Resistive-capacitive deformation sensor
A deformation sensing apparatus comprises an elastic substrate, a first strain-gauge element formed on a first surface of the elastic substrate, and configured to output a first signal in response to a strain applied in a first direction, and a second strain-gauge element formed on a second surface of the elastic substrate opposite to the first surface, and configured to output a second signal in response to a strain applied in the same first direction.
1. A deformation sensing apparatus comprising:
an elastic substrate;
a first strain-gauge element having two distinct terminals comprising a first terminal and a second terminal, wherein the first strain-gauge element is formed on a top surface of the elastic substrate and is configured to output a first signal in response to a strain applied in a first direction, the first signal measurable across the first and second terminals of the first strain-gauge element; and
a second strain-gauge element having two distinct terminals comprising a third terminal and a fourth terminal, wherein the second strain-gauge element is formed on a bottom surface of the elastic substrate opposite to the top surface and is configured to output a second signal in response to a strain applied in the same first direction, the second signal measurable across the third and fourth terminals of the second strain-gauge element.
2. The deformation sensing apparatus of claim 1 , wherein:
the elastic substrate comprises a flexible, electrically-insulating dielectric material; and
the deformation sensing apparatus is configured to output a third signal responsive to an applied deformation, the third signal being measurable between a terminal of the first strain-gauge element and a terminal of the second strain-gauge element.
3. The deformation sensing apparatus of claim 2 , further comprising:
a measurement circuit configured to measure the first signal from the first strain-gauge element and the second signal from the second strain-gauge element in response to the applied deformation; and
a deformation analyzer configured to compute a measure of stretch deformation and a measure of flex deformation of the sensing apparatus, in the applied deformation, based on the measured first signal from the first strain-gauge element, the measured second signal of the second strain-gauge element, and the third signal.
4. The deformation sensing apparatus of claim 3 , wherein:
the first signal is indicative of a first resistance of the first strain-gauge element;
the second signal is indicative of a second resistance of the second strain-gauge element; and
the third signal is indicative of a capacitance across the elastic substrate measured responsive to the applied deformation.
5. The deformation sensing apparatus of claim 4 , wherein the deformation analyzer computes the measure of stretch deformation as a proportion of length change ((ΔL)/L 0 ) of the first and second strain-gauge elements, based on the first, second, and third signals, using the equations:
R 1 =R 2 =R 0 +(GF·Δ L )
C
=
ɛ
Area
gap
=
ɛ
L
0
-
W
0
g
=
ɛ
L
0
-
W
0
(
g
0
-
Δ
L
-
Y
)
=
ɛ
L
0
·
W
0
(
g
0
-
(
Δ
L
1
+
Δ
L
2
2
)
)
,
where R 1 is the first resistance, R 2 is the second resistance, C is the capacitance, and
Area is an overlap between first and second strain-gauge elements,
GF is a Gauge Factor relating strain and resistance,
γ is a Poisson's Ratio of the elastic substrate relating deformations between axes,
L 0 is an undeformed length of the first and second strain-gauge elements,
ΔL, Δ L1 , ΔL 2 are length changes of the first and second strain-gauge elements,
W 0 is an undeformed length of the first and second strain-gauge elements,
c is a dielectric constant of the elastic substrate,
R 0 is a baseline resistance of the first and second strain-gauge elements, and
g, g 0 are, respectively, deformed and baseline widths of the elastic substrate.
6. The deformation sensing apparatus of claim 4 , wherein the deformation analyzer computes the measure of flex deformation as bend radii of the first and second strain-gauge elements, based on the first, second, and third signals, using the equations:
R
1
=
R
0
+
(
GF
·
Δ
L
1
)
≈
R
0
+
(
g
2
ρ
1
·
GF
)
R
2
=
R
0
+
(
GF
·
Δ
L
2
)
≈
R
0
+
(
-
g
2
ρ
2
·
GF
)
,
where R 1 is the first resistance, R 2 is the second resistance, and
GF is a Gauge Factor relating strain and resistance of the first and second strain-gauge elements,
γ is a Poisson's Ratio of the elastic substrate relating deformations between axes,
L 0 is an undeformed length of the first and second strain-gauge elements,
Δ L1 , ΔL 2 are length changes of the first and second strain-gauge elements,
R 0 is a baseline resistance of the first and second strain-gauge elements,
g, is a deformed width of the elastic substrate, and
ρ 1 and ρ 2 are bend radii of the top surface and the bottom surface of the elastic substrate.
7. The deformation sensing apparatus of claim 2 , wherein:
each of the first and second strain-gauge elements has a horse-shoe shape comprising an arcuate head and a pair of elongate leads extending from ends of the arcuate head;
alignment of the shapes of the first and second strain-gauge elements correspond along an axis orthogonal to the top surface and the bottom surface of the elastic substrate;
central axes of the first and second strain-gauge elements are aligned parallel and coplanar to each other along a planes orthogonal to the top surface and the bottom surface of the elastic substrate; and
corresponding leads of the pairs of elongate leads of the first and second strain-gauge elements are respectively length-wise parallel and have substantially the same dimensions.
8. The deformation sensing apparatus of claim 7 , wherein:
a measurement circuit configured to measure the first signal from the first strain-gauge element and the second signal from the second strain-gauge element in response to an applied deformation; and
a deformation analyzer configured to compute a measure of stretch deformation and a measure of flex deformation of the sensing apparatus, in the applied deformation, based on the measured first signal from the first strain-gauge element, the measured second signal of the second strain-gauge element, and the third signal.
9. The deformation sensing apparatus of claim 8 , wherein:
the measure of stretch deformation is indicative of an average change in lengths in relationship to an undeformed length of the first and second strain gauge elements; and
the measure of flex deformation is indicative of a bend radius of an angular bend of surfaces of the elastic substrate on which the first and second strain-gauge elements are formed.
10. The deformation sensing apparatus of claim 8 , wherein the deformation analyzer is further configured to determine whether the stretch deformation corresponds to a compression stretch or an elongation stretch, by comparing the measured first, second, and third signals, based on a sign of changes in resistances of the first and second strain gauge elements and a sign of change in capacitance of the elastic substrate.
11. A deformation sensing apparatus comprising:
an elastic substrate;
a first strain-gauge pair comprising:
a first strain-gauge element formed on a first surface of the elastic substrate, and configured to output a first signal in response to a strain applied in a first direction, and
a second strain-gauge element formed on a second surface of the elastic substrate opposite to the first surface, and configured to output a second signal in response to a strain applied in the same first direction,
wherein the deformation sensing apparatus is configured to output a third signal responsive to an applied deformation, the third signal being measurable between a terminal of the first strain-gauge element and a terminal of the second strain-gauge element; and
a second strain-gauge pair comprising:
a third strain-gauge element formed substantially on the first surface of the elastic substrate, and configured to output a fourth signal in response to a strain applied in a second direction, and
a fourth strain-gauge element formed substantially on the second surface of the elastic substrate opposite to the first surface, and configured to output a fifth signal in response to a strain applied in the same second direction,
wherein the deformation sensing apparatus is configured to output a sixth signal responsive to an applied deformation, the sixth signal being measurable between a terminal of the third strain-gauge element and a terminal of the fourth strain-gauge element,
wherein the first direction is orthogonal to the second direction, and
wherein strain-gauge elements of the first strain-gauge pair and strain-gauge elements of the second strain-gauge pair are mutually orthogonal.
12. The deformation sensing apparatus of claim 11 , further comprising
a measurement circuit configured to measure the first signal from the first strain-gauge element, the second signal from the second strain-gauge element, the fourth signal from the third strain-gauge element, and the fifth signal from the fourth strain-gauge element in response to the applied deformation; and
a deformation analyzer configured to compute a measure of stretch deformation and a measure of flex deformation, respectively, of the sensing apparatus, in the first and second directions, based on the measured first signal from the first strain-gauge element, the measured second signal of the second strain-gauge element, and the measured fourth signal from the third strain-gauge element, and the measured fifth signal from the fourth strain-gauge element.
13. The deformation sensing apparatus of claim 12 , wherein:
the deformation analyzer is further configured to determine a direction of stretch deformation as being either a stretch in the first direction or in the second direction by comparing magnitudes of the first, second, fourth, and fifth signals detected from the first and second strain-gauge pairs;
for a stretch in the first direction, the deformation analyzer is configured to compute a magnitude of stretch using the first and second signals; and
for a stretch in the second direction, the deformation analyzer is configured to compute the magnitude of stretch using the fourth and fifth signals.
14. The deformation sensing apparatus of claim 12 , wherein:
the deformation analyzer is further configured to determine a magnitude of the flex deformation and a direction of the flex deformation based on the measured first, second, fourth, and fifth signals.
15. The deformation sensing apparatus of claim 12 , wherein:
the deformation analyzer is further configured to determine a direction of flex deformation as being either a bend in the first direction or in the second direction by comparing magnitudes of the first, second, fourth, and fifth signals detected from the first and second strain-gauge pairs;
for a bend in the first direction, the deformation analyzer is configured to compute a magnitude of bend using the first and second signals; and
for a bend in the second direction, the deformation analyzer is configured to compute a magnitude of bend using the fourth and fifth signals.
16. The deformation sensing apparatus of claim 12 , wherein the deformation analyzer is further configured to determine, by comparing the measured first, second, fourth, and fifth signals, whether the flex deformation corresponds to a bend toward the first surface of the elastic substrate or a bend toward the second surface of the elastic substrate.
17. A deformation sensing apparatus comprising:
an elastic substrate;
a first strain-gauge element formed on a first surface of the elastic substrate, and configured to output a first signal in response to a strain applied in a first direction; and
a second strain-gauge element formed on a second surface of the elastic substrate opposite to the first surface, and configured to output a second signal in response to a strain applied in a second direction,
wherein the deformation sensing apparatus is configured to output a third signal responsive to an applied deformation, the third signal being measurable between a terminal of the first strain-gauge element and a terminal of the second strain-gauge element,
wherein the first direction is orthogonal to the second direction, and
wherein the first strain-gauge element and the second strain-gauge element are mutually orthogonal.
18. The deformation sensing apparatus of claim 17 , wherein:
a measurement circuit configured to measure the first signal from the first strain-gauge element, the second signal from the second strain-gauge element, and the third signal, responsive to the applied deformation; and
a deformation analyzer configured to compute a measure of stretch deformation and a measure of flex deformation, respectively, of the sensing apparatus, in the first and second directions, based on the measured first signal from the first strain-gauge element, the measured second signal of the second strain-gauge element, and the measured third signal.
19. The deformation sensing apparatus of claim 18 , wherein:
the deformation analyzer is further configured to determine a direction of stretch deformation as being either a stretch in the first direction or in the second direction by comparing magnitudes of the first and second signals detected from the first and second strain-gauge elements;
for a stretch in the first direction, the deformation analyzer is configured to compute a magnitude of stretch using the first and third signals; and
for a stretch in the second direction, the deformation analyzer is configured to compute the magnitude of stretch using the second and third signals.
20. The deformation sensing apparatus of claim 18 , wherein:
the deformation analyzer is further configured to determine a direction of flex deformation as being either a bend in the first direction or in the second direction by comparing magnitudes of the first and second signals detected from the first and second strain-gauge elements;
for a bend in the first direction, the deformation analyzer is configured to compute a magnitude of bend using the first and third signals; and
for a bend in the second direction, the deformation analyzer is configured to compute a magnitude of bend using the second and third signals.
21. A wearable device comprising:
one or more deformation sensors, each including:
an elastic substrate comprising a flexible, electrically-insulating dielectric material;
a first strain-gauge element formed on a first surface of the elastic substrate, and configured to output a first signal in response to a strain applied in a first direction; and
a second strain-gauge element formed on a second surface of the elastic substrate opposite to the first surface, and configured to output a second signal in response to a strain applied in the same first direction,
wherein the deformation sensor is configured to output a third signal responsive to an applied deformation, the third signal being measurable between one of the first and second terminals of the first strain-gauge element and one of the third and fourth terminals of the second strain-gauge element;
a measurement circuit configured to measure the first signal from the first strain-gauge element and the second signal from the second strain-gauge element in response to the applied deformation; and
a deformation analyzer configured to compute a measure of stretch deformation and a measure of flex deformation of the sensing apparatus, in the applied deformation, based on the measured first signal from the first strain-gauge element, the measured second signal of the second strain-gauge element, and the third signal.
22. The wearable device of claim 21 , wherein:
each of the first and second strain-gauge elements of the deformation sensor within the wearable device has a horse-shoe shape comprising an arcuate head and a pair of elongate leads extending from ends of the arcuate head; and
alignment of the shapes of the first and second strain-gauge elements correspond and the shapes are configured to circumscribe an articulating joint, a movement of the joint resulting in a corresponding deformation of the deformation sensor.
23. A method of sensing deformation of a deformation sensor, comprising, in response to an applied deformation:
measuring a first signal from a first strain-gauge element formed on a first surface of an elastic substrate of the deformation sensor, the first signal indicative of a resistance of the first strain-gauge element;
measuring a second signal from a second strain-gauge element formed on a second surface of the elastic substrate of the deformation sensor, the second signal indicative of a resistance of the second strain-gauge element;
measuring a third signal between the first strain-gauge element and the second strain-gauge element, the third signal indicative of a capacitance across the elastic substrate measured responsive to the applied deformation; and
computing a measure of stretch deformation and a measure of flex deformation of the deformation sensor, in the applied deformation, based on the measured first signal from the first strain-gauge element, the measured second signal of the second strain-gauge element, and the third signal.