IEEE SENSORS JOURNAL, VOL. 16, NO. 8, APRIL 15, 2016

2607

Multi-Element Strain Gauge Modules
for Soft Sensory Skins
Edward L. White, Student Member, IEEE, Jennifer C. Case, Student Member, IEEE,
and Rebecca K. Kramer, Member, IEEE

Abstract— In this paper, we describe the fabrication and testingof a sensory module composed of resistive strain gauges in anelastomer substrate. Each module contains three resistive gauges,
providing sufficient information to reconstruct the geometry of
the module. The modules are fabricated from two bonded sheetsof silicone elastomer. The sensing element is a resistive strain
gauge based on room-temperature liquid gallium–indium alloy
contained within microchannels in the substrate. We demonstrate
the functionality of the module by mechanically stretching itover a template and measuring the change in resistance ofthe embedded liquid metal strain gauges. Starting with known
strains, we calibrate the device and fit a quadratic model. With
the model and the measured error distribution, we can predictthe uncertainty in the reconstructed position of the corners of thetriangular modules, which we refer to as nodes.
Index Terms— Mechanical sensors, wearable sensors, sensor
arrays, displacement measurement, electrical resistance measurement.

I. I NTRODUCTION
HE field of soft robotics presents the opportunity to create
devices with capabilities totally unlike those achieved bytraditional robotic systems. As soft robots are built from highly
deformable materials, the joint-linkage paradigm found in rigid
robots breaks down. The result is robotic systems with infinite
degrees of freedom. The downside of flexibility comes in thearea of control. Instead of observing and controlling a fixed
number of states, soft robots have a much more challenging
problem, namely the need to observe a deformation acrossthe entire soft body. In order to provide this proprioceptive
feedback, distributed sensors are required. These sensors caneither be embedded in the body of a robot, or placed on theexterior as a skin. The latter approach is what we pursue inthis work.
In this paper, we describe the fabrication and testing of
sensory skin modules shown in Fig. 1. Each module is composed of an array of resistive strain gauges placed along theedge of its body, providing complete definition of its current

T

Manuscript received October 20, 2015; accepted November 24, 2015. Dateof publication December 10, 2015; date of current version February 24, 2016.
This work was supported by the National Aeronautics and Space Administration within the Early Career Faculty Program through the Space Technology
Research Grants Program under Grant NNX14AO52G. The work of
E. L. White was supported by the National Science Foundation Graduate
Research Fellowship under Grant DGE-1333468. The associate editor
coordinating the review of this paper and approving it for publication was
Prof. Ravinder S. Dahiya.
The authors are with the School of Mechanical Engineering, Purdue
University, West Lafayette, IN 47907 USA (e-mail: white335@purdue.edu;
case15@purdue.edu; rebeccakramer@purdue.edu).
Digital Object Identifier 10.1109/JSEN.2015.2507540

Fig. 1. A completed module, showing resistive strain gauges made fromconductive liquid metal encapsulated in microchannels. The microchannels
are embedded between two elastomers: SIL-950, which is opaque (blue), andSylgard 184, which is transparent, rendering the liquid metal visible between
layers.

state. These modules could be applied to the exterior of asoft robot to measure the state of deformation at that locationin the robot body. Furthermore, this module design could beapplied to other deformable planar systems, such as wearables,
or used to measure state in traditional robots. To measurestate over a larger soft robot body, arrays of these modules
could be connected together, creating large-area sensory skins.
The size of the sensory skin modules described makes themapplicable to larger systems, for example human-scale robots
and wearable devices. We selected a triangular geometry sincemultiple triangular elements can be used to “mesh” a surface
without ambiguity in the resulting configuration. Geometries
with more edges require more strain measurements than thenumber of nodes to define the geometry. For example, asquare requires five measurements to define the location offour nodes. This concept is illustrated in Fig. 2.
We have two goals with this paper. First, we aim to
demonstrate an approach to manufacturing modules which
can be scaled to produce large numbers of devices. Second,
we aim to demonstrate state reconstruction through resistive
strain measurements. To support the first goal, the modules
were fabricated with a laser-based moldless patterning processthat is much more scalable than traditional soft microchannel
patterning approaches. Microchannels were patterned directly
into cured elastomer substrates, rather than curing elastomer
in molds. These microchannels were filled with liquid gallium
indium alloy, forming the resistive sensing element of thestrain gauges. To support the second goal, we calibrated the1558-1748 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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IEEE SENSORS JOURNAL, VOL. 16, NO. 8, APRIL 15, 2016

Fig. 2. Schematic illustration of a (a) 3-sided element, (b) 4-sided element,and (c) 5-sided element. Each solid line represents a length which must
be measured for the geometry of the nodes to be uniquely defined in two
dimentional space. The numbers correspond to these solid lines. The triangle
requires three measurements, the square requires five measurements, and thepentagon requires seven measurements. Thus, the triangular element has anequal number of measurements and nodes, the square requires one moremeasurement than nodes, and the pentagon requires two more measurements
than nodes.

modules against known positions, then recovered the geometry
for unknown positions using measurements of resistance.
The strain sensing elements in our design are placed at
the edge of the structure to maximize their sensitivity to
deformation and to reduce cross-talk between channels asmuch as possible. Ideally, we would have created a single
channel directly between two nodes. This was not possible
for two reasons. First, we wish to increase the overall lengthof the microchannels to increase their resistance, making themeasier to interface with and measure. Second, we wish to offset
the sensors from the node-to-node line so that multiple triangular elements could be attached together without mechanicalinterference. Beyond these considerations, the design of thesensor array and the microchannels was dictated by our
manufacturing capabilities, which include the minimum trace
width, the minimum spacing between traces, and the minimum
distance from the edge of the module to a microchannel.
The minimum channel width is determined by two effects:
the capability of the laser used in this study to fabricate thechannels, and the minimum size channel through which eutectic gallium indium will spontaneously reflow. The minimum
spacing between channels is dictated by bonding between
elastomer layers. As the elastomer substrates are patterned,a small region of the substrate near the microchannel becomes
ablated by the laser patterning process and does not support
good adhesion between layers. Microchannels must be kept
far enough apart so that there is un-ablated elastomer between
the channels. The minimum spacing between a channel andthe edge of the module is based on the alignment accuracy
achieved by manually aligning modules in the laser patterning
system. Doubling or halving these limits would not result ina significant impact to the overall design of the module.
II. P REVIOUS W ORK
The field of sensory skins is populated with many different
approaches and design goals. Some of these devices areintended to sense the external environment, some are intended
to capture some form of user input or other robot-environment
interaction, and some are designed to provide feedback on
the current state of the system. Our design falls into this last
category; it is intended to provide proprioceptive feedback
in a soft robotic system. The field of polymer MEMS, which

includes sensory skin applications, was reviewed by Liu [1].
Biological sensing applications, including artificial skin,were reviewed by Nambiar and Yeow [2]. More specifically,
stretch sensors for human applications were reviewed
by O’Brien, et al. [3]. Our review of sensory skins parallels
the development of the field. We first discuss flexible
polymer substrates used to hold together separate sensing
elements. Next, we describe how flexible polymer itself wastransformed into a sensing element. We continue on to discuss
the emergence of conductive polymer composites, which
are an alternative approach to creating soft sensory skins.
Finally, we review stretchable sensory skins and discuss how
conductive elements may be integrated into soft substrates.
One of the first polymeric materials used in sensory skins
was polyimide, which has proven to be a versatile material,
serving as both an inert substrate supporting active elements
and as a part of the sensing elements themselves. As asupporting element, polyimide has been used to support
hotwire anemometers [4], silicon force sensors [5], and shear
sensors for aerospace and underwater applications [6], [7].
As a sensing element, membranes of polyimide have beenused in resistive force gauges [8], [9], multi-mode sensory
skins, with temperature, thermal conductivity, force, andstiffness sensors [10], and multi-axis force sensors [11].
Thicker polyimide structures have recently been demonstrated
with improved reliability over their thin membranecounterparts [12], [13]. One of the challenges associated withusing polyimide film as a substrate is its limited stretchability.
One approach to increasing the maximum strain of thematerial is through a lattice-like structure of polyimide
and metal film [14]. We have opted to use a stretchable
elastomer instead of a flexible polymer since the former ismore mechanically compatible with soft systems, including
elastomer robots and biological systems such as humans.
The examples presented above all used metal films as resistive sensing elements. An alternative is to create conductive
polymer composites, which have the advantage of supporting
larger strains than metal. Conductive composites have been
fabricated in arrays of dots on a polyimide substrate to sense
force over a surface [15]. A hybrid approach can also be used,combining a single conductive polymer composite with metal
addressing electrodes [16], [17]. In addition to measuringchanges in resistance, alternative sensing mechanisms havebeen described. Variable gain in a field effect transistor [18]and changes in capacitance have also been used to measureapplied loads in polyimide systems [19]. In this work, wehave opted to use resistance-based measurements of strain due
to the simple electrical interface required. Further, we haveelected not to use conductive composites due to their lower
conductivity and reduced mechanical and electrical stability
over multiple cycles [20].
Although polyimide is flexible, it is not stretchable,
making it of limited use in our current application, wherehigh planar deformation is required. Polyimide has beenfrequently employed as a base for MEMS-inspired sensor
skins due to its material compatibility with MEMS processing.
For example, it can be polymerized in place, making it
attractive for spin coating thin features such as membranes

WHITE et al.: MULTI-ELEMENT STRAIN GAUGE MODULES FOR SOFT SENSORY SKINS

and connective layers. It is also more likely to alreadybe found in semiconductor processing equipment, such as
metal evaporators. Despite these advantages, we see themechanical limitations of polyimide as outweighing thebenefits from simpler processing. We believe that this present
work describes an approach to using elastomers that is highly
scalable and overcomes some of the fabrication challenges
that may have restricted adoption of elastomers in the past.
As an alternative to inextensible polymers, stretchable
elastomers can be used to fabricate the entire sensory skin.
One of the most popular is silicone rubber. The most commonof these rubbers is Sylgard 184 from Dow Corning, which isa polydimethylsiloxane (PDMS). Other popular silicones are
EcoFlex and DragonSkin, both from Smooth-On. Unlike inpolyimide sensors, metal films are mechanically incompatible
with the high deformations present in these soft polymers.
Instead, the polymer itself can be turned into a sensing
element by forming a conductive polymer composite by adding
carbon black [21] or expanded intercalated graphite to the bulk
material [20], or by depositing carbon nanotubes [22]–[24],silver nanowires [25], or graphene-nanocellulose on the surface of the elastomer [26]. In summary, there are manydifferent combinations of conductive and silicone materials
which can be combined together. There are trade-offs that drivematerial selection and the choice of loading. These include thechanges in material properties that occur due to the inclusionof the harder and stiffer conductive phase, the decrease instrength that occurs due to stress concentration, the bulk
conductivity of the material, and the gauge factor. As we noted
previously, we have elected not to use conductive composites
in this application due to the degradation of mechanical andelectrical properties over the base elastomer.
An alternative approach to using a solid conductor is
to use a liquid. Within the soft robotics community, theroom-temperature liquid metal alloy of gallium and indium
is a popular choice due to its mechanical compatibility withelastomeric structures [27]. Liquid-metal-filled microchannels
have been used to measure biaxial stretch and appliedpressure [28]–[31], curvature [32], and joint angle [33],and have been integrated with shape memory alloy tocreate an active skin [34]. Liquid-metal-based sensors arefundamentally different from most of the polyimide sensors
described earlier since they are able to measure the stateof the sensor body, and not only the applied loads. This isfunctionally similar to what we are demonstrating in thiscurrent work, since our focus is on proprioceptive sensing.
In these devices, as in the work presented here, hollow
microchannels were created in a silicone substrate, then filledwith liquid metal. However, we are also working to develop
more scalable approaches. Our group has previously demonstrated fabrication of strain sensors by direct writing liquidgallium indium alloy followed by encapsulation in PDMS [35].
We have also demonstrated ink jetting of an ethanol-based
ink containing sub-micron scale particles of liquid metal [36].
These two processes, along with the laser-based approachdescribed in this work, are all attempts to increase the manufacturablity and reliability of liquid-metal. As these alternative
approaches to patterning liquid metals mature, we intend to2609

create devices such as those we describe in this work with the
new methods.
Resistive liquid metal sensors are not the only approach tocreating soft sensor skins. Alternatives resistive approaches
include the use of conductive solutions [37] and ionicliquids [38]. With proper integration, metals can be used insilicone substrates, with similar geometries to those discussed
previously in polyimide, resulting in capacitive force
sensors [39], dual-mode force and proximity sensors [40], andmulti-mode strain, touch and pressure sensors [41]. Hybridsof soft elastomers and flexible polymers have also been
demonstrated [42]–[45]. For our purposes, the use of resistive
liquid metal sensors was based on a combination of experienceand expected device performance. We have extensive
knowledge of how to manufacture this class of devices, andduring the design phase we anticipated that the performance
would be sufficient to achieve our goal of state reconstruction.
In summary, there have been many approaches taken todeveloping sensory skins. The majority of these concepts
have used resistive sensors, as our approach uses. However,many of the sensor skins described in the literature containinextensible elements, making integration with highly
deformable bodies difficult. Our long-term objective is tocreate highly deformable sensory skins, which has caused
us to focus on silicone elastomer substrates. Liquid metal is
attractive to us in this application given its potential for highdeformations and low stiffness. For these reasons, it can be
integrated into a soft sensor skin without negatively impacting
the mechanical response of the skin. Finally, we have chosen
to develop a novel patterning approach to creating traditional
microchannels. While the channels created in this way arerougher than those produced via molding, laser-based ablation
is much more scalable and compatible with large-scale
manufacturing processes such as roll-to-roll fabrication.
III. E XPERIMENTAL
A. Module Fabrication
The sensory skin modules created for this work were fabricated from two sheets of elastomer sandwiching liquid-metalfilled microchannels. We used two platinum-cure silicone
elastomers: Smooth-Sil 950 (Smooth-On) and Sylgard 184(Dow Corning). Both of these elastomers are received as two
liquid parts that are mixed 10:1 by mass. Once the two parts
are added to a plastic cup, we pre-mix the elastomer by handusing a plastic knife to ensure proper blending, followed bymixing and degassing in a THINKY ARE-310 orbital mixer.
The resulting mixed elastomer is ready to cast. The following
steps of the fabrication process are illustrated in Fig. 3.
We prepared the elastomer films, which we call substrates,
used in these experiments using a “rod-coating” technique.
This approach is borrowed from the coating industry, and isfrequently employed to create uniform coatings on long hostsubstrates. Our purpose in using this method instead of themore conventional spin-coating approach is that spin coating
is limited to the size of the substrate that can be created. The
elastomer substrate limits the host substrate onto which it iscast. The most common host substrate used in the soft robotics

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IEEE SENSORS JOURNAL, VOL. 16, NO. 8, APRIL 15, 2016

Fig. 4. Schematic drawing of the module. Black lines are cuts in the material,
while gray lines are microchannels. The serpentine patterns near the edges of
the triangular body are the strain sensitive elements. The rectangular featuresnear the middle of the body are access ports through which the microchannels
are filled. The circles near the center of the body are pass-throughs for copper
wires from the microchannels on the bottom side of the device to the top of
the device. The thicker line in the upper left corner of the image is 1 , thethinner line is 20mm.

Fig. 3.

Fabrication sequence used to manufacture modules.

literature is a silicon wafer. With rod coating, we were able
to create substrates on the meter scale, which enabled us to
produce many (typically 10-12) sensor modules from a single
substrate.
The first step in the rod coating procedure was to placea host substrate onto a flat surface. In our experiments, weused polyethylene terepthalate (PET) on a laboratory counter
top. This film was held in place by Scotch tape to keep
it flat and mitigate wrinkling. We prepared liquid elastomer
using the procedure discussed above. We typically preparedapproximately 60g of elastomer, which resulted in a substrate
10cm wide by 1m long. The final dimensions of the substrate
are not important to the performance of the device, since thesensor modules are cut out from the substrate in a later step.
The coating rod is the placed on the PET film, at one edge ofthe film. For these experiments, we used 12 × 1/2 -13 Acme
threaded rod (McMaster-Carr). Liquid elastomer is thenpoured onto the PET film in front of the rod. The elastomer
substrate is created by scraping the liquid elastomer acrossthe PET film using the threaded rod. The liquid elastomer
flows through the threads of the rod, resulting in a patternof ridges of liquid behind the rod. Since the geometry of theridges is determined by the geometry of the rod, the ridges
are uniform across the length of the substrate, resulting in a
uniform final substrate thickness. Over the next few minutes,
the liquid elastomer in the ridges spreads out, resulting in aflat, uniform substrate over a large area. Although we have notdemonstrated it in this work, we point out that semi-continuous

elastomer substrates could be prepared in this way usingroll-to-roll processing equipment.
We measured the resulting substrate thickness with a
Zeta 20 optical microscope (Zeta Instruments) with the ability
to measure sub-micron variations in thickness and determinedthat the thickness was 283 ± 48.4μm. This was based on
10 observations across the prepared substrate. We should notethat approximately 1cm around the edge of the substrate isvisibly thinner, and should not be used. Although the variation
is higher than what is observed in spin-coating at similar
thicknesses, the variation does not effect sensor performance,
and the substantial increase in substrate size makes this method
preferable.
We attached fabric reinforcements to the Smooth-Sil 950
base substrate to make the mounting holes in the finisheddevice more robust. We began by manually pressing uncured
liquid pre-elastomer into pieces of muslin fabric, then pressed
the infused fabric to the upper side of the Smooth-Sil 950
while the latter was partially cured. Bonding to a partially
cured substrate was found to have superior mechanical performance than bonding to a fully cured substrate. Partial curing toachieve a tacky state required approximately one hour at room
temperature, depending on ambient environmental conditions.
Once the base substrate had cured overnight at room
temperature, it was ready for patterning. In order to pattern
the substrate, we used a Universal Laser Systems VLS2.30
laser system with a 30W C O2 laser module emitting at awavelength of 10.6μm. This allowed us to directly pattern thesubstrate without the use of a mold. The sensor skin pattern isshown in Fig. 4. Once patterned, we cleaned the features byvigorous scrubbing with a paper towel soaked with acetone,
followed by sonication in a Branson 1800 bath sonicator,
followed by washing the sensor array in acetone, isopropanol,
ethanol, and distilled water.

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Thorough cleaning is a critical step in our laser-based fabrication process which produces substantial amounts of soot.
This step is not required in mold-based processes. However,
we believe that the ability to pattern large substrate without
having to manufacture a mold makes up for this deficiency.
We have found that a combination of mechanical and chemicalcleaning is required to adequately clean the surface of thesubstrates after laser processing. We have selected the combination of acetone, isopropanol, and ethanol by balancing theircleaning abilities with the damage caused to the parts. Toluene,
for example, is a superior cleaning agent, but causes >10%
shrinkage of the parts. We have found that a simple visualinspection is sufficient to determine when a part is sufficiently
clean. In the case of the Smooth-Sil 950 used in theseexperiments, the substrate is blue, while the soot resulting
from the laser ablation process is white, making it easy toidentify on the surface. If any soot is observed after cleaning,
the part is re-cleaned using the procedure described above.
To complete the device, we prepared another elastic
substrate of Sylgard 184 using the same rod coating method.
Depending on ambient humidity, curing the Sylgard 184 for
12 to 18 hours at room temperature resulted in a tacky
consistency. We placed the patterned base substrate, channels
down, onto the surface of the partially cured substrate, working
slowing to minimize the bubbles between the layers. This
sandwich is allowed to cure for at least one day to complete thebonding. We have found that tacky bonding has superior adhesion to plasma bonding, and substantially lower probability offilling channels relative to using a liquid “glue” layer. These
results are consistent with the findings of Eddings, et al [46].
Once bonded, a final patterning step was performed to cut thesensor skin to its final size using the VLS 2.30 laser patterning
system. The completed elastomer module is shown in Fig. 1.
At this point, the elastomer module is complete, but does
not contain sensor elements. The last step in the assembly
process is to fill the microchannels created via laser patterningwith eutectic gallium indium alloy. We do this by injecting theliquid metal into the microchannels using a syringe and needle.
Once filled, we insert enamel-coated 34Ga copper wires withapproximately 1cm of insulation stripped from each end into
the ports illustrated in Fig. 4. To finalize the module, dropletsof Sylgard 184 are used to seal the fill ports and wires.
B. Measurement of Strain via Changes in Resistance
The resistance of the sensors embedded along the edges ofthe structure changes as a function of strain. As the resistanceof each element is less than 10, compensating for the effectsof contact resistance becomes important. Our measurements
indicate that contact resistance is approximately 1 acrossboth interfaces, and changes in response to changes in wetted(conducting) area due to inconsistent adhesion between theliquid metal and interface electrodes. Therefore, we employeda four-wire approach. We supply a fixed current to the outer
two terminals, while measuring the voltage drop across theinner terminals. Signal conditioning was accomplished using
a custom-built breadboard composed of three channels readby an Arduino Uno R3 microcontroller connected via USB

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Fig. 5. Electronics used for signal conditioning. Part (a) depicts the voltage
reference. The voltage reference was set to 3.00V using the potentiometer.
Part (b) depicts the transimpedance amplifier used to provide constant current
through the sensor. Part (c) depicts the differential amplifier used to measure
the voltage drop across the sensor element and output the result to an ADC
on an Arduino microcontroller (not shown). A single instance of the voltage
reference was used. Parts (b) and (c) were repeated three times to provide
parallel measurements of the three resistive strain elements on a single sensor.
The circuits in Parts (b) and (c) were implemented using a single quadop amp for each channel.

to a PC running Ubuntu 14.04. Each channel of the signal
conditioning breadboard was composed of a transconductance
amplifier to supply constant current to the resistive strain gauge
element and a differential amplifier to measure the voltage
drop across the gauge. These electronics are shown in Fig. 5.
The modules were tested by pinning the three ends
at an array of locations. We used a polystyrene sheet(McMaster-Carr) with a laser-cut pattern of holes to conduct
this test. 3D printed “push-pins” were used to pin the module
to the polystyrene sheet. We tested various configurations
such that the strain between nodes varied from 0% to 25%.
We note here that we are not interested in the true strain
in the strain gauge. We understand that the strain between
nodes and the strain in the gauge will be different due tovariation in how the module membrane deforms. However,as we are measuring the response of the resistive element
and comparing it to the nodal displacement, the actual strain

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Fig. 6.
Unstretched (left) and stretched (right) modules on polystyrene
pegboard (background). 3D printed pegs are visible at the ends of the stretched
module. Pins protrude from the pegs, through the module, and into the holes
in the pegboard. Pins are held in the board by friction. Note that electricallead wires have been removed from these devices for clarity. The holes in thepegboard are 1/4 apart.

in the gauge is unimportant. The pegboard used in thisexperiment, with a module in place, is shown in Fig. 6.
We used a script written in Python to select test configurations at random and to read the strain gauge data through theArduino Uno R3 microcontroller. During the test, the program
would select a combination of holes to pin the module to, wait
for the operator to pin the module at the required location,then read and record the data. The experimental matrix consisted of 156 observations of 56 unique configurations. Eachobservation included measurements of all three strain gauges
in each module. The measurements performed in this study
are quasi-static. However, our previous work indicates thatloading rate is minor effect in elastomer sensors made fromthese materials, up to 100mm.mi n −1 [47]. In our intended
robotic application, we do not foresee loading rates which
would cause a significantly different response than observedin these quasi-static tests.
The baseline resistance, R0 , was measured once for eachstrain gauge before the test sequence and once after. The
baseline resistance used for the computations described below
was the average of those two observations. The baseline
resistance of the sensors, across all three modules used in
the tests, was 3.75 ± 0.373 (95% confidence, n = 18). The
sequence of 156 measurements took between 6 to 8 hours
to complete. The average change in undeformed resistance
between the start and end of the test across all tests was
0.108 ± 0.504 (95% confidence, n = 9). Excluding one test
which was a clear outlier, this reduces to 0.0354 ± 0.0387
(95% confidence, n = 8). This outlier was element 1 on
module 3, which is visible in Fig. 7(c). We have included
this data in all other calculations. The change in resistance of
0.0354 is 0.943% of the undeformed resistance, which we
believe is sufficiently low that it can be neglected. Therefore,
we are comfortable using only two measurements of baseline
resistance. We also note that the stability of the baseline overthis extensive series of deformations suggests the utility of thisdevice in real-world applications such as robotic proprioception. For a detailed analysis of the response of this type of

Fig. 7. Normalized change in resistance as a function of strain for threemodules. Images (a)-(c) show data for modules 1-3, respectively. Points areexperimentally measured resistance values for the three strain gauges on thedevice. The solid line represents the least squares approximation of the data.
The shaded region represents the 3σ confidence interval taken over all of thedata. Note that the same calibration was used for all three modules, indicating
repeatiblity across modules and between resistive elements within a module.

liquid-embedded elastomer strain sensor, including studies ofloading rate, cyclic load, and stress relaxation, we suggest ourrecently published work [47].

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IV. R ESULTS
Fig. 7 shows the response for three modules. The experimental data in these figures were obtained by fixing the geometry using the pegboard discussed previously and measuring
the change in resistance. In each figure, the data for all threestrain gauges of a given module are presented. The strain in
the horizontal axis is only the strain along the side of thecorresponding strain gauge. The coupling between the output
of a gauge and the strain in the opposite sides of the triangulararray are negligible. For example, the data for element 1 isplotted against the strain in side 1, regardless of the strain insides 2 and 3.
The least squares fit curve in the figures represents theinverse problem, where the normalized change in resistanceis treated as the measured value, and strain is the value to be
determined. The inverse problem is representative of how themodules will be used in practice. We considered a simplified
resistive strain gauge to provide a theoretical basis for ourmodel. We made the assumptions that the conductive liquid
metal within the strain gauge is incompressible, and that thecross-section of the conductive trace is constant throughout
its length. This latter assumption was confirmed by crosssection measurements of the channels with a Zeta 20 optical
microscope (Zeta Instruments). The volume of the liquid
metal, which is conserved, is therefore:V = 6L 0 A(1)

where A is the initial cross-sectional area, L 0 is the undeformed length, and the factor 6 accounts for the 6 parallel pathsin the strain sensor (see Fig. 4). The deformed cross-section is:A∗ =6L 0 A
L0 A
L0 A
= ∗ =
6L ∗
L
L0 + δ

(2)where A∗ is the cross-section in the deformed state, L ∗ is thedeformed length, and δ is the magnitude of the deformation.
We can relate the deformation to the strain by δ =  L 0 .
Substituting and canceling out L 0 , we find that:
A∗ =

A
1+

(3)

This equation is inverted to find a relationship between the normalized change in resistance, which is measured, to the strain:

1 R
(8)
 = −1 + 1 +4 R0
In order to fit the data, we used a generalized least squares
approach. Given the quadratic relationship between strain andnormalized change in resistance from the proceeding analysis,
we assumed a model in the form:
 = a0 + a1r + a2r 0.5

ρ L0
(4a)
A
ρ L∗
R∗ = ∗(4b)A
where R0 and R ∗ are the initial and deformed resistances,respectively. The change in resistance is therefore:
R0 =where ri is the normalized change in resistance of thei t h measurement, i is the applied strain of thei t h measurement, and ai are the parameters of the fit.
We express this system as:

ρ L0
ρ L∗
−
A∗
A
The normalized change in resistance is:(5)

R
AL ∗ − A∗ L 0=
R0
A∗ L 0(6)

Substituting the expressions for A∗ and L ∗ into this equation
results in the final form of the normalized change in resistance:
(7)

(11)

The least-squares fit of this experimental data is:
a = (R T R)−1 R T s(12)Using the data in Fig. 7, we found that the parameters of
the fit are:a = [−0.07320, 0.1342, 0.3711]T

R =

(9)

where  is the applied strain and r is the normalized change
in resistance, namely r = R
R0 .
We created Equation 9 by inspection. The non-linear termcame from inspecting the previous equation and noting that
R/R0 appears with a power 1/2. There are two non-idealities
that complicate this expression. The offset term, a0 , is due
to prestrain caused by material shrinkage. The strain between
nodes is computed based on a nominal initial length. However,during curing, the elastomer contracted slightly, resulting in a
initial, unstrained node-node spacing that was smaller than
the nominal. The linear term a1 is due to the difference
between the node to node strain and the strain observed in thesensing element. Due to the geometry of the module, the strain
observed in the interior of the triangular module where thesensors are located was less than that applied to the exterior,
necessitating the use of a scaling factor.
With this, we cast our experimental data in the form:⎤⎡⎡ ⎤1 r0 r00.5
0
⎡ ⎤
⎥
⎢
⎢1 ⎥
⎢1 r1 r10.5 ⎥ a0⎥⎣ ⎦ ⎢ ⎥⎢(10)⎥⎢1 r2 r 0.5 ⎥ a1 = ⎢⎣2 ⎦⎣2 ⎦ a2..
..
.
.

Ra = s

The resistance is given by:

R= (2 + )
R0

2613

(13)

This solution is what was used to draw the solid lines
on Fig. 7.
Based on the least squares approximation, we also computed
the error between the approximation and the actual data. Theseerrors, across all three elements on three arrays (nine totalelements) are presented as a histogram in Fig. 8. Using
this data, we found that the standard deviation (σ ) in theerror in estimated strain is 0.0152, which is 6.08% of the
full-scale.

2614

IEEE SENSORS JOURNAL, VOL. 16, NO. 8, APRIL 15, 2016

Fig. 8. Histogram showing error between applied and computed strain acrossall strain gauges and modules. Computed strain is based on the measured
normalized change in resistance and the least squares fit of the data. Zeroerror represents no difference between the reconstructed strain and the applied
strain.

Fig. 9.
Example state reconstruction geometry. The solid blue triangle
represents the true geometry of the module. The solid red circles represent
the reconstruced locations of the nodes based on the measured resistance.
The red dashed lines connect the solid red circles. The hollow red circles
represent the reconstructed locations of the nodes based on the perturbed
length values. Only six such perturbed estimates are shown in the figure,although 100 samples were used in practice. The error bars shown on thenodes are based on the observed standard deviation in the reconstructed node
positions (hollow red circles). The geometry in this figure is notional, anderrors have been exaggerated for clarity.

Finally, we reconstructed geometry based on measured
resistance values. Since the modules have no way to establish
their position in a global sense, we applied a local coordinate
system. This coordinate system was centered at one node of
the module, and the X coordinate passing through anothernode. We show the labeled geometry in Fig. 9. The nominal
coordinates (in inches) of the nodes were (0.0, 0.0), (4.0, 0.0),
and (2.0, 3.5). Let L 0 be the distance between nodes 0 and 1,
L 1 be the distance between nodes 1 and 2, and L 2 be thedistance between nodes 2 and 0. In terms of strain, theseFig. 10.
Reconstructed sensor geometry shows the comparison
between the reconstructed geometry based on the resistance measurements(red dashed line) and the known deformed geometry (solid blue triangle)
for three measurements (a-c). Error bars around the nodes represent the3σ uncertainty bounds. There are no error bars around the lower left nodeas that node is defined as the origin of the coordinate system. The only
uncertainty in the position of the node at the lower right is in the horizontal
direction, as the vertical position is defined to be zero. The inset shows anenlargement of the area around the upper node. The dimensions of the inset are
15mm × 15mm.

lengths were:L 0 = L(1 + 0 )(14a)

L 1 = L(1 + 1 )L 2 = L(1 + 2 )

(14b)
(14c)

where L is the undeformed length of a side. Basedon the definition of the local coordinate system,
x 0 = y0 = y1 = 0. The remaining positions were specifiedby:
x1 = L 0
L 2 − L 21 + x 12
x2 = 22x 1
y2 =L 22 − x 22

(15a)
(15b)
(15c)

To compute the strain, i , in Equation 14, we used themodel presented in Equation 9, with the coefficients from

WHITE et al.: MULTI-ELEMENT STRAIN GAUGE MODULES FOR SOFT SENSORY SKINS

Equation 13. The resistance values were measured directlyfrom the strain gauges.
We used a perturbation approach to determine therelationship between the uncertainty in the gauge lengths andthe node positions. Since the relationship between the error
in the measured lengths and the positions of the nodes is
non-linear and depends on the configuration of the module,
we use a Monte Carlo approach to estimate the uncertainties.
To perform this analysis, we assumed that the errors in
the gauge measurements were uniformly distributed with
3σ = 0.0456. This matches the distribution observed in Fig. 8and includes a factor of 3 to include 3σ uncertainties.
To begin the analysis, we started with the nominal gaugemeasurements, then applied a randomly drawn perturbation
based on the distribution described above. We then computed
the resulting node positions, based on Equations 14(a-c). The
resulting positions are shown as open red circles in Fig. 9.
We repeated this random draw procedure 100 times to develop
a population for statistical analysis (only six such positions areshown in the figure for clarity). We computed the geometricdistance between the nominal node location and each
perturbed location and developed an error distribution basedon this measure. From that distribution, we computed theuncertainty in the reconstructed node position. Reconstructed
triangles with uncertainty estimates are shown along withknown geometry in Fig. 10. The six figures shown are
representative of the full set of experiments.
V. C ONCLUSION
In this paper we have demonstrated the fabrication andperformance of a multi-element resistive strain gauge module
for state measurement. This device is an important building
block for soft sensory skins. We have demonstrated that the
manufacturing process is consistent between modules, and thatstrain gauges across different modules, as well as within each
modules, have similar performance characteristics. Further, wedemonstrate that even with the current rudimentary signal
conditioning approach we have achieved sufficient accuracy
to be of use in many soft robotic applications.
One of the significant limitations in the present work is
the interconnection between the modules and the signal conditioning electronics. The current electronics implementation
hinders the application of these modules to soft robots andlimits mobility of the test apparatus. In the future, we will
focus on integrating the signal conditioning into the elastomer
substrate. We believe this is the next step towards state-aware
sensor skins fabricated from elastomeric materials.
ACKNOWLEDGMENT
The authors wish to thank Michelle Yuen for her contributions in the design and manufacturing of the polymer-infused
reinforcement tabs on the ends of the sensor arrays.
Any opinion, findings, and conclusions or recommendations
expressed in this material are those of the authors and do notnecessarily reflect the views of the National Science Foundation or the National Aeronautics and Space Administration.

2615

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Edward L. White received the M.S. degree in mechanical engineering andthe M.B.A. degree from the University of Arizona, Tucson, AZ, USA. He iscurrently pursuing the Ph.D. degree with the Fabrication Laboratory, Schoolof Mechanical Engineering, Purdue University, West Lafayette, IN, USA.
His research is focused on making soft-robotic systems more manufacturerable
and robust.

Jennifer C. Case received the B.S. degree in mechanical engineering from
Northern Illinois University, DeKalb, IL, USA, in 2013. She is currently
pursuing the Ph.D. degree in mechanical engineering from Purdue University,
West Lafayette, IN, USA. Her research is focused on adding closed-loop
control systems to highly deformable robots.

Rebecca K. Kramer received the B.S. degree from Johns Hopkins University
in 2007, the M.S. degree from the University of California, Berkeley, in 2008,
and the Ph.D. degree from Harvard University in 2012. She is currently
an Assistant Professor of Mechanical Engineering with Purdue University.
At Purdue, she founded the Fabrication Laboratory, which contains a leading
facility for the rapid design, fabrication, and analysis of materially soft andmultifunctional robots. Her research interests involve stretchable electronics,
soft actuators, soft material manufacturing, and soft-bodied control. She is
the recipient of a 2014 NASA Early Career Faculty Award and a 2015 NSF
CAREER Award. She was named to the 2015 Forbes’ 30 under 30 lists.