. Although, each of connecting transducer beams  708 ,  710 , and each of connecting transducer beams  714 ,  716 , are spaced considerably further apart from one another as compared to the connecting transducer beams  608 ,  610 ,  614 ,  616  of the load transducer  600  such that the connecting beams  708 ,  710 ,  714 ,  716  are generally axially aligned with the side portions  702   a,    702   c  of the central body portion  702 . 
     With reference again to  FIG. 23 , it can be seen that the illustrated central body portion  702  is generally in the form of square band-shaped element with a central opening  730  disposed therethrough. In  FIG. 23 , it can be seen that the body portion  702  comprises a first pair of opposed side portions  702   a,    702   c  and a second pair of opposed side portions  702   b,    702   d.  The side portion  702   a  is disposed generally parallel to the side portion  702   c,  while the side portion  702   b  is disposed generally parallel to the side portion  702   d.  Each of the side surfaces of the side portions  702   a,    702   b,    702   c,    702   d  is disposed generally perpendicular to the planar top and bottom surfaces thereof. Also, each of the first pair of opposed side portions  702   a,    702   c  is disposed generally perpendicular to each of the second pair of opposed sides portions  702   b,    702   d.  In addition, as shown in  FIG. 23 , each of the opposed side portions  702   b,    702   d  is connected to a respective set of transducer beams  706 ,  708 ,  710  and  712 ,  714 ,  716 . In the illustrated embodiment, it can be seen that each of the opposed side portions  702   a,    702   c  comprises a plurality of apertures  732  (e.g., two apertures  732 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  700  to another object, such as a robotic arm, etc. Also, as depicted in the  FIG. 23 , the central body portion  702  comprises a raised bottom portion or bottom standoff portion  720  for spacing the transducer beams  706 ,  708 ,  710 ,  712 ,  714 ,  716  apart from an object (e.g., robotic arm) to which the load transducer  700  is attached so that forces and/or moments are capable of being accurately measured by the load transducer  700 . 
     As shown in  FIG. 23 , the first set of illustrated transducer beams  706 ,  708 ,  710  of the transducer frame  704  is arranged in a generally T-shaped configuration on a first side of the central body portion  702  (with the wide base of the T-shaped arrangement being formed by the connecting beam transducers  708 ,  710 ). A first side aperture  734  is formed between the side portion  702   d  of the central body portion  702  and the first set of transducer beam side portions  706 ,  708 ,  710 . Referring again to  FIG. 23 , it can be seen that the first transducer beam  706  is connected to the side portion  702   d  of the central body portion  702  by means of two spaced apart connecting transducer beams  708 ,  710 . Specifically, the second transducer beam  708  is connected to an inner side of the first transducer beam  706  on one of its longitudinal ends, and the side portion  702   d  of the central body portion  702  on the other one of its longitudinal ends, and the second transducer beam  708  is disposed generally perpendicular to the side portion  702   d  of the central body portion  702  and to first transducer beam  706 . Similarly, the third transducer beam  710  is connected to the inner side of the first transducer beam  706  on one of its longitudinal ends, and the side portion  702   d  of the central body portion  702  on the other one of its longitudinal ends, and the third transducer beam  710  is disposed generally perpendicular to the side portion  702   d  of the central body portion  702  and to first transducer beam  706 . Turning again to  FIG. 23 , it can be seen that the second set of transducer beams  712 ,  714 ,  716  of the transducer frame  704  is arranged in a generally T-shaped configuration on a second side of the central body portion  702 , which is opposite to the first side of the central body portion  702  (with the wide base of the T-shaped arrangement being formed by the connecting beam transducers  714 ,  716 ). A second side aperture  734  is formed between the side portion  702   b  of the central body portion  702  and the second set of transducer beam side portions  712 ,  714 ,  716 . In  FIG. 23 , similar to the first transducer beam  706 , it can be seen that the fourth transducer beam  712  is connected to the side portion  702   b  of the central body portion  702  by means of two spaced apart connecting transducer beams  714 ,  716 . Specifically, the fifth transducer beam  714  is connected to an inner side of the fourth transducer beam  712  on one of its longitudinal ends, and the side portion  702   b  of the central body portion  702  on the other one of its longitudinal ends, and the fifth transducer beam  714  is disposed generally perpendicular to the side portion  702   b  of the central body portion  702  and to fourth transducer beam  712 . Similarly, the sixth transducer beam  716  is connected to the inner side of the fourth transducer beam  712  on one of its longitudinal ends, and the side portion  702   b  of the central body portion  702  on the other one of its longitudinal ends, and the sixth transducer beam  716  is disposed generally perpendicular to the side portion  702   b  of the central body portion  702  and to fourth transducer beam  712 . Also, in  FIG. 23 , it can be seen that the opposed longitudinal ends of the first transducer beam  706  and the fourth transducer beam  712  are each provided with raised standoff portions  718 . Each raised standoff portion  718  is provided with a mounting aperture  722  disposed therethrough for accommodating a respective fastener (e.g., a screw) that attaches the load transducer  700  to another object, such as a robotic arm, etc. 
     As best shown in the perspective view of  FIG. 23 , the illustrated load cells are located on the transducer beams  706 ,  708 ,  710 ,  712 ,  714 ,  716 . In the illustrated embodiment, each load cell comprises one or more strain gages  724 ,  726 ,  728 . Specifically, in the illustrated embodiment, the first transducer beam  706  and the fourth transducer beam  712  each comprise a pair of spaced apart strain gages  724  disposed on the top surfaces thereof that are sensitive to the vertical force component (i.e., F Z  strain gages). In  FIG. 23 , it can be seen that each of the strain gages  724  is disposed near the raised standoff portions  718  at the opposed ends of the beams  706 ,  712 . Also, in the illustrated embodiment, the second transducer beam  708 , the third transducer beam  710 , the fifth transducer beam  714 , and the sixth transducer beam  716  each comprise a strain gage  726  disposed on an outer side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). The first transducer beam  706  and the fourth transducer beam  712  also each comprise a plurality of spaced apart strain gages  728  (e.g., two spaced apart strain gages  728 ) disposed on an outer side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). 
       FIG. 24  illustrates a load transducer  800  according to a tenth exemplary embodiment of the present invention. With reference to this figure, it can be seen that, in some respects, the tenth exemplary embodiment is similar to that of the preceding embodiments. Moreover, some parts are common to all of the embodiments. For the sake of brevity, the parts that the tenth embodiment of the load transducer has in common with the preceding embodiments will only be briefly mentioned because these components have already been explained in detail above. 
     Initially, referring to the perspective view of  FIG. 24 , it can be seen that the load transducer  800  generally includes a one-piece compact transducer frame  804  with a central body portion  802  and a plurality of L-shaped transducer beams  806 ,  808 ,  810 ,  812  connected thereto. As shown in  FIG. 24 , each of the L-shaped transducer beams  806 ,  808 ,  810 ,  812  is generally disposed at a respective corner of the central body portion  802 . 
     With reference again to  FIG. 24 , it can be seen that the illustrated central body portion  802  is generally in the form of square band-shaped element with a central opening  826  disposed therethrough. In  FIG. 24 , it can be seen that the body portion  802  comprises a first pair of opposed side portions  802   a,    802   c  and a second pair of opposed side portions  802   b,    802   d.  The side portion  802   a  is disposed generally parallel to the side portion  802   c,  while the side portion  802   b  is disposed generally parallel to the side portion  802   d.  Each of the side surfaces of the side portions  802   a,    802   b,    802   c,    802   d  is disposed generally perpendicular to the planar top and bottom surfaces thereof. Also, each of the first pair of opposed side portions  802   a,    802   c  is disposed generally perpendicular to each of the second pair of opposed sides portions  802   b,    802   d.  In addition, as shown in  FIG. 24 , each of the corners of the central body portion  802  is connected to a respective L-shaped transducer beam  806 ,  808 ,  810 ,  812 . In the illustrated embodiment, it can be seen that each of the opposed side portions  802   a,    802   c  comprises a plurality of apertures  828  (e.g., two apertures  828 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  800  to another object, such as a robotic arm, etc. Also, as depicted in the  FIG. 24 , the central body portion  802  comprises a raised bottom portion or bottom standoff portion  816  for spacing the L-shaped transducer beams  806 ,  808 ,  810 ,  812  apart from an object (e.g., robotic arm) to which the load transducer  800  is attached so that forces and/or moments are capable of being accurately measured by the load transducer  800 . 
     As shown in  FIG. 24 , the first generally L-shaped transducer beam  806  comprises a first beam portion  806   a  and a second beam portion  806   b,  wherein the first beam portion  806   a  is disposed generally perpendicular to the second beam portion  806   b.  Similarly, the second generally L-shaped transducer beam  808  comprises a first beam portion  808   a  and a second beam portion  808   b,  wherein the first beam portion  808   a  is disposed generally perpendicular to the second beam portion  808   b.  Also, it can be seen in  FIG. 24  that the first beam portion  806   a  of the first generally L-shaped transducer beam  806  and the first beam portion  808   a  of the second generally L-shaped transducer beam  808  are both generally axially aligned with the side portion  802   a  of the central body portion  802  (i.e., the longitudinal axes of the beam portions  806   a,    808   a  are generally aligned with the longitudinal axis of the side portion  802   a ). With reference again to  FIG. 24 , the third generally L-shaped transducer beam  810  comprises a first beam portion  810   a  and a second beam portion  810   b,  wherein the first beam portion  810   a  is disposed generally perpendicular to the second beam portion  810   b.  Similarly, the fourth generally L-shaped transducer beam  812  comprises a first beam portion  812   a  and a second beam portion  812   b,  wherein the first beam portion  812   a  is disposed generally perpendicular to the second beam portion  812   b.  Also, it can be seen in  FIG. 24  that the first beam portion  810   a  of the third generally L-shaped transducer beam  810  and the first beam portion  812   a  of the fourth generally L-shaped transducer beam  812  are both generally axially aligned with the side portion  802   c  of the central body portion  802  (i.e., the longitudinal axes of the beam portions  810   a,    812   a  are generally aligned with the longitudinal axis of the side portion  802   c ). Also, in  FIG. 24 , it can be seen that the free ends of the second beam portions  806   b,    808   b,    810   b,    812   b  of the L-shaped transducer beams  806 ,  808 ,  810 ,  812  are each provided with raised standoff portions  814 . Each raised standoff portion  814  is provided with a mounting aperture  818  disposed therethrough for accommodating a respective fastener (e.g., a screw) that attaches the load transducer  800  to another object, such as a robotic arm, etc. 
     As best shown in the perspective view of  FIG. 24 , the illustrated load cells are located on the L-shaped transducer beams  806 ,  808 ,  810 ,  812 . In the illustrated embodiment, each load cell comprises one or more strain gages  820 ,  822 ,  824 . Specifically, in the illustrated embodiment, the second beam portions  806   b,    808   b,    810   b,    812   b  of the L-shaped transducer beams  806 ,  808 ,  810 ,  812  are each provided with a strain gage  820  disposed on the top surface thereof that is sensitive to the vertical force component (i.e., an F Z  strain gage). In  FIG. 24 , it can be seen that each of the strain gages  820  is disposed near the raised standoff portions  818  of the second beam portions  806   b,    808   b,    810   b,    812   b.  Also, in the illustrated embodiment, the second beam portions  806   b,    808   b,    810   b,    812   b  of the L-shaped transducer beams  806 ,  808 ,  810 ,  812  each comprise a strain gage  822  disposed on an outer side surface thereof that is sensitive to a first shear force component (i.e., a F X  strain gage). The first beam portions  806   a,    808   a,    810   a,    812   a  of the L-shaped transducer beams  806 ,  808 ,  810 ,  812  each comprise a strain gage  824  disposed on an outer side surface thereof that is sensitive to a second shear force component (i.e., a F Y  strain gage). 
     In the illustrated embodiments of the present invention, the transducer beams do not extend from a top or upper surface of the central body portion. As such, there is no gap formed between the top or upper surface of the central body portion and a bottom or lower surface of one or more of the transducer beams. Rather, in the exemplary embodiments comprising a central body portion, the transducer beams extend outwardly from a side or lateral surface of the central body portion so as to minimize the overall height of the transducer profile (i.e., because the transducer beams are not required to be disposed above the central body portion). Also, in the illustrated embodiments discussed above, the transducer beams are not in the form of generally linear beams, and are not in the form of generally linear beams with generally symmetrical end portions. Rather, the transducer beams of the exemplary embodiments generally either emanate from a central body portion and have only one cantilevered end or are arranged in a continuous band-like configuration. In addition, it can be seen that, except for the top and bottom standoff portions on either the transducer beams or the central body portions, the top and bottom surfaces of the transducer beams of the exemplary embodiments are generally co-planar with the respective top and bottom surfaces of the central body portion. Similarly, in the exemplary embodiments having a band-like configuration of transducer beams, the top surfaces of each of the looped transducer beams are generally co-planar with one another, while the bottom surfaces of each of the looped transducer beams are also generally co-planar with one another. 
       FIGS. 26-29  illustrate a load transducer  900  according to an eleventh exemplary embodiment of the present invention. Referring initially to the top perspective view of  FIG. 26 , it can be seen that the load transducer  900  generally includes a one-piece compact transducer frame  902  having a plurality of transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  connected to one another in succession. As best shown in the perspective views of  FIGS. 26 and 29 , the plurality of transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  are arranged in a circumscribing pattern whereby a central one of the plurality of transducer beam portions (i.e., transducer beam portion  904 ) is at least partially circumscribed by one or more outer ones of the plurality of beam portions (i.e., transducer beam portions  906 ,  908 ,  910 ,  912 ). In other words, the plurality of transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  forming the load transducer  900  are arranged in a looped configuration whereby a central one of the plurality of beam portions (i.e., transducer beam portion  904 ) emanates from a generally central location within a footprint of the load transducer  900  and outer ones of the plurality of beam portions (i.e., transducer beam portions  906 ,  908 ,  910 ,  912 ) are wrapped around the central one of the plurality of beam portions. As best illustrated in the perspective views of  FIGS. 26 and 29 , each of the beam portions  908 ,  910 ,  912  comprise one or more load cells or transducer elements for measuring forces and/or moments. 
     As shown in  FIGS. 26-29 , the illustrated transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  are arranged in a generally spiral-shaped pattern that emanates from the centrally located transducer beam portion  904 . The pattern in which the transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  are arranged is also generally G-shaped (refer to  FIGS. 26 and 29 ). With particular reference to the perspective views of  FIGS. 26 and 29 , it can be seen that the transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  of the load transducer  900  are arranged in such a configuration that each of the successive transducer beam portions are disposed substantially perpendicular to the immediately preceding transducer beam portion. For example, referring to  FIG. 26 , the first transducer beam portion  904  is disposed at the approximate center of the transducer footprint, the second transducer beam portion  906  is connected to the first transducer beam portion  904  and is disposed substantially perpendicular thereto, the third transducer beam portion  908  is connected to the second transducer beam portion  906  and is disposed substantially perpendicular thereto, the fourth transducer beam portion  910  is connected to the third transducer beam portion  908  and is disposed substantially perpendicular thereto, and the fifth transducer beam portion  912  is connected to the fourth transducer beam portion  910  and is disposed substantially perpendicular thereto. In  FIGS. 26 and 29 , it can be seen that the transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  of the load transducer  900  are spaced apart from one another by a generally U-shaped, central gap  942 , which is bounded by each of the transducer beam portions  904 ,  906 ,  908 ,  910 ,  912 . In particular, the first transducer beam portion  904  and the third transducer beam portion  908 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  942 . Similarly, the second transducer beam portion  906  and the fourth transducer beam portion  910 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  942 . Also, the first transducer beam portion  904  and the fifth transducer beam portion  912 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  942 . The third transducer beam portion  908  and the fifth transducer beam portion  912 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  942  and a segment of the first transducer beam portion  904 . 
     Referring again to the top perspective view of  FIG. 26 , it can be seen that the first and second transducer beam portions  904 ,  906  of the load transducer  900  together comprise an L-shaped raised portion or standoff portion  920  with mounting apertures  924  (e.g., three apertures  924 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  900  to another object, such as a plate component of a force plate or force measurement assembly. The mounting apertures  924  pass completely through the first and second transducer beam portions  904 ,  906 , and are provided with respective bottom bore portions  924   a  of increased diameter (see  FIG. 29 ) in order to accommodate fasteners (e.g., screws) with fillister heads that have a larger outer diameter than the threaded portions of the fasteners. In addition, with reference again to  FIG. 26 , it can be seen that the elevated L-shaped top surface of the first and second transducer beam portions  904 ,  906  is provided with pin locating bores  926  (e.g., two bores  926 ) formed therein for receiving locating pins that ensure the proper positioning of the load transducer  900  on the object to which it is mounted, such as a plate component of a force plate or force measurement assembly. The locating pins are received within the pin locating bores  926  on the load transducer  900  and within corresponding pin locating bores provided on the object (e.g., the force plate or force measurement assembly). As depicted in the bottom perspective view of  FIG. 29 , the fifth transducer beam portion  912  of the load transducer  900  comprises a generally rectangular or square raised portion or standoff portion  922  with a mounting aperture  928  (e.g., a single aperture  928 ) disposed therethrough for accommodating a fastener (e.g., a screw) that attaches the load transducer  900  to another object, such as a mounting foot of a force plate or force measurement assembly. Advantageously, the standoff portions  920 ,  922  on the top and bottom of the load transducer  900  elevate the transducer beam portions  904 ,  906 ,  908 ,  910 ,  912  above the object(s) to which the load transducer  900  is attached so that forces and/or moments are capable of being accurately measured by the load transducer  900 . In one or more embodiments, the structural components to which the load transducer  900  is mounted are connected only to the top standoff portion  920  and the bottom standoff  922  so as to ensure that the total load applied to the load transducer  900  is transmitted through the transducer beam portions  904 ,  906 ,  908 ,  910 ,  912 . 
     In the illustrative embodiment, the third, fourth, and fifth transducer beam portions  908 ,  910 ,  912  have a top surface that is disposed at a first elevation relative to a bottom surface of the load transducer  900 , whereas the L-shaped raised portion  920  of the first and second transducer beam portions  904 ,  906  has a top surface that is disposed at a second elevation relative to the bottom surface of the load transducer  900 . As best shown in  FIGS. 26-28 , the second elevation is greater than the first elevation such that a recessed area is created by the difference in elevation between the second elevation and the first elevation. In the illustrated embodiment, the recessed area is used to accommodate electrical components of the transducer load cells (e.g., strain gages  934 ,  936   a,    938   a ). 
     In the illustrative embodiment of  FIGS. 26-29 , each of the transducer beam portions  908 ,  910 ,  912  is provided with a respective aperture  914 ,  916 ,  918  disposed therethrough. In particular, the third transducer beam portion  908  is provided with a generally rectangular aperture  914  disposed vertically through the beam portion. Similarly, the fourth transducer beam portion  910  is provided with a generally rectangular aperture  916  disposed vertically through the beam portion. The fifth transducer beam portion  912  is provided with a generally rectangular aperture  918  disposed horizontally through the beam portion. The apertures  914 ,  916 ,  918 , which are disposed through the respective transducer beam portions  908 ,  910 ,  912 , significantly increase the sensitivity of the load transducer  900  when a load is applied thereto by reducing the cross-sectional area of the transducer beam portions  908 ,  910 ,  912  at the locations of the apertures  914 ,  916 ,  918 . 
     As best shown in the perspective views of  FIGS. 26 and 29 , the illustrated load cells are located on the transducer beam portions  908 ,  910 ,  912 . In the illustrated embodiment, each load cell comprises one or more strain gages  930 ,  932 ,  934 ,  936   a,    936   b,    938   a,    938   b,    940   a,  and  940   b.  Specifically, in the illustrated embodiment, the third transducer beam portion  908  of the load transducer  900  comprises a strain gage  932  disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F Y  strain gage) and substantially centered on the aperture  914 . The third transducer beam portion  908  also comprises a set of strain gages  938   a,    938   b  that are sensitive to a first moment component (i.e., a M Y  strain gages). The strain gages  938   a,    938   b  are disposed on opposed side surfaces (e.g., top and bottom surfaces) of the third transducer beam portion  908 , and are substantially vertically aligned with one another. Turning again to  FIGS. 26 and 29 , in the illustrated embodiment, the fourth transducer beam portion  910  of the load transducer  900  comprises a strain gage  930  disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F X  strain gage) and substantially centered on the aperture  916 . The fourth transducer beam portion  910  also comprises a set of strain gages  936   a,    936   b  that are sensitive to a second moment component (i.e., a M X  strain gages). Like the strain gages  938   a,    938   b,  the strain gages  936   a,    936   b  are disposed on opposed side surfaces (e.g., top and bottom surfaces) of the fourth transducer beam portion  910 , and are substantially vertically aligned with one another. With reference again to  FIGS. 26 and 29 , in the illustrated embodiment, the fifth transducer beam portion  912  of the load transducer  900  comprises a strain gage  934  disposed on the top surface thereof that is sensitive to a vertical force component (i.e., a F Z  strain gage) and substantially centered on the aperture  918 . The fifth transducer beam portion  912  also comprises a set of strain gages  940   a,    940   b  that are sensitive to a third moment component (i.e., a M Z  strain gages). Like the strain gages  936   a,    936   b  and  938   a,    938   b,  the strain gages  940   a,    940   b  are disposed on opposed side surfaces (e.g., first and second lateral surfaces) of the fifth transducer beam portion  912 , and are substantially horizontally aligned with one another. In the illustrated embodiment, the first shear force component is generally perpendicular to the second shear force component, and each of the first and second shear force components are generally perpendicular to the vertical force component. 
     In the illustrated embodiment, the strain gages  930 ,  932 ,  934  are disposed on respective outer surfaces of the transducer beam portions  910 ,  908 ,  912 . The outer surfaces of the transducer beam portions  910 ,  908 ,  912  on which the strain gages  930 ,  932 ,  934  are disposed are generally opposite to the inner surfaces of the respective apertures  916 ,  914 ,  918 . 
     As best shown in  FIGS. 26 and 29 , the illustrated load cells are mounted on top, bottom, or side surfaces of the transducer beam portions  908 ,  910 ,  912  between the standoff portions  920 ,  922  of the load transducer  900 . Alternatively, the strain gages  932 ,  930  can be mounted to the inner side surfaces of the respective third and fourth transducer beam portions  908 ,  910 , rather than to the outer side surfaces of the respective third and fourth transducer beam portions  908 ,  910  as illustrated in  FIGS. 26 and 29 . Similarly, the strain gage  934  can be mounted to the bottom surface of the fifth transducer beam portion  912 , rather than to the top of the transducer beam portion  912  as illustrated in  FIG. 26 . In general, the strain gages  930 ,  932 ,  934  are mounted to surfaces generally normal to the direction of applied vertical and/or shear forces (i.e., F X , F Y , F Z ). It is also noted that alternatively, strain gages  930  can be mounted at both opposed side surfaces of fourth transducer beam portion  910  and/or strain gages  932  can be mounted at both opposed side surfaces of the third transducer beam portion  908 . Similarly, strain gages  934  can be mounted at both the top surface and the bottom surface of the fifth transducer beam portion  912 . These strain gages  930 ,  932 ,  934  measure force either by bending moment or difference of bending moments at two cross sections. As force is applied to the ends of the load transducer  900 , the transducer beam portions bend. This bending either stretches or compresses the strain gages  930 ,  932 ,  934 , which in turn changes the resistance of the electrical current passing therethrough. The amount of change in the electrical voltage or current is proportional to the magnitude of the applied force, as applied to the L-shaped standoff portion  920 . 
     In the illustrated embodiment, each of the strain gages  930 ,  932 ,  934  comprises a full-bridge strain gage configuration (i.e., four (4) active strain gage elements wired in a Wheatstone bridge configuration), while each of the strain gages  936   a,    936   b,    938   a,    938   b,    940   a,  and  940   b  comprises a half-bridge strain gage configuration (i.e., two (2) active strain gage elements). Also, in the illustrative embodiment, the pair of strain gages  936   a,    936   b  are wired together in one Wheatstone bridge configuration (i.e., with a total of four (4) active strain gage elements), the pair of strain gages  938   a,    938   b  are wired together in another Wheatstone bridge configuration (i.e., with a total of four (4) active strain gage elements), and the pair of strain gages  940   a,    940   b  are wired together in yet another Wheatstone bridge configuration (i.e., with a total of four (4) active strain gage elements). 
       FIGS. 30-33  illustrate a load transducer  1000  according to a twelfth exemplary embodiment of the present invention. With reference to these figures, it can be seen that the load transducer  1000  is similar in many respects to the load transducer  900  of the eleventh embodiment described above. However, unlike the aforedescribed load transducer  900 , the load transducer  1000  only measures the force components of a load (i.e., F X , F Y , F Z ), rather than both the force and moment components of a load as explained above with regard to the load transducer  1000 . 
     Initially, referring to the top perspective view of  FIG. 30 , it can be seen that the load transducer  1000  generally includes a one-piece compact transducer frame  1002  having a plurality of transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012  connected to one another in succession. As best shown in the perspective views of  FIGS. 30 and 33 , the plurality of transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012  are arranged in a circumscribing pattern whereby a central one of the plurality of transducer beam portions (i.e., transducer beam portion  1004 ) is at least partially circumscribed by one or more outer ones of the plurality of beam portions (i.e., transducer beam portions  1006 ,  1008 ,  1010 ,  1012 ). In other words, the plurality of transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012  forming the load transducer  1000  are arranged in a looped configuration whereby a central one of the plurality of beam portions (i.e., transducer beam portion  1004 ) emanates from a generally central location within a footprint of the load transducer  1000  and outer ones of the plurality of beam portions (i.e., transducer beam portions  1006 ,  1008 ,  1010 ,  1012 ) are wrapped around the central one of the plurality of beam portions. As best illustrated in the perspective views of  FIGS. 30 and 33 , each of the beam portions  1008 ,  1010 ,  1012  comprise one or more load cells or transducer elements for measuring the various components of an applied force. 
     As shown in  FIGS. 30-33 , the illustrated transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012  are arranged in a generally spiral-shaped pattern that emanates from the centrally located transducer beam portion  1004 . The pattern in which the transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012  are arranged is also generally G-shaped (refer to  FIGS. 30 and 33 ). With particular reference to the perspective views of  FIGS. 30 and 33 , it can be seen that the transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012  of the load transducer  1000  are arranged in such a configuration that each of the successive transducer beam portions are disposed substantially perpendicular to the immediately preceding transducer beam portion. For example, referring to  FIG. 30 , the first transducer beam portion  1004  is disposed at the approximate center of the transducer footprint, the second transducer beam portion  1006  is connected to the first transducer beam portion  1004  and is disposed substantially perpendicular thereto, the third transducer beam portion  1008  is connected to the second transducer beam portion  1006  and is disposed substantially perpendicular thereto, the fourth transducer beam portion  1010  is connected to the third transducer beam portion  1008  and is disposed substantially perpendicular thereto, and the fifth transducer beam portion  1012  is connected to the fourth transducer beam portion  1010  and is disposed substantially perpendicular thereto. In  FIGS. 30 and 33 , it can be seen that the transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012  of the load transducer  1000  are spaced apart from one another by a generally U-shaped, central gap  1032 , which is bounded by each of the transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012 . In particular, the first transducer beam portion  1004  and the third transducer beam portion  1008 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  1032 . Similarly, the second transducer beam portion  1006  and the fourth transducer beam portion  1010 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  1032 . Also, the first transducer beam portion  1004  and the fifth transducer beam portion  1012 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  1032 . The third transducer beam portion  1008  and the fifth transducer beam portion  1012 , which are disposed generally parallel to one another, are laterally spaced apart by the gap  1032  and a segment of the first transducer beam portion  1004 . 
     Referring again to the top perspective view of  FIG. 30 , it can be seen that the first and second transducer beam portions  1004 ,  1006  of the load transducer  1000  comprise an L-shaped arrangement of mounting apertures  1020  (e.g., three (3) apertures  1020 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the load transducer  1000  to another object, such as a plate component of a force plate or force measurement assembly. The mounting apertures  1020  pass completely through the first and second transducer beam portions  1004 ,  1006 , and are provided with respective bottom bore portions  1020   a  of increased diameter (see  FIG. 33 ) in order to accommodate fasteners (e.g., screws) with fillister heads that have a larger outer diameter than the threaded portions of the fasteners. In addition, with reference again to  FIG. 30 , it can be seen that the L-shaped portion of the load transducer  1000  that is formed by the first and second transducer beam portions  1004 ,  1006  is provided with pin locating bores  1022  (e.g., two (2) bores  1022 ) formed therein for receiving locating pins that ensure the proper positioning of the load transducer  1000  on the object to which it is mounted, such as a plate component of a force plate or force measurement assembly. The locating pins are received within the pin locating bores  1022  on the load transducer  1000  and within corresponding pin locating apertures provided on the object (e.g., the force plate or force measurement assembly). As depicted in the perspective views of  FIGS. 30 and 33 , the fifth transducer beam portion  1012  of the load transducer  1000  comprises a mounting aperture  1024  (e.g., a single aperture  1024  proximate to the free end thereof) disposed therethrough for accommodating a fastener (e.g., a screw) that attaches the load transducer  1000  to another object, such as a mounting foot of a force plate or force measurement assembly. In one or more embodiments, the load transducer  1000  is connected to one or more objects in such a manner that the total load applied to the load transducer  1000  is transmitted through the transducer beam portions  1004 ,  1006 ,  1008 ,  1010 ,  1012 . 
     In the illustrative embodiment of  FIGS. 30-33 , each of the transducer beam portions  1008 ,  1010 ,  1012  is provided with a respective aperture  1014 ,  1016 ,  1018  disposed therethrough. In particular, the third transducer beam portion  1008  is provided with a generally rectangular aperture  1014  disposed vertically through the beam portion. Similarly, the fourth transducer beam portion  1010  is provided with a generally rectangular aperture  1016  disposed vertically through the beam portion. The fifth transducer beam portion  1012  is provided with a generally rectangular aperture  1018  disposed horizontally through the beam portion. The apertures  1014 ,  1016 ,  1018 , which are disposed through the respective transducer beam portions  1008 ,  1010 ,  1012 , significantly increase the sensitivity of the load transducer  1000  when a load is applied thereto by reducing the cross-sectional area of the transducer beam portions  1008 ,  1010 ,  1012  at the locations of the apertures  1014 ,  1016 ,  1018 . 
     As best shown in the perspective views of  FIGS. 30 and 33 , the illustrated load cells are located on the transducer beam portions  1008 ,  1010 ,  1012 . In the illustrated embodiment, each load cell comprises one or more strain gages  1026 ,  1028 , and  1030 . Specifically, in the illustrated embodiment, the third transducer beam portion  1008  of the load transducer  1000  comprises a strain gage  1028  disposed on a side surface thereof that is sensitive to a first shear force component (i.e., a F Y  strain gage) and substantially centered on the aperture  1014 . Turning again to  FIGS. 30 and 33 , in the illustrated embodiment, the fourth transducer beam portion  1010  of the load transducer  1000  comprises a strain gage  1026  disposed on a side surface thereof that is sensitive to a second shear force component (i.e., a F X  strain gage) and substantially centered on the aperture  1016 . With reference again to  FIGS. 30 and 33 , in the illustrated embodiment, the fifth transducer beam portion  1012  of the load transducer  1000  comprises a strain gage  1030  disposed on the top surface thereof that is sensitive to a vertical force component (i.e., a F Z  strain gage) and substantially centered on the aperture  1018 . In the illustrated embodiment, the first shear force component is generally perpendicular to the second shear force component, and each of the first and second shear force components are generally perpendicular to the vertical force component. 
     In the illustrated embodiment, the strain gages  1026 ,  1028 ,  1030  are disposed on respective outer surfaces of the transducer beam portions  1010 ,  1008 ,  1012 . The outer surfaces of the transducer beam portions  1010 ,  1008 ,  1012  on which the strain gages  1026 ,  1028 ,  1030  are disposed are generally opposite to the inner surfaces of the respective apertures  1016 ,  1014 ,  1018 . 
     As best shown in  FIGS. 30 and 33 , the illustrated load cells are mounted on top or side surfaces of the transducer beam portions  1008 ,  1010 ,  1012  between the ends of the load transducer  1000 . Alternatively, the strain gages  1028 ,  1026  can be mounted to the inner side surfaces of the respective third and fourth transducer beam portions  1008 ,  1010 , rather than to the outer side surfaces of the respective third and fourth transducer beam portions  1008 ,  1010  as illustrated in  FIGS. 30 and 33 . Similarly, the strain gage  1030  can be mounted to the bottom surface of the fifth transducer beam portion  1012 , rather than to the top of the transducer beam portion  1012  as illustrated in  FIG. 30 . In general, the strain gages  1026 ,  1028 ,  1030  are mounted to surfaces generally normal to the direction of applied vertical and/or shear forces (i.e., F X , F Y , F Z ). It is also noted that alternatively, strain gages  1026  can be mounted at both opposed side surfaces of fourth transducer beam portion  1010  and/or strain gages  1028  can be mounted at both opposed side surfaces of the third transducer beam portion  1008 . Similarly, strain gages  1030  can be mounted at both the top surface and the bottom surface of the fifth transducer beam portion  1012 . These strain gages  1026 ,  1028 ,  1030  measure force either by bending moment or difference of bending moments at two cross sections. As force is applied to the ends of the load transducer  1000 , the transducer beam portions bend. This bending either stretches or compresses the strain gages  1026 ,  1028 ,  1030 , which in turn changes the resistance of the electrical current passing therethrough. The amount of change in the electrical voltage or current is proportional to the magnitude of the applied force, as applied to the load transducer  1000 . 
     In the illustrated embodiment, each of the strain gages  1026 ,  1028 ,  1030  comprises a full-bridge strain gage configuration (i.e., four (4) active strain gage elements wired in a Wheatstone bridge configuration) for measuring the applied vertical and shear forces. 
     An exemplary embodiment of a force measurement system is illustrated in  FIGS. 34-37 . In the illustrative embodiment, the force measurement system generally comprises a force measurement assembly  1040  (i.e., a force plate) that is operatively coupled to a data acquisition/data processing device  1060  (i.e., a data acquisition and processing device or computing device that is capable of collecting, storing, and processing data). The force measurement assembly  1040  illustrated in  FIGS. 34-36  is configured to receive a subject thereon, and is capable of measuring the forces and/or moments applied to its measurement surface by the subject. 
     As shown in  FIG. 34 , the data acquisition and processing device  1060  (e.g., in the form of a laptop digital computer) generally includes a base portion  1064  with a central processing unit (CPU) disposed therein for collecting and processing the data that is received from the force measurement assembly  1040 , and a plurality of devices  1066 - 1070  operatively coupled to the central processing unit (CPU) in the base portion  1064 . Preferably, the devices that are operatively coupled to the central processing unit (CPU) comprise user input devices  1066 ,  1068  in the form of a keyboard  1066  and a touchpad  1068 , as well as a graphical user interface in the form of a laptop LCD screen  1070 . While a laptop type computing system is depicted in the embodiment of  FIG. 34 , one of ordinary skill in the art will appreciate that another type of data acquisition and processing device  1060  can be substituted for the laptop computing system such as, but not limited to, a palmtop computing device (i.e., a PDA) or a desktop type computing system having a plurality of separate, operatively coupled components (e.g., a desktop type computing system including a main housing with a central processing unit (CPU) and data storage devices, a remote monitor, a remote keyboard, and a remote mouse). 
     As illustrated in  FIG. 34 , force measurement assembly  1040  is operatively coupled to the data acquisition/data processing device  1060  by virtue of an electrical cable  1062 . In one embodiment of the invention, the electrical cable  1062  is used for data transmission, as well as for providing power to the force measurement assembly  1040 . Various types of data transmission cables can be used for cable  1062 . For example, the cable  1062  can be a Universal Serial Bus (USB) cable or an Ethernet cable. Preferably, the electrical cable  1062  contains a plurality of electrical wires bundled together, with at least one wire being used for power and at least another wire being used for transmitting data. The bundling of the power and data transmission wires into a single electrical cable  1062  advantageously creates a simpler and more efficient design. In addition, it enhances the safety of the testing environment when human subjects are being tested on the force measurement assembly  1040 . However, it is to be understood that the force measurement assembly  1040  can be operatively coupled to the data acquisition/data processing device  1040  using other signal transmission means, such as a wireless data transmission system. If a wireless data transmission system is employed, it is preferable to provide the force measurement assembly  1040  with a separate power supply in the form of an internal power supply or a dedicated external power supply. 
     Referring again to  FIG. 34 , it can be seen that the force measurement assembly  1040  of the illustrated embodiment is in the form of a force plate assembly with a single, continuous measurement surface. The force plate assembly includes a plate component  1042  supported on a plurality of load transducers  1000 ,  1000 ′. As shown in  FIGS. 34 and 35 , the plate component  1042  comprises a top measurement surface  1044 , a bottom surface  1054  disposed generally opposite to the top measurement surface  1044 , and a plurality of side surfaces  1046 ,  1048 ,  1050 ,  1052  disposed between the top and bottom surfaces  1044 ,  1054 . In the illustrated embodiment, the first side surface  1046  of the plate component  1042  is disposed generally parallel to the second side surface  1048 , and is disposed generally perpendicular to both the third side surface  1050  and the fourth side surface  1052 . The third side surface  1050  of the plate component  1042  is disposed generally parallel to the fourth side surface  1052 , and is disposed generally perpendicular to both the first side surface  1046  and the second side surface  1048 . Turning to the exploded view of  FIG. 36 , it can be seen that the bottom surface  1054  of the plate component  1042  comprises a plurality of transducer mounting recesses  1056  for accommodating respective ones of the load transducers  1000 ,  1000 ′. Also, as shown in  FIG. 36 , it can be seen that an L-shaped transducer standoff plate  1034  is provided in each of the transducer mounting recesses  1056  for spacing the top surfaces of the load transducers  1000 ,  1000 ′ from the mounting surfaces of the recesses  1056 . Referring again to the bottom perspective view of  FIG. 36 , it can be seen that each L-shaped transducer standoff plate  1034  comprises a plurality of mounting apertures  1036  (e.g., three (3) apertures  1036 ) disposed therethrough for accommodating fasteners (e.g., screws) that attach the plate component  1042  of the force measurement assembly  1040  to either the load transducer  1000  or the load transducer  1000 ′. As such, the mounting apertures  1036  in each L-shaped transducer standoff plate  1034  are substantially aligned with the mounting apertures  1020  in the load transducers  1000 ,  1000 ′ such that they correspond thereto. In addition, with reference again to  FIG. 36 , it can be seen that each L-shaped transducer standoff plate  1034  further comprises pin locating apertures  1038  (e.g., two (2) apertures  1038 ) formed therein for receiving locating pins that ensure the proper positioning of the load transducers  1000 ,  1000 ′ on the plate component  1042  of the force measurement assembly  1040 . Thus, the pin locating apertures  1038  in each L-shaped transducer standoff plate  1034  are substantially aligned with the pin locating bores  1022  in the load transducers  1000 ,  1000 ′ such that they correspond thereto. The pin locating apertures  1038  in the L-shaped transducer standoff plates  1034 , and the pin locating bores  1022  in the load transducers  1000 ,  1000 ′, collectively receive locating pins that ensure the proper positioning of the load transducers  1000 ,  1000 ′ on the plate component  1042  of the force measurement assembly  1040 . 
     In illustrated embodiment of  FIGS. 34-36 , the force measurement assembly  1040  comprises a total of four (4) load transducers  1000 ,  1000 ′ that are disposed underneath, and near each of the respective four corners (4) of the plate component  1042 . The load transducers  1000 ′ are generally the same as the load transducers  1000 , expect that they are configured as a mirror image of the load transducers  1000 . Advantageously, because the load transducers  1000 ,  1000 ′ are compact, none of the plurality of load transducers  1000 ,  1000 ′ extend substantially an entire length or width of the plate component  1042  of the force measurement assembly  1040 . The compact construction of the load transducers  1000 ,  1000 ′ not only reduces material costs because less material is used to form the load transducers  1000 ,  1000 ′, but it also allows the load transducers  1000 ,  1000 ′ to be universally used on force plates having a myriad of different lengths and widths because it is not necessary for the load transducers  1000 ,  1000 ′ to conform to the footprint size of the force plate. 
     In an alternative embodiment, rather than using the load transducers  1000 ,  1000 ′ on the force measurement assembly  1040 , the load transducers  900  described above could be provided on the force measurement assembly  1040 . Using the load transducers  900  in lieu of the load transducers  1000 ,  1000 ′ would enable the moment components of the load applied to the plate component  1042  to be measured in addition to the force components of the load. 
     In other embodiments of the invention, rather than using a force measurement assembly  1040  having a plate component  1042  with a single measurement surface  1044 , it is to be understood that a force measurement assembly in the form of a dual force plate may be alternatively employed. Unlike the single force plate assembly  1040  illustrated in  FIGS. 34-36 , the dual force plate comprises two separate plate components, each of which is configured to accommodate a respective one of a subject&#39;s feet thereon (i.e., the left plate component accommodates the subject&#39;s left foot, whereas the right plate component accommodates the subject&#39;s right foot). In these alternative embodiments, each of the two plate components of the dual force plate are supported on four (4) load transducers  1000 ,  1000 ′ (i.e., a load transducer  1000 ,  1000 ′ is disposed in each of the respective four (4) corners of each of the two plate components). As such, the dual force plate comprises a total of eight (8) load transducers  1000 ,  1000 ′ (i.e., four (4) load transducers  1000 ,  1000 ′ under each of the two plate components). 
     Also, as shown in  FIGS. 34-36 , the force measurement assembly  1040  is provided with a plurality of support feet  1058  disposed thereunder. Preferably, each of the four (4) corners of the force measurement assembly  1040  is provided with a support foot  1058  (e.g., mounted on the bottom of each load transducer  1000 ,  1000 ′). In particular, in the illustrated embodiment, each support foot  1058  is attached to an aperture  1024  in a respective one of the load transducers  1000 ,  1000 ′ by means of a fastener (e.g., a screw). In one embodiment, at least one of the support feet  1058  is adjustable so as to facilitate the leveling of the force measurement assembly  1040  on an uneven floor surface. 
     Now, turning to  FIG. 37 , it can be seen that the data acquisition/data processing device  1060  (i.e., the laptop computing device) of the force measurement system comprises a microprocessor  1060   a  for processing data, memory  1060   b  (e.g., random access memory or RAM) for storing data during the processing thereof, and data storage device(s)  1060   c,  such as one or more hard drives, compact disk drives, floppy disk drives, flash drives, or any combination thereof. As shown in  FIG. 37 , the force measurement assembly  1040  and the visual display device  1070  are operatively coupled to the core components  1060   a,    1060   b,    1060   c  of the data acquisition/data processing device  1060  such that data is capable of being transferred between these devices  1040 ,  1060   a,    1060   b,    1060   c,  and  1070 . Also, as illustrated in  FIG. 37 , a plurality of data input devices  1066 ,  1068  such as the keyboard  1066  and mouse  1068  shown in  FIG. 34 , are operatively coupled to the core components  1060   a,    1060   b,    1060   c  of the data acquisition/data processing device  1060  so that a user is able to enter data into the data acquisition/data processing device  1060 . In some embodiments, the data acquisition/data processing device  1060  can be in the form of a laptop computer, while in other embodiments, the data acquisition/data processing device  1060  can be embodied as a desktop computer. 
       FIG. 38  graphically illustrates the acquisition and processing of the load data carried out by the exemplary force measurement system of  FIG. 34 . Initially, as shown in  FIG. 38 , a load L is applied to the force measurement assembly  1040  (e.g., by a subject disposed thereon). The load is transmitted from the plate component  1042  to the load transducers  1000 ,  1000 ′ disposed in each of its four (4) corners. As described above, in the illustrated embodiment, each of the load transducers  1000 ,  1000 ′ includes a plurality of strain gages  1026 ,  1028 ,  1030  wired in one or more Wheatstone bridge configurations, wherein the electrical resistance of each strain gage is altered when the associated beam portion of the load transducer  1000 ,  1000 ′ undergoes deformation resulting from the load (i.e., forces and/or moments) acting on the plate component  1042 . For each plurality of strain gages disposed on the load transducers  1000 ,  1000 ′, the change in the electrical resistance of the strain gages brings about a consequential change in the output voltage of the Wheatstone bridge (i.e., a quantity representative of the load being applied to the measurement surface  1044 ). Thus, in one embodiment, the four (4) load transducers  1000 ,  1000 ′ disposed under the plate component  1042  output a total of twelve (12) analog output voltages (signals). In some embodiments, the twelve (12) analog output voltages from load transducers  1000 ,  1000 ′ disposed under the plate component  1042  are then transmitted to a preamplifier board (not shown) for preconditioning. The preamplifier board is used to increase the magnitudes of the transducer analog voltages, and preferably, to convert the analog voltage signals into digital voltage signals as well. After which, the force measurement assembly  1040  transmits the force plate output signals S FPO1 -S FP12  to a main signal amplifier/converter  1072 . Depending on whether the preamplifier board also includes an analog-to-digital (A/D) converter, the force plate output signals S FPO1 -S FP12  could be either in the form of analog signals or digital signals. The main signal amplifier/converter  1072  further magnifies the force plate output signals S FPO1 -S FP12,  and if the signals S FPO1 -S FP12  are of the analog-type (for a case where the preamplifier board did not include an analog-to-digital (A/D) converter), it may also convert the analog signals to digital signals. Then, the signal amplifier/converter  1072  transmits either the digital or analog signals S ACO1 -S AC12  to the data acquisition/data processing device  1060  (computer  1060 ) so that the forces and/or moments that are being applied to the measurement surface  1044  of the force measurement assembly  1040  can be transformed into output load values OL. In addition to the components  1060   a,    1060   b,    1060   c,  the data acquisition/data processing device  1060  may further comprise an analog-to-digital (A/D) converter if the signals S ACO1 -S AC12  are in the form of analog signals. In such a case, the analog-to-digital converter will convert the analog signals into digital signals for processing by the microprocessor  1060   a.    
     When the data acquisition/data processing device  1060  receives the voltage signals S ACO1 -S AC12 , it initially transforms the signals into output forces by multiplying the voltage signals S ACO1 -S AC12  by a calibration matrix. If the load transducer  900  is used in conjunction with the force measurement assembly  1040 , the data acquisition/data processing device  1060  may additionally transform the signals into output moments by multiplying the voltage signals by the calibration matrix. After which, the force exerted on the surface  1044  of the force measurement assembly  1040 , and the center of pressure of the applied force (i.e., the x and y coordinates of the point of application of the force applied to the measurement surface  1044 ) is determined by the data acquisition/data processing device  1060 . Referring to the perspective view of  FIG. 34 , it can be seen that the center of pressure coordinates (x P     L   , y P     L   ) for the plate component  1042  of the force measurement assembly  1040  are determined in accordance with x and y coordinate axes  1074 ,  1076 . 
     In one exemplary embodiment, the data acquisition/data processing device  1060  determines all three (3) orthogonal components of the resultant forces acting on the plate component  1042  of the force measurement assembly  1040  (i.e., F X , F Y , F Z ). In yet other embodiments of the invention, all three (3) orthogonal components of the resultant forces and moments acting on the plate component  1042  of the force measurement assembly  1040  (i.e., F X , F Y , F Z , M X , M Y , M Z ,) may be determined (i.e., when the load transducer  900  is used in lieu of the load transducers  1000 ,  1000 ′). 
     Any of the features or attributes of the above described embodiments and variations can be used in combination with any of the other features and attributes of the above described embodiments and variations as desired. 
     It is apparent from the above detailed description that the present invention provides a low profile six-component load transducer  10 ,  10 ′,  100 ,  200 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800  which has a significant allowable offset for the line of action of the force. In that, for a given allowable maximum load, this load transducer has a much higher moment capacity than currently available load transducers and the offset value can be as high as five times the diameter (or width dimension) of the transducer. Therefore, the load transducer  10 ,  10 ′,  100 ,  200 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800  according to the present invention is able to withstand and measure moments which are approximately ten times higher than that of a similarly sized and rated conventional load cell. 
     Also, it is readily apparent that the embodiments of the load transducer  900 ,  1000 ,  1000 ′ and the force measurement assembly  1040  using the same offer numerous advantages and benefits. In particular, the load transducer  900 ,  1000 ,  1000 ′ described herein is capable of being interchangeably used with a myriad of different force plate sizes so that load transducers that are specifically tailored for a particular force plate size are unnecessary. Moreover, the universal load transducer  900 ,  1000 ,  1000 ′ described herein is compact and uses less stock material than conventional load transducers, thereby resulting in lower material costs. Furthermore, the aforedescribed force measurement assembly  1040  utilizes the compact and universal load transducer  900 ,  1000 ,  1000 ′ thereon so as to result in a more lightweight and portable force measurement assembly. 
     From the foregoing disclosure and detailed description of certain preferred embodiments, it is also apparent that various modifications, additions and other alternative embodiments are possible without departing from the true scope and spirit of the present invention. The embodiments discussed were chosen and described to provide the best illustration of the principles of the present invention and its practical application to thereby enable one of ordinary skill in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the present invention as determined by the appended claims when interpreted in accordance with the benefit to which they are fairly, legally, and equitably entitled.