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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

Multi-point force sensor based on crossed optical ﬁbers S. Pirozzi Dipartimento di Ingegneria dell’Informazione, Seconda Università degli Studi di Napoli, 81031 Aversa, Italy

a r t i c l e

i n f o

Article history: Received 3 January 2012 Received in revised form 30 May 2012 Accepted 30 May 2012 Available online 8 June 2012 Keywords: Multi-point sensor Force sensor Bending losses Optical ﬁbers

a b s t r a c t The objective of this paper is to present a sensor concept based on optical ﬁbers suitable crossed in order to obtain a multi-point force sensor. The working principle exploits the optical power losses due to the ﬁber bending. The bending losses highly depend on the curvature of the ﬁber. Firstly, an analytical model that relate bending losses to ﬁber curvature is introduced and experimentally validated. After the demonstration of the proposed concept potentiality, a design procedure based on the simultaneous use of the analytical model and a Finite Element (FE) model is described. The procedure is experimentally validated for a single crossing of ﬁbers and it is used to realize a complete sensor prototype. Finally, the sensor prototype is experimentally calibrated as a multi-point force sensor. © 2012 Elsevier B.V. All rights reserved.

1. Introduction In recent years, handheld devices (e.g., mobile phones, tablets, multimedia devices) have become popular due to the increasing number of functionalities and applications that implement with an aesthetic increasingly become slim and miniaturized. To interact with all these features, the user requires a greater variety of user-friendly input devices, such as a mouse, keyboard, touchpad, and touchscreen. In particular, touchscreens and touchpads have rapidly developed in last years together with mobile phones and multimedia devices because of their size limitations. Touchpads began to be introduced in laptops in the late 1980s, becoming in few years an important part of the main input interface of mobile devices. Moreover, since Apple has introduced the iPhone on the market, the user interface is considered a fundamental parameter to make the device appealing to the user. However, most touch devices can measure only the contact point when a user touches the device. As discussed in [1], the forthcoming touch devices require both the contact point and the contact force component. If an input device can estimate both contact point and force component, an innovative variety of mobile devices can be released with new functionalities and applications. The development of touch sensing devices has been actively ongoing. Touch sensing devices are either of touch panel type or pressure/force sensing type. In case of touch panel, the contact point can be measured with an high sensitivity but the measurement of the pressure/force is difﬁcult.

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Pressure/force sensors can detect a subtle pressure/force, but the main drawback is that very thick sheet devices are required because of the structural complexity of the sensor. All commercial touchpads belong to the touch panel type and in practice, they estimate only the contact point. Most of the sensors able to estimate both contact point and contact force component are prototypes developed within research activities conducted in the ﬁelds of robotics and medical instruments [2–12]. However, the developed tactile sensor prototypes cannot use for handheld devices since they typically are not thin and need to manage an high number of signals (al least one for each measuring point). In this paper an innovative sensor concept based on optical ﬁbers is presented. The proposed device exploits the optical power losses due to the ﬁber bending. Additionally, the use of ﬁbers allow to maintain a limited thickness for the sensor. In particular, the ﬁbers are crossed in order to realize a mesh with n × n measuring points, by using only 2n ﬁbers. The obtained prototype is a multipoint sensor which allow to estimate the contact point and the contact force magnitude. Since the sensor concept is based on the optical power losses, ﬁrst of all, an analytical model for bending losses is introduced and experimentally validated. Then, the proposed concept and its potentiality is presented. A design procedure based on the simultaneous use of the validated analytical model and a Finite Element (FE) model is described. The procedure allows to select the design parameters in order to satisfy the desired sensitivity for the sensor and can be easily adapted to different ﬁber type. The procedure is experimentally validated for a single crossing of ﬁbers and it is used to realize a complete sensor prototype. Finally, the sensor prototype is experimentally calibrated as a multi-point force sensor.

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Field distribution

Attenuation in dB km−1

10

Escaping wave

5

Cladding θ < θc Core θ

1.0

θ

θ θ > θc

θ

1550nm

0.5 Rayleigh scattering

Lattice absorption

1310nm 0.1

R

0.05 0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Wavelength [µ m] Fig. 1. Attenuation coefﬁcient vs. wavelength in a typical silica based optical ﬁber.

2. Bending losses in ﬁbers: model and experimental validation When light propagates through a material it experiences attenuation in the direction of propagation due to different phenomena. At an atomic level lattice absorption and scattering play a considerable role in signal attenuation, the one prevailing on the other depending on the wavelength, see [13]. We can deﬁne an attenuation coefﬁcient ˛ as the fractional decrease in optical power per unit distance: 1 dP(z) 2˛ = − , P(z) dz

(1)

where P(z) is the optical power at point z along the ﬁber. Integrating the last equation in the interval [0, z] of the guide gives: 1 2˛ = − ln z

P in P(z)

,

(2)

where Pin = P(0) is the input power. Inverting Eq. (2) we obtain the useful relation: P(z) = Pin exp (−2˛z) ,

(3)

which gives optical power at any z as a function of input power and the attenuation coefﬁcient ˛. A typical silica glass-based optical ﬁber exhibits an attenuation coefﬁcient similar to the one showed in Fig. 1. Apart from absorption and scattering other factors are also cause of attenuation in optical ﬁbers. The most important are micro-bending and macro-bending losses. Micro-bending losses are often simply referred to as bending losses and are given origin by a local bending of the ﬁber that allows some of the light energy being guided to escape the core and radiate away through the cladding. More speciﬁcally if the curvature radius is such that at some point on the core-cladding boundary the TIR (Total Internal Reﬂection) condition is not satisﬁed light rays are refracted and can penetrate the cladding and eventually reach the external coating. The phenomenon is pictured in Fig. 2, where a light ray usually reﬂected at the core-cladding boundary in absence of bending is instead refracted and lost when the ﬁber is bent. Bending losses can be modeled with an attenuation coefﬁcient ˛B , whose deﬁnition is similar to the one of ˛. The calculation of ˛B involves complex analysis of the electromagnetic ﬁeld propagating in the ﬁber. Different methods have been proposed, but the usual approach is the formula introduced by Marcuse in [14].

Fig. 2. Bending loss in an optical ﬁber. A light ray usually reﬂected at core-cladding interface escapes the core when its angle of incidence is inferior to the critical angle c .

According to Marcuse the attenuation coefﬁcient due to bending losses in a weakly guided ﬁber is given by: √ 2 2 exp[−(2/3) 3 /ˇmn R] 2˛B = (4) √ 3/2 2 m V RKm+1 (a)Km−1 (a) where all terms are explained below. Deﬁning with n1 and n2 the refractive indices of the core and the cladding respectively and the free-space propagation constant k0 = 2/ where is the wavelength, and are the ﬁeld decay rates in the core and cladding:

=

2 n21 k02 − ˇmn

(5)

2 − n2 k2 ˇmn 2 0

(6)

=

where ˇmn is the propagation constant of the LPmn (Linearly Polarized) guided mode in the straight guide. R is the curvature radius of ﬁber subjected to bending. V is the V-number deﬁned as

V=

k02 a2 (n21 − n22 )

(7)

where a is the ﬁber core radius. The terms Km (x) are the second kind modiﬁed Bessel functions of order m and argument x. The parameter m is deﬁned as:

m =

2 if m = 0 1 if m = / 0

(8)

being m the azimuthal mode number of the LPmn mode propagating along the ﬁber. For the single mode ﬁbers, used in this work, the propagation mode is the LP01 and then m = 2. Eq. (4) shows that ˛B depends on R and as a consequence, combining Eqs. (4) and (3), the power at the output of a curved ﬁber of length L and constant curvature radius R can be calculated as: P(L) = Pin exp [−2˛B (R)L] ,

(9)

in which explicit dependence from R of the attenuation coefﬁcient is shown. If the stretch of ﬁber in which light propagates has a variable curvature radius a proper integration of the different contributes to the power losses allows the calculation of the total loss. The ﬁbers used in this work are the Standard Corning SMF-28, step index single mode ﬁbers. Before using this type of ﬁber for the proposed sensor design, the model of power losses described above has been experimentally veriﬁed. Table 1 reports the physical properties [15] of this kind of ﬁber at a wavelength of 1550 nm useful for model validation. The power loss has been estimated by using Eq. (9) for different curvature radius R and ﬁber length L values. The comparison between the model results and the experimental data is reported in Fig. 3 that shows power ratio P(L)/Pin as a function of the length L of the ﬁber. The experimental data have been obtained

SMF-28 ﬁber

Refractive index

Radius [m]

Core Cladding Coating

1.4504 1.4447 1.4786

4.15 62.5 125

Crossing 1

Fiber 8

Fiber 7

Fiber 6

Fiber 5

Table 1 Parameters of the Standard Corning SMF-28 ﬁber; the refractive index values are deﬁned at a wavelength of 1550 nm.

3

Crossing 2

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Fiber 1 Crossing 3 Fiber 2

Fiber 3 d

wrapping the ﬁber around cylindrical structures with ﬁxed known radius and by using the same interrogation setup detailed in Section 5. Theoretic curves are compared with experimental data for two different values of the curvature radius R revealing substantial agreement. In particular, for the reported experiments, the percentage mean-square errors are 0.25% and 0.02% for the R = 6 mm and R = 7 mm case, respectively.

Fiber 4

3. Sensor concept description Curvature losses in optical ﬁbers is the main phenomena at the base of the proposed multi-point force sensor. The sensor concept is based on the idea to cross the ﬁbers together to give them an initial curvature, in order to obtain a number of points, coincident with the ﬁber crossing, high sensitive to the applied external forces. Fig. 4 shows a scheme of the sensor concept. As shown, crossing 2n ﬁbers, it is possible to realize a sensor with n × n sensitive points. Each ﬁber passes once above and once below the orthogonal ﬁbers meet, alternately with respect to nearby parallel ﬁbers. For example, in Fig. 4 the ﬁber 1 crosses the ﬁber 5 passing below (crossing 1) and the ﬁber 6 passing above (crossing 2), while the ﬁber 2 crosses the ﬁber 5 passing above (crossing 3) and the ﬁber 6 passing below and so on. The mesh of ﬁbers that results is partially bonded above an elastic deformable layer. In the initial state, when no forces are applied all the ﬁbers have the same total curvature, equivalent to the sum of the curvatures in each crossing, and therefore the same bending losses, equivalent to the sum of the power losses in each crossing. Now consider a single crossing of ﬁbers to explain the working principle of the sensor (a sectional view is reported in Fig. 6): when a force is applied in the orthogonal direction to the plane containing a crossing of ﬁbers, the upper ﬁber stretches (increasing the curvature radius and reducing bending losses) while the lower ﬁber sinks in the elastic layer (decreasing the curvature radius and rising bending losses). Identifying the ﬁbers that show a variation of the output power compared to the output power at rest (no-load applied), it is possible to estimate the coordinates of the contact point with respect to the mesh. Furthermore, the magnitude of the

Fig. 4. A scheme of the sensor working principle.

external force applied to the sensor can be related to the intensity of the output power variation. The sensitivity with respect to the external applied force depends on the initial curvature of the ﬁbers. In particular, combining Eqs. (4) and (3) as in Eq. (9) but for a ﬁxed L length and varying the curvature radius R of the ﬁber the output power can be expressed as: P(R) = Pin exp [−2˛B (R)L] .

(10)

The function P(R)/Pin , reported in Fig. 5, shows that for high or low curvature radius values the output power variations are not sensitive to the curvature radius variations. As a consequence, the initial curvature of the ﬁber has to be chosen so that the gradient of the power ratio P(R)/Pin is high. From Figs. 4 and 6 it is clear that, once selected the type of ﬁber to be used, the distance d between crossed ﬁbers is the fundamental design parameters for the proposed sensor. In particular, an increase of the distance d value implies an increase in the curvature radius, while a decrease of the distance d implies a reduction of the curvature radius. As a consequence, the selection of the distance d value has to be made in order to ﬁx for every crossing an initial curvature for each ﬁber belonging

1

1

R = 6mm experimental data R = 6mm model R = 7mm experimental data R = 7mm model

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d

Not feasible regions

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P (R)/Pin

P (L)/Pin

0.7

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0.2

0.2 0.1

0 0

0.05

0.1

0.15 0.2 Length L [m]

0.25

0.3

0.35

Fig. 3. Power ratio P(L)/Pin as a function of length L of the ﬁber, for different values of the curvature radius R.

0 0

0.005

0.01

Radius of curvature [m] Fig. 5. Power ratio P(R)/Pin for a ﬁxed L value.

0.015

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Fig. 6. Sectional view of the proposed sensor.

As stated above the sensor presented in this paper uses the Standard Corning SMF-28. The ﬁbers are used with coating and without jacket and thus their overall diameter is 250 m (see Table 1). A Finite Element (FE) analysis has been carried out to select the distance d between the ﬁbers that would ensure satisfactory performance. In detail, the model assumes that the ﬁbers at initial condition (with no applied force) are perfectly crossed, i.e. the central axis of a generic ﬁber at each crossing is diverted with respect to the central axis of the crossed ﬁber of a quantity equal to the diameter of the ﬁbers used to realize the sensor (in this work 250 m). Fig. 6 shows the arrangement of the ﬁbers in a generic crossing at initial condition used in the FE analysis with respect to the reference axes. Fig. 7 reports a 3D view captured during a FE simulation. In the initial state, each ﬁber presents total bending losses of optical power that are the sum of bending losses for each crossing. The bending losses for a generic crossing depend on the ﬁber curvature resulting from the choice of the distance d between the crossings. Being all the ﬁbers at the same distance, their curvature in each crossing is always the same and therefore to choose the distance d is sufﬁcient the FE analysis of a single crossing. In order to estimate power losses due to a crossing an accurate estimation of the curvature radius is necessary. In the following analysis, the curvature radius of a ﬁber is assumed equal to the curvature radius of the central axis arrangement of the ﬁber itself. From the FE model, the arrangement of a ﬁber between two consecutive crosses can be carried out for different distances d. For each d value the FE model allow also to estimate the ﬁber arrangement variations due to external forces applied on a cross. Fig. 8 reports the arrangement of the ﬁbers in the cross sketched in Fig. 6 with a distance d = 2.5 mm, in initial condition (no applied force) and with different applied forces. In particular, the reported results have been obtained from the FE model simulating pure vertical forces acting on the crossing along y-axis with imposed vertical displacement y

(a)

0 No forces Vertical displacement 0.01mm Vertical displacement 0.02mm Vertical displacement 0.03mm Vertical displacement 0.04mm Vertical displacement 0.05mm

−0.05

Arrangment along y−axis [mm]

4. Sensor design

values, assuming that the ﬁbers of a neighboring crossing undergo negligible displacements. With these working conditions, the curvature of the ﬁbers is always symmetric with respect to the cross and then to simplify the estimation of power losses can be considered only one half of a ﬁber curvature around the cross. In particular, considering one half of a ﬁber cross, a polynomial that represents the arrangement of the ﬁber can be obtained from the FE model and as a consequence the radius of curvature can be calculated. For example, Fig. 9(a) reports the arrangement of the lower ﬁber in

−0.1

−0.15

−0.2

−0.25

−0.3 −2.5

−2

−1.5

−1

−0.5

0

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1

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Arrangement along x−axis [mm]

(b)

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Arrangment along y−axis [mm]

the feasible region shown in Fig. 5, ensuring a good sensor sensitivity. Additionally, the distance d is also the physical resolution of the sensor in the estimation of the contact point. Obviously, by using software interpolation techniques is possible to estimate the contact point with a resolution lower than the physical one.

−0.1

−0.15 No forces Vertical displacement 0.01mm Vertical displacement 0.02mm Vertical displacement 0.03mm Vertical displacement 0.04mm Vertical displacement 0.05mm

−0.2

−0.25 −2.5

−2

−1.5

−1

−0.5

0

0.5

1

Arrangement along z−axis [mm]

Fig. 7. Screenshot of the FE model.

Fig. 8. Arrangement of the ﬁbers in a cross: (a) arrangement of the lower ﬁber and (b) of the upper ﬁber.

S. Pirozzi / Sensors and Actuators A 183 (2012) 1–10

(a)

5

0

Arrangment along y−axis [mm]

FE model polynomial interpolation −0.05

−0.1

−0.15

−0.2

−0.25 0

0.5

1

1.5

2

2.5

2

2.5

Arrangment along x−axis [mm]

(b)

0.6

Radius of curvature [m]

0.5

0.4

0.3

0.2

0.1

0 0

0.5

1

1.5

x−coordinate [mm] Fig. 9. Arrangement of the lower ﬁber for half cross with the interpolating polynomial (a) and corresponding radius of curvature (b), with no applied force and with y = 0.

rest position (extracted from data shown in Fig. 8(a)) for the half cross with x ∈ [0, d] (d = 2.5 mm) and the corresponding interpolating polynomial. Indicating with fy (x) the analytical expression of the polynomial for a ﬁxed value of y, the radius of curvature Ry (x) can be expressed with the osculating circle formula

(1 + f (x)2 )3/2 y Ry (x) = , fy (x)

output power with respect to the input power, for the half cross with x ∈ [0, d], can be calculated as the sum of the contributions of each part

P(y, d) = P(y, 0) exp −2x

˛B (Ry (xi )) .

(12)

i=1

(11)

(x) and f where fy (x) are the ﬁrst and the second derivative y respectively, analytically calculated, of fy (x). Fig. 9(b) shows the radius of curvature, calculated via Eq. (11), for the part of ﬁber with x ∈ [0, d] (d = 2.5 mm). Since the radius of curvature is not constant, the output power with respect to the input power cannot be calculated using directly Eq. (9). Considering the curvature piecewise constant, it is possible to divide the part of ﬁber in N parts each of length x and with constant radius of curvature Ry (xi ). The Eq. (9) can be apply for each of these parts, and as a consequence, the

N

where the y value indicates the imposed vertical displacement (y = 0 in rest condition with no applied force). Recalling the symmetry of the ﬁber arrangement in a crossing (and as a consequence of the ﬁber curvature), the output power with respect to the input power for the entire crossing, i.e. for x ∈ [− d, d], can be expressed as

P(y, d) = P(y, −d) exp −4x

N

i=1

˛B (Ry (xi )) .

(13)

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(a)

1 d=1.5mm d=2mm d=2.5mm d=3mm

0.9 0.8

P(Δ y,d)/P(0,d)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

Fig. 12. Picture of the sensor prototype used for the FE model validation.

0.05

0.1

0.15

0.2

0.25

0.2

0.25

Δ y [mm]

(b) 7 d=1.5mm d=2mm

6

d=2.5mm

P(Δ y,d)/P(0,d)

d=3mm

5

4

3

2

1 0

0.05

0.1

0.15

Δ y [mm] Fig. 10. Power ratio P(y, d)/P(0, d) vs. vertical displacement y obtained from the FE model for the lower ﬁber (a) and the upper ﬁber (b) in a crossing.

When an external force, with an imposed vertical displacement y > 0, is applied on a crossing, the lower ﬁber arrangement change as shown in Fig. 8(a). Its corresponding interpolating polynomial and the radius of curvature, calculated via Eq. (11), accordingly change. Hence, the output power with respect to the input power for the entire crossing can be recalculated using Eq. (13) with the appropriate values of Ry (xi ). Note that the variable y does not appear explicitly on the right side of Eqs. (12) and (13), but it is evident from the above discussion and from Fig. 8 how the values of Ry (xi ) depend on y. As shown in Fig. 8(a), increasing the

Fig. 13. Picture of the sensor prototype: zoom of the crossing constituted by the red (lower) and white (upper) ﬁbers. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of the article.)

vertical displacement (i.e., increasing external force applied on a crossing), the lower ﬁber curvature increases and as a consequence the output power decreases (the power loss increases). Fixed the input power value P(y, − d), we consider the output power value with no applied force as output power reference P(0, d). For different external force values corresponding to different imposed vertical displacement, the output power variations can be evaluated from the FE model and the results can be reported on a graph (see Fig. 10(a)) where the power ratio P(y, d)/P(0, d) is plotted with respect to vertical displacement y, showing the sensitivity of the power ratio compared to external force. Obviously, for each d value a different curve power ratio P(y, d)/P(0, d) vs. vertical displacement y is obtained.

Fig. 11. Scheme of the interrogation circuit in reﬂection mode used for the experimental evaluation.

S. Pirozzi / Sensors and Actuators A 183 (2012) 1–10

(a)

7

1 FE model experimental data

0.95

P(Δ y,2.5)/P(0,2.5)

0.9 0.85 0.8 0.75 0.7 0.65

0

(b)

0.05

Δ y [mm]

0.1

0.15

2

1.9

FE model experimentl data

P(Δ y,2.5)/P(0,2.5)

1.8 1.7 Fig. 15. Setup for the sensor prototype calibration.

1.6 1.5 1.4 1.3 1.2 1.1 1 0

0.05

Δ y [mm]

0.1

0.15

Fig. 14. Experimental validation of the FE model with experimental data for a single crossing: red (lower) ﬁber (a) and white (upper) ﬁber (b). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of the article.)

The same procedure can be applied to the upper ﬁber of the crossing. It is important to note that, with the same imposed vertical displacement y > 0, the upper ﬁber arrangement change as shown in Fig. 8(b) and then its curvature decreases while the output power increases. As a consequence the corresponding curves, P(y, d)/P(0, d) vs. y, for the upper ﬁber have an opposite monotonicity with respect to the lower ﬁber (see Fig. 10(b)). Fig. 10 reports the power variations for all admissible vertical displacements which depends on the diameter of the ﬁbers used to realize the sensor (in this work 250 m). Evaluating the curves obtained for different d values, reported in Fig. 10, it is possible to select the d value in order to obtain a good sensitivity for a crossing in a ﬁxed vertical displacement range. 5. Experimental results In this section the experimental evaluation of the proposed sensor is presented. First, a single crossing of ﬁbers has been tested in order to verify the FE model results. Then a complete sensor with 16 measuring points has been realized and characterized. For the realization of the prototype presented in this paper d = 2.5 mm has been selected. The proposed sensor concept can be used with an interrogation circuit which works in transmission or in reﬂection mode. In the transmission mode, the light emitted by a source

propagates into a crossed ﬁber and the output power of each ﬁber is measured by using a photodetector. In the reﬂection mode, the crossed ﬁbers are cleaved at one end. The light emitted by a source propagates trough a splitter into a crossed ﬁber, the output power that reach the cleaved interface is partially reﬂected and it comes back trough the crossed ﬁber and the splitter and then it is measured by a photodetector. In the second case the interrogation circuit is more complex and expensive, but the sensitivity of the sensor is higher since the light passes twice in the same crossing, doubling the power losses (and thus the measured signal variations) with the same external applied force. Note that the power losses due to the cleaved interfaces are an undesired effect from the efﬁciency point of view, but the metallization of these interfaces is a solution to reduce it. In this paper, for all presented experimental tests, an interrogation circuit in reﬂection mode is used. A scheme that describes its operating principle is reported in Fig. 11. The source is an EXFO FLS-2200 Broadband Source, SLED-based, with a center wavelength of 1550 nm. The splitter is a classic passive ﬁber optic coupler. The electronic circuit is constituted by an InGaAs-based photodetector for 1550 nm wavelength with responsivity of about 0.9 A/W and a Butterworth ampliﬁed ﬁlter of the fourth order with a bandwidth of 10 kHz. 5.1. Experimental evaluation of the model A ﬁrst sensor prototype has been realized by using 8 Standard Corning SMF-28 ﬁbers in order to obtain 16 crossings, organized as a 4 × 4 matrix. The crossed ﬁbers have been bonded to an elastic layer constituted by PORON® microcellular urethane foam, with about 1 mm of thickness. The stiffness of the elastic layer affects the sensitivity of the sensor, since the sensitivity increases when the stiffness of the elastic material decreases. Instead, the thickness of the elastic layer can be selected to ensure the proper working conditions for the proposed sensor. In fact, the maximum vertical displacement allowed for all ﬁbers is equal to the thickness of the deformable layer, and as a consequence, the working conditions of the sensor can be limited to small displacements by realizing the deformable layer with an equally small thickness. Furthermore, for a ﬁxed thickness value, the full scale can be increased by selecting a material with a higher stiffness. Hence, an appropriate choice of the

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(b)

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(a)

0.8 0.6 0.4 0.2 0

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(f)

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Force [N]

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1

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Force [N]

1.6 1.4 1.2 1 0.8 0

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Fig. 16. Calibration curves for six different crossings: each sub-ﬁgure (a)–(f) reports the power ratio variations vs. applied force for the lower (top) and upper (bottom) ﬁbers of the crossing.

stiffness and the thickness is necessary to ensure a suitable trade-off between the sensitivity and the full scale for the proposed sensor. Fig. 12 reports a picture of the realized sensor prototype. As shown in ﬁgure, only the two central ﬁbers for each matrix side were accessible for measurements, obtaining a total of 4 measuring points. The validation of the FE model can be carried out by characterizing a single crossing of the prototype. Fig. 13 shows a zoom of the crossing constituted by the red (lower) and white (upper) ﬁbers. A vertical force has been applied to this crossing with imposed vertical displacements by using a micropositioning stage like the one shown

in Fig. 15. The experimental data for vertical displacements up to 150 m have been collected and compared with FE model results in Fig. 14, showing a good matching. The validation of the FE model is satisfactory to use its results for the optimal design of sensor prototypes. Note that, for vertical displacements greater than 150 m (and up to ﬁber diameter, i.e., 250 m) the matching (not reported in Fig. 14) is poor because the assumption, considered during the FE analysis, that the ﬁbers of a neighboring crossing undergo negligible displacements, is no longer valid for high vertical displacement values in the experimental case.

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5.2. Experimental characterization of a multi-point sensor prototype After verifying the working principle and the model for a crossing, a multi-point prototype has been realized and completely characterized as multi-point force sensor. In particular, a second prototype has been realized similarly to the ﬁrst one (see Fig. 12), by using 8 Standard Corning SMF-28 ﬁbers organized as a 4 × 4 matrix. In this prototype, all ﬁbers were accessible for measurements with a total of 16 measuring points. The crossed ﬁbers matrix has been bonded between two elastic material layers, improving the robustness of the prototype and obtaining a unique multi-layer structure. The prototype has been calibrated as multi-point force sensor by using a load cell mounted below a micropositioning stage. Fig. 15 shows a picture of the calibration setup. The micropositioning stage moves the load cell that is equipped with a small punch pressing in a neighborhood of a single crossing. The load cell, manufactured by AEP Transducers (model code TCA), has a resolution of 0.2 g and a full-scale of 2 kg. The experimental force measured by the load cell has been collected together the optical power variation exhibited by the ﬁbers. The procedure has been iterated for each crossing, obtaining 16 calibration curves (one for each crossing). Fig. 16 reports the calibration curves for 6 different crossings. For each crossing (see Fig. 16(a)–(f)), the power ratio vs. applied force is reported for the lower (top) and the upper (bottom) ﬁbers. The experimental results show that the curves are very similar for all crossings. The power ratio variations are very high and as a consequence the sensibility of the sensor depends only on optical power source. The sensitivity is directly proportional to the optical power available. As described in Section 3, identifying the ﬁbers that show a variation of the power ratio, it is possible to estimate the contact point and then the applied force magnitude can be evaluate by using the calibration curve corresponding to the crossing where the contact has taken place. For each crossing, the force can be estimated by using one of the two available calibration curves associated to the ﬁbers that constitute the crossing, or by using an appropriate combination of the two curves. Finally, the whole procedure necessary to determine the contact point and the magnitude of the corresponding force is applied for an explicit example. If a force is applied on a crossing during a time interval, by monitoring the power ratio variations of all ﬁbers, the measurements corresponding to the 8 ﬁbers, which constitute the prototype, are similar to those reported in Fig. 17. In detail, Fig. 17

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(top) shows that during the time interval [2.2, 4.7]s the contact point coincides with the crossing constituted by the ﬁbers 2 and 7 (for the numbering of the ﬁbers consider Fig. 4 as reference). After the detection of the contact point, the calibration curves, associated to the couple of ﬁbers that constitute the crossing, are used to convert the power ratio measurements into an estimation of contact force magnitude. As discussed above, for each crossing, two calibration curves, corresponding to the ﬁbers that constitute the crossing, are available. The calibration curves for the crossing constituted by the ﬁbers 2 and 7 are those reported in Fig. 16(c). In this example, the force is estimated from the measurement of the lower ﬁber, by using its calibration curve as a lookup table with a linear interpolation method. The resulting estimated force is reported in Fig. 17 (bottom). 6. Conclusions In this paper has been presented an innovative sensor based on optical ﬁbers suitable crossed in order to obtain a multi-point force sensor. A complete design procedure has been described that allow to ﬁx the sensor characteristics. The procedure uses simultaneously an analytical model of bending losses and a FE model of the sensor structure. In addition, the design procedure described in this work can be easily repeated and/or adapted for the design of a sensor that uses a different type of ﬁber. The obtained prototype demonstrated to be able to measure contact point and contact force magnitude up to 2.5 N. Future developments will be pursued in order to increase full scale measurements. However, the sensitivity, the thickness and the full scale, achieved by the presented prototype, are already sufﬁcient for applications in several ﬁelds. For example, a potential application is the realization of innovative touchpads or buttons to integrate into consumer electronic devices. Such devices could integrate more functionality in a single button or in a limited contact area of the touchpad, by exploiting the measurements of the contact force intensity. As a consequence, for a ﬁxed number of functionalities to be implemented for a device, it is possible to reduce the number of necessary buttons with respect to the current commercial solutions and then the size of the device itself. References [1] K. Dong-Ki, K. Jong-Ho, K. Hyun-Joon, K. Young-Ha, A touchpad for force and location sensing, ETRI Journal 32 (5) (2010) 722–728. [2] E.S. Hwang, J.H. Seo, Y.J. Kim, A polymer-based ﬂexible tactile sensor for both normal and shear load detections and its application for robotics, IEEE/ASME Journal of Microelectromechanical Systems 16 (3) (2007) 556–563. [3] M. Shimojo, A. Namiki, M. Ishikawa, R. Makino, K. Mabuchi, A tactile sensor sheet using pressure conductive rubber with electrical-wires stitched method, IEEE Sensors Journal 4 (5) (2004) 589–596. [4] A. Wisitsoraat, V. Patthanasetakul, T. Lomas, A. Tuantranont, Low cost thin ﬁlm based piezoresistive mems tactile sensor, Sensors and Actuators A: Physical 139 (1–2) (2007) 17–22. [5] L. Beccai, S. Roccella, A. Arena, F. Valvo, P. Valdastri, A. Menciassi, M.C. Carrozza, P. Dario, Design and fabrication of a hybrid silicon three-axial force sensor for biomechanical applications, Sensors and Actuators A: Physical 120 (2) (2005) 370–382. [6] K. Motoo, F. Arai, T. Fukuda, Piezoelectric vibration-type tactile sensor using elasticity and viscosity change of structure, IEEE Sensors Journal 7 (7) (2007) 1044–1051. [7] G.M. Krishna, K. Rajanna, Tactile sensor based on piezoelectric resonance, IEEE Sensors Journal 4 (5) (2004) 691–697. [8] T. Salo, T. Vancura, H. Baltes, Cmos-sealed membrane capacitors for medical tactile sensors, Journal of Micromechanics and Microengineering 16 (4) (2006) 769–778. [9] J.L. Novak, Initial design and analysis of a capacitive sensor for shear and normal force measurement, in: Proceedings of IEEE International Conference on Robotic and Automation, USA, 1989, pp. 137–145. [10] E. Torres-Jara, I. Vasilescu, R. Coral, A soft touch: compliant tactile sensors for sensitive manipulation. CSAIL Technical Report MIT-CSAIL-TR-2006-014, 2006.

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[11] J.S. Heo, J.H. Chung, J.J. Lee, Tactile sensor arrays using ﬁber Bragg grating sensors, Sensors and Actuators A: Physical 126 (2) (2006) 312–327. [12] G. De Maria, C. Natale, S. Pirozzi, Force/tactile sensor for robotic applications, Sensors and Actuators A: Physical 175 (2012) 60–72. [13] S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Prentice Hall, 2001. [14] D. Marcuse, Curvature loss formula for optical ﬁbers, Journal of the Optical Society of America 66 (3) (1976) 216–220. [15] P. Wang, Q. Wang, G. Farrell, G. Rajan, T. Freir, J. Cassidy, Investigation of macrobending losses of standard single-mode ﬁber with small bend radii, Microwave and Optical Technology Letters 49 (9) (2007) 2133–2138.

Biography Salvatore Pirozzi was born in Napoli, Italy, on April 21st, 1977. He received the Laurea and the Research Doctorate degree in Electronic Engineering from the Second University of Naples, Aversa, Italy, in 2001 and 2004, respectively. From 2008 he is an Assistant Professor at the Second University of Naples. His research interests include modeling and control of smart actuators for advanced feedback control systems and design of innovative sensors for robotics applications, as well as identiﬁcation and control of vibrating systems. He published more than 30 international journal and conference papers and he is co-author of the book “Active Control of Flexible Structures”, published by Springer.