Design, analysis and experimental validation of an ungrounded haptic interface using a piezoelectric actuator

Mechatronics 45 (2017) 100–109

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Mechatronics journal homepage: www.elsevier.com/locate/mechatronics

Design, analysis and experimental validation of an ungrounded haptic interface using a piezoelectric actuatorR B. Sauvet∗, T. Laliberté, C. Gosselin Département de génie mécanique – Université Laval, 1065 Avenue de la Médecine, Québec, QC G1V0A6, Canada

a r t i c l e

i n f o

Article history: Received 9 March 2016 Revised 28 July 2016 Accepted 9 June 2017

Keywords: Haptic interface Ungrounded Piezoelectric actuator Asymmetric oscillations Spatial guidance

a b s t r a c t In this paper, a novel small ungrounded haptic device for spatial guidance is presented. The device uses a piezoelectric actuator to generate the haptic illusion of an external force. Using asymmetric accelerations, the device is thus able to generate a pulling or pushing sensation to a user. A dynamic model of the device is developed, which allows the determination of the optimal parameters to be used. These parameters are the frequency of the input signal and the natural frequency of the device including the connection with the user handle. It is shown that by using a particular input frequency, depending on the natural frequency of the device, the acceleration of the moving mass and its asymmetry are both maximized. Experimental tests show that the device is able to generate a haptic perception in two opposite directions with a success rate ranging from 80% to 86%.

1. Introduction Several recent research initiatives are focusing on improving guidance and positioning in space. The applications of such technologies are numerous, ranging from the personal assistance for the physical orientation of people with visual impairments [1], to the teleoperation used especially in micro-robotics [2] and medicine, and the training with simulators [3,4]. In order to enhance the guidance and positioning, one approach is to use haptics to provide feedback to the user. Haptic devices used for this purpose can be classified into three categories following their force reference system [5] namely : grounded, body grounded, and ungrounded. To render the guidance even more intuitive and understandable, one can use asymetric accelerations to generate illusion forces [6–9] (see Table 1). Along these lines, a pseudo-attraction force method is proposed in [7]. This technique consists in moving an internal mass according to two phases: at first, the mass undergoes a large acceleration for a short period of time, which is perceived by the user. Secondly, a smaller acceleration is generated over a longer period of time in the opposite direction. This small acceleration is barely detected by the human user, who hence perceives

R This paper was recommended for publication by Associate Editor Edmond Richer. ∗ Corresponding author. E-mail addresses: [email protected], [email protected] (B. Sauvet), [email protected] (T. Laliberté), [email protected] (C. Gosselin).

http://dx.doi.org/10.1016/j.mechatronics.2017.06.006 0957-4158/© 2017 Elsevier Ltd. All rights reserved.

© 2017 Elsevier Ltd. All rights reserved.

a unidirectional force. The device is capable of generating illusion forces, but only in one predetermined direction. Amemiya and colleagues proposed different ungrounded designs based on this technique. The first devices use the same actuation module consisting of a swinging slider-crank mechanism. In [10], the module is controlled by a belt and pulley attached to a stepper motor which directs the user towards the desired direction. The main disadvantage of this arrangement is the rotational slowness. The device presented in [11] is composed of four force modules which are arranged as a cross. This system provides the possibility of generating eight diagonal directions. Its performances are better than those of the device proposed in [10], despite some problems in the haptic feedback perception. These problems are due to the combined synchronized movement of two modules, which limits the overall precision. In [12], the authors addressed the haptic guidance problem, examining different possible designs and proposed a prototype that generates a force illusion in a single direction. However, the proposed design has two disadvantages : it does not allow to reduce the size of the system and, most importantly, the properties of this device are determined at the design stage. In recent research initiatives, the miniaturization of the ungrounded interfaces has been addressed by replacing slider-crank mechanisms with oscillators (see Table 1). Firstly, this substitution enables to simplify the mechanism, replacing the motor and slidercrank mechanism by a simple oscillator. Secondly, this simplification makes it possible to decrease the size of the system. Thirdly, the use of oscillators allows more flexibility for the input trajec-

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Table 1 Characteristics of some ungrounded haptic devices. The papers presented in this table are those in which the most detailed information could be found. n/a stands for ‘not available’. References

Size(mm or mm3 )

Weight (g)

Nb of directions

System

[6,18] [7,19] [9] [20] [11] [12] [13] [13] [14] [14]

∅ : 300 (approx) 130 × 200 × 48 90 × 105 × n/a 56 × 175 × 27 ∅ : 300 90 × 130 × 90 18 × 18 × 37 18 × 37 × 74 35 × 7.5 × 5 35 × 7.5 × 13

10 0 0 (approx) 500 650 250 750 336 19 42 5 10

8 2 yaw and pitch 2 8 2 2 8 2 8

Magnetic levitation Slider crank Gyroscopic effect Slider crank slider crank slider crank Vibrating actuators Vibrating actuators Vibrating actuators Vibrating actuators

tories. Also, the system’s large accelerations can be produced using a high frequency oscillator. For instance, the Buru-Navi3, proposed in [13] has a mass of only 19 g for a one-degree-of-freedom (DOF) force display and 42 g for a two-DOF force display. Reference [14] also succeeded in miniaturizing a device to a mass of only 5 g. This miniaturization is required for the system to be integrated into a small device like a phone for example. Nonetheless, an ungrounded haptic device could also be used with a larger system, like a simulator or to provide an additional feedback in a context of teleoperation [15]. The main interest in using such an ungrounded interface, is that it does not constrain the working space of the user. However, as stated in Weber’s law [16,17], the perception of a stimulus is proportional to the magnitude of this stimulus. This means that small–sized devices produce essentially small forces. For example in [14], the author measured the force feedback produced by the haptic device with a comparative test. This system can generate 0.2N. This low value suggests that the miniaturization does not allow the generation of significant forces. In order to benefit from the advantages of ungrounded haptic systems and integrate them into more complex environments, two criteria must be in place namely, the haptic system must be capable of producing a stimulus of significant magnitude and the portable device should have a relatively small size. In other words, the haptic device must generate a clearly perceptible force feedback and it should have a ratio of the mass of the internal moving part over its total mass as close as possible to 1. In order to fulfill these criteria, the use of piezoelectric actuators is proposed here. Piezoeletric actuators have several advantages like a high resonant frequency (around 100 Hz and more) and a high stiffness (0.3 N/μm to 2.3 N/μm). Besides, they can generate a high force despite a low amplitude and size. To the best of the knowledge of the authors, piezoelectric actuators have not yet been used for portable haptic devices with an asymmetric acceleration approach. In this paper, a new ungrounded haptic device is developed, analyzed and experimentally validated. The novel device uses a piezo-actuator to generate a force illusion using asymmetric accelerations. A dynamic analysis of the system is conducted in order to understand the influence of the dynamics and to optimize the user’s perception. Experimental tests are reported for the determination of the force generated by the system and to validate the user’s perception. This paper is organized as follows: The next section describes the proposed device and its dynamic model. Section 3 presents the methods and the parameters used for the experimental validation, as well as the protocols of evaluation. Finally, the results are presented and analyzed in Section 4. 2. Proposed device and dynamic analysis The proposed haptic device (Fig. 1) consists of a piezo actuator P-602-3SL from Physik Instrumente (specifications in Table 2),

Table 2 Specifications of the actuator P-602-3SL from PI. Travel Stiffness Resonant frequency Maximum push force Maximum pull force Dimensions Mass

300μm 350,0 0 0 N/m 330 Hz 100 N 5N 46 mm× 19 mm× 9 mm 40 g

Table 3 Mass of the device. Component

Material

Mass (g)

Support Guide rail Carriage on ball bearing Brass movable part Actuator Handle Others

Aluminum Stainless steel Stainless steel Brass Stainless steel ABS plastic

61.34 6.5 7.5 111.3 40 34.7 ࣃ 0.66

Total Movable part Support

− − −

262 139.2 (53.1%) 122.8 (46.9%)

Volume

−

55mm× 50mm× 25.4mm

a linear guide-way (a carriage on ball bearing 8438K1 and a guide rail 6725K23 from Mc-Master), an aluminum mechanical structure and a brass movable part (see specifications in Table 3). The piezo– actuator is mounted between the mechanical structure (the support) and the movable part. The mobile part is excited by the piezo–actuator. The main axis of the actuator and the centre of mass of the movable part are aligned in order to decrease the torques applied on the support. The movable part is fixed on a linear guide-way to decrease the torques on the actuator as well. The actuator includes an integrated position sensor: both of them are driven by a controller/amplifier (the E-610-S0 LVPZT from Physik Instrumente). A handle, made of 3D-printed ABS plastic, is rigidly attached to the support in order to allow the user to hold the haptic device by hand. The acceleration of the moving part and the support are measured using 3-axis accelerometers (MMA7361 and ADXL335 from Sparkfun, respectively). The complete setup is connected to a PC through an A/D converter (Sensoray 626), as shown in Fig. 2. The device has a total mass of 262 g. The movable part and the support represent 53% and 47% of the total mass, respectively (Table 3). In order to measure the inertial forces produced, the haptic device was mounted on an ATI force/torque sensor mini40 (SI-80-4) which is rigidly attached to a table. The specifications like the stiffness, the resonant frequency and the damping between the support and the moving part are determined with the device fixed to the force sensor in the following subsection.

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Fig. 1. The proposed ungrounded haptic device.

Fig. 4. Schematic representation of the mechanical system consisting of the device held by a user’s hand.

haviour is considered linear to simplify the modelling. Thus, the system can be described by the following linear differential equation

mx¨ + cx˙ + kx = Fext

Fig. 2. Schematic of the connections to the haptic device. The lines indicate the links (power or data transmission) between the components.

(1)

where m is the mass of the moving part (which is equal to 139.2 g), c is the damping coefficient, k is the stiffness and Fext is the external force. By exciting the device with a square-wave input (duration of 10 s) to have free oscillations between two impulses, the resonant frequency is calculated using a Fast Fourier Transform (FFT) and is found to be equal to 166 Hz. The damping coefficient, c, is calculated from the logarithmic decrement and is equal to 11.8 Ns/m. The stiffness is then deducted by the relation (k = m(2π fn )2 ) where fn stands for the resonant frequency, which yields k =1510 0 0 N/m. 2.2. Dynamic modelling of the device held by hand

Fig. 3. Schematic representation of the system mounted on the force sensor. The device can be described as a one-DOF mass-spring-damper system.

2.1. Dynamic analysis of the device mounted on the force sensor When mounted on the force sensor (which is considered rigid), the device can be described as a one–DOF mass-spring-damper system (see Fig. 3). The actuator is position controlled. Its be-

When the device is held by hand, the resulting mechanical system is then considered as a two-DOF system (see Fig. 4). The mechanical connection between the user and the system is achieved through the human skin, through which the haptic information is transmitted. The human skin can be considered as a viscoelastic material that is modeled by a Kelvin-Voigt model [21], [22], i.e., a purely viscous damper cskin and a purely elastic spring kskin connected in parallel. Using this assumption and the model shown in Fig. 4, the dynamic model of the 2-DOF system can be assembled as





m1 0

 +





0 m2

  x¨1



x¨2



M

k −k

−k (k + kskin )

 K

c −c

+



−c (c + cskin )

 C    x1



x2

=

Fext −Fext

  x˙ 1



x˙ 2

 (2)

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where x1 and x2 are respectively the position coordinate of the moving mass and of the support, m1 and m2 are the mass of the moving part and of the support (see Table 3), and matrices M, C and K are the mass matrix, the damping matrix and the stiffness matrix of the two-DOF system. The natural frequency of the device without handle but not fixed to the force sensor (i.e., two-DOF free system) is equal to 242Hz and can be calculated as

1 fn = 2π



k ( m1 + m2 ) . ( m1 m2 )

(3)

3. Methods The haptic principle proposed by Amemiya [13,19,20,23] is used here. This principle is based on a pseudo-attraction force generated by asymmetric accelerations. In this approach, a movable mass is first moved in one direction with a large acceleration profile; then this mass is brought back to the initial position with a smaller acceleration applied in the opposite direction for a longer time. The haptic perception resulting from this asymmetry is mainly stimulated by the large acceleration. 3.1. Trajectory profile The generic trajectory planning scheme used is described in [24]. In this trajectory profile, one complete period is equal to 2T. This time period is the reciprocal of the frequency of the impetus, also referred to as the perception frequency. Using this trajectory profile, the theoretical large acceleration (ah ) and the low acceleration (al ) can be written as a function of the half time period T, the amplitude of the motion A, and α the cyclic ratio between ah and al (with 0 < α < 1). One has

ah = al =

2A

αT 2 2A

( α − 1 )T 2

(4) (5)

Therefore, using this trajectory profile, the accelerations cannot be modified independently from the perception frequency. In order to be able to control these two parameters independently, the original trajectory profile described in [24] (shown in Fig. 5) has been modified. A variable delay has been introduced between the accelerations, as shown in Fig. 6. The new complete period is equal to 2T + delay. The accelerations ah and al do no longer depend on this new period and are always calculated using the parameter T. With this modification, two frequencies coexist: the first one is the frequency that allows us to calculate the accelerations using parameter T (referred to as the acceleration frequency) and the second one is the frequency of the impetus (referred to as the perception frequency). Hence, the acceleration frequency and the perception frequency can be chosen independently. For example in Fig. 5 the perception frequency is 1 Hz. The introduction of a 1s delay (Fig. 6) decreases the perception frequency to 0.5 Hz while keeping the same parameters and values of acceleration. In other words, the introduction of a delay makes it possible to optimize the parameters independently. 3.2. Parameter selection Experiments were conducted with the device held by hand and different additional masses mounted on the moving part (100 g, 20 0 g, and 50 0 g). Thus, in the different experiments, the mass of the moving part is 139.2 g (no mass added), 239.2 g, 339.2 g, or 639.2 g. The amplitude of travel is equal to 300 μm and the parameter α is fixed to 0.2, based on the results reported in [24].

Fig. 5. Trajectories generated for different values of the cyclic ratio α . Figures (a) (α = 0.1) and (b) (α = 0.9) represent trajectories which generate opposite force rendering. The space between the dotted lines shows the time period during which the feeling acceleration is produced by the device. The term ”perception period” indicated on Fig.(b) corresponds to the term ”perception frequency” used in the text.

The acceleration frequencies range from 40Hz to 70Hz by steps of 10 Hz. Using these parameters, the theoretical large accelerations are 19.2, 30, 43.2, and 58.8m/s2 respectively. 3.3. Experimental protocol for the frequency evaluation An evaluation has been conducted in order to determine the perception frequencies that are the most effective for the users. A mass can be added to the moving part to create a larger force (see Section 4.3.3). In this experiment, a mass of 200 g has been chosen. This mass is a compromise to keep the device reasonably light. The subject holds the device by the handle and changes the perception frequency between 10 and 50 Hz with either 5 Hz or 0.5 Hz steps. The user stops the evaluation when he/she finds that his/her perception of the force in one direction is the strongest. Fifteen subjects, ranging from 24 to 32 years of age and with no

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B. Sauvet et al. / Mechatronics 45 (2017) 100–109 Table 4 Maximum average values of the force (in N) measured by the sensor and computed with the measured acceleration of the moving part. Values are calculated from the average of 220 samples. Acc freq (Hz)

40

50

60

70

Computed with measured acc measured

3.92 4.46

4.68 5.36

4.81 5.42

4.92 5.6

in this experiment (14 males and 1 female). Each subject tested the device during a period of 80 s, which corresponds to 40 occurrences of the force stimulus. In the second experiment (experiment B), a force (forward or backward) is randomly generated every 2 seconds followed by a period of 2 s during which the device is switched off. Sixteen subjects, ranging from 24 to 32 years of age and with no known abnormalities, participated in this experiment (14 males and 2 females). For this experiment, the period of test ranges from 108 to 120 s, which corresponds to 27 to 30 occurrences of the force stimulus. In both experiments, the subjects were asked to provide their answers by pressing the up or down arrow key on a keyboard. During the evaluation, the subjects had either closed eyes or could not see the device. Moreover, the device did not emit enough sound to give any auditory indication to the subject. The frequency of acceleration is set to 50 Hz and the perception frequency is set to 30 Hz. A mass can be added to the moving part to create a stronger acceleration (see Section 4.3.3). A mass of 200 g has been chosen. This mass is a compromise to keep the device reasonably light. 4. Results and analysis 4.1. Description of the acceleration patterns Fig. 7 shows the characteristic pattern produced by the device (in force or acceleration) when the acceleration profile presented above is used. In this figure, the asymmetry of the acceleration is clearly visible when comparing the maximal value and the minimal value. This asymmetry enables the user to feel a haptic force illusion. Moreover, the positive values of the force indicate one given direction of perception while the negative values correspond to the opposite direction. Fig. 6. Trajectory planning scheme used in this paper. The parameters are the same as in Fig. 5 except that a delay (here 1s) is introduced between the acceleration steps. Figures (a) (α = 0.1) and (b) (α = 0.9) represent trajectories which generate opposite force perceptions. The time period between the accelerations can be changed independently from the value of the accelerations. The term ”Perception period” indicated on the Fig.b corresponds to the term ”perception frequency” used in the text.

known abnormalities, participated in this experiment (14 males and 1 female). The resonant frequencies are measured with a FFT. To ensure the validity of the measure (i.e., allow the device to oscillate freely between two impulses), each evaluation starts with a frequency of 3 Hz. 3.4. Experimental protocol for the haptic evaluation The evaluations of the device have been conducted in order to verify the effectiveness of the virtual force. In these experiments, the subjects are asked to find the direction of the force stimulus generated by the device (forward or backward). To assure that the users really feel the direction of the virtual force, and not just the change of its direction, two experiments are proposed. In the first experiment (experiment A), a force (forward or backward) is randomly generated every 2 s. Fifteen subjects, ranging from 24 to 32 years of age and with no known abnormalities, participated

4.2. Evaluation of the accelerometer As shown in Fig. 2, an accelerometer is mounted on the moving part in order to determine its acceleration. In order to validate the measured acceleration of the moving part, the device was rigidly mounted on a force sensor. The forces induced by the acceleration of the moving part (computed by multiplying the measured acceleration and the mass) and the forces measured by the sensor are shown in Fig. 7. The average forces computed based on the measured accelerations and the average forces measured by the force sensor are shown in Table 4. The force computed based on the measured acceleration is lower than the force measured by the force sensor. The average difference is within a range of 0.46 to 0.60 N which corresponds to a percentage of 10%–15%. It can be observed that the accelerometer fixed on the moving part underestimates its acceleration. The underestimation of the force induced by the mass comes most probably from the assumption that was made on the mass of the piezo-actuator. Indeed, it was assumed that the mass of the actuator is divided in two equal parts: one for the mass of the support and one for the mass of the moving part. In practice, the mass of the moving part of the actuator is probably larger than the mass of the fixed part. Nevertheless,

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Fig. 7. Comparison between the force measured by the sensor and the force computed by multiplying the acceleration of the moving part with its mass. Figure (a) represents the acceleration frequencies of 60 Hz in each direction alternately. Figure (b) is an enlargement.

the measurements from the accelerometer can reasonably be used to infer the forces induced by the device.

Fig. 8. Acceleration pattern of the moving part versus the perception frequency for the hand held device, for an acceleration frequency of 60Hz. The figure presents from left to right the variation of the acceleration of the moving part over time for a perception frequency of 20, 25, 30, 35, and 40 Hz in one direction. Figure (b) shows the pattern of oscillation during three time periods, the data was filter with a Butterworth filter.

4.3. Experiments with the hand held device 4.3.1. Perception frequency Figs. 8 and 9 show the variations of the acceleration of the moving part as a function of the perception frequency. Fig. 8(a) and (b) present, from left to right, the results obtained with a perception frequency of 20, 25, 30, 35, and 40 Hz in one direction for the hand held device. It can be observed that the variation of the perception frequency has an impact on the maximum and the minimum of the acceleration of the moving part. Thus, this parameter can be adjusted to improve (see for example Fig. 8(a) and (b) for 30 Hz) or minimize (see Fig. 8(a) and (b) for 40 Hz) the asymmetry of the acceleration. The same observation can be made in Fig. 9. For example, for a moving mass of 239.2 g, the maximum acceleration is achieved for a perception frequency of 35 Hz and decreases for all other frequencies. Moreover, although Fig. 9(a) and (b) present the results

for two different acceleration frequencies (60 Hz and 50 Hz respectively), the maximum accelerations occur for the same perception frequencies and the same mass. Hence, the maximum acceleration can be roughly predicted for a given perception frequency and a given mass of the moving part. In order to better understand the effect of the perception frequency, the hand held device is excited with a frequency of 3 Hz. At this low frequency, the device undergoes free oscillations between two impulses (see Fig. 10). A FFT analysis is performed on the measured accelerations to determine the natural frequencies of the device (Table 5). The hand held device can be considered as a two-DOF system (the moving part and the support, Eq. (2)) and thus two resonant frequencies exist. Table 5 shows the resonant frequencies obtained from the FFT analysis for the same user that led to the results of Fig. 9. It can be observed that the resonant fre-

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B. Sauvet et al. / Mechatronics 45 (2017) 100–109 Table 5 Resonant frequencies obtained from the FFT analysis of the hand held device.

139.2 239.2 339.2 639.2

g g g g

f1 (Hz)

f2 (Hz)

47.9 35.9 32.9 26.9

230 203 206 206

Table 6 Comparison of the resonant frequencies determined experimentally and the answers from the user tests.

Fig. 9. Variation of the acceleration for different masses of moving parts versus the perception frequency for the hand held device. The acceleration frequency is equal to 60 Hz for figure (a) and 50 Hz for figure (b).

Fig. 10. Acceleration pattern of the moving part with an impulse of frequency of 3 Hz.

Users

fanswer (Hz)

fmeasured (Hz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

25 30 30 29 35 27 27.5 25 35 32.5 23 28 33.2 28 34

24.5 31.9 29.5 30.6 31.9 28.7 30.6 26.9 31.9 31.9 27.5 26.3 30.8 29.4 32.5

quencies closely correspond to the frequencies that produced the best response in Fig. 9(a) and (b). The same method (i.e., impulses at 3 Hz with FFT) was repeated with 15 users to measure their resonant frequencies when they held the device. The frequency evaluation (see Table 6) shows that the frequency which optimizes the perception for a user is close to the measured resonant frequency (with an average error of 2Hz). Moreover, this test shows that the resonant frequency is user dependent, with a range from 24.5Hz to 32.5Hz. The average of the measured resonant frequencies is equal to 29.7 Hz with a standard deviation of 2.3 Hz. Several observations can be made from these results. Firstly, Figs. 8 and 9 show that the maximal acceleration of the moving part and the asymmetry are linked to the perception frequency. Secondly, based on Fig. 9(a) and (b), and Table 5 it is observed that the optimal perception frequency is very close to and appears to correspond to one of the resonant frequencies of the device. Thirdly, Table 6 confirms that the optimum perception for the user corresponds to a frequency close to the resonant frequency (with a small average error of 2 Hz). This result also shows that the value of the resonant frequency is user dependent. Based on this result, it can be conjectured that when the perception frequency is in agreement with the resonant frequency, the energy of the device is maximized. Thus, the maximum of the acceleration is higher and the asymmetry increases. These results confirm the assumption made in [13], according to which the actuator and the perception frequency are important parameters for the rendering, as well as the role of the natural frequency. More specifically, these results show the impact of these parameters on the acceleration and its asymmetry, and thus on the performance of the device. Moreover, this clarifies the role of the natural frequency of the device including the link skin/device. Indeed, the mechanical properties of the human skin change through the life cycle [25]. These modifications could affect the natural frequency of the user/device.

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Fig. 11. Acceleration pattern of the moving part when the device is held by hand for an acceleration frequency of 60 Hz, the first half in one direction, then the second half in the other direction.

Table 7 Maximum average values of the accelerations and the forces of the moving part. Asterisks (∗ ) represent the values measured by a sensor. Values are calculated from the average of 220 samples. Acc freq (Hz)

40

50

60

70

No mass added

12.7 1.77

19.3 2.68

24.1 3.36

25.3 3.53

m/s2 N

100 g added

10.5 2.50

13.8 3.30

16.7 3.99

17.5 4.18

m/s2 ∗ N

200 g added

8.38 2.84

11.6 3.92

14.3 4.84

14.6 4.96

m/s2 ∗ N

500 g added

6.6 4.22

9.41 6.01

11.2 7.13

11.6 7.43

m/s2 ∗ N

Thus, to improve the performance of the device, it is not only required to improve the acceleration of the moving part, it is also crucial to adjust the frequency (i.e., the perception frequency) to the resonance frequency of the device, included the link user’s hand/device.

4.3.2. Moving part Fig. 11 shows the acceleration pattern of the moving part having a mass of 139.2 g. Table 7 shows the maximum average values of the acceleration for different masses. These values are shown graphically in Fig. 12. Fig. 12(b) and Table 7 show that the acceleration of the moving part decreases as its mass is increased. Although the acceleration is decreasing, this decrease is more than compensated by the increase in mass. Therefore, the force produced by the moving part increases (see Fig. 12(a)). These results also suggest that an increase of the mass and of the acceleration frequency both contribute to the force produced by the moving part. Ideally, the moving part should constitute the largest possible percentage of the total mass in order to optimize the performance of the device. However, Fig. 13 shows that this increase does not have the same impact on the acceleration of the support. In a similar way, the increase of acceleration frequency has a different impact on the acceleration of the moving part and the acceleration of the support. Besides, the user does not directly feel the acceleration of the moving part; he rather feels the acceleration of the support.

Fig. 12. Force generated by the acceleration of the moving part and acceleration of the moving part as a function of the mass of the moving part. The points corresponding to the same acceleration frequency are connected to highlight the trend (40 Hz, 50 Hz, 60 Hz, and 70 Hz). The percentage in brackets refers to the mass of the moving part over the total mass of the device.

Table 8 Average values of the acceleration of the support. Each values are calculated from the average of 220 samples. Acc freq (Hz)

40

50

60

70

No mass added 100 g added 200 g added 500 g added

5.49 7 7.12 6.92

7.75 9.4 9.43 9.3

8.55 10.1 10.2 10.2

9 10.2 10.7 10.4

m/s2 m/s2 m/s2 m/s2

4.3.3. Support When the user is holding the device with the handle, the support can undergo some motion. Fig. 14 shows the acceleration of the support for a moving part having a mass of 239.2 g (additional mass of 100 g). This figure shows that the acceleration pattern of the support is almost symmetrical, as opposed to the acceleration of the moving part which is clearly asymmetrical (Fig. 11). Fig. 13 and Table 8 show the acceleration of the support as a function of the mass of the moving part for different accelera-

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Fig. 13. Acceleration of the support as a function of the mass of the moving part. The points corresponding to a given acceleration frequency are connected to highlight the trend (40 Hz, 50 Hz, 60 Hz, and 70 Hz). The percentage in brackets refers to the mass of the moving part over the total mass of the device.

Fig. 15. Boxplot of the percentage of correct answers for the two evaluations. The average of the percentage of correct answers is indicated by asterisk. The average percentage for A is 85.8% and for B the average is 79.7%. The boxplot indicate interquartile range (IQR, distance between 0.25 and 0.75 percentile of data, denoted by the outline of the box), data range (lines) and outliers (defined by a distance of more than 1.5 IQR lower or higher than the 0.25 or 0.75 percentile respectively, denoted by crosses).

part (see Figs. 14 and 11) and could also explain the clear plateau observed in Fig. 13. In addition, the total weight of the device must be comfortable for the user. In the case of the present system, the ideal mass of the moving part seems to be with an additional mass between 100 and 200 g. With an additional mass of 100 g, the total mass of the device is 362 g. The moving part represents then 66% of the total mass. For an additional mass of 200 g, the moving part represents 73% of the total mass (462 g). The use of heavier weights would be uncomfortable for the user for an extended operating time. 4.4. Evaluation of the haptic perception

Fig. 14. Acceleration pattern of the support for an acceleration frequency of 60 Hz and a moving mass of 239.2 g (additional mass of 100 g), the first half in one direction, then the second half in the other direction.

tion frequencies. Firstly, the acceleration of the support increases when the mass of the moving part increases, contrary to the acceleration of the moving part (see Fig. 12(b)). Moreover, the acceleration of the support also increases when the acceleration frequency increases. However, the acceleration of the support eventually plateaus. Indeed, the acceleration of the support does not increase significantly when the mass of the moving part is larger than 339.2 g. Similarly, it does not increase significantly beyond an acceleration frequency of 60 Hz (see Fig. 13). Fig. 14 shows that the acceleration pattern of the support is different from that of the moving part (see Fig. 11). One possible explanation for this is that the user significantly damps the movement of the support. Indeed, the link between the handle and the user’s hand can be modeled with a damper and a spring. Additionally, the hand of the user is not fixed in space. Hence, the user can react to the movement of the device through his hand, in addition of the damping induced by the skin, and impart an acceleration to the support during the experiment. This explains why the acceleration pattern of the support is different from that of the moving

In the experiments described above, the user must determine in which direction each of the stimuli is perceived (forward or backward). The answers collected are then compared with the direction of the forces generated. The results of this comparison are shown in Fig. 15. Results from experiments A and B indicate that the majority of subjects are able to correctly perceive the direction of the submitted virtual force. The average percentage of correct answers is 85.8% for experiment A and 79.7% for experiment B. The boxplots show that 75% of the users have a percentage of correct answers higher than 80% for experiment A and higher than 71% for experiment B. Besides 50% of the users have a percentage of correct answers higher than 88% in experiment B. However, three users had a percentage of success lower than 50%. The difference in success rate between the two experiments can be explained by the protocol of each experiment. In experiment A, a force is randomly defined 2 s. During this experiment, the subject feels the direction of the virtual force but also the change of the direction between two opposite forces. This variation constitute additional haptic information for the user. This type of experiment stimulates mainly the mechanoreceptors named the Meissner corpuscles [13]. These structures have a frequency range of 5 – 50 Hz and are most responsive to changing contact or to sliding [26]. Thus, the perception of the change of the direction increases the sensitivity of these sensors. On the other hand, during experiment B, all generated forces are separated by a period of time during which the device is switched off. The user can only perceive the direction of the virtual force without being helped by

B. Sauvet et al. / Mechatronics 45 (2017) 100–109

the change of the direction. Therefore, it is more difficult in the second experiment (B) to determine the direction of the force than in the first experiment (A). Yet, the percentage of correct answers in the second experiment is satisfactory (79.7% of correct answers). The results show that this device is able to generate a haptic perception in two directions with good results.

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5. Conclusion Portable haptic devices are an interesting approach to provide guidance to visually impaired users or in other situations such as simulators. Different systems already exist but they mainly focus on the miniaturization of both volume and force. Hence, there is a need for systems that provide at the same time a small volume and the generation of large forces. This paper proposes to fill this gap by using a piezoelectric actuator together with asymmetric acceleration profiles. A prototype was built that is able to generate an acceleration of the moving part corresponding to a force between 1.7 and 7.4 N, depending on the mass of the moving part. The volume is small and is equal to 55 mm× 50 mm× 25.4 mm. The experimental results reported highlight the importance of the dynamic characterization of the device for optimizing the human perception. Generating large accelerations is not sufficient, the frequency of the impulses must also be taken into account. This frequency, referred to as the perception frequency, needs to be adjusted to the resonant frequency of the device, including the hand/device interaction. When such a frequency is used, both the acceleration and the asymmetry are maximized therefore optimizing the haptic perception. The tests performed with human subjects have demonstrated that the presented prototype of a haptic device is able to provide information on the direction with a percentage of correct answers ranging from 80% to 86%. This work shows the potential of piezoelectric actuators for the design of portable haptic devices. Piezoelectric actuators have the potential to improve the range of forces that can be generated by a portable haptic device while keeping a small volume. Also, this paper provides a comprehensive study that can lead to a better use of this type of device. Future developments include a new prototype with compliant joints to reduce the number of mobiles parts (ball bearing), and the use of new optimized input trajectories.

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[10] [11]

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[17] [18]

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Acknowledgments [20]

The authors would like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada and of the Canada Research Chair Program for their financial support (grant number : DG-89715). This project was approved by the Ethics Research Committee of Laval University: Certificate No 2015159 / 30-06-2015.

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