Force sensor based on discrete optoelectronic components and compliant frames

Force sensor based on discrete optoelectronic components and compliant frames

Sensors and Actuators A 165 (2011) 239–249 Contents lists available at ScienceDirect Sensors and Actuators A: Physical journal homepage: www.elsevie...

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Sensors and Actuators A 165 (2011) 239–249

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical journal homepage:

Force sensor based on discrete optoelectronic components and compliant frames G. Palli b , S. Pirozzi a,∗ a b

Dipartimento di Ingegneria dell’Informazione, Seconda Università degli Studi di Napoli, 81031 Aversa, Italy Dipartimento di Elettronica, Informatica e Sistemistica Università di Bologna, 40136 Bologna, Italy

a r t i c l e

i n f o

Article history: Received 19 July 2010 Received in revised form 15 October 2010 Accepted 17 November 2010 Available online 25 November 2010 Keywords: Force sensors Tendon driven robots Compliant frames Robotic hands

a b s t r a c t In this paper, a novel force sensor based on commercial discrete optoelectronic components mounted on a compliant frame is described. The compliant frame has been designed through an optimization procedure to achieve a desired relation between the applied force and the angular displacement of the optical axes of the optoelectronic components. The narrow-angle characteristics of Light Emitting Diode (LED) and PhotoDetector (PD) couples have been exploited for the generation of a signal proportional to very limited deformation of the compliant frame caused by the external traction force. This sensor is suitable for applications in the field of tendon driven robots, and in particular the use of this sensor for the measurement of the actuator side tendon force in a robotic hand is reported. The design procedure of the sensor is presented together with the sensor prototype, the experimental verification of the calibration curve and of the frame deformation and the testing in a force feedback control system. The main advantages of this sensor are the simplified conditioning electronics, the very high noise-to-signal ratio and the immunity to electromagnetic fields. © 2010 Published by Elsevier B.V.

1. Introduction Since the dawn of robotics, the availability of joint torque sensors improves the dynamic performance of the servomechanisms that are basic components of any robot, from the industrial manipulators to antropomorphic robotic hands [1–5]. The main reason can be attributed to the rejection capabilities of disturbance torques acting on the transmission chain of the motion from the motor to the load via torque feedback. The most relevant disturbance affecting torque transmission is known to be the dry friction, and when a torque feedback is not available, the only possibility is the friction compensation usually based on more or less accurate friction models [6]. Unfortunately, most of the friction compensation algorithms require a good model of the phenomenon whose parameters are usually very difficult to identify. The relevance of friction compensation is of most importance when not only position control of the robot is of concern but also a force or impedance control has to be implemented, and this is especially true when the interaction control is implemented on industrial robots. In such a case robot joints are actuated via gear trains affected by significant friction and therefore only a robust inner position loop making the robot insensitive to torque disturbances allows the user to specify the desired impedance behaviour [7,8]. In fact, if a classical, i.e. not position-based, impedance or compliance control is applied, the lower is the desired stiffness the

∗ Corresponding author. E-mail address: [email protected] (S. Pirozzi). 0924-4247/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.sna.2010.11.007

lower is the disturbance rejection of the control loop, therefore the dynamic performance of the system significantly degrades. In this case, only the availability of joint torque/force sensors can help in obtaining the desired dynamic performance. Another important field of application of torque/force sensors is the control of robotic hands, in fact such complex systems are specifically designed to allow the robot to interact with the environment, usually very unstructured and so generic that a safe interaction can be ensured only if the mechanism possesses a compliant behaviour. When integrated robotic hands are considered, such a compliance has to be provided by torque control, hence finger joint force/torque sensors appear mandatory [9–11]. The same objective exists for tendon-driven artificial hands which are the most used solutions for prosthetic applications [12] and when the torque/force control could be useful not only for overcoming friction and other disturbances but specifically also for reproducing nonlinear characteristic of human-like tendons [13]. Since the first prototypes of robotic hands, it was clear how important were the requirement of limited invasiveness for every kind of sensor to be integrated into the device. From the first solutions provided for tendon-driven fingers [14] only limited progress has been made [15] and the sensor solutions adopted appear still cumbersome and quite invasive. The sensors developed for the DEXMART project [16] are mainly based on optic technology, i.e. optical fibers [17] and optoelectronic components. This choice is based on some interesting properties typical of these devices as immunity to electromagnetic fields, lightness, low power consumption. In particular, the force sensor proposed in this paper takes advantage of the angle-varying


G. Palli, S. Pirozzi / Sensors and Actuators A 165 (2011) 239–249

Fig. 1. Scheme of the actuation system of the robotic finger.

Fig. 2. Finger prototype with the twisted string actuation system [18].

radiation pattern of common Light Emitting Diodes (LEDs) and responsivity pattern of PhotoDetectors (PDs) and on mechanical properties of a compliant mechanism specially designed for the sensor. The paper presents design, realization, calibration and testing in a feedback control system of the sensor prototype. 2. Sensor design The sensor described in this paper has been developed to be integrated in a tendon-driven robotic hand. Fig. 1 reports a scheme of a typical robotic finger with a linear actuation module connected

to a tendon. In order to directly measure the force applied by the actuator to the tendon it is necessary to introduce a force sensor in the system, as shown in Fig. 1. Fig. 2 shows a picture of the tendondriven robotic finger together with the actuation module [18] and the integrated sensors, developed within the DEXMART project. The proposed solution makes use of an optoelectronic components couple, an infrared LED and a PD, mounted on a compliant frame that is deformed under the action of the tendon tension. The compliant frame is a monolithic metallic structure suitably designed to obtain an angular displacement of the optical axes of the optoelectronic components linearly proportional to the force

µ ¯1 ¯2


LED I( ¯1 )

R( ¯2 ) Photodetector Fig. 3. Working principle of the proposed force sensor.

G. Palli, S. Pirozzi / Sensors and Actuators A 165 (2011) 239–249


Fig. 4. Characteristics of the Honeywell optoelectronic components taken from datasheets: LED (code SEP8736) on the left and PD (code SDP8436) on the right.

applied in the direction of the tendon. Compliant mechanisms are often used also for the implementation of linear actuators using smart materials [19], for the development of compliant transmission systems [20] or as displacement/force magnifiers [21,22]. The designed compliant frame has been mounted between the actuation module and the tendon that drives the phalanx. The advantages of this implementation consist in the very high sensitivity and in the simplicity of the conditioning electronics, with respect to strain gauge based load cells, together with the high immunity to electromagnetic disturbances. The drawbacks of this solution may be the thermal drift, as in the case of strain gauges, and the cross coupling due to other similar sensors mounted in the neighborhood. This latter effect can be annihilated by means of a suitable design of the sensor cover or by modulating/demodulating the LED supply and the output signals, with an additional conditioning electronics. Instead in the presence of high thermal drift, it could be minimized by using differential measurements. 2.1. Working principle The working principle of the proposed sensor takes advantage of the angle-varying radiation pattern of common LEDs and responsivity pattern of PDs. Fig. 3 shows a LED and a PD positioned with an initial relative angle between their mechanical axes  = ˇ1 + ˇ2 . In this figure, ˇ1 represents the angle between the LED mechanical axis and the segment that indicates the distance d from the tip of the PD to the tip of the LED, and ˇ2 representing the angle between the PD mechanical axis and the same segment. In this state a certain amount of light emitted by the LED reaches the PD and it is proportionally converted into an electrical current, I . When the angle  between the mechanical axes of the emitter and of the receiver experiences a variation with respect to its initial value a different amount of light will be sensed by the PD and converted into a current different from I . This happens because the radiation pattern of the LED varies with the angle ˇ1 , so that the receiver detects different values of radiant flux for different values of ˇ1 . At the same time also the way the PD weighs received light varies, according to the variations of its responsivity pattern with ˇ2 . The combination of these two effects leads to the observed variations of the photocurrent. Recalling the theory on LED radiation patterns [23], it is possible to model the system in order to optimize the design of the sensor, selecting initial relative angle  between the mechanical axes of the two devices. In particular, if the distance d is large enough to render the far-field approximation valid, the LED could be regarded as a point source. In this case the pho-

tocurrent I (and thus the received radiant flux by the PD) will be proportional to the product between the radiant intensity pattern of the LED, evaluated in ˇ1 (denoted as I(ˇ1 )) and the responsivity pattern of the PD, evaluated in ˇ2 (denoted as R(ˇ2 )1 ), and inversely proportional to the square of the distance d I ≈

I(ˇ1 )R(ˇ2 ) . d2


For the specific sensor presented in this paper optoelectronic components with a very narrow angle of view have been chosen with the aim of obtaining a large sensitivity of the sensor with a very limited angular variations. In particular the selected LED, manufactured by Honeywell (code SEP8736), is an aluminum gallium arsenide infrared emitting diode molded in a side-emitting smoke gray plastic package. The selected PD, manufactured by Honeywell (code SDP8436), is an NPN silicon phototransistor molded in a black plastic package. The LED and PD have a nominal beam angle of 10 and 18, respectively. They are mechanically and spectrally matched with a peak wavelength of 880 nm. Fig. 4 reports the characteristics of the LED and of the PD, taken from the datasheets. In these figures the large variation of radiant intensity pattern and responsivity pattern of the selected optoelectronic components over a very limited variation of the angular displacement in a suitably selected region has been highlighted. These characteristics have been exploited to implement the force sensor based on these optoelectronic components. As shown in Fig. 10(a) that will be detailed later, the LED and the PD has been mounted with an initial relative angle  = 15◦ , such that the no-load working point (I(ˇ1 ) and R(ˇ2 ) for the LED and the PD, respectively) is located in the lower part of the response characteristics indicated by the blue stars in Fig. 4. By rotating the axes of the optoelectronic components of an angle , the relative response of the LED and of the PD changes of I and R, respectively, as highlighted in windows of Fig. 4. These changes can be detected by measuring the output voltage Vout of the simple circuit shown in Fig. 5. 3. Compliant frame design As simplifying assumption, the characteristics of the optoelectronic components have been considered linear within the region of interest highlighted in Fig. 4 and the compliant frame has been designed to achieve a variation of the angle between the optical

1 The ϕ-dependence of the radiation and responsivity patterns is here omitted since the devices only move within a plane at constant ϕ.


G. Palli, S. Pirozzi / Sensors and Actuators A 165 (2011) 239–249



470 Ω

PD Vout


100 k Ω

in the direction of the tendon. The maximum allowed deflection is 3◦ with a load of 80 N. To achieve the symmetry of the structure, the compliant frame has been split into two identical parts, each of those can be seen as a Slider–Crank mechanism (SCM) (see Fig. 6), and the optoelectronic components have been mounted on only one of this two parts. Each part can be schematized as reported in Fig. 6, where the scheme of the half compliant frame equivalent pseudo-rigid SCM is reported. In the compliant frame, the linear torsional springs K1 , K2 and K3 have been implemented by means of corner-filleted Flexural Hinges (FHs) [24], anyway due to the very small fillet radius, the FHs have been designed considering the simple beam model (small length flexural pivot [25]). From Fig. 6 it is clear that the tendon tension causes the slider movement in the upward direction. Moreover, due to the mechanism symmetry, the total tendon tension Ft is split equally on the two sides of the compliant frame, so the load applied to each SCM is Fl = Ft /2.

3.1. Pseudo-rigid body modeling of the SCM Fig. 5. Measuring circuit for the force sensor based on optoelectronic components.

axes of the optoelectronic components linearly proportional to the external traction force applied to the force sensor within the range of interest (0–80 N). As a design improvement, the compliant frame can be designed to achieve a linear proportional relation between the load force and the output voltage of the sensor, when the characteristics of the optoelectronic components are known precisely enough. In this implementation, the output voltage of the sensor has been then interpolated by a suitable polynomial expression during the sensor calibration to compute the corresponding load, as will be shown in Section 4. The compliant frame has been then suitably designed to impose to the LED and PD a relative angular displacement of their axes linearly proportional to the applied force

For the design of the SCM, let’s start considering its kinetostatic closed-form equations. The no-load configuration of the SCM is described by the parameters  20 ,  30 and r10 . Note that, while  20 ,  30 and r10 change when the compliant frame is deformed (i.e. the slider moves in the upward direction), all the other parameters remain constant even if a load (i.e. a suitable tendon tension) is applied. The relations between the no-load dimensions of the SCM are 20 = a cos


2 r10

30 = 2 − a sin

+ r42

+ a cos

2 − r2 − r2 r32 − r10 4 2


2 + r2 r10 4

r4 + r2 sin 20 r3










µ2 K1

r2 LED

Crank r4

Fig. 6. Scheme of the pseudo-rigid SCM and equivalence with half model compliant frame.


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When a load Fl is applied, the SCM parameters change satisfying the relations r1 = r2 cos 2 + r3 cos 3

r12 + r42

3 = 2 − a sin

+ a cos

(4) r32 − r12 − r42 − r22 2r2

r4 + r2 sin 2 r3

r12 + r42



The pseudo-rigid SCM approximation of the compliant frame is obtained by considering the scheme reported in Fig. 6 and by considering all the hinges as linear torsional springs. Introducing the SCM joints displacement 1 = 2 − 20


2 = 2 − 20 − 3 + 30


3 = 3 − 30


× 10



Measured Theoretical Verification FEManalysis


Compliant Frame Elongation [m]

2 = a cos




10 8 6 4 2 0










Tendon Tension [N]

the torques resulting on the SCM joints can be easily calculated as T1 = K1 1


T2 = K2 2


T3 = K3 3


Linear displacement of the compliant frame Vs. Tension force.


0.06 Desired Real Verification

−r3 cos 3 (T1 + T2 − Fl r2 sin 2 ) +r2 cos 2 (T3 − T2 − Fl r3 sin 3 ) = 0


Due to its complexity, Eq. (13) has been numerically solved within the MATLAB computational framework to obtain the value of r1 that corresponds to the load Fl in static conditions r1 = Ginv (Fl , r10 )




[2 (Fl ) − ˛Fl ] dFl



where ˛ ∈ R is the coefficient that define the desired linear characteristic. Introducing the vector of the SCM geometric parameters  = [r10 , r2 , r3 , r4 , K1 , K2 , K3 ] the design optimization process then consists in finding the optimal SCM parameters that minimize the cost function: min J : min <  < max 

where  min and  max are suitable bounds on the SCM geometric parameters necessary to avoid unfeasible solutions. In Fig. 7(b) it is possible to see the very good linearity of the angular deformation






The value of  2 and  3 can be then computed by means of Eqs. (5) and (6). Obviously, r10 = Ginv (0, r10 ). Due to the way how the optoelectronic components are mounted on the compliant frame, the variation of the relative angle between LED–PD mechanical axes, caused by the tendon tension Fl , is equal to  2 . Note that the initial relative position of the optoelectronic components can be independently selected by means of the configuration of the slender parts visible in Fig. 6 used to host and to align the LED and the PD. The paramenters of the SCM have been then optimized to obtain a linear relation between Fl and  2 . By explicitly expressing the dependence of  2 from the load Fl as  2 (Fl ), the cost function used during the optimization process can be defined as

Angular Displacement [rad]


It’s worth noticing that, due to the pseudo-rigid body approximation, the SCM joint displacements and torques correspond to the FH’s ones. By applying the principle of the virtual works, it is possible to write











Tendon Tension [N] Angular displacement of the optoelectronic components Vs. Tension force. Fig. 7. Linear and angular displacement of the compliant frame.

characteristic obtained by means of the proposed design procedure with respect to the desired one, while Fig. 7(a) shows that the axial deformation of the sensor is very limited. The proposed optimization process has been implemented with the MATLAB computational framework and solved numerically by means of the lsqnonlin algorithm, which solves nonlinear least-squares problems, including nonlinear data-fitting problems. The final step of the compliant frame design consists in the definition of the FH geometry. By adopting the ideal beam model [25], the center of rotation of the FH can be assumed at the middle point of the beam and the FH’s stiffness can be easily calculated by the relations Ii =

h3i b 12


EIi li


li > 5hi


Ki =

where Ii , Ki , li and hi are the area moment of inertia, the torsional stiffness, the length and the height of the i-th FH, respectively, E


G. Palli, S. Pirozzi / Sensors and Actuators A 165 (2011) 239–249


xi2 xi1


y i2

y i1 Detailed view of the FH reference frames. x21



x11 y11 KT1

x22 y21








y31 P





Half compliant frame reference frames. Fig. 8. Compliant frame analysis.

is the Young’s modulus of the material and b is the thickness of the compliant frame that is constant (b = 4.6 × 10−3 m) to allow a simpler manufacturing by means of wire electro-erosion. Note that the slender beam condition (19) is necessary to allows the simple beam model to be valid. It is also important to remark that the compliant mechanisms is symmetric to obtain the same deformation on both the sides of the compliant frame and to allow its elongation along the direction of the traction force to be measured.

3.2. Compliant frame design verification Due to the compliant frame design and in particular to the dimensions of the rigid links that connects the FHs with respect to the FH’s dimensions itself, some of the assumptions needed to assume the pseudo-rigid body approximation of the SCM, like the ratio of the FH length with respect to the rigid link length and the negligible thickness of the FHs with respect to the arm of the resulting moment acting on the FH produced by the force applied to the rigid link, may be no longer satisfied when large displacements are considered. Anyway, considering the limited range of the compliant frame deformations and with the aim of verifying the reliability of the design procedure proposed in Section 3.1, the characteristic of the compliant frame can be verified by assuming Timoshenko-beam model of the FH. Due to the structure and to the symmetry of the compliant frame, the analysis reported in this section will be restricted to planar movements and forces. This allows a simplified formulation of the Timoshenko-like model of the FH, and in particular of its stiffness matrix [26]. With reference to Fig. 8(a) where the configuration of a FH subjected to generic load and deformation is depicted (even if restricted to the planar case) and considering the previous assumptions, the force/deformation equation of the FH can be

written in the form [27] Fi = KTi (Pi − Pi0 ) = KTi Pi T

Fi = [FTi

FTi ] ,


Pi{0} = [PTi {0}


Fi(1,2) = [ Fxi(1,2)

(20) PTi {0} ]



Pi(1,2){0} = [ xi(1,2){0}

Mi(1,2) ]







i(1,2){0} ]



where Fi1 and Fi2 are the vector of the planar forces and moment acting on the left and the right side of i-th FH, respectively, Pi1 and Pi2 are the position and orientation vector of the reference frames rigidly fixed at the left and right side of the beam, respectively (Pi(1,2)0 denotes the no-load configuration of the reference frames). The stiffness matrix of the i-th FH is defined as


0 12Ii

⎢ 0 ⎢ li2 ⎢ ⎢ 6Ii ⎢ 0 E⎢ li KTi = ⎢ 0 li ⎢ −Ai ⎢ i ⎢ 0 −12I ⎢ li2 ⎣ 6I 0



0 6Ii li




0 −6Ii li






0 −12Ii li2 −6Ii li 0 12Ii li2 −6Ii li

0 6Ii li

⎥ ⎥ ⎥ ⎥ 2Ii ⎥ ⎥ ⎥ 0 ⎥ −6Ii ⎥ ⎥ li ⎥ ⎦



where Ai = bi hi is the cross-section area of the i-th FH and Ii is defined in (17). With reference to the compliant frame schematic structure reported in Fig. 8(b) and by assuming perfectly rigid connections between the FH and the rigid link, it is possible to write the relations between forces and displacements in the references frames of each FH as Fj1 = Gij Fi2 ,

Pj1 = Ri PLij + Pi2 ,

PLij = [ lxij





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Fig. 9. FEM analysis of the compliant frame stress (×5 scale).

Gij =

Ri =

1 0 0

0 −lyij 1 lxij 0 1

cos i2 sin i2 0

Fx32 = Fl ,

− sin i2 cos i2 0

32 = 320 .


0 0 1

Eqs. (20)–(29) define a map between the external force Fl and the compliant frame configuration. This nonlinear system of equations has been numerically solved to evaluate both the compliant frame elongation and the angular displacement between the two rigid links. These results have been then compared with the data obtained from the compliant frame design procedure based on the pseudo-rigid body approximation of the SCM. The results of these analysis are reported if Fig. 7 and identified as “verification”: it is possible to note the very good fitting between the results obtained


The boundary condition for the solution of the system (20)–(27) is 0]







Detail A 5:1 2.40

PD 8.02





P11 = P110 = [ 0

y32 = y320 ,







4.60 0.47


LED Support

Detail of the compliant SCM.

Detail B 5:1 Detail C 5:1

Front view

Lateral view

Detail of the compliant hinges implementation.

Fig. 10. Detailed view of the compliant frame (all dimensions in [mm]).


G. Palli, S. Pirozzi / Sensors and Actuators A 165 (2011) 239–249

Fig. 11. Prototypes of the optical force sensor.

from the proposed design procedure and the verification of the compliant frame characteristics. Moreover, a suitable Finite Element Method (FEM) analysis has been performed with the aim of both verifying the accuracy of the design procedure and to check if the limits of the adopted materials (Aluminum 7075-T6) in terms of yield strength are satisfied. The maximum stress condition of the compliant frame is shown in Fig. 9 while its measured elongation is reported in Fig. 7(a): it is also worth noting that the FEM analysis confirms the effectiveness of the proposed design. The final dimensions of the selected compliant frame are reported in Fig. 10, while a picture of the manufactured frames and a sensor prototype provided with the optoelectronic components are reported in Fig. 11(a) and (b), respectively. The frames has been manufactured by means of wire electro-erosion, using the same material adopted in FEM analysis: Aluminum 7075-T6. The slender parts marked as “support” in Fig. 10(a) are designed to place in the correct initial position the optoelectronic components. These component are simply bonded with a cyanoacrylate-based glue on the support and aligned using as reference the compliant frame borders. 4. Experimental verification of the sensor A suitable experimental setup, depicted in Fig. 12, has been implemented with the aim of calibrating the sensor, measuring the compliant frame deformation and testing a feedback control algorithm where the information acquired by the proposed force sensor are exploited. With reference to Fig. 12, the setup is composed by two linear motors (Linmot P01-37 × 120): for force measuring purposes, the Linear Motor 1 (LM1) is equipped with the proposed force sensor based on optoelectronic components while the Linear Motor 2 (LM2) is equipped with a custom made strain gauge based load cell with a maximum measurable force of 100 N. The

two linear motors have an integrated incremental encoder with a resolution of 1 ␮m for the measurements of their position and they are mounted on a common frame in a counter-posed configuration along the same axis. While the strain gauge load cell is connected to the amplifier through a shielded cable for noise rejection, the optoelectronic components of the proposed sensor are connected to circuit reported in Fig. 5 by means of single-wire cables to both simplifying the connection and verifying the robustness of the sensor versus electromagnetic noise. A Sensoray 526 data acquisition board mounted on a PC-104 with RTAI-Linux real time operating system has been used both for collecting the data and control the system during the experiments. Both the force sensors are directly connected to the sliders of the linear motors by means of a screw that pass through the axis of the slider and of the load cell. 4.1. Sensor characterization During the sensor calibration, the tendon has been removed and the two load cells have been rigidly connected together. Moreover, the slider of the LM2 has been mechanically blocked in a fixed position for the measurement of the compliant frame elongation. The calibration curve has been defined simply by applying, by means of LM1, a suitable load to the force sensor and by measuring the corresponding output voltage Vout of the circuit shown in Fig. 5. These data have been then compared with the information coming from the strain gauge load cell mounted on LM2. The calibration curve obtained during the experiments is reported in Fig. 13, together with the characteristics obtained by means of a 3-rd order polynomial interpolation. These plots show that this interpolation is suitable for describing the response of the sensor. In Fig. 14 the output signal of the sensor is shown to highlight that, since it is of 1 V order, amplification is not strictly required. The shape of the signal is given by the controller and control objective used during

Fig. 12. Experimental setup used for the evaluation of the control system.

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70 3rd-order interp. Measured

Strain-Gauge Load Cell Optical Load Cell



Tendon Tension [N]

Tendon Tension [N]

65.7 50




65.6 65.5 65.4 65.3 65.2 65.1

10 65.0 0 1.8

8.8 2








Output Voltage [V] Fig. 13. Calibration curve of the of the load cell based on optoelectronic components.

this experiments. This particular signal has been selected because of its non-trivial harmonic content. Fig. 14 shows also the Power Spectral Density (PSD) of the same signal, demonstrating that the noise level is below the signal level of about three orders of magnitude, since the signal bandwidth is limited to a few Hertz. With the aim of showing the effect of the electromagnetic noise on the sensor, in Fig. 15 the tendon force measured (without any filtering) close to the maximum force range by means of both the straingauge and the optical load cell is reported: from this comparison it is quite evident the effects of the electromagnetic noise generated by the linear motors on the strain-gauge load cell, due also to the high amplifier gain needed to achieve a suitable signal level with respect to the optical based load cell. It follows that, for our application, other than the reduced dimensions, the reduced cost and the simplified conditioning electronics achievable with the proposed sensor, the signal-to-noise ratio of the optical load cell is more or


less an order of magnitude better that the one of the strain-gauge load cell. From Fig. 15, together with the Fig. 16(a), it is also evident a sensor resolution of about 0.1 N. With the aim of validating the design of the compliant frame and the results of the FEM analysis, also its elongation has been measured during the experiments. Due to the very limited deformation of the compliant frame, this measure has been obtained by the difference between the overall axis deformation of the experimental setup when the sensor is mounted and the overall deformation without the sensor. The results reported in Fig. 7(a) confirm the validity of the compliant frame design and analysis. 4.2. Application test bed For the verification of the sensor properties, a feedback control system has been implemented using the information collected

Output Voltage [V]

3 2.8 2.6 2.4 2.2 2 1.8 0.2










Time [s]

Power/Frequency [dB/Hz]

20 0 -20 -40 -60 -80 -100




Fig. 15. Comparison between the signals acquired form the strain-gauge load cell and the load cell based on optoelectronic components.




Time [s]




Frequency [Hz] Fig. 14. Typical sensor time signal (top) and its power spectral density (bottom).



G. Palli, S. Pirozzi / Sensors and Actuators A 165 (2011) 239–249



Force [N]

40 39 Sensor Measure Force Setpoint


LM2 Position [m] Force Error [N]

37 2 1 0 -1 -2 0.02

0.015 0.01

0.005 0










Time [s]



Sensor Measure Force Setpoint

Force [N]

25 20 15 10

Force Error [N]

2 1 0 -1 -2










Time [s] Fig. 16. Experimental results of the force feedback controller.

by means of the proposed force sensor. In these experiments, a polymeric fiber is used as tendon to connect the strain gauge load cells with the proposed force sensor, as shown in Fig. 12, for the emulation of the working conditions the proposed force sensor is designed for. The system controller acts independently on the two motors: the load applied to the tendon is controlled using the LM1 by means of a force feedback loop based on the information coming from the optoelectronic components based force sensor, while a standard proportional-derivative position controller is used to move the LM2. Two different experiments have been performed. During the first experiment the tendon load is kept constant by LM1, while the LM2 moves along a programmed trajectory: the plots reported in Fig. 16(a) show how the force sensor signal is successfully used to track the reference tendon load, with a maximum error <1%. In the second experiment LM2 has been kept in a fixed position and the reference trajectory of the tendon load is sinusoidal: from Fig. 16(b) it is possible to see that also in this case the tendon load is successfully controlled thanks to the proposed force sensor based on optoelectronic components, with a limited error.

5. Conclusions This paper reports the development of an innovative force sensor based on optoelectronic components and compliant frames. The basic working principle has been presented together with a simplified design procedure for the definition of the compliant frame geometry. Moreover, the verification of the design procedure performed both by means of a Timoshenko beam model of the flexural hinges and by FEM analysis confirms the feasibility of the proposed design procedure. A prototype of the proposed sensor has been realized by means of wire electro-erosion and the calibration of the sensor has been performed. The force information has been reconstructed from the sensor output by means of a 3-rd order interpolation and the sensor response shows a very good noise-to-signal ratio and repeatability. As a demonstration of the applicability of the sensor, a force feedback control algorithm has been implemented using the information gathered by the proposed sensor. The experimental results show that the sensor is suitable for the replacement of traditional strain gauge-based load cell for the measurement of tendon traction force. In addition, the very limited requirements in terms of

G. Palli, S. Pirozzi / Sensors and Actuators A 165 (2011) 239–249

conditioning electronics make this solution more feasible for the implementation of highly integrated devices like robotic hands and the dimension of the designed sensor are compatible with the actuation module of the University of Bologna (UB) Hand IV that is under development within the DEXMART project. Moreover, the presented results are even more interesting, also from a commercialization point of view, considering that the used optoelectronic devices are not particular components manufactured specifically for this application, but they are simply off-the-shelf very cheap components. The use of aluminum to manufacture the compliant frame guarantees a low cost and a good mechanical robustness. Different sensor prototypes have been tested in laboratory and the reproducibility appears high, requiring only a standard calibration phase for each sensor.


[14] [15]

[16] [17]



Acknowledgment [20]

The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 216239 (DEXMART project).



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Biographies G. Palli was born in Forlì, Italy, on January 6th, 1977. He received the Laurea and the Ph.D. degrees in automation engineering from the University of Bologna, Italy, in 2003 and 2006, respectively. Currently he is a post-doc at the University of Bologna. His research interests include the design and control of robotic hands, the modeling and control of robots with variable stiffness joints, the design of compliant structures and actuation systems for robotics applications, the development of real time systems for automatic control applications. S. Pirozzi was born in Napoli, Italy, on April 21st, 1977. He received the Laurea and the Ph.D. degrees in electronic engineering from the Second University of Naples, Aversa, Italy, in 2001 and 2004, respectively. Currently he is an Assistant Professor at the Second University of Naples. His research interests include modelling 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 20 international journal and conference papers and he is co-author of the book “Active Control of Flexible Structures”, published by Springer.