SPREAD BRIDGE XY FORCE SENSOR

A force sensor comprising a beam having a longitudinal center axis and a neutral axis that extends along a beam surface parallel to the center axis. A first half-bridge includes tension resistors. A second half-bridge includes tension resistors. A third half-bridge includes compression resistors. A fourth half-bridge includes compression resistors. The half-bridges are arranged on the beam surface such that redundant measurements of orthogonal components of a force imparted to the beam can be made using four different combinations of three of the half-bridges. The redundant measurements can be used to identify a malfunction of one or more of the resistors.

BACKGROUND

Force sensing and feedback during a minimally invasive surgical procedure may bring better immersion, realism and intuitiveness to a surgeon performing the procedure. For the best performance of haptics rendering and accuracy, force sensors may be placed on a surgical instrument and as close to the anatomical tissue interaction as possible. One approach is to embed a force sensor at a distal end of a surgical instrument shaft with electrical strain gauges formed on the force transducer, through overlay of a conducive sheet having cut-out circuit pattern, printing or additive deposition processes, for example, to measure strain imparted to the surgical instrument.

FIG.1is an illustrative drawing representing a prior force sensor that includes a rectangular beam with four full-Wheatstone bridges (full-bridges). A typical bridge circuit includes an electrical circuit topology in which two circuit branches (usually in parallel with each other) are bridged by a third branch between the first two branches to provide an offset voltage between the two branches at some intermediate point along them. The illustrative force sensor includes two full-bridges on each of two adjacent orthogonal sides of the beam to measure forces orthogonal to a longitudinal axes of the beam. The beam can be secured to a distal portion of a surgical instrument shaft to sense forces orthogonal to a longitudinal axis of the shaft. For example, a forces applied orthogonal to a side of the beam (i.e. an X or Y force) can be determined by subtracting force measurements determined by the full-bridges at proximal and distal end portions of that side of the beam.

A force sensor can experience a variety of different strain sources including: an orthogonal force of interest to be measured, moment, off axis force, off axis moment, compression/tension, torsion, ambient temperature and gradient temperature. Each of the example full-bridges can cancel the following stress: temperature, torsion, off axis force, and off axis moment. Each individual full-bridge output can indicate stress due to force, moment, and compression/tension. In the example force sensor, the subtraction of an output value produced by a proximal full-bridge formed on a side from an output value produced by a distal full-bridge on the same side, can cancel a moment, resulting in an output value that represents the orthogonal force of interest to be measured.

A surgical instrument force sensor can be critical to ensuring patient safety. Accordingly, force sensor error detection can be required to protect against harm by detecting force sensor failures. One approach to error detection can be to provide additional full-bridges to produce redundant force measurements that can be compared to detect errors. However, limited space on beam sides can make adding more full-bridges on a side impractical. Moreover, some manufacturing processes typically are limited to formation of bridges at most on two sides. Formation of bridges on four sides increases manufacturing cost significantly.

SUMMARY

A force sensor includes a beam with four Wheatstone half-bridges (“half bridges”) located on a beam surface. The beam includes a proximal portion and a distal portion, a longitudinal center axis and a neutral axis that extends along a beam surface parallel to the center axis. First and second half-bridges include tension resistors. Third and fourth half-bridges include compression resistors. The first and third half-bridges are arranged along a first side axis. The second and fourth half-bridges are arranged along a second a side axis. The first and second side axes extend along the beam surface parallel to the neutral axis on opposite sides of the neutral axis and equidistant from the neutral axis.

Each of four combinations of the three half-bridges can be used to produce separate measurements of orthogonal components of a force imparted to the beam. Comparison of the separate measurements provides an indication of whether one or more of the half-bridges has a malfunction. A malfunction is reported as a sensor error.

DETAILED DESCRIPTION

Spread Bridge Adjacent Sided XY Force Sensor

FIG.2is an illustrative side view of a distal portion of an example surgical instrument202with an elongated shaft204, shown in partially cut way, and a force sensor205. The force sensor205is mounted to a distal end portion of the shaft204and includes a beam206having multiple strain gauge resistors212located thereon. The surgical instrument202includes an end effector208, which can include articulatable jaws, for example. During a surgical procedure, the end effector208contacts anatomical tissue, which can result in imparting of X, Y, or Z direction forces to the force sensor206and that may result in moment forces such as a moment My about a Y-direction axis, for example. The force sensor205, which includes a longitudinal axis210, can be used to measure X and Y forces perpendicular to the longitudinal axis210.

FIG.3Ais an illustrative perspective view of an example force sensor302that includes a rectangular beam304with spread Wheatstone bridge circuits located on each of two adjacent sides thereof. A first full-Wheatstone bridge352(indicated by dashed lines) includes first (RP1), second (RD1), third (RP2), and fourth (RD2) resistors. A second full-Wheatstone bridge354(indicated by dashed lines) includes fifth (RP3), sixth (RD3), seventh (RP4), and eighth (RD4) resistors. In an example first full-Wheatstone bridge352, the first and second resistors are coupled in a first half bridge, and the third and fourth resistors are coupled in a second half bridge. In an example second full-Wheatstone bridge, the fifth and sixth resistors are coupled in a third half bridge, and the seventh and eighth resistors are coupled in a fourth half bridge. An (X, Y, Z) beam coordinate system305is shown to explain force directions relative to the beam304. An example beam304can have a rectangular cross-section with planar side faces. More particularly, an example beam can have a square cross-section. The beam304includes a proximal beam portion304P and a distal beam portion304D and includes a longitudinal center axis306extending between the proximal and distal beam portions. The force sensor302includes example resistors RP1-RP4and RD1-RD4that have matching resistor values.

The resistors can be placed on the beam304manually or using automated machinery and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly on to the beam304. In both cases, an electrical circuit can be completed externally using wirebonds and flexible printed circuit.

A first proximal strain gauge resistor (‘resistor’) RP1and a second proximal resistor RP2are located at a proximal beam portion304P of a first side308of the beam304. A first distal resistor RD1and a second distal resistor RD2are located at a distal beam portion of the first side308of the beam304. A first set of resistors RP1-RP2and RD1-RD2located on the first side308of the beam are arranged in a first spread full-Wheatstone bridge, explained below. A third proximal resistor RP3and a fourth proximal resistor RP4are located at a proximal beam portion304P of a second side310of the beam304. A third distal resistor RD3and a fourth distal resistor RD4are located at a distal beam portion304D of the second side310of the beam304. The first side308of the example beam304is adjacent to the second side310of the example beam304. A second set of resistors RP3-RP4and RD3-RD4are arranged in a second spread full-Wheatstone bridge, explained below.

As explained more fully below, the first and second full-bridge circuits are ‘spread’ in that portions of each bridge circuit are laterally spaced apart from one another on the beam304. For example, each full-bridge can include two half-bridges that are laterally spread apart from each other. An advantage of laterally spreading apart the half-bridges is that conductor traces that couple resistors to bias voltages or to one another, for example, can be routed to pass through the middle of a face of a beam304or close a neutral axis of the beam304, on each face of the beam. Alternatively, in a circular cross-section beam (not shown), conductor traces advantageously can be routed along the neutral axes of individual half-bridges. This routing helps reduce strain on the traces and in turn improves the accuracy of the sensor, by rejecting unwanted signal. As explained more fully below, the first and second proximal resistors RP1, RP2and the first and second distal resistors RD1, RD2located at the first side308of the beam304act as Y-direction force sensor elements, and the third and fourth proximal resistors RP3, RP4and the third and fourth distal resistors RD3, RD4located at the second side310of the beam act as X-direction force sensor elements.

Each of resistors RP1-RP4and RD1-RD4is the same type of strain gauge resistor. More particularly in the example force sensor302described herein, the resistors RP1-RP4and RD1-RD4are tension type gauge resistors used to measure tensile strain. In an alternative example force sensor, the set of resistors can be compression type gauge resistors used to measure compression strain. As used herein reference to a set resistors having ‘matching type’ refers to a set of resistors in which either all resistors are tension resistors or all resistors are compression resistors. Resistors that have matching type are more likely to have similar sensitivity and performance, making a sensor better suited for situation of low signal to noise ratio where the common mode cancellation is crucial and much better. In general, although either tension or compression gauge resistors can be used to determine X direction and Y direction forces, which are orthogonal to each other, tension strain gauge resistors, in general, are more sensitive than compression gauge resistors.

FIG.3Bshows the illustrative perspective view of the force sensor302ofFIG.3Athat further shows an imaginary first plane P1and an imaginary second plane P2. The first proximal resistor RP1and the first distal resistor RD1are arranged upon the first side of the beam304within the first imaginary plane P1in which the center axis extends306and that defines a first lateral side axis312at a location on the first side308of the beam304along which the first plane P1intersects the first side. The first lateral axis312and the center axis306extend parallel to one another. An example first lateral side axis312extends through the first proximal resistor RP1and through the first distal resistor RD1. Moreover, an example first lateral side axis312bisects the example first proximal resistor RP1and bisects an example first distal resistor RD1.

Still referring toFIG.3B, the second proximal resistor RP2and the second distal resistor RD2are arranged upon the first side of the beam304within a second imaginary plane P2in which the center axis306extends and that defines a second lateral side axis314at a location on the first side308of the beam304along which the second plane P2intersects the first side308. The second later axis314and the center axis306extend parallel to one another. An example second lateral side axis314extends through the second proximal resistor RP2and through the second distal resistor RD2. Moreover, an example second lateral side axis314bisects the example second proximal resistor RP2and bisects an example second distal resistor RD2.

FIG.3Cshows the illustrative perspective view of the force sensor302ofFIG.3Athat further shows an imaginary third plane P3and an imaginary fourth plane P4. The third proximal resistor RP3and the third distal resistor RD3are arranged upon the second side310of the beam304, (adjacent to the first side308, within the third imaginary plane P3in which the center axis306extends and that defines a third lateral side axis316at a location on the second side310of the beam304along which the third plane P3intersects the second side310. An example third lateral side axis316extends through the third proximal resistor RP3and through the third distal resistor RD3. Moreover, an example third side axis bisects the example third proximal resistor RP3and bisects an example third distal resistor RD3.

Still referring toFIG.3C, the fourth proximal resistor RP4and the fourth distal resistor RD4are arranged upon the second side310of the beam304within a fourth imaginary plane P4in which the center axis306extends and that defines a fourth lateral side axis318at a location on the second side310of the beam304along which the fourth plane P4intersects the second side310of the beam304and that includes the center axis306. An example fourth lateral side axis318extends through the fourth proximal resistor RP4and through the fourth distal resistor RD4. More particularly, an example fourth lateral side axis bisects an example fourth proximal resistor RP4and bisects an example first distal resistor RD4.

FIG.4is an illustrative proximal direction cross-section view of the example beam304ofFIGS.3A-3Bshowing intersection of the imaginary planes at the longitudinal center axis306.FIG.5Ais a side view showing arrangement of resistors RP1-RP2, RD1-RD2on the first side308of the beam304.FIG.5Bis a side view showing arrangement of resistors RP3-RP4, RD3-RD4on the second side310of the beam304.

Referring toFIG.4, the proximal direction end view of the beam304shows side views of the imaginary first through fourth planes P1-P4that intersect along the longitudinal center axis306. The (X, Y, Z) beam coordinate system305is shown to explain force directions relative to the beam304. It is noted that inFIG.4, the Z axis is shown emerging from the page. The first and second planes P1, P2are separated from one another about the center axis by a first separation angle A1. The second and third imaginary planes are separated from one another by a second separation angle B1. In an example force sensor302, the first separation angle equals the second separation angle.

Referring toFIG.5A, the first plane P1is shown extending through the first proximal resistor RP1and the first distal resistor RD1, which are arranged along the first lateral side axis312on the first side308of the beam304, and the second plane P2is shown extending through the second proximal resistor RP2and the second distal resistor RD2, which are arranged along the second lateral side axis314on the first side308of the beam304. The (X, Y, Z) beam coordinate system305is shown to explain force directions relative to the beam304. It is noted that inFIG.5A, the X axis is shown directed into the page. Size of the first separation angle A1corresponds to lateral spacing distance at the first side308, between the first and second lateral side axes312,314, and therefore, corresponds to lateral spacing between the a first resistor pair including the first proximal and distal resistors RP1, RD1and a second resistor pair including the second proximal and distal resistors RP2, RD2. In an example force sensor302the first lateral side axis312and the second lateral side axis314are equidistant from a neutral axis315of the first side308of the beam304, which extends within the first side face and which is equidistant from the opposite lateral edges of the first side308, although equidistant spacing is not required.

Referring toFIG.5B, the third plane P3is shown extending through the third proximal resistor RP3and the third distal resistor RD3, which are arranged along the third lateral side316axis on the second side310of the beam304, and the fourth plane P4is shown extending through the fourth proximal resistor RP4and the fourth distal resistor RD4, which are arranged along the fourth lateral side axis318of the beam304on the second side310of the beam304. The (X, Y, Z) beam coordinate system305is shown to explain force directions relative to the beam304. It is noted that inFIG.5B, the Y axis is shown emerging from the page. Size of the second separation angle B1corresponds to lateral spacing distance at the second side310, between the third and fourth lateral side axes316,318, and therefore, corresponds to lateral spacing between a third resistor pair including the third proximal and distal resistors RP3, RD3, and a fourth resistor pair including the fourth proximal and distal resistors RP4, RD4are arranged. In an example force sensor302the third lateral side axis316and the fourth lateral side axis318are equidistant from a neutral axis319of the second side310of the beam304, which extends within the second side face and which is equidistant from the opposite lateral edges of the second side310.

Thus, a first pair of resistors, RP1, RD1and a second pair of resistors, RP2, RD2are positioned upon the first side308of the beam304laterally spread apart. In an example beam304, the first pair of resistors is positioned in alignment with the first lateral side axis312and the second pair or resistors is positioned in alignment with the second lateral side axis314, and the first and second lateral side axes are equally laterally spaced apart from and on opposite sides of the neutral axis315of the first side of the beam304. More particularly, the first pair of resistors is positioned in alignment with the first lateral side axis312and the second pair or resistors is positioned in alignment with the second lateral side axis314. Moreover, a third pair of resistors, RP3, RD3and a fourth pair of resistors, RP4, RD4are positioned upon the second side310of the beam304laterally spread apart. In an example beam304, the third pair of resistors is positioned in alignment with the third lateral side axis316and the fourth pair or resistors is positioned in alignment with the fourth lateral side axis318, and the first and second lateral side axes316,318are equally laterally spaced apart from, and on opposite sides of, the neutral axis319of the second side of the beam304. More particularly, the third pair of resistors is positioned in alignment with the third lateral side axis316and the fourth pair or resistors is positioned in alignment with the fourth lateral side axis318.

In an example force sensor, proximal and distal resistors that are part of the same full-bridge are laterally aligned. Moreover, in an example force sensor, spacing between the first and second lateral side axis matches spacing between the third and fourth lateral side axes. In an example force sensor, the proximal resistors RP1-RP4are positioned at matching longitudinal locations of the beam. In an example force sensor, the distal resistors RD1-RD4are positioned at matching longitudinal locations of the beam.

As explained below, resistors of the first bridge352are arranged laterally separated to measure force in a first direction perpendicular to the beam center axis306, based upon off-neutral axis forces imparted along the first and second planes P1, P2. Similarly, resistors of the second bridge354are arranged laterally to measure force in a second direction that is perpendicular to the beam center axis306and perpendicular to the first direction, based upon measuring off-axis forces imparted along the second and third planes P3, P4. As shown inFIG.8A, lateral separation of the resistors of the first bridge352makes possible routing of first center conductor traces356parallel to the beam center axis306in a region of the beam304between proximal and distal resistors of the first bridge352. Likewise, lateral separation of the resistors of the second bridge352makes possible routing of second center conductor traces358parallel to the beam center axis306in a region of the beam304between proximal and distal resistors of the second bridge354.

FIG.6Ais an illustrative side elevation view of an example beam304showing an first example layout topology of an example full-Wheatstone bridge602. The first example full-Wheatstone bridge layout includes resistors RPA-RPBand RDA-RDB. In an example force sensor304, the resistors RP1-RP2and RD1-RD2located on the first side308of the beam304can be coupled consistent with the topology of the first full-Wheatstone bridge layout, and likewise, resistors RP3-RP4and RD3-RD4located on the second side310of the beam304can be coupled consistent with the topology of the first full-Wheatstone bridge layout. The first Wheatstone bridge layout is coupled in a first configuration to input bias voltage conductors (EP, EN) and output voltage conductors (Vo−, Vo+).FIG.6Bis an illustrative first schematic circuit diagram604representation of the full-Wheatstone bridge layout topology. Referring toFIGS.6A-6B, the first proximal resistor RPAis electrically coupled between a positive first DC electrical potential (EP) and a second (also referred to as ‘negative’ potential) output Vo−. The second proximal resistor RPBis electrically coupled between a negative second DC electrical potential (EN) and the second output Vo−. The first distal resistor RDAis electrically coupled between the positive first DC electrical potential (EP) and a first output Vo+ (also referred to as a ‘positive’ output). The second distal resistor RDBis electrically coupled between the negative second DC electrical potential (EN) and the first output Vo+.

FIG.7Ais an illustrative side elevation view of an example beam304showing a second circuit layout toplogy of an example full-Wheatstone bridge702. The second example full-Wheatstone bridge layout includes resistors RPA-RPBand RDA-RDB. In an example force sensor304, the resistors RP1-RP2and RD1-RD2located on the first side308of the beam304can be coupled consistent with the topology of the second full-Wheatstone bridge layout, and likewise, resistors RP3-RP4and RD3-RD4located on the second side310of the beam304can be coupled consistent with the topology of the second full-Wheatstone bridge layout. The second Wheatstone bridge layout is coupled in a second configuration to input bias voltage conductors (EP, EN) and output voltage conductors (Vo−, Vo+).FIG.7Bis an illustrative first schematic circuit diagram704representation of the second full-Wheatstone bridge layout topology. Referring toFIGS.7A-7B, the first proximal resistor RPAis electrically coupled between the positive first DC electrical potential (EP) and the first output Vo+. The second proximal resistor RPBis electrically coupled between the positive first DC electrical potential (EP) and the second output Vo−. The first distal resistor RDAis electrically coupled between the negative second DC electrical potential (EN) and the first output Vo+. The second distal resistor RDBis electrically coupled between the negative second DC electrical potential (EN) and the second output Vo−.

In general, the layout inFIG.6Ais better for reducing the number of traces that must span the length of the beam and also reduces the effect of traces picking up strain. On the other hand, the layout inFIG.7Alayout is preferred if the force sensor uses half bridge voltage measurements.

FIG.8Ais an illustrative flattened side view of two adjacent sides of an example beam304showing a spread layout of first and second full-Wheatstone bridges352,354and routing of center conductor traces356,358that extend within the centers of the bridges, between proximal and distal resistors of the bridges. The first bridge352is located at a first side304-1of the beam304. The second bridge354is located at a second side304-2of the beam304. The first and second sides304-1,304-2share a side edge303of the beam304.

The first full Wheatstone bridge352includes RP1, RP2and distal resistors RD1, RD2and has a first neutral axis362that extends parallel to the beam axis306between proximal resistors RP1, RP2and the distal resistors RD1, RD2. In an example first bridge, the first neutral is equally spaced from each of RP1and RP2and is equally spaced from each of RD1and RD2. The first bridge352is longitudinally split in that the proximal resistors RP1, RP2are longitudinally separated from the distal resistors RD1, RD2. The first bridge is laterally spread in that proximal resistors RP1, RP2are laterally spread apart and the distal resistors RD1, RD2are laterally spread apart from one another. The second full Wheatstone bridge354has a first neutral axis364that extends along the outer surface of the beam304parallel to the beam axis306between proximal resistors RP3, RP4and between distal resistors RD3, RD4. In an example second bridge, the second neutral is equally spaced from each of RP3and RP4and is equally spaced from each of RD3and RD4. The second bridge354is longitudinally split in that the proximal resistors RP3, RP4are longitudinally separated from the distal resistors RD3, RD4. The second bridge is laterally spread in that proximal resistors RP3, RP4are laterally spread apart and the distal resistors RD3, RD4are laterally spread apart from one another.

It will be appreciated that since the resistors of the first full-Wheatstone bridge352are laterally spread apart, they do not occupy the first neutral axis362. Likewise, since the resistors of the second full-Wheatstone bridge354are laterally spread apart, they do not occupy the second neutral axis364. Therefore conductor traces can be routed close to and in parallel with the first and second neutral axes362,364, which can reduce the amount of strain imparted to the traces. Also, routing of traces along the neutral axis of a bridge circuit can be easier to produce to manufacture or assembly.

An example first full-bridge includes a first group of center conductor traces356that extend longitudinally along a center portion of the first bridge352, parallel to the first neutral axis362, along a region of the outer surface304-1of the beam304between the pair of proximal resistors RP1, RP2and the pair of distal resistors RD1, RD2of the first bridge352. The first group of center traces356include trace segments356-1coupled to a first positive output voltage VO1+. The first group of center traces356includes trace segments356-1coupled to a first negative voltage output VO1−. The first group of center traces356include trace segments356-3coupled to a negative voltage potential EN.

Similarly, an example second full-bridge includes a second group of center conductor traces358that extend longitudinally along a center portion of the second bridge354, parallel to the second neutral axis364, along a region of the outer surface304-2of the beam304between the pair of proximal resistors RP3, RP4and the pair of distal resistors RD3. RD4of the second bridge352. The second group of center traces358include trace segments358-1coupled to a second positive output voltage VO2+. The second group of center traces358include trace segments358-2coupled to a second negative voltage output VO2−. The second group of center traces358include trace segments358-3coupled to the negative voltage potential EN.

FIG.8Bis an illustrative first schematic circuit diagram representation of the first and second full-Wheatstone bridges ofFIG.8A. The first full-Wheatstone bridge352includes RP1and RD1coupled between EP and EN to provide a first half-bridge voltage divider circuit that includes a trace conductor coupled to the first positive output voltage VO1+. The first full-Wheatstone bridge352also includes RP2and RD2coupled between EP and EN to provide a second half-bridge voltage divider circuit that includes a trace conductor coupled to the first negative output voltage VO1−. The second full-Wheatstone bridge354includes RP3and RD3coupled between EP and EN to provide a third half-bridge voltage divider circuit that includes a trace conductor coupled to the second negative output voltage VO2−. The second full-Wheatstone bridge354also includes RP4and RD4coupled between EP and EN to provide a fourth half-bridge voltage divider circuit that includes a trace conductor coupled to the second positive output voltage VO2+.

FIG.9Ais an illustrative cross-sectional end view of the example beam304ofFIG.4indicating the resistors on the first side and indicating a first plane force FP1and a second plane force FP2.FIG.9Bis an illustrative force diagram that indicates orthogonal X and Y force components of the first plane force FP1imparted to the first proximal resistor RP1and the first distal resistor RD1in response to an applied force F.FIG.9Cis an illustrative force diagram that indicates X and Y force components of the second plane force FP2imparted to the second proximal resistor RP2and the second distal resistor RD2in response to the applied force F.

In an example force sensor302, resistance values of the first pair of resistors, RP1, RD1, match resistance values of the second pair of resistors, RP2, RD2. In an example force sensor302, the first and second pairs of resistors are positioned upon an example beam304, such that an applied force F imparted to the example beam304imparts a first plane strain force FP1to the first pair of resistors within the first plane P1and imparts a second plane strain force FP2to the second pair of resistors within the second plane P2. It will be appreciated that the first plane strain force FP1is an off-axis force since it is a force imparted along the first lateral side axis312, which is laterally offset from a neutral axis315of the first bridge352. Likewise, it will be appreciated that the second plane strain force FP2is an off-axis force since it is a force imparted along the second lateral side axis314, which is laterally offset from a neutral axis315of the first bridge352. The first and second pairs of resistors are positioned upon an example beam304, such that a magnitude of the components of the first plane strain force FP1matches a magnitude of the components of the second plane strain force FP2. Force directions of the first plane strain force FP1and second plane strain force FP2are separated from one another by the first separation angle ‘A’.

An advantage of using strain gauge resistors of the same type is that magnitude of a force imparted perpendicular to the center axis306of a beam304can be determined based upon a difference in magnitude of off-axis forces imparted to the different half-bridges of a full-bridge located on the beam. In the example force sensor302, magnitude of a Y-direction force component FYimparted to the beam304by an applied force F can be determined based upon difference between the first off-axis force FP1and the second off-axis force FP2as follows.

Let A be angle between P1and P2.

Let X axis bisect the angle A. Therefore, an angle between P1and X is A/2 and an angle between P2and X is A/2.

Let θ be an angle between the X axis and an applied force F.

Force along X axis Fx=F cos θ

Force along y axis Fy=F sin θ

we get

When we subtract FP1and FP2

Thus, the difference between FP1and FP2is proportional to the Y-direction force component FYimparted to the beam by the applied force F.

Moreover, it will be appreciated that,

where VS1O+is positive output voltage and VS1O−is negative output voltage of the first bridge circuit352, and VS1O+−VS1O−is a voltage offset produced by the first bridge circuit352located on the first side308of the beam304.

FIG.10is an illustrative cross-sectional end view of the example beam ofFIG.4indicating the resistors on the second side310of the beam304and indicating third plane X-force and fourth plane X-force. In an example force sensor302, resistance values of the third pair of resistors, RP3, RD3, match resistance values of the fourth pair of resistors, RP4, RD4. In an example force sensor302, the third and fourth pairs of resistors are positioned upon an example beam304, such that an applied force imparted to the example beam304imparts a third plane strain force FP3to the third pair of resistors within the third plane P3and imparts a fourth plane strain force FP4to the fourth pair of resistors within the fourth plane P4. It will be appreciated that the third plane strain force FP3is an off-axis force since it is a force imparted along the third lateral side axis316, which is laterally offset from a neutral axis315of the second bridge354. Likewise, it will be appreciated that the fourth plane strain force FP4is an off-axis force since it is a force imparted along the fourth lateral side axis318, which laterally is offset from a neutral axis315of the second bridge354. The third and fourth pairs of resistors are positioned upon an example beam304, such that a magnitude of the components of third plane strain force FP3matches a magnitude of the components of fourth plane strain force FP4. Force directions of the third plane strain force FP3and the fourth plane strain force FP4are separated from one another by the second separation angle A.

In this example, the difference between FP3and FP4is proportional to the X-direction force component Fximparted to the beam by the applied force F. Persons skilled in the art will understand the process for determining the difference between FP3and FP4based upon the above explanation of a determination of a difference between FP1and FP2.

Moreover, it will be appreciated that,

where VS2O+is the positive output voltage and VS2O−is the negative output voltage of the second bridge354and VS2O+−VS2O−is a voltage offset produced by the second bridge circuit354on the second side310of the beam304.

FIG.11is an illustrative drawing representing a metal sheet1102containing cut-outs that define example resistors RP1-RP4and RD1-RD4for assembly into respective first and second full-Wheatstone bridges on adjacent first and second sides308,310of the beam304. A first region1104of the metal sheet1102includes resistors RP1-RP2and RD1-RD2for coupling in a first full-bridge configuration located on the first side308of the beam304. A second region1106of the metal sheet1102includes resistors RP3-RP4and RD3-RD4for coupling in a second full-bridge configuration located on the second (Y-axis) side of an example beam. The first and second refion are separated by a fold line1108.

FIG.12Ais an illustrative drawing representing a process of folding the metal sheet1102at the fold line1108to wrap the first and second regions of the metal sheet about a beam304to position first pair of resistors RP1-RP2and RD1-RD2at the side308of the beam304and to position the second pair of resistors RP3-RP4and RD3-RD4at the second side310of the beam304.FIG.12Bis an illustrative perspective view of the beam304showing the first and second regions1104-1106of the metal sheet1102overlaying respective first and second sides308-310of an example beam304. In an example rectangular beam, the first and second sides include adjacent side faces of the beam. The metal sheet1102can be glued on or welded on to the beam304or a combination of both. During the attachment process caution is taken to line up the metal sheet1102with the beam304.

Redundant Multiple Half-Bridge XY Force Sensor

In a sensor having four half-bridges and all gauges of same type on first and reverse sides, subtracting the half bridge voltages of adjacent two half bridges provides a force measurement in the axis parallel to the plane having all the gauges of the two half bridge. There are four ways to do this which provides two measurements of Fx and Fy.

FIG.13A-13Bshow an illustrative first side perspective view (FIG.13A) and second side perspective view (FIG.13B) of an example force sensor2302that includes a rectangular beam2304with two four strain gauge resistors RP1-RP4, RD1-RD4coupled in two half Wheatstone bidge circuits (‘half-bridges”) located on each of two reverse sides thereof. A second side308of the beam2304shown inFIG.13Bfaces in a direction that is reverse of a direction faced by a first side308of the beam2304shown inFIG.13A. An (X, Y, Z) beam coordinate system2305is provided to explain force directions relative to the beam2304. An example beam2304can have a rectangular cross-section with planar side faces. More particularly, an example beam can have a square cross-section. The beam2304includes a proximal beam portion2304P and a distal beam portion2304D and includes a longitudinal center axis306extending between the proximal and distal beam portions2304P,2304D.

Referring toFIG.13A, a first proximal strain gauge resistor (‘resistor’) RP1and a second proximal resistor RP2are located at the proximal beam portion2304P of the first side308of the beam2304. A first distal resistor RD1and a second distal resistor RD2are located at the distal beam portion2304D of the first side308of the beam2304. As explained below with reference toFIGS.14A-4B,15A-15B, a first pair of resistors, RP1-RD1, are electrically coupled in series and arranged in a first half-bridge, and a second pair of resistors, RP2-RD2, are electrically coupled in series and arranged in a second half-bridge.

Referring toFIG.13B, a third proximal resistor RP3and a fourth proximal resistor RP4are located at the proximal beam portion2304P of the second side2310(also referred to as the ‘reverse’ side) of the beam2304that faces in a reverse direction to a direction faced by the first side308of the beam2304. A third distal resistor RD3and a fourth distal resistor RD4are located at a distal beam portion2304D of the reverse second side2310of the beam2304. As explained below with reference toFIGS.14A-14B,15A-15B, a third pair of resistors, RP3-RD3, are electrically coupled in series and arranged in a third half-bridge, and a fourth pair of resistors, RP4-RD4, are electrically coupled in series and arranged in a fourth half-bridge arranged in a fourth half-bridge.

FIG.14Ais an illustrative side view of an example beam including a first example half-bridge circuit layout2402having proximal and distal tension gauge strain resistors RTP, RTDelectrically coupled in series and having a voltage node coupled between them. The first example half-bridge bridge circuit layout2402includes input bias voltage conductors (EP, EN) and output an voltage node (Vo) between the proximal and distal tension resistors RTP, RTD.FIG.14Bis an illustrative first schematic circuit diagram2404representation of the first half-bridge circuit layout2402. Referring toFIGS.14A-14B, a proximal tension resistor RTPis electrically coupled between a positive first DC electrical potential (EP) and an output voltage node Vo. A distal tension resistor RTDis electrically coupled between a negative second DC electrical potential (EN) and the output voltage node Vo. In an example force sensor2302, each of the first, second, third and fourth half-bridges has a layout2402and circuit schematic2404represented inFIGS.14A-14B.

FIG.15Ais an illustrative side view of an example beam showing a second example half-bridge circuit layout2502having proximal and distal compression gauge strain resistors RCP, RCDelectrically coupled in series and having a voltage node coupled between them. The second example half-bridge bridge circuit layout2502includes input bias voltage conductors (EP, EN) and output an voltage node (Vo) between the proximal and distal compression resistors RCP, RCD.FIG.15Bis an illustrative second schematic circuit diagram2504representation of the second half-bridge circuit layout2502. Referring toFIGS.15A-15B, a proximal compression resistor RCPis electrically coupled between a positive first DC electrical potential (EP) and an output voltage node Vo. A distal compression resistor RCDis electrically coupled between a negative second DC electrical potential (EN) and the output voltage node Vo. In another example force sensor2302, each of the first, second, third and fourth half-bridges has a layout2502and circuit schematic2504represented inFIGS.15A-15B.

As shown inFIGS.14A-14BandFIGS.15A-15B, each half-bridge of an example force sensor2302includes a pair of strain gauge resistors having matching type, which can be either tension type (FIGS.14A-14B) or compression type (FIGS.15A-15B). As used herein reference to a set resistors having ‘matching type’ refers to a set of resistors in which either all resistors are tension resistors or all resistors are compression resistors. Although either tension or compression gauge resistors can be used to determine X direction and Y direction forces, in general, tension strain gauge resistors are more sensitive than compression gauge resistors.

Referring again toFIGS.13A-13B, as explained more fully below, a voltage offset between a first half-bridge voltage at a first voltage node between the first pair of resistors RP1, RD1and a second half-bridge voltage at a second voltage node between the second pair of resistors RP2, RD2can be used to measure X-direction force imparted to the beam2304. Additionally, a voltage offset between the third half-bridge voltage at a third voltage node between the third pair of resistors RP3, RD3and a fourth half-bridge voltage at a fourth voltage node between the fourth pair of resistors RP4, RD4can be used to measure X-direction force imparted to the beam2304. Thus, together, the first, second, third, and fourth half-bridges provide redundant measures of X-direction force upon the beam.

Further, as explained more fully below, a voltage offset between the first half-bridge voltage at a first voltage node between the first pair of resistors RP1, RD1and the fourth half-bridge voltage at the fourth voltage node between the fourth pair of resistors RP4, RD4can be used to measure Y-direction force imparted to the beam2304. Additionally, an offset between the second half-bridge voltage at the second voltage node between the second pair of resistors RP2, RD2and the third half-bridge voltage at the third voltage node between the third pair of resistors RP3, RD3can be used to measure Y-direction force imparted to the beam2304.

Thus, together, the first, second, third, and fourth half-bridges can provide redundant measures of X-direction force upon the beam2304and can provide redundant measures of Y-direction forces upon the beam2304. A malfunction of any one of resistors RP1-RP4and RD1-RD4results in differences in X-direction force measurements determined using the first and second half-bridges on the one hand and X-direction force determined measurements using the third and fourth half-bridges on the other. Similarly, a malfunction of any one of resistors RP1-RP4and RD1-RD4results in differences in Y-direction force measurements determined using the first and fourth half-bridges on the one hand and Y-direction force measurements determined using the second and third half-bridges on the other.

Still referring toFIG.13A, the first proximal resistor RP1and the first distal resistor RD1are arranged upon the first side308of the beam2304within a first imaginary plane P1in which the center axis306extends and that defines a first lateral side axis2312at a location on the first side308of the beam2304along which the first plane P1intersects the first side308. The first lateral side axis2312and the center axis306extend parallel to one another. An example first lateral side axis2312extends through the first proximal resistor RP1and through the first distal resistor RD1. More particularly in an example force sensor, the example first lateral side axis2312bisects the example first proximal resistor RP1and bisects the example first distal resistor RD1.

Referring toFIG.13A, the second proximal resistor RP2and the second distal resistor RD2are arranged upon the first side308of the beam within a second imaginary plane P2in which the center axis306extends and that defines a second lateral side axis2314at a location on the first side308of the beam2304along which the second plane P2intersects the first side. The second lateral axis2314and the center axis306extend parallel to one another. An example second lateral side axis2314extends through the second proximal resistor RP2and through the second distal resistor RD2. More particularly in an example force sensor, the example second lateral side axis bisects2314the example second proximal resistor RP2and bisects an example second distal resistor RD2.

Referring toFIG.13B, the third proximal resistor RP3and the third distal resistor RD3are arranged upon the reverse second side2310of the beam2304within the first imaginary plane P1, in which the center axis extends306, and that defines a third lateral side axis2316at a location on the second side2310of the beam2304along which the first plane P1intersects the second side2310. An example third lateral side axis2316extends through the third proximal resistor RP3and through the third distal resistor RD3. More particularly in an example force sensor, the example third side axis2316bisects the example third proximal resistor RP3and bisects an example third distal resistor RD3.

Referring toFIG.13B, the fourth proximal resistor RP4and the fourth distal resistor RD4are arranged upon the reverse second side2310of the beam2304within the second imaginary plane P2, in which the center axis306extends, and that defines a fourth lateral side axis2318at a location on the second side2310of the beam2304along which the second plane P2intersects the second side2310of the beam2304and that includes the center axis306. An example fourth lateral side axis2318extends through the fourth proximal resistor RP4and through the fourth distal resistor RD4. More particularly in an example force sensor, the example fourth lateral side axis bisects an example fourth proximal resistor RP4and bisects an example first distal resistor RD4.

FIG.16is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bshowing the first and second imaginary planes P1, P2.FIG.17Ais a side view of the beam2304showing the first side308of the beam ofFIGS.13A-13B, which includes first (RP1) and second (RD1) and second resistors coupled in a first half-bridge HB1and includes third (RP2) and fourth (RD2) resistors coupled in a second half-bridge HB2.FIG.17Bis a side view of the beam2304showing the reverse second side308of the beam ofFIGS.13A-13B, which includes A second bridge includes fifth (RP3) and sixth (RD3) resistors coupled in a third half-bridge HB3and includes seventh (RP4) and eighth (RD4) resistors coupled in a fourth half-bridge HB4.

The resistors can be placed on the beam2304manually or using automated machinery and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly on to the beam2304. In both cases, an electrical circuit can be completed externally using wirebonds and flexible printed circuit.

Referring toFIG.16, a proximal direction end view of the beam2304shows side views of the first and second planes P1, P2that intersect one another along the center axis306, which extends within both the first and second planes. The first plane P1extends through the first and third half-bridges HB1, HB3and through the center axis306. The second plane P1extends through the second and fourth half bridges HB2, HB4and through the center axis306. Portions of the first and second planes P1, P2that extend through the respective first and second half bridges HB1, HB2intersect the center axis306separated by a first separation angle A1. Portions of the first and second planes P1, P2that extend through the respective third and fourth half bridges HB3, HB4also intersect the center axis306separated by the first separation angle A1.

Referring toFIG.17A, the first plane P1is shown extending through the first half bridge HB1, which includes the first (proximal resistor RP1and the first distal resistor RD1, which are arranged along the first lateral side axis2312on the first side308of the beam2304, and the second plane P2is shown extending through the second half-bridge HB2, which includes the second proximal resistor RP2and the second distal resistor RD2, which are arranged along the second lateral side axis2314on the first side308of the beam2304. Size of the first separation angle A1corresponds to lateral spacing distance at the first side308, between the first and second lateral side axes2312,2314, and therefore, corresponds to lateral spacing between the first half-bridge HB1including the first proximal and distal resistors RP1, RD1and a second resistor pair including the second proximal and distal resistors RP2, RD2. In an example force sensor2302, the first lateral side axis2312and the second lateral side axis2314are equidistant from a neutral axis of the first side of the beam2304, which is equidistant from the first and second lateral side edges2312,2314of the first side308of the beam2304.

Referring toFIG.17B, the first plane P1is shown extending through the third half bridge HB3, which includes the third proximal resistor RP3and the third distal resistor RD3, which are arranged along the third lateral side axis2316on the second side2310of the beam2304, and the second plane P2is shown extending through the fourth half bridge HB4, which includes the fourth proximal resistor RP4and the fourth distal resistor RD4, which are arranged along the fourth lateral side axis2318on the second side2310of the beam2304. Size of the first separation angle A1corresponds to lateral spacing distance at the second side2310of the beam2304, between the third and fourth lateral side axes2316-2318, and therefore, corresponds to lateral spacing between the third half-bridge HB3including the third resistor pair including RP3, RD3, and the fourth half-bridge HB4including the fourth resistor pair including RP4, RD4. In an example force sensor the third lateral side axis2316and the fourth lateral side axis2318are equidistant from a neutral axis of the second side2310of the beam2304, which is equidistant from the third and fourth lateral side edges2316,2318of the second side2310of the beam2304.

The half-bridges HB1-HB4are laterally located symmetrically about the beam2304. separation angle A1between the first and second half-bridges matches the first separation angle A1between the third and fourth half-bridges HB3-HB4. Moreover, in an example force sensor2302, spacing between the first and second lateral side axes2312,2314matches spacing between the third and fourth lateral side axes2316,2318, although equidistant spacing is not required. The half-bridges HB1-HB4are longitudinally located symmetrically along the beam2304. Proximal resistors RP1-RP4are positioned at matching longitudinal locations of the beam. In an example force sensor, the distal resistors RD1-RD4are positioned at matching longitudinal locations of the beam.

FIG.18Ais an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a second plane strain force FP2and a third plane strain force FP3imparted to the respective second and third half-bridges HB2, HB3by an applied force F upon the beam2304. In the example beam ofFIG.18A, the second and third half-bridges HB2, HB3contain only tension resistors.FIG.18Bis an illustrative force diagram that indicates X and Y force components of the second plane strain force FP2imparted to the second half-bridge HB2that includes the second proximal resistor RP2and the second distal resistor RD2, in response to the applied force F.FIG.18Cis an illustrative force diagram that indicates orthogonal X and Y force components of the third plane strain force FP3imparted to the third half-bridge HB3, which includes the third proximal resistor RP3and the third distal resistor RD3, in response to the applied force.

In an example force sensor2302, resistance values of the second pair of resistors, RP2, RD2, of the second half-bridge HB2match resistance values of the third pair of resistors, RP3, RD3, of the third half-bridge HB3. In an example force sensor2302, the second and third half-bridges HB2, HB3are positioned upon an example beam2304, such that an applied force imparted to the example beam2304imparts a second plane strain force FP2to the second half-bridge HB2within the second plane P2and imparts a third plane strain force FP3to the third half-bridge HB3within the third plane P3. It will be appreciated that the second plane strain force FP2is an off-axis force since it is a force imparted along the second lateral side axis2314. Likewise, it will be appreciated that the third plane strain force FP3is an off-axis force since it is a force imparted along the third lateral side axis2316. In an example force sensor2302, the second and third half-bridges HB2, HB3are positioned upon an example beam2304, such that a magnitude of the components of second plane strain force FP2matches magnitude of the components of third plane strain force FP3.

An advantage of using strain gauge resistors of the same type is that magnitude of a force imparted perpendicular to the center axis306of a beam2304can be determined based upon a difference in magnitude of off-axis forces imparted to the different half-bridges of a full-bridge located on the beam. In the the example force sensor2302, magnitude of a Y-direction force component FYimparted to the beam2304by an applied force F can be determined based upon difference between the first off-axis force FP2and the second off-axis force FP3as follows.

Let A be angle between P2and P3.

Let X axis bisect the angle A. Therefore, an angle between P2and X is A/2 and an angle between P3and X is A/2.

Let θ be an angle between the X axis and an applied force F.

Force along X axis Fx=F cos θ

Force along y axis Fy=F sin θ

we get

When we subtract FP1and FP2

Thus, the difference between FP2and FP3is proportional to the Y-direction force component FYimparted to the beam by the applied force F.

Moreover, it will be appreciated that,

where VO2the output voltage of HB2and VO3is the output voltage of HB3.

FIG.19is an illustrative proximal direction cross-section view of the example beam ofFIGS.13A-13Bindicating a first plane strain force FP1and a fourth plane strain force FP4imparted to the respective first and fourth half-bridges HB1, HB4by an applied force F upon the beam2304. In the example beam ofFIG.19, the first and fourth half-bridges HB1, HB4contain only tension resistors resistors. In an example force sensor2302, resistance values of the first pair of resistors, RP1, RD1, of the first half-bridge HB1match resistance values of the fourth pair of resistors, RP4, RD4, of the fourth half-bridge HB4. In an example force sensor2302, the first and fourth half-bridges HB1, HB4are positioned upon an example beam2304, such that an applied force F imparted to the example beam2304imparts a first plane strain force FP1to the first half-bridge HB1within the first plane P1and imparts a fourth plane strain force FP4to the fourth half-bridge HB4within the second plane P4. In an example force sensor2302, the first and fourth half-bridges HB1, HB4are positioned upon an example beam2304, such that a magnitude of components of the first plane strain force FP1matches a magnitude of components of the fourth plane strain force FP4.

In this example, the difference between FP1and FP4is proportional to the Y-direction force component FYimparted to the beam by the applied force F. Persons skilled in the art will understand the process for determining the difference between FP1and FP4based upon the above explanation of a determination of a difference between FP2and FP3.

Moreover, it will be appreciated that,

where VO1the output voltage of HB1and VO4is the output voltage of HB4.

FIG.20is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a first plane strain force FP1and a second plane strain force FP2imparted to the respective first and second half-bridges HB1, HB2by an applied force upon the beam2304. In an example force sensor2302, resistance values of the first pair of resistors, RP1, RD1, of the first half-bridge HB1match resistance values of the second pair of resistors, RP2, RD2, of the second half-bridge HB2. In an example force sensor2302, the first and second half-bridges HB1, HB2are positioned upon an example beam2304, such that an applied force imparted to the example beam2304imparts a first plane strain force FP1to the first half-bridge HB1within the first plane P1and imparts a second plane strain force FP2to the second half-bridge HB2within the second plane P2. It will be appreciated that the first plane strain force FP1is an off-axis force since it is a force imparted along the first lateral side axis2312. Likewise, it will be appreciated that the second plane strain force FP2is an off-axis force since it is a force imparted along the second lateral side axis2314. The first and second half-bridges HB1, HB2are positioned upon an example beam2304, such that a magnitude of the first plane strain force FP1Xmatches a magnitude of the second plane strain force FP2. Force directions of the first plane strain force FP1Xand the first plane P1are separated from one another by the first separation angle A1.

In this example, the difference between FP1and FP2is proportional to the X-direction force component Fximparted to the beam by the applied force F. Persons skilled in the art will understand the process for determining the difference between FP1and FP2based upon the above explanation of a determination of a difference between FP2and FP3.

Moreover, it will be appreciated that,

where VO1the output voltage of HB1and VO2is the output voltage of HB2.FIG.21is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a third plane strain force FP3and a fourth plane strain force FP4imparted to the respective third and fourth half-bridges HB3, HB4by an applied force FXupon the beam. In an example force sensor2302, resistance values of the third pair of resistors, RP3, RD3, of the third half-bridge HB3match resistance values of the fourth pair of resistors, RP4, RD4, of the fourth half-bridge HB4. In an example force sensor2302, the third and fourth half-bridges HB3, HB4are positioned upon an example beam2304, such that an applied force imparted to the example beam2304imparts a third plane strain force FP3to the third half-bridge HB3within the third plane P3and imparts a fourth plane strain force FP4to the fourth half-bridge HB4within the fourth plane P4. It will be appreciated that the third plane strain force FP3is an off-axis force since it is a force imparted along the third lateral side axis2316. Likewise, it will be appreciated that the fourth plane strain force FP4is an off-axis force since it is a force imparted along the fourth lateral side axis2318. In an example force sensor2302, the third and fourth half-bridges HB3, HB4are positioned upon an example beam2304, such that a magnitude of theFIG.21is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a third plane strain force FP3and a fourth plane strain force FP4imparted to the respective third and fourth half-bridges HB3, HB4by an applied force FXupon the beam.

In this example, the difference between FP3and FP4is proportional to the X-direction force component FXimparted to the beam by the applied force F. Persons skilled in the art will understand the process for determining the difference between FP3and FP4based upon the above explanation of a determination of a difference between FP2and FP3.

Moreover, it will be appreciated that,

where VO3the output voltage of HB3and VO4is the output voltage of HB4.

Furthermore, it will be appreciated that FXand FYcan be determined more generally based upon each one of the following four combinations of three half-bridges (HBs) set forth in the following Table 1.

Thus, the half-bridge combinations in the above Table 1 can be used to make redundant determinations of FXand FY. A comparison of the FXand FYvalues determined based upon the above combinations of half-bridges can be used to determine whether the force sensor2304contains a malfunctioning resistor. If even a single resistor malfunctions, then then all four combinations would produce different FXand FYvalues thus indicating failure. Since all four HBs would produce different results in the event of a failure, it will not be possible to determine the failing resistor. Adding one or more additional half-bridges to the beam can be used to achieve an error-tolerant design in that comparisons of five or more combinations of three bridges can be used to make a determination as to which half-bridge is defective, whereupon and measurements from the defective half-bridge can be ignored.

Redundant Single Sided XY Force Sensor

An example single sided XY force sensor includes a beam that includes four half-bridges located on a single side thereof. Two half-bridges are one of compression type and two half-bridges are tension type. Since compression and tension strain gauge resistors measure experience opposite direction strain in response to a force imparted to the beam, measurements by a combination of three half-bridges located on the same side of the beam in which one of the three has a different strain gauge resistor type than the other two can be used to measure both X-direction forces and Y-direction forces. The example single sided XY force sensor that includes four half-bridges, in which two are compression type and two are tension type, can perform redundant XY measurements.

In a sensor having four half-bridges and all gauges of same type on first and reverse sides, subtracting the half bridge voltages of adjacent two half bridges provides a force measurement in the axis parallel to the plane having all the gauges of the two half bridge. There are four ways to do this which provides two measurements of Fx and Fy.

FIG.13A-13Bshow an illustrative first side perspective view (FIG.13A) and second side perspective view (FIG.13B) of an example force sensor2302that includes a rectangular beam2304with two four strain gauge resistors RP1-RP4, RD1-RD4coupled in two half Wheatstone bidge circuits (‘half-bridges”) located on each of two reverse sides thereof. A second side308of the beam2304shown inFIG.13Bfaces in a direction that is reverse of a direction faced by a first side308of the beam2304shown inFIG.13A. An (X, Y, Z) beam coordinate system2305is provided to explain force directions relative to the beam2304. An example beam2304can have a rectangular cross-section with planar side faces. More particularly, an example beam can have a square cross-section. The beam2304includes a proximal beam portion2304P and a distal beam portion2304D and includes a longitudinal center axis306extending between the proximal and distal beam portions2304P,2304D.

Referring toFIG.13A, a first proximal strain gauge resistor (‘resistor’) RP1and a second proximal resistor RP2are located at the proximal beam portion2304P of the first side308of the beam2304. A first distal resistor RD1and a second distal resistor RD2are located at the distal beam portion2304D of the first side308of the beam2304. As explained below with reference toFIGS.14A-4B,15A-15B, a first pair of resistors, RP1-RD1, are electrically coupled in series and arranged in a first half-bridge, and a second pair of resistors, RP2-RD2, are electrically coupled in series and arranged in a second half-bridge.

Referring toFIG.13B, a third proximal resistor RP3and a fourth proximal resistor RP4are located at the proximal beam portion2304P of the second side2310(also referred to as the ‘reverse’ side) of the beam2304that faces in a reverse direction to a direction faced by the first side308of the beam2304. A third distal resistor RD3and a fourth distal resistor RD4are located at a distal beam portion2304D of the reverse second side2310of the beam2304. As explained below with reference toFIGS.14A-14B,15A-15B, a third pair of resistors, RP3-RD3, are electrically coupled in series and arranged in a third half-bridge, and a fourth pair of resistors, RP4-RD4, are electrically coupled in series and arranged in a fourth half-bridge arranged in a fourth half-bridge.

FIG.14Ais an illustrative side view of an example beam including a first example half-bridge circuit layout2402having proximal and distal tension gauge strain resistors RTP, RTDelectrically coupled in series and having a voltage node coupled between them. The first example half-bridge bridge circuit layout2402includes input bias voltage conductors (EP, EN) and output an voltage node (Vo) between the proximal and distal tension resistors RTP, RTD.FIG.14Bis an illustrative first schematic circuit diagram2404representation of the first half-bridge circuit layout2402. Referring toFIGS.14A-14B, a proximal tension resistor RTPis electrically coupled between a positive first DC electrical potential (EP) and an output voltage node Vo. A distal tension resistor RTDis electrically coupled between a negative second DC electrical potential (EN) and the output voltage node Vo. In an example force sensor2302, each of the first, second, third and fourth half-bridges has a layout2402and circuit schematic2404represented inFIGS.14A-14B.

FIG.15Ais an illustrative side view of an example beam showing a second example half-bridge circuit layout2502having proximal and distal compression gauge strain resistors RCP, RCDelectrically coupled in series and having a voltage node coupled between them. The second example half-bridge bridge circuit layout2502includes input bias voltage conductors (EP, EN) and output an voltage node (Vo) between the proximal and distal compression resistors RCP, RCD.FIG.15Bis an illustrative second schematic circuit diagram2504representation of the second half-bridge circuit layout2502. Referring toFIGS.15A-15B, a proximal compression resistor RCPis electrically coupled between a positive first DC electrical potential (EP) and an output voltage node Vo. A distal compression resistor RCDis electrically coupled between a negative second DC electrical potential (EN) and the output voltage node Vo. In another example force sensor2302, each of the first, second, third and fourth half-bridges has a layout2502and circuit schematic2504represented inFIGS.15A-15B.

As shown inFIGS.14A-14BandFIGS.15A-15B, each half-bridge of an example force sensor2302includes a pair of strain gauge resistors having matching type, which can be either tension type (FIGS.14A-14B) or compression type (FIGS.15A-15B). As used herein reference to a set resistors having ‘matching type’ refers to a set of resistors in which either all resistors are tension resistors or all resistors are compression resistors. Although either tension or compression gauge resistors can be used to determine X direction and Y direction forces, in general, tension strain gauge resistors are more sensitive than compression gauge resistors.

Referring again toFIGS.13A-13B, as explained more fully below, a voltage offset between a first half-bridge voltage at a first voltage node between the first pair of resistors RP1, RD1and a second half-bridge voltage at a second voltage node between the second pair of resistors RP2, RD2can be used to measure X-direction force imparted to the beam2304. Additionally, a voltage offset between the third half-bridge voltage at a third voltage node between the third pair of resistors RP3, RD3and a fourth half-bridge voltage at a fourth voltage node between the fourth pair of resistors RP4, RD4can be used to measure X-direction force imparted to the beam2304. Thus, together, the first, second, third, and fourth half-bridges provide redundant measures of X-direction force upon the beam.

Further, as explained more fully below, a voltage offset between the first half-bridge voltage at a first voltage node between the first pair of resistors RP1, RD1and the fourth half-bridge voltage at the fourth voltage node between the fourth pair of resistors RP4, RD4can be used to measure Y-direction force imparted to the beam2304. Additionally, an offset between the second half-bridge voltage at the second voltage node between the second pair of resistors RP2, RD2and the third half-bridge voltage at the third voltage node between the third pair of resistors RP3, RD3can be used to measure Y-direction force imparted to the beam2304.

Thus, together, the first, second, third, and fourth half-bridges can provide redundant measures of X-direction force upon the beam2304and can provide redundant measures of Y-direction forces upon the beam2304. A malfunction of any one of resistors RP1-RP4and RD-RD4results in differences in X-direction force measurements determined using the first and second half-bridges on the one hand and X-direction force determined measurements using the third and fourth half-bridges on the other. Similarly, a malfunction of any one of resistors RP1-RP4and RD1-RD4results in differences in Y-direction force measurements determined using the first and fourth half-bridges on the one hand and Y-direction force measurements determined using the second and third half-bridges on the other.

Still referring toFIG.13A, the first proximal resistor RP1and the first distal resistor RD1are arranged upon the first side308of the beam2304within a first imaginary plane P1in which the center axis306extends and that defines a first lateral side axis2312at a location on the first side308of the beam2304along which the first plane P1intersects the first side308. The first lateral side axis2312and the center axis306extend parallel to one another. An example first lateral side axis2312extends through the first proximal resistor RP1and through the first distal resistor RD1. More particularly in an example force sensor, the example first lateral side axis2312bisects the example first proximal resistor R pi and bisects the example first distal resistor RD1.

Referring toFIG.13A, the second proximal resistor RP2and the second distal resistor RD2are arranged upon the first side308of the beam within a second imaginary plane P2in which the center axis306extends and that defines a second lateral side axis2314at a location on the first side308of the beam2304along which the second plane P2intersects the first side. The second lateral axis2314and the center axis306extend parallel to one another. An example second lateral side axis2314extends through the second proximal resistor RP2and through the second distal resistor RD2. More particularly in an example force sensor, the example second lateral side axis bisects2314the example second proximal resistor RP2and bisects an example second distal resistor RD2.

Referring toFIG.13B, the third proximal resistor RP3and the third distal resistor RD3are arranged upon the reverse second side2310of the beam2304within the first imaginary plane P1, in which the center axis extends306, and that defines a third lateral side axis2316at a location on the second side2310of the beam2304along which the first plane P1intersects the second side2310. An example third lateral side axis2316extends through the third proximal resistor RP3and through the third distal resistor RD3. More particularly in an example force sensor, the example third side axis2316bisects the example third proximal resistor RP3and bisects an example third distal resistor RD3.

Referring toFIG.13B, the fourth proximal resistor RP4and the fourth distal resistor RD4are arranged upon the reverse second side2310of the beam2304within the second imaginary plane P2, in which the center axis306extends, and that defines a fourth lateral side axis2318at a location on the second side2310of the beam2304along which the second plane P2intersects the second side2310of the beam2304and that includes the center axis306. An example fourth lateral side axis2318extends through the fourth proximal resistor RP4and through the fourth distal resistor RD4. More particularly in an example force sensor, the example fourth lateral side axis bisects an example fourth proximal resistor RP4and bisects an example first distal resistor RD4.

FIG.16is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bshowing the first and second imaginary planes P1, P2.FIG.17Ais a side view of the beam2304showing the first side308of the beam ofFIGS.13A-13B, which includes first (RP1) and second (RD1) and second resistors coupled in a first half-bridge HB1and includes third (RP2) and fourth (RD2) resistors coupled in a second half-bridge HB2.FIG.17Bis a side view of the beam2304showing the reverse second side308of the beam ofFIGS.13A-13B, which includes A second bridge includes fifth (RP3) and sixth (RD3) resistors coupled in a third half-bridge HB3and includes seventh (RP4) and eighth (RD4) resistors coupled in a fourth half-bridge HB4.

The resistors can be placed on the beam2304manually or using automated machinery and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly on to the beam2304. In both cases, an electrical circuit can be completed externally using wirebonds and flexible printed circuit.

Referring toFIG.16, a proximal direction end view of the beam2304shows side views of the first and second planes P1, P2that intersect one another along the center axis306, which extends within both the first and second planes. The first plane P1extends through the first and third half-bridges HB1, HB3and through the center axis306. The second plane P1extends through the second and fourth half bridges HB2, HB4and through the center axis306. Portions of the first and second planes P1, P2that extend through the respective first and second half bridges HB1, HB2intersect the center axis306separated by a first separation angle A1. Portions of the first and second planes P1, P2that extend through the respective third and fourth half bridges HB3, HB4also intersect the center axis306separated by the first separation angle A1.

Referring toFIG.17A, the first plane P1is shown extending through the first half bridge HB1, which includes the first (proximal resistor RP1and the first distal resistor RD1, which are arranged along the first lateral side axis2312on the first side308of the beam2304, and the second plane P2is shown extending through the second half-bridge HB2, which includes the second proximal resistor RP2and the second distal resistor RD2, which are arranged along the second lateral side axis2314on the first side308of the beam2304. Size of the first separation angle A1corresponds to lateral spacing distance at the first side308, between the first and second lateral side axes2312,2314, and therefore, corresponds to lateral spacing between the first half-bridge HB1including the first proximal and distal resistors RP1, RD1and a second resistor pair including the second proximal and distal resistors RP2, RD2. In an example force sensor2302, the first lateral side axis2312and the second lateral side axis2314are equidistant from a neutral axis of the first side of the beam2304, which is equidistant from the first and second lateral side edges2312,2314of the first side308of the beam2304.

Referring toFIG.17B, the first plane P1is shown extending through the third half bridge HB3, which includes the third proximal resistor RP3and the third distal resistor RD3, which are arranged along the third lateral side axis2316on the second side2310of the beam2304, and the second plane P2is shown extending through the fourth half bridge HB4, which includes the fourth proximal resistor RP4and the fourth distal resistor RD4, which are arranged along the fourth lateral side axis2318on the second side2310of the beam2304. Size of the first separation angle A1corresponds to lateral spacing distance at the second side2310of the beam2304, between the third and fourth lateral side axes2316-2318, and therefore, corresponds to lateral spacing between the third half-bridge HB3including the third resistor pair including RP3, RD3, and the fourth half-bridge HB4including the fourth resistor pair including RP4, RD4. In an example force sensor the third lateral side axis2316and the fourth lateral side axis2318are equidistant from a neutral axis of the second side2310of the beam2304, which is equidistant from the third and fourth lateral side edges2316,2318of the second side2310of the beam2304.

The half-bridges HB1-HB4are laterally located symmetrically about the beam2304. separation angle A1between the first and second half-bridges matches the first separation angle A1between the third and fourth half-bridges HB3-HB4. Moreover, in an example force sensor2302, spacing between the first and second lateral side axes2312,2314matches spacing between the third and fourth lateral side axes2316,2318, although equidistant spacing is not required. The half-bridges HB1-HB4are longitudinally located symmetrically along the beam2304. Proximal resistors RP1-RP4are positioned at matching longitudinal locations of the beam. In an example force sensor, the distal resistors RD1-RD4are positioned at matching longitudinal locations of the beam.

FIG.18Ais an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a second plane strain force FP2and a third plane strain force FP3imparted to the respective second and third half-bridges HB2, HB3by an applied force F upon the beam2304. In the example beam ofFIG.18A, the second and third half-bridges HB2, HB3contain only tension resistors.FIG.18Bis an illustrative force diagram that indicates orthogonal X and Y force components of the second plane strain force FP2imparted to the second half-bridge HB2that includes the second proximal resistor RP2and the second distal resistor RD2, in response to the applied force F.FIG.18Cis an illustrative force diagram that indicates orthogonal X and Y force components of the third plane strain force FP3imparted to the third half-bridge HB3, which includes the third proximal resistor RP3and the third distal resistor RD3, in response to the applied force.

In an example force sensor2302, resistance values of the second pair of resistors, RP2, RD2, of the second half-bridge HB2match resistance values of the third pair of resistors, RP3, RD3, of the third half-bridge HB3. In an example force sensor2302, the second and third half-bridges HB2, HB3are positioned upon an example beam2304, such that an applied force imparted to the example beam2304imparts a second plane strain force FP2to the second half-bridge HB2within the second plane P2and imparts a third plane strain force FP3to the third half-bridge HB3within the third plane P3. It will be appreciated that the second plane strain force FP2is an off-axis force since it is a force imparted along the second lateral side axis2314. Likewise, it will be appreciated that the third plane strain force FP3is an off-axis force since it is a force imparted along the third lateral side axis2316. In an example force sensor2302, the second and third half-bridges HB2, HB3are positioned upon an example beam2304, such that a magnitude of the components of second plane strain force FP2matches magnitude of the components of third plane strain force FP3.

An advantage of using strain gauge resistors of the same type is that magnitude of a force imparted perpendicular to the center axis306of a beam2304can be determined based upon a difference in magnitude of off-axis forces imparted to the different half-bridges of a full-bridge located on the beam. In the the example force sensor2302, magnitude of a Y-direction force component FYimparted to the beam2304by an applied force F can be determined based upon difference between the first off-axis force FP2and the second off-axis force FP3as follows.

Let A be angle between P2and P3.

Let X axis bisect the angle A. Therefore, an angle between P2and X is A/2 and an angle between P3and X is A/2.

Let θ be an angle between the X axis and an applied force F.

Force along X axis Fx=F cos θ

Force along y axis Fy=F sin θ

we get

When we subtract FP1and FP2

Thus, the difference between FP2and FP3is proportional to the Y-direction force component Fyimparted to the beam by the applied force F.

Moreover, it will be appreciated that,

where VO2the output voltage of HB2and VO3is the output voltage of HB3.

FIG.19is an illustrative proximal direction cross-section view of the example beam ofFIGS.13A-13Bindicating a first plane strain force FP1and a fourth plane strain force FP4imparted to the respective first and fourth half-bridges HB1, HB4by an applied force F upon the beam2304. In the example beam ofFIG.19, the first and fourth half-bridges HB1, HB4contain only tension resistors. In an example force sensor2302, resistance values of the first pair of resistors, RP1, RD1, of the first half-bridge HB1match resistance values of the fourth pair of resistors, RP4, RD4, of the fourth half-bridge HB4. In an example force sensor2302, the first and fourth half-bridges HB1, HB4are positioned upon an example beam2304, such that an applied force F imparted to the example beam2304imparts a first plane strain force FP1to the first half-bridge HB1within the first plane P1and imparts a fourth plane strain force FP4to the fourth half-bridge HB4within the second plane P4. In an example force sensor2302, the first and fourth half-bridges HB1, HB4are positioned upon an example beam2304, such that a magnitude of components of the first plane strain force FP1matches a magnitude of components of the fourth plane strain force FP4.

In this example, the difference between FP1and FP4is proportional to the Y-direction force component FYimparted to the beam by the applied force F. Persons skilled in the art will understand the process for determining the difference between FP1and FP4based upon the above explanation of a determination of a difference between FP2and FP3.

Moreover, it will be appreciated that,

where VO1the output voltage of HB1and VO4is the output voltage of HB4.

FIG.20is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a first plane strain force FP1and a second plane strain force FP2imparted to the respective first and second half-bridges HB1, HB2by an applied force upon the beam2304. In an example force sensor2302, resistance values of the first pair of resistors, RP1, RD1, of the first half-bridge HB1match resistance values of the second pair of resistors, RP2, RD2, of the second half-bridge HB2. In an example force sensor2302, the first and second half-bridges HB1, HB2are positioned upon an example beam2304, such that an applied force imparted to the example beam2304imparts a first plane strain force FP1to the first half-bridge HB1within the first plane P1and imparts a second plane strain force FP2to the second half-bridge HB2within the second plane P2. It will be appreciated that the first plane strain force FP1is an off-axis force since it is a force imparted along the first lateral side axis2312. Likewise, it will be appreciated that the second plane strain force FP2is an off-axis force since it is a force imparted along the second lateral side axis2314. The first and second half-bridges HB1, HB2are positioned upon an example beam2304, such that a magnitude of the first plane strain force FP1Xmatches a magnitude of the second plane strain force FP2. Force directions of the first plane strain force FP1Xand the first plane P1are separated from one another by the first separation angle A1.

In this example, the difference between FP1and FP2is proportional to the X-direction force component Fximparted to the beam by the applied force F. Persons skilled in the art will understand the process for determining the difference between FP1and FP2based upon the above explanation of a determination of a difference between FP2and FP3.

Moreover, it will be appreciated that,

where VO1the output voltage of HB1and VO2is the output voltage of HB2.FIG.21is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a third plane strain force FP3and a fourth plane strain force FP4imparted to the respective third and fourth half-bridges HB3, HB4by an applied force FXupon the beam. In an example force sensor2302, resistance values of the third pair of resistors, RP3, RD3, of the third half-bridge HB3match resistance values of the fourth pair of resistors, RP4, RD4, of the fourth half-bridge HB4. In an example force sensor2302, the third and fourth half-bridges HB3, HB4are positioned upon an example beam2304, such that an applied force imparted to the example beam2304imparts a third plane strain force FP3to the third half-bridge HB3within the third plane P3and imparts a fourth plane strain force FP4to the fourth half-bridge HB4within the fourth plane P4. It will be appreciated that the third plane strain force FP3is an off-axis force since it is a force imparted along the third lateral side axis2316. Likewise, it will be appreciated that the fourth plane strain force FP4is an off-axis force since it is a force imparted along the fourth lateral side axis2318. In an example force sensor2302, the third and fourth half-bridges HB3, HB4are positioned upon an example beam2304, such that a magnitude of theFIG.21is an illustrative proximal direction cross-section view of the example beam2304ofFIGS.13A-13Bindicating a third plane strain force FP3and a fourth plane strain force FP4imparted to the respective third and fourth half-bridges HB3, HB4by an applied force Fxupon the beam.

In this example, the difference between FP3and FP4is proportional to the X-direction force component Fximparted to the beam by the applied force F. Persons skilled in the art will understand the process for determining the difference between FP3and FP4based upon the above explanation of a determination of a difference between FP2and FP3.

Moreover, it will be appreciated that,

where VO3the output voltage of HB3and VO4is the output voltage of HB4.

Furthermore, it will be appreciated that FXand FYcan be determined more generally based upon each one of the following four combinations of three half-bridges (HBs) set forth in the following Table 1.

Thus, the half-bridge combinations in the above Table 1 can be used to make redundant determinations of FXand FY. A comparison of the FXand FYvalues determined based upon the above combinations of half-bridges can be used to determine whether the force sensor2304contains a malfunctioning resistor. If even a single resistor malfunctions, then then all four combinations would produce different FXand FYvalues thus indicating failure. Since all four HBs would produce different results in the event of a failure, it will not be possible to determine the failing resistor. Adding one or more additional half-bridges to the beam can be used to achieve an error-tolerant design in that comparisons of five or more combinations of three bridges can be used to make a determination as to which half-bridge is defective, whereupon and measurements from the defective half-bridge can be ignored.

Redundant Single Sided XY Force Sensor

An example single sided XY force sensor includes a beam that includes four half-bridges located on a single side thereof. Two half-bridges are one of compression type and two half-bridges are tension type. Since compression and tension strain gauge resistors measure experience opposite direction strain in response to a force imparted to the beam, measurements by a combination of three half-bridges located on the same side of the beam in which one of the three has a different strain gauge resistor type than the other two can be used to measure both X-direction forces and Y-direction forces. The example single sided XY force sensor that includes four half-bridges, in which two are compression type and two are tension type, can perform redundant XY measurements.

More generally, however, based upon any three of the four half-bridge measurements one would be able to measure Fx, Fy and temperature gradient. For a beam with four half-bridges, two tension and two compression, there are four ways to pick three of four half-bridges, and therefore, we can get four measurements of Fx and Fy and thus provide redundancy in measurement.

FIG.22shows an illustrative top perspective view of an example force sensor21102that includes a rectangular beam21104that includes two example tension resistor half-bridges and two example compression resistor half-brigs located on an outer first side surface21108thereof. An example beam21104includes a planar first side surface21108. The beam21104includes a proximal beam portion21104P and a distal beam portion21104D and includes a center axis21106extending between the proximal and distal beam portions. The two example tension half-bridges have the first circuit layout2402and the first circuit schematic2404ofFIGS.14A-14B. The two example compression half-bridges have the second circuit layout2502and the second circuit schematic2504ofFIGS.15A-15B.

A first pair of tension resistors includes a first proximal tension resistor RTP1located at the proximal beam portion21104P and a first distal tension resistor RTD1located at the distal beam portion21104D. The first proximal tension resistor RTP1and the first distal tension resistor RTD1are electrically coupled in series and arranged in a first tension half-bridge HB1T. A second pair of tension resistors includes a second proximal tension resistor (RTP2) located at the proximal beam portion21104P and a second distal tension resistor (RTD2) located at the distal beam portion21104D. The second proximal tension resistor RTP2and the second distal tension resistor RTD2are electrically coupled in series and arranged in a second tension half-bridge HB2T. A first pair of compression resistors includes a first proximal compression resistor (RCP1) located at the proximal beam portion21104P and a first distal compression resistor (RCD1) located at the distal beam portion21104D. The first proximal compression resistor (RCP1) and the first distal compression resistor (RCD1) are electrically coupled in series and arranged in a third compression resistor half-bridge HB3C. A second pair of compression resistors includes a second proximal compression resistor resistor (RCP2) located at the proximal beam portion21104P and an second distal compression resistor resistor (RCD2) located at the distal beam portion21104D. The second proximal compression resistor (RCP2) and the second distal compression resistor (RCD2) are electrically coupled in series and arranged in a fourth compression resistor half-bridge HB4c.

As will be appreciated from the explanation of illustrativeFIGS.14A-14BandFIGS.15A-15Band as explained more fully below, a respective output voltage node is located between each of the respective first pair of tension resistors RTP1, RTD1of HB1T, the respective second pair of tension resistors RTP2, RTD2of HB2T, the respective first pair of compression resistors RCP1, RCD1of HB3C, and the respective second pair of compression resistors RCP2, RCD2of HB4T. Voltage offsets between certain combinations of these different output voltages can be used to determine redundant measures of X-force imparted to the beam. Voltage offsets between certain combinations of these different output voltages can be used to determine redundant measures of Y-force imparted to the beam. A malfunction of any one of resistors RTP1, RTP2, RTD1, RTD2, RCP1, RCP2, RCD1, RCD2results in differences in redundant X-direction force measurements. Similarly, a malfunction of any one of the resistors results in differences in redundant Y-direction force measurements. A difference in the redundant X-direction force measurements and/or redundant Y-direction force measurements indicates a malfunction of the force sensor.

Still referring toFIG.22, the first proximal tension resistor RTP1, the first distal tension resistor RTD1, the first proximal compression resistor RCP1and the first distal compression resistor RCD1are arranged upon the first side21108of the beam within a first imaginary plane P1, in which the center axis21108extends, and that defines a first lateral side axis21112at a location on the first side21108of the beam21104along which the first plane P1intersects the first side21108. The first lateral side axis21112and the center axis21106extend parallel to one another. An example first lateral side axis21112extends through the first proximal and distal tension resistors RTP1-RTD1and through the first proximal and distal compression resistors RCP1-RCD1. An example first lateral side axis21112bisects the example first proximal and distal tension resistor and the example first proximal and distal compression resistors.

The second proximal tension resistor RTP2, the second distal tension resistor RTD2, the second proximal compression resistor RCP2and the second distal compression resistor RCD2are arranged upon the first side21108of the beam21104within a second imaginary plane P2, in which the center axis21106extends, and that defines a second lateral side axis21114at a location on the first side21108of the beam21104along which the second plane P2intersects the first side21108. The second lateral side axis21114and the center axis21106extend parallel to one another. An example second lateral side axis21114extends through the second proximal and distal tension resistors RTP2-RTD2and through the second proximal and distal compression resistors RCP2-RCD2. An example second lateral side axis21114bisects the example second proximal and distal tension resistor and the example second proximal and distal compression resistors.

FIG.23is an illustrative proximal direction cross-section view of the example beam21104ofFIG.22. The proximal direction end view of the beam shows side views of the first and second planes P1, P2that intersect one another along the center axis21106, which extends within both the first and second planes. The first and third half-bridges HB1T, HB3Care longitudinally aligned along one lateral edge of the beam21104, and the second and fourth half-bridges HB2T, HB4Care longitudinally aligned along an opposite edge of the beam21104. A portion of the first plane that extend through half-bridge circuits HB1T, HB3Cand a portion of the second plane P2that extends through half-bridge circuits HB2T, HB4Cintersect the center axis306separated by a first separation angle B1.

FIG.24is a side view of the outer surface first side21108of the example beam21104ofFIG.22on which the two tension resistor half bridges HB1T, HB2Tand the two compression resistor half-bridges HB3C, HB4Care located. The first plane FP1is shown extending through the first tension resistor half-bridge HB1Tcontaining the first proximal and distal tension resistors and proximal resistor RTP1, RTD1and through the third compression resistor half-bridge HB3Ccontaining the first proximal and distal compression resistors RCP1, RCD1. The second plane P2is shown extending through the second tension resistor half-bridge HB2Tcontaining the second proximal and distal tension resistors and proximal resistor RTP2, RTD2and through the fourth compression resistor half-bridge HB4Ccontaining the second proximal and distal compression resistors RCP2, RCD2. Size of the first separation angle B1corresponds to lateral spacing distance at the first side21108, between the first and second lateral side axes21112,21114, and therefore, corresponds to lateral spacing between the first tension resistor pair RP1, RD1and the first compression resistor pair RCP1, RCD1on the one hand and the second tension resistor pair RP2, RD2and the second compression resistor pair RCP2, RCD2on the other. In an example force sensor21102the first lateral side axis21112and the second lateral side axis21114are equidistant from a neutral axis21115that extends within a surface of the of the first side21108of the beam21104, parallel to the center axis21106and equidistant from opposite lateral edges of the first side21108.

The resistors of the first and third half-bridges HB1Tand HB3Care interleaved. RCD1is aligned with the first lateral side axis21112between RTD1and RTP1. RTP1is aligned along the first lateral side axis21112between between RCD1and RCP1.

The resistors of the second and fourth half-bridges HB2Tand HB4Care interleaved. RCD4is aligned with the second lateral side axis21114between RTD2and RTP2. RTP2is aligned along the second lateral side axis21114between RCD3and RCP4.

A first voltage node VO1is coupled between first tension resistor pair RTD1and RTP1. A second voltage node VO2is coupled between second tension resistor pair RTD2and RTP2. A third voltage node VO3is coupled between first compression resistor pair RCD1and RCP1. A fourth voltage node VO4is coupled between second compression resistor pair RCD2and RCP2.

In an example force sensor, the first and second proximal tension resistors RTP1, RTP2are positioned at matching longitudinal locations of the beam21104. In an example force sensor, the first and second distal resistors tension RTD1, RTD2are positioned at matching longitudinal locations of the beam21104. Similarly, in an example force sensor, the first and second proximal compression resistors RCP1, RCP2are positioned at matching longitudinal locations of the beam21104. In an example force sensor, the first and second distal resistors compression RCD1, RCD2are positioned at matching longitudinal locations of the beam21104.

FIG.25is an illustrative cross-sectional end view of the example beam21104ofFIG.22indicating a first plane strain force FP1and a second plane strain force FP2imparted to the respective first and second tension resistor half-bridges HB1T, HB2Tby an applied force F force upon the beam21104. In an example force sensor21102, resistance values of the first pair of resistors, RTP1, RTD1, of the first half-bridge HB1Tmatch resistance values of the second pair of resistors, RTP2, RTD2, of the second half-bridge HB2T. In an example force sensor21102, the first and second half-bridges HB1T, HB2Tare positioned upon an example beam21104, such that an X-direction force imparted to the example beam21104imparts a first plane strain force FP1to the first half-bridge HB1Twithin the first plane P1and imparts a second plane strain force FP2to the second half-bridge HB2Twithin the second plane P2. HB1Tand HB2Tcan be used to determine X-direction component of the applied force by determining differences between plane forces.

FIG.26is an illustrative cross sectional end cross-section view of the example beam21104ofFIG.22indicating a first plane strain force FP1and a second plane strain force FP2imparted to the respective third and fourth compression resistor half-bridges HB3C, HB4Cby an applied force upon the beam21104. In an example force sensor21102, the third and compression fourth half-bridges HB3C, HB4Care positioned upon an example beam21104, such that an applied force imparted to the example beam21104imparts a third plane strain force FP3to the third compression half-bridge HB3Cwithin the first plane P1and imparts a fourth plane strain force FP4to the fourth compression half-bridge HB4Cwithin the second plane P2. HB3Cand HB4Ccan be used to determine X-direction component of the applied force by determining differences between plane forces.

FIG.27is an illustrative cross-sectional end view of the example beam21104ofFIG.22indicating a first plane strain force FP1and a fourth plane strain force FP2imparted to the respective first tension and fourth compression resistor half-bridges HB1T, HB4Cby an applied force upon the beam21104. In an example force sensor21102, the first tension and fourth compression half-bridges HB1T, HB4Care positioned upon an example beam21104, such that an applied force imparted to the example beam21104imparts a first plane strain force FP1to the first tension half-bridge HB1Twithin the first plane P1and imparts a fourth plane strain force FP4to the fourth compression half-bridge HB4Cwithin the second plane P2. HB1Tand HB4Ccan be used together with one of HB2Tor HB3Cto determine Y-direction component of the applied force as explained below with reference toFIG.29.

FIG.28is an illustrative cross-sectional end view of the example beam21104ofFIG.22indicating a reverse second plane strain force FP2and a third plane strain force FP3imparted to the respective second tension and third compression resistor half-bridges HB2T, HB3Cby an applied force upon the beam21104. In an example force sensor21102, the second tension and third compression half-bridges HB2T, HB3Care positioned upon an example beam21104, such that an applied force imparted to the example beam21104imparts a third plane strain force FP2to the third compression half-bridge HB3Cwithin the first plane P1and imparts a second plane strain force FP2to the second tension half-bridge HB2Twithin the second plane P2. HB2Tand HB3Cbe used together with one of HB1Tor HB4Cto determine Y-direction component of the applied force as explained below with reference toFIG.29.

Determining a force components by subtracting off-axis force components does not work for half-bridge pairs that have different resistor types since compression and tension resistor have non-matching sensitivities. However, in the example sensor21102, which includes both tension resistor type half-bridges and compression resistor-type half-bridges, any combination of three half bridges can be used to determine both an FXcomponent and an FYcomponent, which are orthogonal to one another, of an applied force F, which is explained as follows with reference toFIG.29.

FIG.29is an illustrative end cross-section view of the example beam21504indicating forces imparted to the three example half-bridges HBA, HBB, HBClocated thereon. In the following explanation, two half-bridges can be same type (either tension resistor type or compression resistor type) and a third half-bridge can be of the same type or opposite type. It is noted that unlike the beam21102ofFIG.22, which has four half-bridges on one side, the beam21504has two half-bridges, HBAand HBB, both located together on a same side of a beam and has a third half-bridge, HBC, located on an opposite side of the beam. Persons skilled in the art will appreciate that following process to determine of FXand FYcomponents of an applied force F, based upon force measurements using three half-bridges in which two half-bridges have matching resistor type that may or may not match the resistor type of a third half-bridge, is agnostic as to circumferential location of the half-bridges on the beam and is agnostic as to half-bridge type.

Let the applied force F=(FX, FY).

Then force along,

Where VΔTis voltage due to temperature gradient along the half bridge; giis the sensitivity/gain of the HB toward force along FPi.

Values for giand θi are known by design or calibration, and therefore, the unknowns are FX, FY, and VΔT. We have three equations and three unknowns. This is a straight forward linear algebra problem.

A value of gi for HBidepends on the type of HB.

If we assume sensitivity for all tension gauge HBs is g thene following is gi

If we assume value of gi is g for a tension gauge HB; then value of gi is −ρg if HB is compression gauge, where ρ is the Poisson ratio of the material.

Thus, it will be appreciated that FXand FYcan be determined based upon each one of the following four combinations of three half-bridges (HBs) set forth in the following Table 2.

The following is an example of use of the process described with reference toFIG.29to determine example FXand FYforce component for the example ofFIG.26.

This example assumes the following values in Table 3:

The value θ is the half-angle (A/2) between the FP1and FP2force planes inFIG.26. The value g is the sensitivity of the tension gauge half-bridge.

In this example, we use HB1T, HB2T, and HB3C, with equations (10), (11) to determine,

Thus, the half-bridge combinations in the above Table 2 can be used to make redundant determinations of FXand FY. A comparison of the FXand FYvalues determined based upon the above combinations of half-bridges can be used to determine whether the force sensor21102contains a malfunctioning resistor. If even a single resistor malfunctions, then then all four combinations would produce different FXand FYvalues thus indicating failure. Since all four HBs would produce different results in the event of a failure, it will not be possible to determine the failing resistor.

FIG.30is an illustrative drawing representing an computer system21902configured to monitor force sensor2302voltage measurements. An example computer system21902includes a display screen21904. The computer system21902is configured to receive voltage measurements VO1, VO2, VO3, and VO4on lines21903produced by the force sensor2302.FIG.31is an illustrative flow diagram22000representing an example diagnostic process to detect an occurrence of a malfunctioning strain gauge resistor in a force sensor2302or21102. The computer system21902is configured with computer readable instructions to perform steps of the diagnostic process22000. At block22002, the computer system receives voltage measurements VO1, VO2, VO3, and VO4. At block22004, determines whether respective FXvalues match and whether respective FYvalues match for each of the HB combinations 1-4 of Table 1. More particularly, for example the computer system21902uses voltage measurements from HB1, HB2, HB3, and HB4to determine FXand FY. If values match, then control flows back to block22002. If values do not match then block22006sends an electronic signal to report an error. In an example computer system21902, the electronic signal causes display of an error message on the display screen21904It will be understood that the process200also can be performed for the sensor21102and the combinations 1-4 of Table 2.

Spread Bridge Reverse Disded XY Force Sensor

FIGS.32A-32Bshow an illustrative top perspective view (FIG.32A) and bottom perspective view (FIG.32B) of an example force sensor3302that includes a rectangular beam3304with Wheatstone bidge circuits (‘full-bridges’) located on two reverse sides thereof. A first full-Wheatstone bridge includes first (RP1), second (RD1), third (RP2), and fourth (RD2) resistors. A second bridge includes fifth (RP3), sixth (RD3), seventh (RP4), and eighth (RD4) resistors. In an example first full-Wheatstone bridge3352, the first and second resistors are coupled in a first half bridge, and the third and fourth resistors are coupled in a second half bridge. A second side3308of the beam3304shown inFIG.32Bfaces in a direction that is reverse of a direction faced by a first side3308of the beam3304shown inFIG.32A. An (X, Y, Z) beam coordinate system3305is shown to explain force directions relative to the beam3304. An example beam3304can have a rectangular cross-section with planar side faces. More particularly, an example beam can have a square cross-section. The beam3304includes a proximal beam portion3304P and a distal beam portion3304D and includes a longitudinal center axis3306extending between the proximal and distal beam portions. Referring toFIG.32A, a first proximal strain gauge resistor (‘resistor’) RP1and a second proximal resistor RP2are located at a proximal beam portion3304P of a first side3308of the beam3304. A first distal resistor RD1and a second distal resistor RD2are located at a distal beam portion3304D of the first side3308of the beam3304. Resistors RP1-RP2and RD1-RD2of a first set of resistors located on the first side3308of the beam are arranged in a first spread full-Wheatstone bridge, explained below in which a first pair of resistors RP1-RD1and a second pair of resistors RP2-RD2are located laterally spread apart from one another on opposite sides of a first side neutral axis3315. Referring toFIG.32B, a third proximal strain gauge resistor (‘resistor’) RP3and a fourth proximal resistor RP4are located at a proximal portion of a second side (also referred to as the ‘reverse’ side) of the beam. A third distal resistor RD3and a fourth distal resistor RD4are located at a distal portion of the second side of the beam. Resistors RP3-RP4and RD3-RD4of a second set of resistors are arranged in a second split full-Wheatstone bridge aligned with a third axis3319, which is a neutral axis, of the second side of the beam.

As explained more fully below, the first and second full-bridge circuits are ‘spread’ in that portions of each bridge circuit are laterally spaced apart from one another on the beam3304. For example, each full-bridge can include two half-bridges that are laterally spread apart from each other. An advantage of laterally spreading apart the half-bridges is that conductor traces that couple resistors to bias voltages or to one another, for example, can be routed to pass through the middle of a face of a beam3304or close a neutral axis of the beam3304, on each face of the beam. Alternatively, in a circular cross-section beam (not shown), conductor traces advantageously can be routed along the neutral axes of individual half-bridges. This routing helps reduce strain on the traces and in turn improves the accuracy of the sensor, by rejecting unwanted signal.

The resistors can be placed on the beam3304manually or using automated machinery and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly on to the beam3304. In both cases, an electrical circuit can be completed externally using wirebonds and flexible printed circuit.

As explained more fully below, a first pair of resistors RP1-RP2and second pair of resistors RD1-RD2located at the first3304side of the beam act as Y-direction force sensor elements, and third pair of resistors RP3-RP4and a fourth pair of resistors RD3-RD4located at the reverse second side of the beam act as X-direction force sensor elements. Referring again toFIG.32A, the first proximal resistor RP1and the first distal resistor RD1are arranged upon the first side3308of the beam3304within a first imaginary plane P1in which the longitudinal center axis3306extends and that defines a first lateral side axis3312at a location on the first side3308of the beam3304along which the first plane P1intersects the first side3308. The first later axis3312and the center axis3306extend parallel to one another and parallel to the first side neutral axis3315. An example first lateral side axis3312extends through the first proximal resistor RP1and through the first distal resistor RD1. Moreover, an example first lateral side axis3312bisects the example first proximal resistor RP1and bisects an example first distal resistor RD1.

Still referring toFIG.32Athe second proximal resistor RP2and the second distal resistor RD2are arranged upon the reverse first side3308of the beam3304within a second imaginary plane P2in which the longitudinal center axis3306extends and that defines a second lateral side axis3314at a location on the first side3308of the beam3304along which the second plane P2intersects the first side3308. The second later axis3314and the center axis3306extend parallel to one another and parallel to the first side neutral axis3315. An example second lateral side axis3314extends through the second proximal resistor RP2and through the second distal resistor RD2. Moreover an example second lateral side axis3314bisects the example second proximal resistor RP2and bisects an example second distal resistor RD2.

Each of resistors of the first and second pairs of resistors RP1-RD1and RP2-RD2is the same type of strain gauge resistor. More particularity in the example force sensor3302described herein, the resistors RP1-RD1and RP2-RD2are tension type gauge resistors used to measure tensile strain. In an alternative example force sensor, the first and second pairs of resistors can be compression type gauge resistors used to measure compression strain. As used herein reference to a set resistors having ‘matching type’ refers to a set of resistors in which either all resistors are tension resistors or all resistors are compression resistors. Resistors that have matching type are more likely to have similar sensitivity and performance, making a sensor better suited for situation of low signal to noise ratio where the common mode cancellation is crucial and much better. In general, although either tension or compression gauge resistors can be used to determine X direction and Y direction forces, in general, tension strain gauge resistors are more sensitive than compression gauge resistors.

Referring toFIG.32B, a third pair of resistors RP3-RD3and fourth pair of resistors RP4-RD4are arranged along a second side third axis3319of the second reverse side3310of the beam3304. The second side third axis3319is a neutral axis that extends within the second side face, parallel to the center axis3306, equidistant from the lateral edges of the second side. The third and fourth pairs of resistors include non-matching types of resistors. In particular, one of RP3, RP4is a tension resistor and the other is a compression resistor, and one of RD3, RD4is a tension resistor and the other is a compression resistor. The pitch between tension gauges and compression gauges also are matching.

FIG.33is an illustrative proximal direction cross-section view of the example beam3304ofFIGS.32A-32B.FIG.34Ais a side elevation view of the beam showing the first side3308of the beam3304.FIG.34Bis a side elevation view of the beam showing the second side3310of the beam3304.

Referring toFIG.33, the proximal direction end view of the beam3304shows side views of the first and second planes P1, P2that intersect one another along the longitudinal center axis3306, which extends within both the first and second planes P1, P2. The (X, Y, Z) beam coordinate system3305is shown to explain force directions relative to the beam3304. It is noted that inFIG.33, the Z axis is shown emerging from the page. The first and second planes P1, P2are separated from one another about the center axis3306by a first separation angle A1.

Referring toFIG.34A, the first lateral side axis3312is shown extending through the first proximal resistor RP1and the first distal resistor RD1on the first side3308of the beam3304. It is noted that inFIG.34A, the X-axis extends into the page. The second lateral side axis3314is shown extending through the second proximal resistor RP2and the second distal resistor RD2on the first side3308of the beam3304. Size of the first separation angle A1corresponds to lateral spacing distance at the first side3308, between the first and second lateral side axes3312,3314, and therefore, corresponds to lateral spacing between the a first resistor pair RP1, RD1from the second resistor pair RP2, RD2. In an example force sensor the first lateral side axis3312and the second lateral side axis3314are equidistant from the first side neutral axis3315, which extends within a first side face of the beam and is equidistant from the opposite lateral edges of the first side3308.

Referring toFIG.34B, the resistors RP3-RP4and RD3-RD4are aligned along the second third axis3319, which extends within a second side face of the beam3304and is equidistant from the opposite lateral edges of the second side3310. It is noted that inFIG.34A, the X-axis emerges from the page.

As explained below, resistors of the first bridge circuit are arranged laterally separated to measure force in a first direction perpendicular to the beam center axis3306, based upon off-neutral axis forces imparted along the first and second planes P1, P2. As shown inFIG.37A, lateral separation of the resistors of the first bridge3352makes possible routing of first center conductor traces3356parallel to the beam center axis3306in a region of the beam3304between proximal and distal resistors of a full-Wheatstone bridge.

FIG.35Ais an illustrative side elevation view of an example beam3304showing a first example layout of a first full-Wheatstone bridge3602that includes resistors RP1-RP2and RD1-RD2. The first Wheatstone bridge layout is coupled in a first configuration to input bias voltage conductors (EP, EN) and output voltage conductors (Vo−, Vo+).FIG.35Bis an illustrative first schematic circuit diagram3604representation of the first full-Wheatstone bridge layout topology. Referring toFIGS.35A-35B, the first proximal resistor RP1is electrically coupled between a positive first DC electrical potential (EP) and a second (also referred to as ‘negative’ potential) output Vo−. The second proximal resistor RP2is electrically coupled between a negative second DC electrical potential (EN) and the second output Vo−. The first distal resistor RD1is electrically coupled between the positive first DC electrical potential (EP) and a first output Vo+(also referred to as a ‘positive’ output). The second distal resistor RD2is electrically coupled between the negative second DC electrical potential (EN) and the first output Vo+.

FIG.36Ais an illustrative side elevation view of an example beam3304showing an alternative second example layout of a first full-Wheatstone bridge3702that includes resistors RP1-RP2and RD1-RD2. The second Wheatstone bridge layout is coupled in a second configuration to input bias voltage conductors (EP, EN) and output voltage conductors (Vo−, Vo+).FIG.36Bis an illustrative first schematic circuit diagram3704representation of the second alternative example layout of the first full-Wheatstone bridge circuit. Referring toFIGS.36A-36B, the first proximal resistor RP1is electrically coupled between the positive first DC electrical potential (EP) and the first output Vo+. The second proximal resistor RP2is electrically coupled between the positive first DC electrical potential (EP) and the second output Vo−. The first distal resistor RD1is electrically coupled between the negative second DC electrical potential (EN) and the first output Vo+. The second distal resistor RD2is electrically coupled between the negative second DC electrical potential (EN) and the second output Vo−.

In general, the layout inFIG.35Ais better for reducing the number of traces that must span the length of the beam and also reduces the effect of traces picking up strain. On the other hand, the layout inFIG.36Alayout is preferred if the force sensor uses half bridge voltage measurements.FIG.37Ais an illustrative side view of an example beam3304showing an example layout of a second example full-Wheatstone bridge3802located at the second side3310of the beam3304and including resistors RP3-RP4and RD3-RD4. Proximal resistor RP3is located proximal of proximal resistor RP4. Distal resistor RD3is located proximal of distal resistor RD4. Proximal resistor RP3and distal resistor RD3are tension gauge resistors and proximal resistor RP4and distal resistor RD4are compression gauge resistors. In the second bridge's first layout shown inFIG.37A, the second bridge is coupled in a first configuration to input bias voltage conductors (EP, EN) and to output voltage conductors (Vo−, Vo+).FIG.37Bis an illustrative schematic circuit diagram3804representation of the first example layout of the second full-bridge circuit. Referring toFIGS.37A-37B, the third proximal resistor RP3is electrically coupled between the negative second DC electrical potential (EN) and the first output Vo+. The fourth proximal resistor RP4is electrically coupled between the positive first DC electrical potential (EP) and the first output Vo+. The third distal resistor RD3is electrically coupled between the negative second DC electrical potential (EN) and the second output Vo−. The fourth distal resistor RD4is electrically coupled between the positive first DC electrical potential (EP) and the second output Vo−.

FIG.37Ais an illustrative side view of an example beam3304showing an example second layout of a second example full-Wheatstone bridge3902located at the second side3310of the beam3304and including resistors RP3-RP4and RD3-RD4. Proximal resistor RP3is located proximal of proximal resistor RP4. Distal resistor RD3is located proximal of distal resistor RD4. Proximal resistor RP3and distal resistor RD3are tension gauge resistors and proximal resistor RP4and distal resistor RD4are compression gauge resistors. In the second bridge's second layout shown inFIG.37A, the second full-bridge is coupled in a first configuration to input bias voltage conductors (EP, EN) and to output voltage conductors (Vo−, Vo+).FIG.37Bis an illustrative schematic circuit diagram904representation of the second example layout of the second full-bridge circuit. Referring toFIGS.37A-37B, the third proximal resistor RP3is electrically coupled between the positive first DC electrical potential (EP) and the first output Vo+. The fourth proximal resistor RP4is electrically coupled between the positive first DC electrical potential (EP) and the second output Vo−. The third distal resistor RD3is electrically coupled between the negative second DC electrical potential (EN) and the first output Vo+. The fourth distal resistor RD4is electrically coupled between the negative second DC electrical potential (EP) and the second output Vo−.

FIG.38Ais an illustrative side view of an example beam3304showing a spread layout of the Wheatstone bridge3352located on the first side3308of the beam3304and showing and routing of center conductor traces3356that extend within the center of the bridge, between proximal and distal resistors of the bridge. The bridge3352includes RP1, RP2and distal resistors RD1, RD2and has a first neutral axis3362that extends parallel to the beam axis3306between proximal resistors RP1, RP2and the distal resistors RD1, RD2. In an example bridge, the first neutral is equally spaced from each of RP1and RP2and is equally spaced from each of RD1and RD2. The first bridge3352is longitudinally split in that the proximal resistors RP1, RP2are longitudinally separated from the distal resistors RD1, RD2. The first bridge is laterally spread in that proximal resistors RP1, RP2are laterally spread apart and the distal resistors RD1, RD2are laterally spread apart from one another.

It will be appreciated that since the resistors of the first full-Wheatstone bridge3352are laterally spread apart, they do not occupy the first neutral axis3362. Therefore conductor traces can be routed close to and in parallel with the first neutral axes3362, which can reduce the amount of strain imparted to the traces. Also, routing of traces along the neutral axis of a bridge circuit can be easier to produce to manufacture or assembly.

An example first full-bridge includes a first group of center conductor traces3356that extend longitudinally along a center portion of the first bridge3352, parallel to the first neutral axis3362, along a region of an outer surface of the beam3304between the pair of proximal resistors RP1, RP2and the pair of distal resistors RD1, RD2of the first bridge3352. The first group of center traces3356include trace segments3356-1coupled to a first positive output voltage VO1+. The first group of center traces3356includes trace segments3356-1coupled to a first negative voltage output VO1−. The first group of center traces3356include trace segments3356-3coupled to a negative voltage potential EN.

FIG.38Bis an illustrative first schematic circuit diagram representation of the first and second full-Wheatstone bridges ofFIG.38A. The full-Wheatstone bridge3352includes RP1and RD1coupled between EP and EN to provide a first half-bridge voltage divider circuit that includes a trace conductor coupled to the first positive output voltage VO1+. The first full-Wheatstone bridge3352also includes RP2and RD2coupled between EP and EN to provide a second half-bridge voltage divider circuit that includes a trace conductor coupled to the first negative output voltage VO1−.

FIG.39Ais an illustrative cross-sectional end view of the example beam3304ofFIG.33indicating the resistors on the first side and indicating a first plane force FP1and a second plane force FP2.FIG.39Bis an illustrative force diagram that indicates X and Y force components of the first plane force FP1imparted to the first proximal resistor RP1and the first distal resistor RD1in response to an applied force F.FIG.39Cis an illustrative force diagram that indicates X and Y force components of the second plane Y-force FP2imparted to the second proximal resistor RP2and the second distal resistor RD2in response to the applied force F.

In an example force sensor3302, resistance values of the first pair of resistors, RP1, RD1, match resistance values of the second pair of resistors, RP2, RD2. In an example force sensor3302, the first and second pairs of resistors are positioned upon an example beam3304, such that an applied force F imparted to the example beam3304imparts a first plane strain force FP1to the first pair of resistors within the first plane P1and imparts a second plane strain force FP2to the second pair of resistors within the second plane P2. It will be appreciated that the first plane strain force FP1is an off-axis force since it is a force imparted along the first lateral side axis3312, which is laterally offset from a neutral axis3315of the first bridge3352. Likewise, it will be appreciated that the second plane strain force FP2is an off-axis force since it is a force imparted along the second lateral side axis3314, which is latterly offset from a neutral axis3315of the first bridge3352. The first and second pairs of resistors are positioned upon an example beam3304, such that a magnitude of the first plane strain force FP1matches a magnitude of the second plane strain force FP2. Force directions of the first plane strain force FP1and second plane strain force FP2are separated from one another by the first separation angle ‘A’.

An advantage of using strain gauge resistors of the same type is that magnitude of a force imparted perpendicular to the center axis3306of a beam3304can be determined based upon a difference in magnitude of off-axis forces imparted to the different half-bridges of a full-bridge located on the beam. In the example force sensor3302, magnitude of a Y-direction force component FYimparted to the beam3304by an applied force F can be determined based upon difference between the first off-axis force FP1and the second off-axis force FP2as follows.

Let A be angle between P1and P2.

Let X axis bisect the angle A. Therefore, an angle between P1and X is A/2 and an angle between P2and X is A/2.

Let θ be an angle between the X axis and an applied force F.

Force along X axis Fx=F cos θ

Force along y axis Fy=F sin θ

we get

When we subtract FP1and FP2

Thus, the difference between FP1and FP2is proportional to the Y-direction force component FYimparted to the beam by the applied force F.

Moreover, it will be appreciated that,

where VS1O+is positive output voltage and VS1O−is negative output voltage of the first bridge circuit3352, and VS1O+−VS1O−is a voltage offset produced by the first bridge circuit3352located on the first side3308of the beam3304.

FIG.40is an illustrative proximal direction cross-section view of the example beam3304ofFIG.33indicating the resistors RP3, RP4, RD3, RD4, of an example second full bridge3802or3902on the second side3310and indicating an X-axis force FX. The example second full-bridge3802or3902measures the X-axis force, which is perpendicular to the longitudinal axis3306and to the third axis3319of the second side3310. An example full bridge circuit includes tension resistors and compression resistors longitudinally aligned parallel with a beam center axis and along a neutral axis is disclosed in PCT/US2018/061113 filed Nov. 14, 2018, which is expressly incorporated herein in its entirety by this reference.

FIG.41is an illustrative drawing representing a metal sheet31102containing cut-outs that define example resistors RP1-RP4and RD1-RD4for assembly into respective first and second full-Wheatstone bridges on reverse-facing first and second sides3308,3310of a beam3304. A first region31104of the metal sheet31102includes resistors RP1-RP2and RD1-RD2to be coupled within a first full-bridge to be located at a first side3308of an example beam. A second region31106of the metal sheet includes resistors RP3-RP4and RD3-RD4to be coupled within a second full-bridge to be located at a reverse second side3310of an example beam3304. A middle third region31108that extends between the first and second regions and is sized to overlay a third intermediate side3320of the beam3304located between the first and second sides3308,3310of the beam3304. A first fold line1110separates the first region from the second region and a second fold line1112separates the second region from the middle region.

FIG.42Ais an illustrative drawing representing a process of folding the metal sheet31102along the first and second fold lines1110,1112to wrap the first, second, and third31104,31104,31106regions of the metal sheet31102about an example beam3304to position a first set of resistors, RP1-RP2and RD1-RD2, at the first side3308of the beam3304and to position a second set of resistors RP3-RP4and RD3-RD4at the second side3310of the beam3304, and to position the middle third refion31108over the third intermediate side3320of the beam3304.FIG.42Bis an illustrative top perspective view of the beam3304with the metal sheet31102wrapped around three sides thereof. In particular,FIG.42Bshows the first region31104of the metal sheet31102overlaying the first side3310of the beam3304to position the first set of resistors at the first side.FIG.42Cis an illustrative bottom perspective view of the beam3304with the metal sheet31102wrapped around three sides thereof. In particular,FIG.42Cshows the second region31106of the metal sheet31102overlaying the second side3310of the beam3304to position the second set of resistors at the second side. In an example rectangular beam, the first side includes a first face of the beam and the second side includes a second side face that is reverse to the first side face.

Although illustrative examples have been shown and described, a wide range of modification, change and substitution is contemplated in the foregoing disclosure and in some instances, some features of the examples may be employed without a corresponding use of other features. For example, a rectangular beam is described herein. However, beams having alternate example beams having circular cross sections or octagonal cross-sections can be used. More generally, an example beam can be used that has a second area moment of inertia that is isotropic for all axes within a cross section plane extending through a proximal portion of the beam perpendicular to the center axis of the beam and that also is isotropic for all axes within a distal cross section plane extending through a distal portion of the beam perpendicular to the center axis of the beam.

The second area moment of inertia requirement is expressed as,

where IXrepresents a moment of inertia about an arbitrarily chosen X axis lying on the plane perpendicular to the central axis and IYrepresents a moment of inertia about an axis that lies on the same plane but perpendicular to the X axis and

where IXYrepresents a product moment of inertia for the cross section of the beam.

FIG.43is an illustrative cross-sectional view of a beam1500having cross-section area A. For cross section A of the beam1500,

Let Ix, Iy, Ixybe the 2nd moment of Inertia

For a new frame inclined at angle θ

For I to be isotropic in all directions, the requirement is that,

The second area moment of inertia requirement is expressed as,

where IXrepresents a moment of inertia about an arbitrarily chosen X axis lying on the plane perpendicular to the central axis and IYrepresents a moment of inertia about an axis that lies on the same plane but perpendicular to the X axis and

where IXYrepresents a product moment of inertia for the cross section of the beam.

EXAMPLES

Example 1 can include a force sensor comprising: a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first full-bridge circuit including: a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output; a second full-bridge circuit including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output; and a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor type; wherein the first, second, third, and fourth resistors are located at a first side face of the beam, such that a voltage offset between the first and second voltage divider outputs represents magnitude of a first force imparted to the beam in a first force direction normal to the longitudinal axis and parallel to a face of the beam; and wherein the fifth, sixth, seventh, and eighth resistors are located at a second side face of the beam adjacent to the first side face, such that a voltage divider offset between the third and fourth voltage divider outputs represents magnitude of a second force imparted to the beam in a second force direction normal to the longitudinal axis and normal to the first force direction.

Example 2 can include the subject matter of Example 1 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

Example 3 can include the subject matter of Example 1 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

Example 4 can include the subject matter of Example 3 wherein the first and third resistors have matching values, second and fourth resistors have matching values, the fifth and seventh resistors have matching values, and the sixth and eighth resistors have matching values.

Example 5 can include the subject matter of Example 3 wherein the first and third resistors have matching longitudinal locations of the beam, second and fourth resistors have matching longitudinal locations of the beam, the fifth and seventh resistors have matching longitudinal locations of the beam, and the sixth and eighth resistors have matching longitudinal locations of the beam.

Example 6 can include a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first full-bridge circuit including: a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output, arranged to extend along a first side axis that extends along the beam parallel to the longitudinal center axis; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output, arranged to extend along a second side axis that extends along the beam parallel to the longitudinal center axis; a second full-bridge circuit including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output, arranged to extend along a third side axis that extends along the beam parallel to the longitudinal center axis, and a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output, arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal center axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor type; wherein the first and second resistors that extend along the first side axis, and the third and fourth resistors that extend along the second side axis, are positioned upon the beam such that a voltage offset between the first and second voltage divider outputs represents magnitude of a first force imparted to the beam in a first force direction normal to the longitudinal axis and normal to the first and second side axes and parallel to the third and fourth side axis; and wherein the fifth and sixth resistors that extend along the third side axis, and the seventh and eighth resistors that extend along the fourth side axis, are positioned upon the beam such that a voltage offset between the third and fourth voltage divider outputs represents magnitude of a second force imparted to the beam in a second force direction normal to the longitudinal axis, parallel to the first and second axes and normal to the third and fourth side axes.

Example 7 can include the subject matter of Example 6 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

Example 8 can include the subject matter of Example 6 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 9 can include the subject matter of Example 6 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

Example 10 can include the subject matter of Example 6 wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal locations of the beam.

Example 11 can include the subject matter of Example 6 wherein the first and third resistors are located in a proximal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the proximal cross-section plane that pass through the longitudinal center axis; wherein the fifth and seventh resistors are located in a proximal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the proximal cross-section plane that pass through the longitudinal center axis; wherein the second and fourth resistors are located in a distal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the distal cross-section plane that pass through the longitudinal center axis; and wherein the sixth and eighth resistors are located in a distal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the distal cross-section plane that pass through the longitudinal center axis.

Example 12 can include the subject matter of Example 6 wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first and second planes; wherein the third side axis extends within a third plane that includes the longitudinal center axis; wherein the fourth side axis extends within a fourth plane that includes the longitudinal center axis; and wherein the first force direction bisects a second separation angle between the third and fourth planes.

Example 13 can include the subject matter of Example 12 wherein the first separation angle equals the second separation angle.

Example 14 can include the subject matter of Example 6 wherein the first gauge resistor, the second gauge resistor, the third gauge resistor, and the fourth gauge resistor are located at respective locations of the beam that have matching cross sections; and wherein the fifth gauge resistor, the sixth gauge resistor, the seventh gauge resistor, and the eighth gauge resistor are located at respective locations of the beam that have matching cross sections.

Example 15 can include the subject matter of Example 9 wherein the first gauge resistor, the second gauge resistor, the third gauge resistor, and the fourth gauge resistor are located at respective locations of the beam that have matching cross sections; and wherein the fifth gauge resistor, the sixth gauge resistor, the seventh gauge resistor, and the eighth gauge resistor are located at respective locations of the beam that have matching cross sections.

Example 16 can include, for use with a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion, a metal sheet comprising: a first cut-out section configured to overlay a first side face of the beam, including: a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output; a second cut-out section configured to overlay a second side face of the beam adjacent to the first side face of the beam, including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output; and a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output, arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal center axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor type; wherein the first, second, third, and fourth resistors arranged to overlay first side face of the beam, are located at a first side face of the beam, such that a voltage offset between the first and second voltage divider outputs represents magnitude of a first force imparted to the beam in a first force direction normal to the longitudinal axis; and wherein the fifth, sixth, seventh, and eighth resistors arranged to overlay a second side face of the beam adjacent to the first side face of the beam, are positioned upon the beam such that a voltage offset between the third and fourth are located at a second side face of the beam adjacent to the first side face, such that a voltage divider offset between the first and second voltage divider outputs represents magnitude of a second force imparted to the beam in a second force direction normal to the longitudinal axis and normal to the first force direction.

Example 17 can include the subject matter of Example 16 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

Example 18 can include the subject matter of Example 16 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 19 can include the subject matter of Example 16 wherein the first, third, fifth, and seventh resistors are arranged to be located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are arranged to be located at the proximal portion of the beam.

Example 20 can include the subject matter of Example 16 wherein the first, third, fifth, and seventh resistors are arranged to be positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are arranged to be positioned at matching longitudinal locations of the beam.

Example 21 can include, for use with a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion, a metal sheet comprising: a first cut-out section configured to overlay a first portion of the beam including: a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output, arranged to overlay the first portion of the beam and to extend along a first side axis that extends along the beam parallel to the longitudinal center axis; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output, arranged to overlay the first portion of the beam and to extend along a second side axis that extends along the beam parallel to the longitudinal center axis; a second cut-out section configured to overlay a second portion of the beam including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output, arranged to overlay the second portion of the beam and to extend along a third side axis that extends along the beam parallel to the longitudinal center axis; and a seventh gauge resistor (‘seventh resistor’) and a eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output, arranged to overlay the second portion of the beam and to extend along a fourth side axis that extends along the beam parallel to the longitudinal center axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor type; wherein the first and second resistors arranged to overlay the first portion of the beam and to extend along the first side axis, and the third and fourth resistors arranged to overlay the first portion of the beam and extend along the second side axis, are arranged to be positioned upon the beam such that a voltage offset between the first and second voltage divider outputs represents magnitude of a first force imparted to the beam in a first force direction normal to the longitudinal axis and normal to the first and second side axes and parallel to the third and fourth side axis; and wherein the fifth and sixth resistors arranged to overlay the second portion of the beam and to extend along the third side axis, and the seventh and eighth resistors arranged to overlay the second portion of the beam and to extend along the fourth side axis, are arranged to be positioned upon the beam such that a voltage offset between the third and fourth voltage divider outputs represents magnitude of a second force imparted to the beam in a second force direction normal to the longitudinal axis, parallel to the first and second axes and normal to the third and fourth side axes.

Example 22 can include the subject matter of Example 22 wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first and second planes; wherein the third side axis extends within a third plane that includes the longitudinal center axis; wherein the fourth side axis extends within a fourth plane that includes the longitudinal center axis; and wherein the first force direction bisects a second separation angle between the third and fourth planes.

Example 23 can include the subject matter of Example 22 wherein the first separation angle equals the second separation angle.

Example 24 can include a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first full-bridge circuit on the beam, having a first neutral axis and including: a first half-bridge circuit first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) arranged along a first lateral side axis parallel to the longitudinal center axis and coupled to provide a first voltage divider output; and a second half-bridge circuit including third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) arranged along a second lateral side axis parallel to the longitudinal center axis and coupled to provide a second voltage divider output; wherein the first and second lateral side axes are laterally spaced apart from one another on opposite sides of the first neutral axis; further including: multiple first center conductor traces extending parallel to the neutral axis in a region of the beam that is between the first resistor and the second resistor and that is between the third resistor and the fourth resistor.

Example 25 can include a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first full-bridge circuit on the beam, having a first neutral axis and including: a first half-bridge circuit first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) arranged along a first lateral side axis parallel to the longitudinal center axis and coupled to provide a first voltage divider output; and a second half-bridge circuit including third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) arranged along a second lateral side axis parallel to the longitudinal center axis and coupled to provide a second voltage divider output; wherein the first and second lateral side axes are laterally spaced apart from one another on opposite sides of the first neutral axis, wherein the first, second, third, and fourth resistors have a matching resistor type; and wherein the first full-bridge circuit is arranged on the beam such that a component of an applied force in a first direction perpendicular to the longitudinal center axis can be determined based upon a difference between a first off-axis force imparted to the first half-bridge and a second off-axis force imparted to the second half-bridge.

Example 26 includes the subject matter of claim25further including: a second full-bridge circuit on the beam, having a second neutral axis and including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) arranged along a third lateral side axis parallel to the longitudinal center axis and coupled to provide a third voltage divider output; and a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘eighth resistor’) arranged along a fourth lateral side axis parallel to the longitudinal center axis and coupled to provide a fourth voltage divider output; wherein the third and fourth lateral side axes are laterally spaced apart from one another on opposite sides of the second neutral axis; further including: multiple first center conductor traces extending parallel to the second neutral axis in a region of the beam that is between the fifth resistor and the sixth resistor and that is between the seventh resistor and the eighth resistor.

Example 27 includes the subject matter of claim26wherein the first, second, third, and fourth resistors have a matching resistor type; wherein the first full-bridge circuit is arranged on the beam such that a component of an applied force in a first direction perpendicular to the longitudinal center axis can be determined based upon a difference between a first off-axis force imparted to the first half-bridge and a second off-axis force imparted to the second half-bridge; wherein the fifth, sixth, seventh, and eighth resistors have a matching resistor type; and wherein the second full-bridge circuit is arranged on the beam such that a component of the applied force in a second direction perpendicular to the longitudinal center axis and perpendicular to the first direction can be determined based upon a difference between a third off-axis force imparted to the third half-bridge and a fourth off-axis force imparted to the fourth half-bridge.

Example 28 includes a force sensor comprising: a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-bridge circuit that includes a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output; a second half-bridge circuit that includes a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output; a third half-bridge circuit that includes a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output; and a fourth half-bridge circuit that includes a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘sixth resistor’) coupled to provide a fourth voltage divider output; wherein the first, second, third, fourth, fifth, sixth, seventh and eighth resistors have matching resistor type; wherein the first, second, third, and fourth resistors are positioned upon a first face of the beam and the fifth, sixth, seventh, and eighth resistors are positioned upon a second face of the beam that is reverse to the first face of the beam, such that, a voltage offset between the first and second voltage divider outputs represents magnitude of a first force imparted to the beam in a first force direction normal to the longitudinal axis; a voltage offset between the third and fourth voltage divider outputs represents magnitude of the first force; a voltage offset between the first and fourth voltage divider outputs represents magnitude of a second force imparted to the beam in a second force direction normal to the longitudinal axis and normal to the first force direction; and a voltage offset between the second and third voltage divider outputs represents magnitude of the second force.

Example 29 includes the subject matter of claim28wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

Example 29 includes the subject matter of claim28wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 30 includes the subject matter of claim28wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the distal portion of the beam.

Example 31 includes the subject matter of claim30wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal locations of the beam.

Exam 32 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-bridge circuit that includes a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output, arranged to extend along a first side axis that extends along the beam parallel to the longitudinal center axis; a second half-bridge circuit that includes a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output, arranged to extend along a second side axis that extends along the beam parallel to the longitudinal center axis; a third half-bridge circuit that includes a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output, arranged to extend along a third side axis that extends along the beam parallel to the longitudinal center axis; and a fourth half-bridge circuit that includes a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘sixth resistor’) coupled to provide a fourth voltage divider output, arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal center axis; wherein the first, second, third, fourth, fifth, sixth, seventh and eighth resistors have matching resistor type; wherein the first and second resistors that extend along the first side axis, and the third and fourth resistors that extend along the second side axis, are positioned upon the beam such that a voltage offset between the first and second voltage divider outputs represents magnitude of a first force imparted to the beam in a first force direction normal to the longitudinal axis and normal to the first, second, third, and fourth side axes; wherein the fifth and sixth resistors that extend along the third side axis, and the seventh and eighth resistors that extend along the fourth side axis, are positioned upon the beam such that a voltage offset between the third and fourth voltage divider outputs represents magnitude of the first force imparted to the beam in the first force direction normal to the longitudinal axis and normal to the first, second, third, and fourth side axes; wherein the first and second resistors that extend along the first side axis, and the seventh and eighth resistors that extend along the fourth side axis, are positioned upon the beam such that a voltage offset between the first and fourth voltage divider outputs represents magnitude of a second force imparted to the beam in a second force direction normal to the longitudinal axis and parallel to the first, second, third, and fourth side axes; and wherein the third and fourth resistors that extend along the first side axis, and the fifth and sixth resistors that extend along the third side axis, are positioned upon the beam such that a voltage offset between the second and third voltage divider outputs represents magnitude of the second force imparted to the beam in the second force direction normal to the longitudinal axis and parallel to the first, second, third, and fourth side axes.

Example 33 includes the subject matter of Example 32 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

Example 34 includes the subject matter of Example 32 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 35 includes the subject matter of Example 32 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the distal portion of the beam.

Example 36 includes the subject matter of Example 35 wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal locations of the beam.

Example 37 includes the subject matter of Example 35 wherein the first, third, fifth, and seventh resistors are located in a proximal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the proximal cross-section plane that pass through the longitudinal center axis; and wherein the second, fourth, sixth, and eighth resistors are located in a distal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the distal cross-section plane that pass through the longitudinal center axis.

Example 38 includes the subject matter of Example 32 wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first and second planes; wherein the third side axis extends within a third plane that includes the longitudinal center axis; wherein the fourth side axis extends within a fourth plane that includes the longitudinal center axis, and wherein the first force direction bisects a second separation angle between the first and fourth planes.

Example 39 includes the subject matter of claim37wherein the first and second angles are supplementary angles.

Example 40 includes a force sensor comprising: a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-bridge circuit that includes a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output; a second half-bridge circuit that includes a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output; a third half-bridge circuit that includes a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output; and a fourth half-bridge circuit that includes a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘sixth resistor’) coupled to provide a fourth voltage divider output; wherein the first, second, third, and fourth resistors are one of tension type and compression type and the fifth, sixth, seventh and eighth resistors are the other of tension type and compression type.

Example 41 includes the subject matter of Example 40 wherein the first, second, third, and fourth resistors are strain type resistors and the fifth, sixth, seventh, and eighth resistors are compression type resistors.

Example 42 includes the subject matter of Example 40 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 43 includes the subject matter of Example 40 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the distal portion of the beam.

Example 44 includes the subject matter of Example 43 wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal locations of the beam.

Example 45 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-bridge circuit that includes a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output, arranged to extend along a first side axis that extends along the beam parallel to the longitudinal center axis; a second half-bridge circuit that includes a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output, arranged to extend along a second side axis that extends along the beam parallel to the longitudinal center axis; a third half-bridge circuit that includes a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) coupled to provide a third voltage divider output, arranged to extend along a third side axis that extends along the beam parallel to the longitudinal center axis; and a fourth half-bridge circuit that includes a seventh gauge resistor (‘seventh resistor’) and an eighth gauge resistor (‘sixth resistor’) coupled to provide a fourth voltage divider output, arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal center axis; wherein the first, second, third, and fourth resistors are tension type resistors; wherein the fifth, sixth, seventh, and eighth resistors are compression type resistors.

Example 46 includes the subject matter of Example 45 wherein the first, second, third, and fourth resistors are tension type resistors and the fifth, sixth, seventh, and eighth resistors are compression type resistors.

Example 47 includes the subject matter of Example 45 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 48 includes the subject matter of Example 45 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

Example 49 includes the subject matter of Example 48 wherein the first, third, fifth, and seventh resistors are arranged to be positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are arranged to be positioned at matching longitudinal locations of the beam.

Example 50 includes the subject matter of Example 48 wherein the first, third, fifth, and seventh resistors are located in a proximal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the proximal cross-section plane that pass through the longitudinal center axis; and wherein the second, fourth, sixth, and eighth resistors are located in a distal cross-section plane of the beam that is normal to the center axis and that has a second area moment of inertia that is isotropic for all axes within the distal cross-section plane that pass through the longitudinal center axis.

Example 51 includes the subject matter of claim45wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first and second planes; wherein the third side axis extends within a third plane that includes the longitudinal center axis; wherein the fourth side axis extends within a fourth plane that includes the longitudinal center axis; and wherein the first force direction bisects a second separation angle between the third and fourth planes.

Example 52 includes the subject matter of claim51wherein the first and second angles are supplementary angles.

Example 53 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first full-bridge circuit including: a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output; and a second full-bridge circuit including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) a seventh gauge resistor (‘seventh resistor’) coupled to provide a third voltage divider output and an eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output; wherein the first, second, third, and fourth resistors have matching resistor type; wherein the fifth and sixth resistors are a one of tension and compression resistor type and the seventh and eighth resistors are the other of tension and compression resistor type; wherein the first, second, third, and fourth resistors are located at a first side face of the beam, such that a voltage offset between the first and second voltage divider outputs represents magnitude of first force imparted to the beam in a first force direction normal to the longitudinal axis; and wherein the fifth, sixth, seventh, and eighth resistors are located at a second side face of the beam that is reverse to the first side face of the beam, such that a voltage offset between the third and fourth voltage divider outputs represents magnitude of second force imparted to the beam in a second force direction normal to the longitudinal axis and normal to the first force direction.

Example 54 includes the subject matter of Example 53 wherein the first, second, third, and fourth resistors are strain type resistors.

Example 54 includes the subject matter of Example 53 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 55 includes the subject matter of Example 53 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

Example 56 includes the subject matter of Example 55 wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal locations of the beam.

Example 57 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first full-bridge circuit including: a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output, arranged to extend along a first side axis that extends along the beam parallel to the longitudinal center axis; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output, arranged to extend along a second side axis that extends along the beam parallel to the longitudinal center axis; and a second full-bridge circuit including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) a seventh gauge resistor (‘seventh resistor’) coupled to provide a third voltage divider output and an eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output, arranged to extend along a third side axis that extends along the beam parallel to the longitudinal center axis; wherein the first, second, third, and fourth resistors have matching resistor type; wherein the fifth and sixth resistors are a one of tension and compression resistor type and the seventh and eighth resistors are the other of tension and compression resistor type; wherein the first and second resistors that extend along the first side axis, and the third and fourth resistors that extend along the second side axis, are positioned upon the beam such that a voltage offset between the first and second voltage divider outputs represents magnitude of first force imparted to the beam in a first force direction normal to the longitudinal axis and normal to the first and second side axes; and wherein the fifth, sixth, seventh, and eighth resistors that extend along the third side axis, are positioned upon the beam such that a voltage offset between the third and fourth voltage divider outputs represents magnitude of second force imparted to the beam in a second force direction normal to the longitudinal axis and parallel to the first and second side axes.

Example 58 includes the subject matter of Example 57 wherein the first, second, third, and fourth resistors are strain type resistors.

Example 59 includes the subject matter of Example 57 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 60 includes the subject matter of Example 57 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

Example 61 includes the subject matter of Example 60 wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal locations of the beam.

Example 61 includes the subject matter of Example 57 wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first and second planes.

Example 62 includes, for use with a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion, a metal sheet comprising: a first cut-out section configured to overlay a first side face of the beam including; a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output; and a second cut-out section configured to overlay a second side face of the beam that faces reverse to the first side face of the beam including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) a seventh gauge resistor (‘seventh resistor’) coupled to provide a third voltage divider output and an eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output; wherein the first, second, third, and fourth resistors have matching resistor type; wherein the fifth and sixth resistors have a one of tension and compression resistor type and the seventh and eighth resistors have the other of tension and compression resistor type; wherein the first, second, third, and fourth resistors arranged to overlay the first side face of the beam, such that a voltage offset between the first and second voltage divider outputs represents magnitude of first force imparted to the beam in a first force direction normal to the longitudinal axis; and wherein the fifth, sixth, seventh, and eighth resistors are arranged to overlay the second side face of the beam that is reverse to the first side face of the beam, such that a voltage offset between the third and fourth voltage divider outputs represents magnitude of second force imparted to the beam in a second force direction normal to the longitudinal axis and normal to the first force direction.

Example 63 includes the subject matter of Example 61 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

Example 64 includes the subject matter of Example 61 wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

Example 65 includes the subject matter of Example 61 wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

Example 66 includes the subject matter of Example wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal locations of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal locations of the beam.

Example 68 includes, for use with a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion, a metal sheet comprising: a first cut-out section configured to overlay a first portion of the beam including: a first gauge resistor (‘first resistor’) and a second gauge resistor (‘second resistor’) coupled to provide a first voltage divider output, arranged to overlay the first portion of the beam and to extend along a first side axis that extends along the beam parallel to the longitudinal center axis; and a third gauge resistor (‘third resistor’) and a fourth gauge resistor (‘fourth resistor’) coupled to provide a second voltage divider output, arranged to overlay the first portion of the beam and to extend along a second side axis that extends along the beam parallel to the longitudinal center axis; and a second cut-out section configured to overlay a second portion of the beam including: a fifth gauge resistor (‘fifth resistor’) and a sixth gauge resistor (‘sixth resistor’) a seventh gauge resistor (‘seventh resistor’) coupled to provide a third voltage divider output and an eighth gauge resistor (‘eighth resistor’) coupled to provide a fourth voltage divider output, arranged to overlay the second portion of the beam and to extend along a third side axis that extends along the beam parallel to the longitudinal center axis; wherein the first, second, third, and fourth resistors have matching resistor type; wherein the fifth and seventh resistors are strain type resistors; wherein the sixth and eighth resistors compression type resistors; wherein the first and second resistors arranged to overlay the first portion of the beam and to extend along the first side axis, and the third and fourth resistors arranged to overlay the first portion of the beam and to extend along the second side axis, are arranged to be positioned upon the beam such that a voltage offset between the first and second voltage divider outputs represents magnitude of first force imparted to the beam in a first force direction normal to the longitudinal axis and normal to the first and second side axes; and wherein the fifth, sixth, seventh, and eighth resistors arranged to overlay the second portion of the beam and to extend along the third side axis, are arranged to be positioned upon the beam such that a voltage offset between the third and fourth voltage divider outputs represents magnitude of second force imparted to the beam in a second force direction normal to the longitudinal axis and parallel to the first and second side axes; wherein the first side axis extends within a first plane that includes the longitudinal center axis; wherein the second side axis extends within a second plane that includes the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first and second planes.

Example 69 includes the subject matter of Example 68 wherein the first side axis extends within a first plane that includes the longitudinal center axis; and wherein the first side axis extends within a first plane that includes the longitudinal center axis.

Example 70 includes a force sensor comprising: a beam including a proximal portion and a distal portion, a longitudinal center axis and a neutral axis that extends along a beam surface parallel to the center axis; a first Wheatstone half-bridge (“half-bridge”) including tension resistors; a second half-bridge including tension resistors; a third half-bridge including compression resistors; a fourth half-bridge including compression resistors; the first and third half-bridges arranged along a first side axis; the second and fourth half-bridges are arranged along a second a side axis; the first and second side axes extend along the beam surface parallel to the neutral axis on opposite sides of the neutral axis and equidistant from the neutral axis.

Example 71 includes method to identify a malfunction of the force sensor of Example 70 comprising: imparting a force to the force sensor; measuring a pair of orthogonal components of the imparted force using each of four different combinations of three half-bridges from a group, the group consisting of the first half-bridge, the second half-bridge, the third half-bridge, and the fourth half-bridge, to produce four pairs of force measurements, each pair of force measurements including a first force component measurement of the imparted force and a second force component measurement of the imparted force, the first force component orthogonal to the second force component; comparing the first force component measurements from each pair of force measurements; comparing the second force component measurements from each pair of force measurements; producing an electronic signal to report an error in response to a mismatch of a first force component measurement of one of the pairs of force measurements and a first force component measurement of at least one other of the pairs of force measurements; and producing an electronic signal to report an error in response to a mismatch of a second force component measurement of one of the pairs of force measurements and a second force component measurement of at least one other of the pairs of force measurements.

One of ordinary skill in the art would recognize many variations, alternatives, and modifications. Thus, the scope of the disclosure should be limited only by the following claims, and it is appropriate that the claims be construed broadly and, in a manner, consistent with the scope of the examples disclosed herein. The above description is presented to enable any person skilled in the art to create and use a force sensor with a beam and a distributed bridge circuit. Various modifications to the examples will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other examples and applications without departing from the scope of the invention. In the preceding description, numerous details are set forth for the purpose of explanation. However, one of ordinary skill in the art will realize that the invention might be practiced without the use of these specific details. In other instances, well-known processes are shown in block diagram form in order not to obscure the description of the invention with unnecessary detail. Identical reference numerals may be used to represent different views of the same or similar item in different drawings. Thus, the foregoing description and drawings of examples in accordance with the present invention are merely illustrative of the principles of the invention. Therefore, it will be understood that various modifications can be made to the examples by those skilled in the art without departing from the scope of the invention, which is defined in the appended claims.