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ResearchCite this article: Droogendijk H, de Boer MJ,

Sanders RGP, Krijnen GJM. 2014 A biomimetic

accelerometer inspired by the cricket’s clavate

hair. J. R. Soc. Interface 11: 20140438.

http://dx.doi.org/10.1098/rsif.2014.0438

Received: 26 April 2014

Accepted: 21 May 2014

Subject Areas:biomimetics, biomechanics, mathematical

physics

Keywords:accelerometer, cricket, MEMS, bio-inspired,

clavate hair

Author for correspondence:H. Droogendijk

e-mail: h.droogendijk@utwente.nl

& 2014 The Author(s) Published by the Royal Society. All rights reserved.

A biomimetic accelerometer inspired bythe cricket’s clavate hair

H. Droogendijk, M. J. de Boer, R. G. P. Sanders and G. J. M. Krijnen

MESAþ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands

Crickets use so-called clavate hairs to sense (gravitational) acceleration to

obtain information on their orientation. Inspired by this clavate hair system,

a one-axis biomimetic accelerometer has been developed and fabricated

using surface micromachining and SU-8 lithography. An analytical model is

presented for the design of the accelerometer, and guidelines are derived to

reduce responsivity due to flow-induced contributions to the accelerometer’s

output. Measurements show that this microelectromechanical systems

(MEMS) hair-based accelerometer has a resonance frequency of 320 Hz, a

detection threshold of 0.10 ms22 and a dynamic range of more than 35 dB.

The accelerometer exhibits a clear directional response to external accelerations

and a low responsivity to airflow. Further, the accelerometer’s physical limits

with respect to noise levels are addressed and the possibility for short-term

adaptation of the sensor to the environment is discussed.

1. IntroductionIn biology, mechanosensors, equipped with differing hair-like structures for

signal pick-up, are sensitive to a variety of physical quantities such as acceleration,

flow, rotational rate, balancing and IR-light [1,2]. As an example, crickets have

various types of hair-like receptors for measurement of several environmental

quantities. For sensing of low-frequency flows (typically less than 1 kHz) to

obtain information about the environment and avoid, for example, predator

attacks, crickets use filiform hairs, which are situated on the dorsal side of two

abdominal appendages called cerci and which are able to sense airflows with vel-

ocity amplitudes down to 30 mm s21 [3,4] and operate around the energy levels of

thermal noise [5]. Crickets gather also information about their environment by the

use of bristle hairs, which activate interneurons that respond to tactile stimuli of

the cercus and abdomen [6]. Further, crickets have club-shaped sensilla, called cla-

vate hairs, located on their cerci (figure 1), with hair lengths of 20–250 mm [8].

These clavate hairs turn out to be sensitive to (gravitational) acceleration, provid-

ing the cricket information on its orientation [7–10]. For example, a cricket uses its

clavate hairs to compensate head movement when it is rotated around its longi-

tudinal axis [11], for which such rotations can be measured with a resolution of

about 0.18 [9]. Additionally, Bischof [9] showed that these clavate hairs can

respond to harmonic accelerations with frequencies up to 300 Hz.

For measuring (gravitational) acceleration, numerous types of accelerometers

have been realized over the past years using microelectromechanical systems

(MEMS) technology, with applications in, for example, the automotive industry

and navigation [12]. Current state-of-the-art commercialized MEMS acceler-

ometers show formidable performance in range, resolution and noise floor. In

contrast to the cricket’s clavate system, MEMS accelerometers are usually not

hair-based systems and frequently contain feedback electronics. To explore

some of the intricacies of the clavate hair system and assess its potential for engin-

eering applications (e.g. automotive industry, robotics and motion tracking), we

aim to design, fabricate and characterize a biomimetic accelerometer. Biomimetic

hair-based structures have been exploited earlier with applications in both

actuation and sensing of physical quantities [13,14], but seldom for inertial

measurement. Previously, a hair-like accelerometer has been investigated by

Tang et al. [15], but its response to external accelerations was not demonstrated.

40

60

14

10

90806040

10

Figure 1. Artist’s reconstruction of the clavate hair-based sensory system (adapted from [7]).

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In this paper, we present the design and fabrication of

a biomimetic accelerometer using MEMS technology and

report on its characterization with respect to externally applied

accelerations. We also assess, both theoretically and experimen-

tally, responsivity due to flow-induced contributions to the

accelerometer’s output and derive design guidelines on how

to reduce these effects. Further, we address the accelerometer’s

physical limits with respect to noise levels and discuss the possi-

bility for short-term adaptation of the sensor to the environment

by electrostatically tuning the sensor’s responsivity.

2. Theory and modelling2.1. Hair mechanicsMechanically, the hair-based accelerometer can be under-

stood as a so-called inverted pendulum which is subjected

to external accelerations (figure 2). It is described as a

second-order rotational-mechanical system with moment

of inertia J, a rotational stiffness S and a rotational damping

R, resulting in a description of the system’s response to

harmonic accelerations by

u(v) ¼ Ta

S� Jv2 þ jvR, (2:1)

where for a cylindrical hair, the moment of inertia can be

expressed as

J ¼ prd2

484L3 þ 3

4d2L

� �: (2:2)

In these expressions, u(v) is the rotational angle amplitude

of the hair and Ta is the amplitude of the torque acting on

the hair. Usually, in the models the hairs are treated as cylind-

rical structures [4], but here the hair is modelled as an

inverted conical shape to take the MEMS-hair-shape into

account. We will show that this eventually will only lead to

a geometry-dependent factor h such that J � hrd2L3.

From (2.2), the moment of inertia J depends strongly on the

hair diameter d and hair length L. The torque Ta is a

consequence of external accelerations, or the projections

thereof, in the direction perpendicular to the hair and perpen-

dicular to its rotation axis, denoted here by aext. Using

Newton’s second law, Ta is found by integrating the inertial

contributions by over the hair

Ta ¼ðL

0

aextrpd(z)

2

� �2

zdz ¼ J � aext, (2:3)

where J can be expressed as

J ¼ phr

8d2L2: (2:4)

In these expressions, r is the density of the hair and h a par-

ameter that depends on the precise geometry of the hair.

Further, we assume that the rotational angle amplitudes u are

small, so the torque Ta can be considered directly proportional

to the external acceleration aext.

2.2. DesignThe hair mechanical system behaves like a classical second-

order system and consequently exhibits the trade-off between

responsivity and bandwidth. The responsivity of the hair accel-

erometer for frequencies well below the system’s resonance

frequency (v� vr) is defined as

responsivity ¼ du(v)

daext

����v¼0

¼ ph

8

rd2L2

S: (2:5)

The bandwidth of the system is estimated from the system’s

resonance frequency

bandwidth ¼ vr ¼

ffiffiffiSJ

s: (2:6)

By taking the product of responsivity and bandwidth, a

figure of merit (FoM) can be defined for the biomime-

tic hair accelerometer, similar to the approach described by

Krijnen et al. [16]

FoM ¼ responsivity� bandwidth: (2:7)

SR

J

acceleration

Ta

q (w)

Figure 2. Schematic view of inertial measurement by hair-like structures.

Table 1. Experimental values of the biomimetic hair-based accelerometer.

quantity symbol value

hair geometry

hair length L 800 mm

hair diameter d 80 mm

mechanical parameters

torsional stiffness S 9.07 � 1029 N m rad21

torsional resistance R 2.44 � 10213 N m s rad21

moment of inertia J 2.25 � 10215 kg m2

flow contributions (80 Hz)

added damping Rm 1.91 � 10214 N m s rad21

added mass Jr 1.07 � 10218 kg m2

added mass Jm 1.94 � 10217 kg m2

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When the hair length is considerably larger than the hair

diameter (L� d), this FoM can be simplified to

FoM/

ffiffiffiffiffiffiffiffiffiffird2L

S

s: (2:8)

As a result, to achieve a ‘good’ hair-based accelerometer, the

sensor should have a long and thick hair (high d and L), as

well as a compliant mechanical suspension (low S).

2.3. Flow contributionsAlthough the hair structure is responsive to external accelera-

tions, dynamic accelerations will lead to a net flow velocity

[9]. That is, the hair is moving with a relative velocity vthrough its surrounding medium, for which we consider

the medium velocity itself to be zero

v ¼ aext

jv: (2:9)

As a consequence, viscous forces will contribute to the

total hair mechanical response for external accelerations.

Following the approach given by Shimozawa et al. [3], these

flow-induced contributions can be taken into account.

The angular deflection amplitude um(v) for a hair subject to

external harmonic acceleration at frequency v, including

flow-induced torque, is found to be

um(v) ¼aext

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiJ

2 þ (x=v)2q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi[S� (J þ Jr þ Jm)v2]2 þ [(Rþ Rm)v]2

q : (2:10)

Here, J is the inertial-induced torque contribution as defi-

ned in (2.4), and x represents the flow-induced torque

contribution (see appendix A)

x ¼ jZSjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA2

f þ B2f

q, (2:11)

where the variables Af and Bf are defined as

Af ¼ðL

0

k(z)z cos (zz þ hS)dz and

Bf ¼ðL

0

k(z)z sin (zz þ hS)dz, (2:12)

with k(z) a parameter that depends on the flow-profile

k(z) ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ e�2bz � 2e�bz cos (bz)

p: (2:13)

The quantities Jr and Jm are often referred to as virtual added

mass, and Rm as virtual added damping [17]

Jr ¼prd2L3

12, Jm ¼ �

p2mGL3

3gvand

Rm ¼4

3pmGL3, (2:14)

where m is the air dynamic viscosity, and r is the air density.

The dimensionless parameters g and G are defined in appen-

dix A. Note that when the flow contributions are small

(x=v� J, Jr þ Jm � J and Rm � R), the expression for the

rotational angle um(v) will simplify to (2.1).

To evaluate the analytical model, the values for the par-

ameters of the hair-flow sensory system as given in table 1

are used. In this work, given the mechanical parameters Sand R listed in table 1, the hair geometry (L and d ) is

chosen such that the inertial-induced Ta is large with respect

to Tf (generally about 100�), so that the hair-based acceler-

ometer is primarily inertially responsive. Also, the torsional

stiffness S is chosen such—by proper dimensioning the

torsional beams which act as the torsional spring—that

the resonance frequency of the sensor lies between 100 and

1000 Hz. The torsional damping R is usually determined by

squeezed film damping and needs to be found experimen-

tally. The flow contributions contain a (slight) frequency

dependency, and therefore a frequency needs to be chosen

to evaluate these contributions. As several experiments (e.g.

linearity) were performed at 80 Hz, this frequency was used

for evaluation.

2.4. Thermal noiseAn important characteristic of a sensory system is its signal-

to-noise ratio (SNR). Generally, when the SNR is equal

SU-8

(a) (b)

Al

SixNy

SiO2

Si

Figure 3. (a) Design and (b) fabrication of the MEMS hair-based accelerometer fabricated by surface micromachining and using SU-8 lithography. (Online versionin colour.)

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or higher than one, a system may detect the input signal.

Hence, besides the responsivity of the sensor, the noise

level of the system determines the fundamental detec-

tion threshold of the system. To find the detection threshold

of our system, we consider the power spectral density

due to the Johnson–Nyquist (thermal) white noise in the

system [18]

�T2n ¼ 4kBT0(Rþ Rm), (2:15)

where kB is the Boltzmann constant, T0 is the ambient temp-

erature and �T2n the square of the noise-induced equivalent

torque per unit of bandwidth. The mechanical transfer func-

tion H(v) of the system determines the resulting mechanical

response to the noise

H(v) ¼ 1

S� (J þ Jr þ Jm)v2 þ j(Rþ Rm)v: (2:16)

The equivalent noise angle Qn is found by integrating the

noise power over the full spectrum and taking the square root

Qn ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1

0

�T2njH(v)j2dv

s: (2:17)

The detection limit ath is found by dividing the sensor’s

equivalent noise angle Qn by the rotational angle Qm for an

acceleration of 1 m s22

ath ¼Qn

Qmjaext¼1 m s�2

: (2:18)

Thermal noise calculations for our hair mechanical system

indicate a detection threshold for acceleration sensing of

about 1.1 � 1023 m s22 for frequencies within a bandwidth

of 1 kHz.

3. FabricationThe fabrication process for the biomimetic accelerometer is

based upon the process for cricket-inspired biomimetic hair

flow sensors, previously developed in our group [19,20].

A schematic overview of the biomimetic accelerometer with

the materials indicated is shown in figure 3a.

The sensor is fabricated on a silicon-on-insulator wafer.

Trenches are etched in the silicon device layer using DRIE.

A layer of 200 nm stoichiometric Si3N4 is used for covering

and protecting the trenches. The device layer contains two

electrodes, which are used for capacitive read-out of the accel-

eration-induced movement. On top of the Si3N4 layer, a

sacrificial layer of poly-silicon (1.5 mm) is deposited by

LPCVD. The sensor membrane and springs are constructed

by depositing and patterning a 1 mm SiRN layer on top of

the poly-silicon. Aluminium (80 nm) is sputtered on top

of the membrane to create the electrodes for capacitive

read-out. Our artificial clavate hair is created by two layers

of SU-8, to realize both the centre of mass towards the

top of the hair structure and a total hair length of about

800 mm with an average diameter of about 80 mm. Finally,

to release the membrane the sacrificial poly-silicon layer

is removed using XeF2 etching. The fabrications results are

shown by the SEM image in figure 3b.

4. Material and methods4.1. Experimental set-upExperiments to measure the sensor’s response are performed using

the set-up shown in figure 4. A waveform generator (Agilent

33220A-001) is used to produce a sinusoidal signal at a frequency

f (v ¼ 2pf ) that is supplied to an amplifier. This amplifier drives a

voice-coil shaker (MB Electronics PM 50) to generate harmonic

acceleration. Carrier signals at 1 MHz are supplied to the bottom

electrodes of the accelerometer for capacitive read-out. The top

electrode is connected to a charge amplifier, and after demodula-

tion and filtering (Stanford SR 650) the sensor’s response is

monitored on an oscilloscope (Agilent DS1024). For calibration,

the applied accelerations were measured by mounting a reference

accelerometer (STEVAL-MKI021V1) on the shaker.

4.2. Frequency responseFirst, the frequency response of the hair-based accelerometer

was measured using capacitive read-out in the direction per-

pendicular to the rotational axis. Frequencies within a range of

50–1000 Hz were applied to the shaker. The reference acceler-

ometer was used to determine the externally applied acceleration

amplitude. The resulting measured magnitude response of the bio-

mimetic accelerometer is shown in red in figure 5. Here, the circles

represent the measurements and the dashed line exhibits the

analytical model based on (2.1), where the resonance frequency

v0 and the quality factor Q were fitted. We observe good agree-

ment between model and measurements, where the resonance

frequency is found to be about 320 Hz.

AC voltage

carrier signals

shaker

oscilloscope filter

demodulation

charge amplifier

amplifier

Figure 4. Capacitive measurement set-up for determining the membrane rotation of the biomimetic accelerometer. (Online version in colour.)

0.001

0.01

0.1

1

10

1000100mec

hani

cal t

rans

fer

(VR

MS

m–1

s2 )

frequency (Hz)

frequency response – magnitude

accelerationflow

Figure 5. Measured mechanical transfer of the hair-based accelerometerusing capacitive read-out. (Online version in colour.)

–270

–180

–90

0

90

1000100

phas

e (°

)

frequency (Hz)

frequency response – phase

measurementsanalytical model

Figure 6. Measured phase-shift of the hair-based accelerometer usingcapacitive read-out. (Online version in colour.)

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Additionally, flow measurements have been performed by

replacing the shaker by a loudspeaker to apply an oscillating air-

flow. The measured response for accelerations induced flow is

shown in blue in figure 5, where the measured flow response

per metre per second has been normalized to acceleration equiv-

alent flow response using (2.9). Here, the squares represent the

measurements and the dash-dotted line exhibits the analytical

model based on (2.10) with J ¼ 0. Again, good agreement

between model and measurements is observed, with a similar

resonance behaviour. Furthermore, the overall responsivity

to acceleration-induced flow is significantly lower than the

responsivity to acceleration, as desired.

In addition to the magnitude of the response of the hair-

based accelerometer, the phase of its response was also

measured. Both measurements (points) and analytical model

(dashed line) are shown in figure 6. We observe good agreement

between measurements and model, and the phase-shift of about

1808 around resonance is clearly visible.

4.3. DirectivityThe sensor’s directivity was measured by rotating it over 3608,with steps of 108, with respect to the direction of the applied

external acceleration, while using capacitive read-out. To this

end, harmonic acceleration with a frequency of 80 Hz was

applied, and the output voltage was measured by a multimeter

(Keithley 2000). The obtained results are shown in figure 7.

We observe that the measurements are in close agreement with

the theoretical response for a so-called figure of eight. The

measurements indicate that the hair-based accelerometer has a

maximum responsivity for both 08 and 1808, which coincides

with the direction perpendicular to the rotational axis of the

hair sensor.

4.4. Threshold and linearityTo obtain a model that describes the sensor’s SNR as a function

of acceleration amplitude as well as the sensor’s detection

threshold, the signal and noise powers are considered. The

signal is assumed to have a linear relationship with respect to

the acceleration amplitude a0, given by the coefficient Sc(v).

This coefficient is directly related to the sensor’s rotational

angle u(v) and therefore has a dependency on the acceleration

frequency v. Nc is a constant representing the total noise,

giving for the measured output z due to the uncorrelated sources

z(v) ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(Sc(v)aext)

2 þN2c

q: (4:1)

From this expression, the measured detection threshold amin can

be found by equating the noise and signal powers (or alterna-

tively by calculating the intersection value of the asymptotes)

which requires only the values for Sc and Nc

amin(v) ¼ Nc

Sc(v): (4:2)

0

0.1

0.2

outp

ut v

olta

ge (

VR

MS)

0.3

directivity measurement

0

30

6090

120

150

180

210

240270

300

330

measurements theoretical

Figure 7. Measured directivity of the hair-based accelerometer using capaci-tive read-out at an acceleration frequency of 80 Hz. (Online version in colour.)

0.01

0.1

1

0.1 1 10

outp

ut v

olta

ge (

VR

MS)

acceleration (m s−2)

linearity and noise level at 80 Hz

measurementsanalytical model

Figure 8. Measured response versus acceleration amplitudes at a frequency of80 Hz using capacitive read-out. (Online version in colour.)

0.01

1

Alla

n de

viat

ion

(ms–2

)

averaging time (s)

Allan deviation results

measurementsbias instability

velocity random walk

10 100

Figure 9. Measured Allan deviation using capacitive read-out. (Online versionin colour.)

Table 2. Experimental values of the biomimetic hair-based accelerometer.

quantity symbol value

mechanical parameters

quality factor Q 12.5

resonance frequency f0 319.6 Hz

sensor performance (80 Hz)

threshold amin 0.10 m s22

dynamic range DR �35.6 dB

full-scale error 1FS 3.3%

velocity random walk VRW 1.67 m s21ffiffiffiffiffiffih�1p

bias instability sb 5 � 1023 m s22

thermal noise limit ath 1.1 � 1023 m s22

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Experiments to determine the sensor’s linearity were performed

by choosing first a specific acceleration frequency (80 Hz) and

then by varying the acceleration amplitude. Subsequently, from

the measured output RMS-voltage the sensor’s detection limit

and linearity are derived. The results are shown in figure 8,

where the points represent the measurements, the solid line is

based on (4.1), and the dashed lines indicate the constant equiv-

alent noise amplitude and ideal linear response asymptotes. We

observe that for accelerations with an amplitude of more than

0.1 m s22, indicated by the intersection of the asymptotes, the

hair-based accelerometer exhibits a clear linear relationship

with the applied acceleration. Below this amplitude, the sensor’s

output is dominated by noise (SNR , 1).

To get some insight in the accelerometer’s noise performance

and stability, an Allan variance measurement was performed.

The zero-acceleration output RMS-voltage was measured with

a time interval of 20 ms for a period of 2 h using a multimeter

(Agilent 34401A) connected to LABVIEW. The results of the sub-

sequently calculated Allan deviation are shown in figure 9,

together with asymptotic lines for both the velocity random

walk and the bias instability.

From the linearity measurements, the error on full-scale (i.e. the

measurement taken at highest acceleration of 6.12 m s22; figure 8)

was calculated and found to be 3.3%. By considering the detection

threshold and the full-scale acceleration amplitude, the dynamic

range of the hair-based accelerometer is about 35.6 dB. The Allan

variance results showed a velocity random walk of 1.67 m s21

ffiffiffiffiffiffiffiffih�1

pand a bias instability of 5 � 1023 m s22. To summarize, an

overview of the sensor performance is shown in table 2.

5. DiscussionThe measured threshold of the biomimetic accelerometer is

about 0.10 m s22, which is about a factor 100 larger than the

calculated thermal noise based value of 1.1�1023 m s22. The

relative large detection threshold is due to the presence of com-

paratively strong noise sources in the read-out electronics [21].

Improvement of these electronics, by reduction of its noise, will

help to bring the detection threshold for the accelerometer

towards the thermal noise-limited threshold. Similar dif-

ferences between measured and (calculated) thermal noise

levels have been observed for our previously reported

biomimetic hair flow sensors [21,22].

As stated in §2, the hair sensor is designed in such a way to

have a negligible flow-induced response. Therefore, the ratio

between responsivity to acceleration and responsivity to accel-

eration-induced flow is desired to be large. This ratio is shown

in figure 10, and the various graphs indicate its dependence

on L and d. As stated earlier, the hair length L and diameter dhave a large impact on both inertial and flow-induced sensing,

and can be used to reduce the sensor’s flow responsivity relative

to its acceleration responsitivity. In figure 10, the dashed red

line indicates the original response ratio, together with the

measurements based upon data from figure 5 represented by

10

100

1000

100010010ratio

acc

eler

atio

n/flo

w r

espo

nses

frequency (Hz)

ratio between acceleration and flow response

analytical modelshorter hair (L/2)thicker hair (2d)

Figure 10. Dependence of the ratio of the acceleration to flow-inducedresponses. (Online version in colour.)

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circles. Although the hair length L has significant impact on both

flow and inertial responsivity, only a slight improvement is

gained in response ratio for lower frequencies when shortening

the hair (dashed-dotted blue line). However, by maintaining the

hair length and increasing the thickness of the hair by a factor 2,

an improvement of more than 300% can be gained for all fre-

quencies within the sensor’s bandwidth (dotted green line).

Also, by considering the FoM for a hair flow sensor [16], the

FoMflow scales with d1/3, while the FoMacc of the accelerometer

scales with d2 following (2.8). Therefore, to realize a ‘good’ accel-

erometer, the hair diameter is important for having both a good

FoM and minimal flow responsivity. This result is in coincidence

with observations for the cricket, as the cricket uses long and

thin (filiform) hairs for measurement of flow [23] and shorter

and thick (clavate) hairs for measurement of acceleration [8].

Additionally, to minimize the disturbance of surrounding air-

flow, the clavate hairs should be short, which coincides with

biological observations for the hair lengths (Lflow � Lacc):

As stated in Theory and modelling, the rotational angle

amplitudes u are assumed to be small. However, the presence

of the Earth’s gravitational field will lead to a projection of the

acceleration g in the direction of movement of the hair when

operating in the horizontal plane, comparable to a pendulum.

As a consequence, the torque exerted on the hair due to gcan be calculated using (2.3), which leads to an additional

angle-dependent term and can be regarded as a contribution

to the system’s torsional stiffness. Consequently, the system’s

frequency response changes to

u(v) ¼ Ta

[S� Sg]� Jv2 þ jvR, (5:1)

where Sg is the contribution due to the Earth’s gravitational

acceleration

Sg ¼ hpr

8d2L2g: (5:2)

In our case, this contribution due to g is negligible, as Sg has

a value of 1.88� 10211 N m rad21 in the case of a straight hair

(h ¼ 1), and the value of the system’s mechanical torsional

stiffness is about three orders of magnitude larger.

Generally, the susceptibility for (gravitational) acceleration

is used by crickets for determination of their position and orien-

tation. The hair-based accelerometer described in this work in

principle also allows for determination of orientation using the

Earth’s gravitational field. That is, by measuring the projection

of the Earth’s gravitational acceleration, the angle of rotation of

the accelerometer with respect to the Earth can be determined.

However, as the fabricated accelerometer has limits with respect

to resolution, an error in this angle will result. Based on the

experimental data listed in table 2, this error is calculated to

be in the order of 0.78 for accelerations well below resonance

(v! 0), which emphasizes the potential use of this accelero-

meter to determine orientation. Note that this value approaches

the resolution of the cricket’s clavate hair system of 0.18 [9].

As shown in figure 7, the hair-based accelerometer has a

strong directivity. In our MEMS version, this directivity

stems from both the mechanical design, which primarily

allows rotation around the torsional axis of the sensor, and

the differential capacitive read-out, which causes a strong

reduction of signals caused by tilting of the hair. As a conse-

quence, multiple hair-based accelerometers may be used

simultaneously to sense acceleration in three dimensions. In

crickets, filiform hairs have been shown to have preferential

directions of rotations with ratios in stiffness of ‘hard’ over

’easy’ directions between 4 and 8 [24]. Bischof [8] demonstrated

that such directivity exists in the cricket’s clavate hairs.

Additionally, Sakaguchi & Murphey [10] have shown that

crickets use the many clavate hair-sensors on their cerci for

determination of their orientation relative to the gravitational

field and that they do so both with respect to roll (rotation

around longitudinal axis of the animal) and pitch.

Continuing with biology-inspired systems, the perform-

ance of a sensory system can be adapted to the environment.

For example, the bullfrog’s internal ear displays adaptation

by mechanical relaxation of hair bundles [25], leading to a

change in stiffness of the saccular hair cell. A similar technique

can be applied to the biomimetic accelerometer by electrostati-

cally reducing the torsional stiffness S and could be useful for,

for example, robotic applications in which adaptation to the

environment is required. The technique of electrostatic spring

softening (ESS) has been investigated thoroughly for our

biomimetic hair-based flow sensors and can lead to an

improvement in responsivity of more than 80% and a reduced

sensory threshold of more than 50% in the case of noise which

is dominated by, for example, electronics [22]. As the acceler-

ometer’s geometry and parameters are similar to those of the

hair flow sensor, comparable results can be expected.

6. ConclusionA biomimetic accelerometer has been developed and fabri-

cated using surface micromachining and SU-8 lithography,

inspired by the clavate hair system of the cricket. We showed

that this MEMS hair-based accelerometer has a resonance

frequency of 320 Hz, a detection threshold of 0.10 m s22 and

a dynamic range of more than 35 dB. Further, the acceler-

ometer has low responsivity to airflow, clear directivity and a

bias instability of 5 � 1023 m s22. We have argued that the

accelerometer can be further optimized by increasing the hair

diameter, and that it principally allows for adaptation to the

environment by exploiting the mechanism of ESS.

Funding statement. This work is carried out within the BioEARS-project,funded by STW/NWO.

Appendix A. Flow contributionsAssuming that the flow with relative velocity v(t) is oscillat-

ing over a flat surface, the no-slip boundary condition gives

rise to the height z-dependent velocity profile [26]

v(t) ¼ V0 sin (vt)� V0e�bz sin (vt� bz), (A 1)

rsif.royalsocietypublishing.orgJ.R.Soc.Interface

11:20140438

8

on July 9, 2018http://rsif.royalsocietypublishing.org/Downloaded from

where b is proportional to the reciprocal of the boundary layer

thickness, with n the kinematic viscosity (b ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiv=(2n)

p):Using

trigonometric identities, expression (A 1) is written as a

sinusoidal function with an amplitude Vz and phase-shift zz

vz(t) ¼ Vz sin (vtþ zz), (A 2)

where

Vz ¼ V0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ e�2bz � 2e�bz cos (bz)

p(A 3)

and

zz ¼ arctane�bz sin (bz)

1� e�bz cos (bz)

� �: (A 4)

With the velocity profile given, the viscous forces exerted on

the hair are described in [27], under the assumption of small

angular displacements and low Reynolds and Strouhal num-

bers [4]. Following the analysis of Shimozawa et al. [3], the

torque Tf, due to the relative air-movement, acting upon the

hair can be expressed as

Tf ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA2 þ B2

p, (A 5)

where A and B are torque contributions given by

A ¼ðL

0

jZSjVzz cos (zz þ hS)dz and

B ¼ðL

0

jZSjVzz sin (zz þ hS)dz: (A 6)

In both A and B, the parameter Zs expresses the relation between

the oscillating airflow V and the force per unit length F

ZS ¼FV¼ ZSR þ jZSX, (A 7)

where

ZSR ¼ 4pmG and ZSX ¼prd2

4v� p2mG

g: (A 8)

In these expressions, G and g are dimensionless parameters

G ¼ �g

g2 þ (p=4)2, g ¼ gþ ln (s) and s ¼ d

4

ffiffiffiffiv

n

r: (A 9)

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