# Studying the influence of contact force on thermal perception at the fingertip

Danilo Troisi, Jeanne Hecquard, Ferran Argelaguet, Justine Saint-Aubert, Marc J.-M. Macé, Anatole Lécuyer, Claudio Pacchierotti, Monica Malvezzi

<figure><img src="image_1.png" /></figure>

## To cite this version:

Danilo Troisi, Jeanne Hecquard, Ferran Argelaguet, Justine Saint-Aubert, Marc J.-M. Macé, et al. Studying the influence of contact force on thermal perception at the fingertip. 2024 - Eurohaptics conference, Hiroyuki Kajimoto; Pedro Lopes; Claudio Pacchierotti, Jun 2024, Lille, France. pp.1-8. hal-04551672

HAL Id: hal-04551672

https://hal.science/hal-04551672

Submitted on 18 Apr 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

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<figure><img src="image_2.png" /></figure>
# Studying the influence of contact force on thermal perception at the fingertip

Danilo Troisi, Jeanne Hecquard, Ferran Argelaguet, Justine Saint-Aubert, Marc J.-M. Macé, Anatole Lécuyer, Claudio Pacchierotti, Monica Malvezzi

<figure><img src="image_1.png" /></figure>

## To cite this version:

Danilo Troisi, Jeanne Hecquard, Ferran Argelaguet, Justine Saint-Aubert, Marc J.-M. Macé, et al. Studying the influence of contact force on thermal perception at the fingertip. EUROHAPTICS 2024 - 14th International Conference on Human Haptic Sensing and Touch Enabled Computer Applications, Jun 2024, Lille, France. pp.154-161, 10.1007/978-3-031-70061-3_13. hal-04551672

HAL Id: hal-04551672

https://hal.science/hal-04551672v1

Submitted on 18 Apr 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>
# Studying the influence of contact force on thermal perception at the fingertip

Danilo Troisi¹,², Jeanne Hecquard³, Ferran Argelaguet³, Justine Saint-Aubert⁴, Marc Macé⁴, Anatole Lécuyer³, Claudio Pacchierotti⁴, and Monica Malvezzi¹

¹ Dept. Information Engineering and Mathematics, University of Siena – Siena, Italy

² Department of Information Engineering, University of Pisa – Pisa, Italy

³ Inria, Univ Rennes, CNRS, IRISA – Rennes, France

⁴ CNRS, Univ Rennes, Inria, IRISA – Rennes, France

**Abstract.** This paper investigates the influence of contact force applied to the human's fingertip on the perception of hot and cold temperatures, studying how variations in contact force may affect the sensitivity of cutaneous thermoreceptors or their interpretation. A psychophysical experiment involved 18 participants exposed to cold (20 °C) and hot (38 °C) thermal stimuli at varying contact forces, ranging from gentle (0.5 N) to firm (3.5 N) touch. Results show a tendency to overestimate hot temperatures (hot feels hotter than it really is) and underestimate cold temperatures (cold feels colder than it really is) as the contact force increases. This result might be linked to the increase in the fingertip contact area that occurs as the contact force between the fingertip and the plate delivering the stimuli grows.

**Keywords:** Thermal feedback, Contact force, Haptic perception, Fingertip haptics

## 1 Introduction

Thermal feedback can be used to augment real and virtual interactions, by conveying information on the environment or as affective touch [5,8,12,13]. Peltier cells are the most common devices used in that regard, as they are compact, can display a wide range of temperatures from hot to cold, and are easy to control. However, they present significant flaws, one of them being their slow dynamics [8]. While their technical efficiency can always be improved, the use of thermal illusions is another way of attaining a target sensation faster or with less energy [8,9]. Indeed, thermal perception hinges on spatial [18] and temporal [10] thresholds of the human skin receptors [14], which can be manipulated through haptic devices to modulate thermal sensations [9]. Notable examples include the thermal grill illusion, demonstrated by Thunberg in 1896 [15]; interlaced together, innocuous warm and cool stimuli feel painfully burning. Another prominent thermal illusion is the Thaler, or temperature-weight illusion by Weber et al. in 1846 [17], in which colder objects felt heavier than neutral ones.

In this paper, we seek to evaluate the potential of contact force to modulate thermal perception. Galie et al. [2,3] studied the increase of the contact area of
Studying the influence of contact force
on thermal perception at the fingertip

Danilo Troisi¹,², Jeanne Hecquard³, Ferran Argelaguet³, Justine Saint-Aubert⁴,
Marc Macé⁴, Anatole Lécuyer³, Claudio Pacchierotti⁴, and Monica Malvezzi¹

¹ Dept. Information Engineering and Mathematics, University of Siena – Siena, Italy

² Department of Information Engineering, University of Pisa – Pisa, Italy

³ Inria, Univ Rennes, CNRS, IRISA – Rennes, France

⁴ CNRS, Univ Rennes, Inria, IRISA – Rennes France

**Abstract.** This paper investigates the influence of contact force applied to the human's fingertip on the perception of hot and cold temperatures, studying how variations in contact force may affect the sensitivity of cutaneous thermoreceptors or their interpretation. A psychophysical experiment involved 18 participants exposed to cold (20 °C) and hot (38 °C) thermal stimuli at varying contact forces, ranging from gentle (0.5 N) to firm (3.5 N) touch. Results show a tendency to overestimate hot temperatures (hot feels hotter than it really is) and underestimate cold temperatures (cold feels colder than it really is) as the contact force increases. This result might be linked to the increase in the fingertip contact area that occurs as the contact force between the fingertip and the plate delivering the stimuli grows.

**Keywords:** Thermal feedback, Contact force, Haptic perception, Fingertip haptics

# 1 Introduction

Thermal feedback can be used to augment real and virtual interactions, by conveying information on the environment or as affective touch [5,8,12,13]. Peltier cells are the most common devices used in that regard, as they are compact, can display a wide range of temperatures from hot to cold, and are easy to control. However, they present significant flaws, one of them being their slow dynamics [8]. While their technical efficiency can always be improved, the use of thermal illusions is another way of attaining a target sensation faster or with less energy [8,9]. Indeed, thermal perception hinges on spatial [18] and temporal [10] thresholds of the human skin receptors [14], which can be manipulated through haptic devices to modulate thermal sensations [9]. Notable examples include the thermal grill illusion, demonstrated by Thunberg in 1896 [15]; interlaced together, innocuous warm and cool stimuli feel painfully burning. Another prominent thermal illusion is the Thaler, or temperature-weight illusion by Weber et al. in 1846 [17], in which colder objects felt heavier than neutral ones.

In this paper, we seek to evaluate the potential of contact force to modulate thermal perception. Galie et al. [2,3] studied the increase of the contact area of
the skin when increasing the force applied on it through a plate. They found that between 0 N and 4 N, the contact area increased following a logarithmic trend. They also noted that the thermal sensitivity of participants' fingers was negatively affected by a prolonged increase in the contact force. Dou et al. [1] also observed that an increase in contact force led to an increase in the heat flux of materials. To our knowledge, no work has been carried out on the influence of contact force on thermal perception. However, some studies evaluated the reverse: the effect of thermal feedback on the perception of contact force or stiffness [2,4]. In this respect, Gallo et al. [4] found an increase in stiffness perception and precision when felt in combination with warm thermal feedback, significantly higher than with cold feedback. With these observations in mind, we hypothesize that thermal perception is modulated by the contact force.

This work aims to evaluate the influence of contact force on thermal perception, and if such force is effective to enhance both warm and cold thermal perception. A psychophysical experiment was carried out, where participants repeatedly compared pairs of stimuli combining force and thermal feedback. Two thermal conditions were studied: hot, at 38 °C, and cold, at 20 °C. Participants reported which stimuli in the pair felt hotter or colder, depending on the thermal condition. Our primary hypothesis is that an increase in contact force will heighten thermal perception: hot will feel hotter, cold will feel colder.

# 2 Methods

## 2.1 Experimental Setup

**Device.** We designed a 1-degree-of-freedom (1-DoF) haptic interface able to provide different temperatures and contact forces stimuli to a user's fingertip. The device is shown in Fig. 1a; it includes a flat plate moving upwards and downwards, towards and away from the fingertip. It houses a 3×3 cm Peltier cell (P in Fig. 1, model GM250-71-14-16) powered with a 5.3 V power supply and maximum current absorbed of 1.1 A, a temperature sensor (T, LM35) with a sensitivity of 10 mV/°C, and a heat sink (H, SK57720SA). The Peltier cell is located on the upper part of the plate, contacting the user's fingertip during the interaction. The temperature sensor is attached to one of the cell's corners to not interfere with the finger-platform interaction. To ensure precise temperature measurements, we assessed any discrepancies between the temperature at the center and the temperature at the corner of the cell. The heat sink is located in the lower part of the moving plate to absorb the heat produced by the Peltier cell. Moreover, a fan is located outside the device (not shown in Fig. 1), pointing towards the heat sink, to increase dissipation without providing any additional undesirable stimuli to the user.

The moving plate is actuated by two servomotors (S, HS-625MG) through two racks (R) and gears (G), enabling the platform to move up and down with respect to the grounding base B1. On the sides of the moving plate, two racks (R) are securely attached using screws. The maximum stroke of the moving plate is 15 mm. All these components are mounted on a fixed floating base (B2).
the skin when increasing the force applied on it through a plate. They found that between 0 N and 4 N, the contact area increased following a logarithmic trend. They also noted that the thermal sensitivity of participants' fingers was negatively affected by a prolonged increase in the contact force. Dou et al. [1] also observed that an increase in contact force led to an increase in the heat flux of materials. To our knowledge, no work has been carried out on the influence of contact force on thermal perception. However, some studies evaluated the reverse: the effect of thermal feedback on the perception of contact force or stiffness [2,4]. In this respect, Gallo et al. [4] found an increase in stiffness perception and precision when felt in combination with warm thermal feedback, significantly higher than with cold feedback. With these observations in mind, we hypothesize that thermal perception is modulated by the contact force.

This work aims to evaluate the influence of contact force on thermal perception, and if such force is effective to enhance both warm and cold thermal perception. A psychophysical experiment was carried out, where participants repeatedly compared pairs of stimuli combining force and thermal feedback. Two thermal conditions were studied: hot, at 38 °C, and cold, at 20 °C. Participants reported which stimuli in the pair felt hotter or colder, depending on the thermal condition. Our primary hypothesis is that an increase in contact force will heighten thermal perception: hot will feel hotter, cold will feel colder.

# 2 Methods

## 2.1 Experimental Setup

**Device.** We designed a 1-degree-of-freedom (1-DoF) haptic interface able to provide different temperatures and contact forces stimuli to a user's fingertip. The device is shown in Fig. 1a; it includes a flat plate moving upwards and downwards, towards and away from the fingertip. It houses a 3×3 cm Peltier cell (P in Fig. 1, model GM250-71-14-16) powered with a 5.3 V power supply and maximum current absorbed of 1.1 A, a temperature sensor (T, LM35) with a sensitivity of 10 mV/°C, and a heat sink (H, SK57720SA). The Peltier cell is located on the upper part of the plate, contacting the user's fingertip during the interaction. The temperature sensor is attached to one of the cell's corners to not interfere with the finger-platform interaction. To ensure precise temperature measurements, we assessed any discrepancies between the temperature at the center and the temperature at the corner of the cell. The heat sink is located in the lower part of the moving plate to absorb the heat produced by the Peltier cell. Moreover, a fan is located outside the device (not shown in Fig. 1), pointing towards the heat sink, to increase dissipation without providing any additional undesirable stimuli to the user.

The moving plate is actuated by two servomotors (S, HS-625MG) through two racks (R) and gears (G), enabling the platform to move up and down with respect to the grounding base B1. On the sides of the moving plate, two racks (R) are securely attached using screws. The maximum stroke of the moving plate is 15 mm. All these components are mounted on a fixed floating base (B2).
To register the force exerted by the plate on the user's fingertip, we installed a triaxial high-precision force and torque sensor (F, ATI Nano43), with a resolution of 0.002 N and 0.025 N mm, respectively. Finally, a fingertip mount (M in Fig. 1b) enables a comfortable fingertip positioning and a controlled interaction force. The setup is firmly attached to a table with two clamps. The structure of the device is 3D-printed in ABS on a Raise3D N2 Plus printer.

We implemented a closed-loop PID-based force and temperature control using the data registered by the force and temperature sensors.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Experimental setup. A 1-DoF platform housing a Peltier element provides different temperature and pressure stimuli to the user's fingertip.</figcaption></figure>

## 2.2 Experimental Protocol and Measures

**Participants.** Eighteen participants took part in the study (16 males, 2 females), aged between 23 and 36 years old (M = 27.06, SD = 3.27). All participants had no known hand or finger impairment. They all gave written informed consent and did not receive any form of compensation.

**Procedure.** During the experiment, the room's heating system was set to maintain a temperature of 24°C. Participants sat before the setup and placed their right index finger inside the finger mount, as shown in Fig. 1b. Then, the experimenter carefully ensured that the finger pulp was placed right above the center of the Peltier element to guarantee a good contact interaction. Finally, the device and finger mount were secured to the table through two clamps to avoid undesired movements during the experiment.

The experiment included two blocks, “hot” and “cold”, featuring interactions when the Peltier element on the plate had a temperature of 38°C and 20°C, respectively. We chose these two temperatures as they stand equally distant from the standard temperature of our fingertips, which Vergara et al. reported
To register the force exerted by the plate on the user's fingertip, we installed a triaxial high-precision force and torque sensor (F, ATI Nano43), with a resolution of 0.002 N and 0.025 N mm, respectively. Finally, a fingertip mount (M in Fig. 1b) enables a comfortable fingertip positioning and a controlled interaction force. The setup is firmly attached to a table with two clamps. The structure of the device is 3D-printed in ABS on a Raise3D N2 Plus printer.

We implemented a closed-loop PID-based force and temperature control using the data registered by the force and temperature sensors.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Experimental setup. A 1-DoF platform housing a Peltier element provides different temperature and pressure stimuli to the user's fingertip.</figcaption></figure>

## 2.2 Experimental Protocol and Measures

**Participants.** Eighteen participants took part in the study (16 males, 2 females), aged between 23 and 36 years old (M = 27.06, SD = 3.27). All participants had no known hand or finger impairment. They all gave written informed consent and did not receive any form of compensation.

**Procedure.** During the experiment, the room's heating system was set to maintain a temperature of 24°C. Participants sat before the setup and placed their right index finger inside the finger mount, as shown in Fig. 1b. Then, the experimenter carefully ensured that the finger pulp was placed right above the center of the Peltier element to guarantee a good contact interaction. Finally, the device and finger mount were secured to the table through two clamps to avoid undesired movements during the experiment.

The experiment included two blocks, “hot” and “cold”, featuring interactions when the Peltier element on the plate had a temperature of 38°C and 20°C, respectively. We chose these two temperatures as they stand equally distant from the standard temperature of our fingertips, which Vergara et al. reported
to be in the range [28, 30]°C [16]. In particular, a pilot test aimed to identify
temperatures that produced both hot and cold sensations with comparable in-
tensity. Results indicated that 38°C felt as hot as 20°C felt cold. Within each
block, participants carried out 48 comparisons of two subsequent force stimuli
at the given temperature (38°C or 20°C), comparing the reference force vs. a
test force. For this experiment, we considered 2N as the reference force and [0.5,
1.0, 1.5, 2.5, 3.0, 3.5] N as the test forces to apply at the fingertip. The range
of forces was inspired from Galie et al.'s work on the influence of force on the
contact area of skin [2]. Each test/reference couple was compared 4 times within
each block, resulting in 8 repetitions for each tested force. Participants had no
information about the rendered sensations (e.g., they did not know that the
temperature within each block was the same). For each comparison, the device
makes contact with the user's fingertip for 2 s, then breaks contact for 4 s, and
again makes contact for 2 s (see the video). These timings were chosen to enable
the user to remember the two stimuli while giving time to the fingertip to return
to its rest temperature before the second interaction [7]. After each comparison,
participants responded to "Which contact felt hotter?" during the hot block and
"Which contact felt colder?" during the cold block. Throughout the experiment,
participants could answer this question by pressing "1" or "2" on the keyboard
with their left hand for the first or second feedback. Participants took a 1-minute
break every 24 comparisons. The order in which the blocks were presented and
the order in which the reference and test forces were applied were counterbal-
anced. The order in which the comparisons were presented within each block was
randomized. The duration of the experiment depended on the participants' re-
sponsiveness in providing answers. Considering this factor, the experiment lasted
approximately 45 minutes.

Throughout the experiment, we recorded the target and measured forces/tem-
peratures for each interaction, as well as the users' response and response time
for each comparison.

According to the literature, increasing contact pressure on the fingertip leads to an expanded contact surface between the skin and the interacting device (up to a certain level) [2]. With this in mind, our main hypothesis was that: Increased contact force exacerbates temperature perception (hot feels hotter than it really is, and cold feels colder than it really is) (H).

3 Analysis and Results

Following the data collection from the experiment, we removed trials in which
the difference between target and registered forces/temperatures in the refer-
ence or comparison stimuli surpassed three standard deviations (73 out of 1728
trials), i.e., trials in which the system failed to reach the target stimulus level.
We also removed data from two participants. For the first one, the temperature
sensor partially detached from the Peltier cell during the experiment, leading to
an unpredictable (and unknown) level of applied temperature. The second par-
ticipant did not understand the comparative question for the feedback couples,
to be in the range [28, 30]°C [16]. In particular, a pilot test aimed to identify
temperatures that produced both hot and cold sensations with comparable in-
tensity. Results indicated that 38°C felt as hot as 20°C felt cold. Within each
block, participants carried out 48 comparisons of two subsequent force stimuli
at the given temperature (38°C or 20°C), comparing the reference force vs. a
test force. For this experiment, we considered 2N as the reference force and [0.5,
1.0, 1.5, 2.5, 3.0, 3.5] N as the test forces to apply at the fingertip. The range
of forces was inspired from Galie et al.'s work on the influence of force on the
contact area of skin [2]. Each test/reference couple was compared 4 times within
each block, resulting in 8 repetitions for each tested force. Participants had no
information about the rendered sensations (e.g., they did not know that the
temperature within each block was the same). For each comparison, the device
makes contact with the user's fingertip for 2 s, then breaks contact for 4 s, and
again makes contact for 2 s (see the video). These timings were chosen to enable
the user to remember the two stimuli while giving time to the fingertip to return
to its rest temperature before the second interaction [7]. After each comparison,
participants responded to "Which contact felt hotter?" during the hot block and
"Which contact felt colder?" during the cold block. Throughout the experiment,
participants could answer this question by pressing "1" or "2" on the keyboard
with their left hand for the first or second feedback. Participants took a 1-minute
break every 24 comparisons. The order in which the blocks were presented and
the order in which the reference and test forces were applied were counterbal-
anced. The order in which the comparisons were presented within each block was
randomized. The duration of the experiment depended on the participants' re-
sponsiveness in providing answers. Considering this factor, the experiment lasted
approximately 45 minutes.

Throughout the experiment, we recorded the target and measured forces/tem-
peratures for each interaction, as well as the users' response and response time
for each comparison.

According to the literature, increasing contact pressure on the fingertip leads to an expanded contact surface between the skin and the interacting device (up to a certain level) [2]. With this in mind, our main hypothesis was that: Increased contact force exacerbates temperature perception (hot feels hotter than it really is, and cold feels colder than it really is) (H).

**3 Analysis and Results**

Following the data collection from the experiment, we removed trials in which
the difference between target and registered forces/temperatures in the refer-
ence or comparison stimuli surpassed three standard deviations (73 out of 1728
trials), i.e., trials in which the system failed to reach the target stimulus level.
We also removed data from two participants. For the first one, the temperature
sensor partially detached from the Peltier cell during the experiment, leading to
an unpredictable (and unknown) level of applied temperature. The second par-
ticipant did not understand the comparative question for the feedback couples,
leading to random, uninformative answers for studying the considered hypothe-
ses. After this step, the data from 16 participants (1462 trials) was analyzed
with regard to our hypotheses. The difference between target and registered
forces/temperatures (i.e., the error in delivering the stimuli) were M = 0.12 N,
SD=0.19 N and M=0.00°C, SD=0.08°C, respectively.

Then, we computed for each user, feedback couple, and thermal condition the percentage of answers where the reference stimulus (2 N) was selected as being colder/warmer (see Fig. 2). A general linear mixed model analysis was performed, considering the *percentage* as the dependent variable, the comparison force and the temperature condition as within-subject variables, and the user as a random factor. The results showed only a significant effect on force ($F_{4,12,61.81} = 17.62, p < 0.001, \eta_P^2 = 0.54$), but not on the temperature condition ($F_{1,15} = 0.33, p = 0.86, \eta_P^2 = 0.002$) nor on their interaction ($F_{3,69,55.29} = 0.66, p = 0.61, \eta_P^2 = 0.04$). Figure 2 summarizes the results of the post-hoc tests. A line between two force levels means a significant difference ($p < 0.05$, t-tests with Bonferroni correction). We observe that the percentage of answers - wherein the reference stimulus was selected as being warmer/colder - was higher when the compared forces were smaller, and this effect does not change with the considered temperatures.

Finally we fitted a psychometric function for each user, to compute the
point of subjective equality (PSE) (M =0.22, SD=0.87) and the just-noticeable
differences (JND) (M = -2.04, SD = 1.86). Similarly to the previous results,
there were no significant differences between hot/cold conditions for the PSE
(t(15) = -0.47 p = 0.65) and the JND (t(15) = 0.05 p = 0.96), thus only the global
PSE and JND are reported.

4 Discussion and Conclusion

We explored the impact of contact force at the fingertip on the perception of hot and cold temperatures. We conducted an empirical study to compare the perceived temperature of a moving plate by applying different forces at their index fingertips. Results show a tendency to overestimate hot temperatures and to underestimate cold temperatures with increasing contact force, supporting **H.** In other words, the hot plate felt hotter as the force increased; similarly, the cold plate felt colder as the force increased. This exacerbation of the temperature perception seems stronger at lower forces (<2.5 N), e.g., results at 3 N (+1) vs. 3.5 N (+1.5) show no difference, while results 0.5 N (-1.5) vs. 1 N (-1) show a statistically significant difference. In addition to the change of pressure, this trend may be also associated with the concurrent increase in fingertip contact area as the force between the fingertip and the plate rises. Indeed, Galie and Jones [3] identified a logarithmic trend between contact force and contact area on the fingertips, with a fast increase of the contact area for low forces (<2 N) and close-to-zero increase when applying high forces (>3 N). Our study mostly addresses the former range, considering forces from 0.5 N to 3.5 N. Moreover, as stated by Jay et al. [6], pressure-induced changes in skin temperature perception might be associated to changes in blood flow. Thus, additional experiments are
leading to random, uninformative answers for studying the considered hypothe-
ses. After this step, the data from 16 participants (1462 trials) was analyzed
with regard to our hypotheses. The difference between target and registered
forces/temperatures (i.e., the error in delivering the stimuli) were M = 0.12 N,
SD=0.19 N and M=0.00°C, SD=0.08°C, respectively.

Then, we computed for each user, feedback couple, and thermal condition the percentage of answers where the reference stimulus (2 N) was selected as being colder/warmer (see Fig. 2). A general linear mixed model analysis was performed, considering the *percentage* as the dependent variable, the comparison force and the temperature condition as within-subject variables, and the user as a random factor. The results showed only a significant effect on force ($F_{4,12,61.81} = 17.62, p < 0.001, \eta_P^2 = 0.54$), but not on the temperature condition ($F_{1,15} = 0.33, p = 0.86, \eta_P^2 = 0.002$) nor on their interaction ($F_{3,69,55.29} = 0.66, p = 0.61, \eta_P^2 = 0.04$). Figure 2 summarizes the results of the post-hoc tests. A line between two force levels means a significant difference ($p < 0.05$, t-tests with Bonferroni correction). We observe that the percentage of answers - wherein the reference stimulus was selected as being warmer/colder - was higher when the compared forces were smaller, and this effect does not change with the considered temperatures.

Finally we fitted a psychometric function for each user, to compute the
point of subjective equality (PSE) (M =0.22, SD=0.87) and the just-noticeable
differences (JND) (M = -2.04, SD = 1.86). Similarly to the previous results,
there were no significant differences between hot/cold conditions for the PSE
(t(15) = -0.47 p = 0.65) and the JND (t(15) = 0.05 p = 0.96), thus only the global
PSE and JND are reported.

4 Discussion and Conclusion

We explored the impact of contact force at the fingertip on the perception of hot and cold temperatures. We conducted an empirical study to compare the perceived temperature of a moving plate by applying different forces at their index fingertips. Results show a tendency to overestimate hot temperatures and to underestimate cold temperatures with increasing contact force, supporting **H.** In other words, the hot plate felt hotter as the force increased; similarly, the cold plate felt colder as the force increased. This exacerbation of the temperature perception seems stronger at lower forces (<2.5 N), e.g., results at 3 N (+1) vs. 3.5 N (+1.5) show no difference, while results 0.5 N (-1.5) vs. 1 N (-1) show a statistically significant difference. In addition to the change of pressure, this trend may be also associated with the concurrent increase in fingertip contact area as the force between the fingertip and the plate rises. Indeed, Galie and Jones [3] identified a logarithmic trend between contact force and contact area on the fingertips, with a fast increase of the contact area for low forces (<2 N) and close-to-zero increase when applying high forces (>3 N). Our study mostly addresses the former range, considering forces from 0.5 N to 3.5 N. Moreover, as stated by Jay et al. [6], pressure-induced changes in skin temperature perception might be associated to changes in blood flow. Thus, additional experiments are
<figure><img src="image_4.png" /><figcaption>Fig. 2: Box-plot showing the ratio of the trials wherein the reference stimulus (2 N) was considered colder/warmer. The lines on the top represent significant differences between force conditions ($p < 0.05$). The difference between temperature conditions was not significant. The colored oblique lines represent the binomial regression model using measured forces.</figcaption></figure>

needed to analyze this temperature vs. force relationship at higher forces to further verify the relationship between thermal perception and contact area. For example, a potential approach to prevent the increase in contact area with the application of rising forces could be to utilize Peltier cells smaller than the fingertip.

At the end of the experiment, participants provided feedback on their strategy. The majority of the participants were surprised upon discovering that the temperature remained constant within a block, while only one speculated that only pressure changed during the comparisons. Finally, in this work, we only considered two reference temperatures and short sustained contacts (2 s) from when we reached the target contact force, meaning that higher forces were also applied for a (very slightly) longer time; these variables might impact the relationship between temperature and contact force. For example, we expect the behavior to vary depending on which set of thermal receptors are activated [7,11]. Similarly, the local shape of the end-effector at the contact point – a flat surface in our case – might change the way the temperature is delivered and, therefore, its interpretation. These observations leave a substantial space for further experimentation and application in relevant scenarios.

Indeed, these (and previous) results on the topic pave the way for the development of new thermal devices, in which the target thermal sensation can be modulated by controlling the actual temperature of the end-effector as well as the pressure it applies on the skin. As Peltier cells have slow dynamics, it
<figure><img src="image_4.png" /><figcaption>Fig. 2: Box-plot showing the ratio of the trials wherein the reference stimulus (2 N) was considered colder/warmer. The lines on the top represent significant differences between force conditions ($p < 0.05$). The difference between temperature conditions was not significant. The colored oblique lines represent the binomial regression model using measured forces.</figcaption></figure>

needed to analyze this temperature vs. force relationship at higher forces to further verify the relationship between thermal perception and contact area. For example, a potential approach to prevent the increase in contact area with the application of rising forces could be to utilize Peltier cells smaller than the fingertip.

At the end of the experiment, participants provided feedback on their strategy. The majority of the participants were surprised upon discovering that the temperature remained constant within a block, while only one speculated that only pressure changed during the comparisons. Finally, in this work, we only considered two reference temperatures and short sustained contacts (2 s) from when we reached the target contact force, meaning that higher forces were also applied for a (very slightly) longer time; these variables might impact the relationship between temperature and contact force. For example, we expect the behavior to vary depending on which set of thermal receptors are activated [7,11]. Similarly, the local shape of the end-effector at the contact point – a flat surface in our case – might change the way the temperature is delivered and, therefore, its interpretation. These observations leave a substantial space for further experimentation and application in relevant scenarios.

Indeed, these (and previous) results on the topic pave the way for the development of new thermal devices, in which the target thermal sensation can be modulated by controlling the actual temperature of the end-effector as well as the pressure it applies on the skin. As Peltier cells have slow dynamics, it
is promising to be able to rapidly modulate the perceived temperature through pressure variation.

**Acknowledgement.** This research has been funded by the EU Horizon 2020 research and innovation program under grant agreement No. 101017884 (GuestXR) and by the Next Generation EU project ECS00000017 "Ecosistema dell'Innovazione" Tuscany Health Ecosystem (THE, PNRR: Spoke 9: Robotics and Automation for Health).

## References

1. Dou, R., Ge, T., Liu, X., Wen, Z.: Effects of contact pressure, interface temperature, and surface roughness on thermal contact conductance between stainless steel surfaces under atmosphere condition. International Journal of Heat and Mass Transfer **94**, 156–163 (2016)

2. Galie, J., Ho, H.N., Jones, L.A.: Influence of contact conditions on thermal responses of the hand. In: World Haptics 2009 - Third Joint EuroHaptics conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems. pp. 587–592 (March 2009)

3. Galie, J., Jones, L.A.: Thermal cues and the perception of force. Experimental brain research **200**, 81–90 (2010)

4. Gallo, S., Rognini, G., Santos-Carreras, L., Vouga, T., Blanke, O., Bleuler, H.: Encoded and crossmodal thermal stimulation through a fingertip-sized haptic display. Frontiers in Robotics and AI **2** (10 2015)

5. Haliburton, L., Schött, S.Y., Hirsch, L., Welsch, R., Schmidt, A.: Feeling the temperature of the room: Unobtrusive thermal display of engagement during group communication. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol. **7**(1) (mar 2023)

6. Jay, O., Havenith, G.: Differences in finger skin contact cooling response between an arterial occlusion and a vasodilated condition. Journal of Applied Physiology **100**(5), 1596–1601 (2006)

7. Jones, L.: Thermal touch. Scholarpedia **4**(5), 7955 (2009)

8. Jones, L.A., Ho, H.N.: Warm or cool, large or small? the challenge of thermal displays. IEEE Transactions on Haptics **1**(1), 53–70 (2008)

9. Karmakar, S., Kesh, A., Muniyandi, M.: Thermal illusions for thermal displays: a review. Frontiers in human neuroscience **17**, 1278894 (12 2023)

10. Kenshalo, D.R., Scott, H.A.: Temporal course of thermal adaptation. Science **151**(3714), 1095–1096 (1966)

11. Pacchierotti, C., Prattichizzo, D.: Cutaneous/tactile haptic feedback in robotic teleoperation: Motivation, survey, and perspectives. IEEE Trans. Robotics (2023)

12. Pacchierotti, C., Sinclair, S., Solazzi, M., Frisoli, A., Hayward, V., Prattichizzo, D.: Wearable haptic systems for the fingertip and the hand: taxonomy, review, and perspectives. IEEE Trans. Haptics **10**(4), 580–600 (2017)

13. Prattichizzo, D., Otaduy, M., Kajimoto, H., Pacchierotti, C.: Wearable and handheld haptics. IEEE Trans. Haptics **12**(3), 227–231 (2019)

14. Stevens, J.C., Choo, K.K.: Temperature sensitivity of the body surface over the life span. Somatosensory & motor research **15** 1, 13–28 (1998)
is promising to be able to rapidly modulate the perceived temperature through
pressure variation.

**Acknowledgement.** This research has been funded by the EU Horizon 2020 re-
search and innovation program under grant agreement No. 101017884 (GuestXR)
and by the Next Generation EU project ECS00000017 "Ecosistema dell'Innova-
zione" Tuscany Health Ecosystem (THE, PNRR: Spoke 9: Robotics and Au-
tomation for Health).

References

1. Dou, R., Ge, T., Liu, X., Wen, Z.: Effects of contact pressure, interface temperature, and surface roughness on thermal contact conductance between stainless steel surfaces under atmosphere condition. International Journal of Heat and Mass Transfer **94**, 156–163 (2016)

2. Galie, J., Ho, H.N., Jones, L.A.: Influence of contact conditions on thermal responses of the hand. In: World Haptics 2009 - Third Joint EuroHaptics conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems. pp. 587–592 (March 2009)

3. Galie, J., Jones, L.A.: Thermal cues and the perception of force. Experimental brain research **200**, 81–90 (2010)

4. Gallo, S., Rognini, G., Santos-Carreras, L., Vouga, T., Blanke, O., Bleuler, H.: Encoded and crossmodal thermal stimulation through a fingertip-sized haptic display. *Frontiers in Robotics and AI* **2** (10 2015)

5. Haliburton, L., Schött, S.Y., Hirsch, L., Welsch, R., Schmidt, A.: Feeling the temperature of the room: Unobtrusive thermal display of engagement during group communication. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol. **7**(1) (mar 2023)

6. Jay, O., Havenith, G.: Differences in finger skin contact cooling response between an arterial occlusion and a vasodilated condition. Journal of Applied Physiology **100**(5), 1596–1601 (2006)

7. Jones, L.: Thermal touch. Scholarpedia **4**(5), 7955 (2009)

8. Jones, L.A., Ho, H.N.: Warm or cool, large or small? the challenge of thermal displays. IEEE Transactions on Haptics **1**(1), 53–70 (2008)

9. Karmakar, S., Kesh, A., Muniyandi, M.: Thermal illusions for thermal displays: a review. *Frontiers in human neuroscience* **17**, 1278894 (12 2023)

10. Kenshalo, D.R., Scott, H.A.: Temporal course of thermal adaptation. *Science* **151**(3714), 1095–1096 (1966)

11. Pacchierotti, C., Prattichizzo, D.: Cutaneous/tactile haptic feedback in robotic teleoperation: Motivation, survey, and perspectives. IEEE Trans. Robotics (2023)

12. Pacchierotti, C., Sinclair, S., Solazzi, M., Frisoli, A., Hayward, V., Prattichizzo, D.: Wearable haptic systems for the fingertip and the hand: taxonomy, review, and perspectives. IEEE Trans. Haptics **10**(4), 580–600 (2017)

13. Prattichizzo, D., Otaduy, M., Kajimoto, H., Pacchierotti, C.: Wearable and hand-held haptics. IEEE Trans. Haptics **12**(3), 227–231 (2019)

14. Stevens, J.C., Choo, K.K.: Temperature sensitivity of the body surface over the life span. Somatosensory & motor research **15** 1, 13–28 (1998)
8

D. Troisi et al.

15. Thunberg, T.: Förnimmelserne vid till samma ställe lokaliserad, samtidigt pågående köld-och värmeretning - sensations localized at the same place, simultaneously ongoing cold and heat. Uppsala Läkfören Förh 1, 489-95 (1896)

16. Vergara, R.C., Moënne-Loccoz, C., Maldonado, P.E.: Cold-blooded attention: finger temperature predicts attentional performance. Frontiers in human neuroscience 11, 454 (2017)

17. Weber, E.: E. h. weber on the tactile senses. In: E. H. Weber on the tactile senses (2nd ed., H. E. Ross & D. J. Murray, Eds.) (1996)

18. Yang, G.H., Kwon, D.S., Jones, L.A.: Spatial acuity and summation on the hand: The role of thermal cues in material discrimination. Perception & Psychophysics 71, 156-163 (2009)
8

D. Troisi et al.

15. Thunberg, T.: Förnimmelserne vid till samma ställe lokaliserad, samtidigt pågående köld-och värmeretning - sensations localized at the same place, simultaneously ongoing cold and heat. Uppsala Läkfören Förh 1, 489-95 (1896)

16. Vergara, R.C., Moënne-Loccoz, C., Maldonado, P.E.: Cold-blooded attention: finger temperature predicts attentional performance. Frontiers in human neuroscience 11, 454 (2017)

17. Weber, E.: E. h. weber on the tactile senses. In: E. H. Weber on the tactile senses (2nd ed., H. E. Ross & D. J. Murray, Eds.) (1996)

18. Yang, G.H., Kwon, D.S., Jones, L.A.: Spatial acuity and summation on the hand: The role of thermal cues in material discrimination. Perception & Psychophysics 71, 156-163 (2009)