**2. Psychophysical experiment**

#### **2.1 Subjective equality and difference threshold**

In the psychophysical experiments of this study, the relationships between the stimulus magnitudes of fine step-heights and the sensitivity of the finger's tactile sensing mechanism are examined. Subjective equalities and difference thresholds for fine step-heights

dots, respectively (Heller, 1989). On the other hand, the psychophysical experiments (Miyaoka et al., 1993, 1996, 1997) determined that the human tactile mechanism is able to detect a mechanical vibration of 0.2 µm in amplitude and a surface unevenness of 3 µm in amplitude. Also, the psychophysical experiment (Kawamura et al., 1996) revealed that FA I plays an important role in discriminating the magnitudes of step-height of around 10 µm. From these experimental results, it is considered that, like the human visual sense, the human tactile sense has several kinds of module mechanisms, and it is supposed that the human tactile modules are classified based on the stimulus magnitudes they can detect and discriminate and their information processing characteristics: the subtle stimulation detection module, fine texture recognition module, two-dimensional pattern recognition module, and three-dimensional shape recognition module. So far the authors have been investigated the tactile sensation capability of recognizing fine step-heights with respect to

Using a measurement system that presents fine step-heights of about 10 µm to subjects' fingers (Miyaoka et al., 1996; Kawamura et al., 1996), the difference thresholds for a 10 µm step-height were determined when the subjects actively touched the step-height with their fingers moving over the step-height and when they were passively touched the step-height presented to their fingers by the movement of the step presentation device. As a result, the difference thresholds for a 10 µm step-height in the active- and passive-touch experiments agreed approximately. Therefore, it was concluded that the finger's discrimination capability of fine step-heights of about 10 µm does not depend on the touching manners. Also, the paper (Kawamura et al., 1998) suggested that when the subjects discriminated a pair of the 10 µm step-heights presented at the different presentation velocities of 20 and 40 mm/s to their fingers, they perceived the height of the fast moving step-height to be a larger stimulus than that of the slowly moving step-height due to the influence of the stimulus velocity. Furthermore, the authors developed a measurement system that can create fine step-heights of 0 to 1000 µm and present the step-heights to subjects' fingers at various

In this paper, to measure the finger's tactile sensation capability of discriminating fine stepheights, the developed measurement system is used. In the psychophysical tests, the presentation angle of a step is defined as the angle to finger's length and several pairs of fine step-heights of 0 to 100 µm are presented to subjects' fingertips at various presentation angles. This paper first describes the measurement system that controls the amounts of step-heights according to the experiment procedure based on the PEST method in order to determine subjective equalities and difference thresholds for fine step-heights, then examines the effects of the touching manner of human finger, finger's motion direction, and fingertip region on the tactile recognition of fine step-heights. In the psychophysical tests, first, the subjects discriminate step-heights of 10 to 100 µm in active- and passive-touch manners using the center of their fingertips. Next, the subjects discriminate step-heights of around 10 µm using

In the psychophysical experiments of this study, the relationships between the stimulus magnitudes of fine step-heights and the sensitivity of the finger's tactile sensing mechanism are examined. Subjective equalities and difference thresholds for fine step-heights

the top and center of their fingertips in various motion directions of their fingers.

the fine texture recognition module.

presentation angles (Kawamura et al., 2009).

**2. Psychophysical experiment** 

**2.1 Subjective equality and difference threshold** 

determined using the experiments are important values for investigating the human tactile sensation. The meanings of those values are explained in the following (Gescheider, 1985).

In an experiment, human subjects touch several pairs of stimuli with their fingers and try to distinguish them. One of the stimulus pair is the standard stimulus and the other is the comparison stimulus. The magnitudes of the standard and comparison stimuli are denoted by *δs* and *δc*, respectively. The standard stimulus is designed to be constant and the comparison stimulus is variable. Several pairs of *δs* and *δc* are presented to the subjects and for each pair they are asked to tell which stimulus of *δs* and *δc* they feel stronger. When *δc* is smaller than *δs*, the proportion of the responses that *δc* is chosen as stronger than *δs* is supposed to be low. Conversely, when *δ<sup>c</sup>* is greater than *δs*, the proportion of the responses that *δc* is chosen as stronger than *δs* is supposed to be high. Figure 1 shows a characteristic curve of the proportion that *δc* is chosen as stronger than *δs*. The horizontal axis shows the comparison stimulus while the vertical axis shows the proportion of the subjects selecting the comparison stimulus. The comparison stimulus magnitudes for the proportions equal to 0.25, 0.5, and 0.75 are denoted by *S*0.25, *S*0.5, and *S*0.75, respectively. The value of *S*0.5 is called the subjective equality for *δs*. If the standard and comparison stimuli are presented under the same condition, *S*0.5 should be equal to *δs*.

Fig. 1. An example of a discrimination characteristics curve.

The values of *Δ<sup>U</sup>* = *S*0.75 − *S*0.5 and *Δ<sup>L</sup>* = *S*0.5 − *S*0.25 are the upper and lower thresholds for *δs*, respectively. Moreover, the average of the thresholds, *Δ =* (*ΔU* + *ΔL*)/2, is called the difference threshold. In addition, these thresholds usually have very close values because the upper and lower thresholds become almost equal. Also the value of the ratio of *Δ* to *δs* is called the Weber fraction. The value is known to be constant over the range of stimulus magnitude in tactile sensing mechanisms, as well as in visual and auditory.

Measurement System of Fine Step-Height

satisfied. Equations (3) and (4) are given as follows:

**Rule #2: Incremental stimulus magnitude** 

given as follows:

8

10

12

14

16

Comparison step-height,

18

20

*δcn* µm

22

*Rn* is set half *Rn*-1.

Discrimination Capability of Human Finger's Tactile Sense 167

is satisfied, then the experiment continues with the same comparison stimulus. If the condition is not satisfied, then *δcn* is varied and the trial block is incremented to the (*n* + 1)-th trial block. *δcn*+1 is decreased whenever (3) is satisfied and increased whenever (4) is

Fig. 3. An example of variation in comparison step-height calculated by the PEST algorithm.

0 10 20 30 40 50 60 70

Trial number, *T*

The incremental range of the comparison stimulus magnitude in the *n*-th trial block, *Rn*, should decrease in order for *δcn*+1 to converge as the number of trials increases. Here *δcn*+1 is

> *cn cn n* <sup>1</sup>

If *δcn* differs considerably from the convergent value, *Rn* should increase to reach rapidly the convergent value. Taylor and Creelman empirically determined the rules for the adjustment of the incremental range. In their rules, the convergence condition is judged by the variation in fluctuation direction of the stimulus magnitude. The fluctuation direction (increase or

a. If the direction *Dn* becomes contrary to the direction *Dn*-1 of the (*n* - 1)-th trial block, then

A trial block

decrease) in the *n*-th trial block is denoted by *Dn*. *Rn* is specified as follows:

b. If *Dn*-1 and *Dn* are the same direction, then *Rn* is set the same as *Rn*-1.

*E E <sup>n</sup> <sup>p</sup>* , (3)

*E E <sup>n</sup> <sup>p</sup>* . (4)

*δs* **=** 10 µm *δc***1=** 20 µm *R***1=** 3 µm *P* **=** 0.75 *Ep***=** 1.0 *Rmin***=** 0.3 µm

Trial ○: true ×: false

*R* . (5)

Upper threshold

#### **2.2 Parameter Estimation by Sequential Testing (PEST) method**

Taylor and Creelman developed the PEST method to determine the above-mentioned difference thresholds and subjective equalities through the process of a psychophysical experiment without calculating the characteristics curve (Taylor & Creelman, 1982). The PEST algorithm consists of three groups of rules in the following, and, as shown in Fig. 2, calculates the magnitudes of comparison stimuli to present to a subject based on the subject's responses in the experiment. In this study, the authors have developed the measurement system that calculates the magnitudes by computer based on the PEST algorithm and determines the difference thresholds and subjective equalities.

Fig. 2. Flowchart of changing the magnitude of comparison stimulus using the PEST algorithm.

#### **Rule #1: Condition for changing the magnitude of comparison stimulus**

A PEST sequence consists of several trial blocks composed of several trials as shown in Fig. 3. Let us consider the *n*-th trial block. The magnitude of comparison stimulus is constant throughout the same block. Let *δcn*, *Tn* and *Cn* be the comparison stimulus magnitude, the trial number and the number of the human subject's correct answers in the current *n*-th trial block, respectively. For a specified *P*, the proportion of *Cn* against *Tn*, the error number *En* is given as follows:

$$E\_n = P \cdot T\_n - \mathbb{C}\_{n \text{ \textquotedblleft}} \tag{1}$$

where the value of *P* is 0.25, 0.5, or 0.75 to obtain the lower threshold, the subjective equality, or the upper threshold, respectively. Let *Ep* be the permitted error number. If the condition:

$$\begin{array}{ccccc} \| \, E\_n \| \, < & E\_p \end{array} \tag{2}$$

Taylor and Creelman developed the PEST method to determine the above-mentioned difference thresholds and subjective equalities through the process of a psychophysical experiment without calculating the characteristics curve (Taylor & Creelman, 1982). The PEST algorithm consists of three groups of rules in the following, and, as shown in Fig. 2, calculates the magnitudes of comparison stimuli to present to a subject based on the subject's responses in the experiment. In this study, the authors have developed the measurement system that calculates the magnitudes by computer based on the PEST

**2.2 Parameter Estimation by Sequential Testing (PEST) method** 

algorithm and determines the difference thresholds and subjective equalities.

**Increase** the comparison stimulus

algorithm.

given as follows:

condition:

Error number *En* **=** *P*・*Tn* - *Cn*

Next trial Next trial Same trial

Fig. 2. Flowchart of changing the magnitude of comparison stimulus using the PEST

A PEST sequence consists of several trial blocks composed of several trials as shown in Fig. 3. Let us consider the *n*-th trial block. The magnitude of comparison stimulus is constant throughout the same block. Let *δcn*, *Tn* and *Cn* be the comparison stimulus magnitude, the trial number and the number of the human subject's correct answers in the current *n*-th trial block, respectively. For a specified *P*, the proportion of *Cn* against *Tn*, the error number *En* is

where the value of *P* is 0.25, 0.5, or 0.75 to obtain the lower threshold, the subjective equality, or the upper threshold, respectively. Let *Ep* be the permitted error number. If the

**Rule #1: Condition for changing the magnitude of comparison stimulus** 

Difficult to discriminate

Shortage of trial number

**|***En***| <** *Ep*

Easy to discriminate

*Tn*: Trial number

*E PT C n nn* , (1)


*Cn*: Correct-answer number *Ep*: Permitted error number

*En* **≥** *Ep En* **≤ -** *Ep*

**Discriminate two stimuli**

Input the subject's answer

**Decrease** the comparison stimulus

*P* : 0.75 for upper threshold 0.50 for subjective equality 0.25 for lower threshold

is satisfied, then the experiment continues with the same comparison stimulus. If the condition is not satisfied, then *δcn* is varied and the trial block is incremented to the (*n* + 1)-th trial block. *δcn*+1 is decreased whenever (3) is satisfied and increased whenever (4) is satisfied. Equations (3) and (4) are given as follows:

$$E\_n \quad \le \quad -E\_{p\\_\ast} \tag{3}$$

$$E\_n \quad \ge \quad E\_p \tag{4}$$

#### **Rule #2: Incremental stimulus magnitude**

The incremental range of the comparison stimulus magnitude in the *n*-th trial block, *Rn*, should decrease in order for *δcn*+1 to converge as the number of trials increases. Here *δcn*+1 is given as follows:

$$
\delta\_{cn+1} = \delta\_{cn} \pm R\_n \,. \tag{5}
$$

If *δcn* differs considerably from the convergent value, *Rn* should increase to reach rapidly the convergent value. Taylor and Creelman empirically determined the rules for the adjustment of the incremental range. In their rules, the convergence condition is judged by the variation in fluctuation direction of the stimulus magnitude. The fluctuation direction (increase or decrease) in the *n*-th trial block is denoted by *Dn*. *Rn* is specified as follows:


Measurement System of Fine Step-Height

Discrimination Capability of Human Finger's Tactile Sense 169

**Cover plate 0 - 1000 µm**

**Rotary table**

**Peltier element**

**Z-stage Stepping motor**

Fig. 5. Scene of psychophysical experiment of active-touch manner.

Fig. 6. Scene of psychophysical experiment of passive-touch manner.

**AC servo motor**

Fig. 4. Step-height presentation device.

**Stainless steel plate**

**X-table**


#### **Rule #3: Condition of termination**

*Rn* becomes small as *δcn* approaches the standard stimulus magnitude, *δs*. The minimum incremental range, *Rmin*, is specified by the PEST algorithm. If the condition of termination:

$$\mathcal{R}\_n \quad \le \quad \mathcal{R}\_{\min} \tag{6}$$

is satisfied, then the processing is terminated. The difference between *δcn* and *δs* is the threshold if the value of *P* is 0.25 or 0.75, and *δcn* is the subjective equality if *P* is 0.5.

Experimental results using the PEST method are exemplified in Fig. 3 to explain the abovementioned PEST procedure. In the example, *P*, *Ep*, and *Rmin* are set at 0.75, 1.0, and 0.3 µm, respectively. Also, the standard step-height *δs* and the initial comparison step-height *δc*1, the initial increment *R*1 are 10 µm, 20 µm, and 3 µm, respectively. While the calculated result of (1) satisfies the condition given by (2), the human subject repeats the comparison of *δs* of 10 µm with *δc*1 of 20 µm. Since after twelve trials the right side of (1) yields 0.75 × 12 − 10 = − 1 and the result satisfies the condition given by (3), *δc*2 is reduced to 17 µm (*δc*2 = *δ<sup>c</sup>*<sup>1</sup> − *R*1) according to Rule #2 (incremental stimulus magnitude). As is evident from Fig. 3, the comparison step-height decreases as the trial number increases. Thereafter, *δc*5 is increased to 12.5 µm (*δc*5 = *δc*4 + *R*4; *R*4 = *R*<sup>3</sup> 2) when the condition given by (4) is satisfied for a trial block with an 11 µm step-height. In the continuous blocks, the comparison step-height is bounded because the calculated results alternately satisfy the conditions given by (3) and (4). However, the comparison step-height decreases gradually due to Rule #2. Finally the calculated *R*8 satisfies the condition of (6). The terminated comparison step-height is 11.375 µm and its upper threshold is obtained from the experiment as *ΔU* = 1.375 µm.

In the experiments of the paper, *Ep* is set a constant value of 1.0 and the other values are determined according to the experiment conditions.

#### **3. Measurement system**

To measure the human finger's tactile sensation capability of recognizing fine step-heights using psychophysical experiments, a measurement system that creates step-heights of 0 to 1000 µm and presents several pairs of the step-heights to human subject's fingers according to the PEST algorithm were developed (Fig. 4). In the psychophysical experiments of this paper, the subjects touch fine step-heights in active-touch manner (Fig. 5) and passive-touch manner (Fig. 6). The step-height presentation device has the capability of controlling four parameters of the step-height presentation, i.e., the step-height, presentation velocity, presentation angle, and presentation temperature. The first three parameters are controlled by a computer that drives the wedge-shaped Z stage, the X-table and the rotary table, and the presentation temperature is controlled by the Peltier elements.

A fine step is formed between two fine finished stainless steel plates, and the height of the step is a stimulus magnitude. The stepping motor-driven Z stage slides one of the stainless

c. If *Dn*-2, *Dn*-1 and *Dn* are the same direction and *Rn*-2 is half *Rn*-3, then *Rn* is set the same as *Rn*-1. However, if *Dn*-2, *Dn*-1, and *Dn* are the same direction and *Rn*-2 is equal to *Rn*-3, then

d. If *Dn*-3, *Dn*-2, *Dn*-1, *Dn*, … continue in the same direction, then *Rn*, *Rn*+1, *Rn*+3, … are each

*Rn* becomes small as *δcn* approaches the standard stimulus magnitude, *δs*. The minimum incremental range, *Rmin*, is specified by the PEST algorithm. If the condition of termination:

is satisfied, then the processing is terminated. The difference between *δcn* and *δs* is the

Experimental results using the PEST method are exemplified in Fig. 3 to explain the abovementioned PEST procedure. In the example, *P*, *Ep*, and *Rmin* are set at 0.75, 1.0, and 0.3 µm, respectively. Also, the standard step-height *δs* and the initial comparison step-height *δc*1, the initial increment *R*1 are 10 µm, 20 µm, and 3 µm, respectively. While the calculated result of (1) satisfies the condition given by (2), the human subject repeats the comparison of *δs* of 10 µm with *δc*1 of 20 µm. Since after twelve trials the right side of (1) yields 0.75 × 12 − 10 = − 1 and the result satisfies the condition given by (3), *δc*2 is reduced to 17 µm (*δc*2 = *δ<sup>c</sup>*<sup>1</sup> − *R*1) according to Rule #2 (incremental stimulus magnitude). As is evident from Fig. 3, the comparison step-height decreases as the trial number increases. Thereafter, *δc*5 is increased to 12.5 µm (*δc*5 = *δc*4 + *R*4; *R*4 = *R*<sup>3</sup> 2) when the condition given by (4) is satisfied for a trial block with an 11 µm step-height. In the continuous blocks, the comparison step-height is bounded because the calculated results alternately satisfy the conditions given by (3) and (4). However, the comparison step-height decreases gradually due to Rule #2. Finally the calculated *R*8 satisfies the condition of (6). The terminated comparison step-height is 11.375

threshold if the value of *P* is 0.25 or 0.75, and *δcn* is the subjective equality if *P* is 0.5.

µm and its upper threshold is obtained from the experiment as *ΔU* = 1.375 µm.

determined according to the experiment conditions.

the presentation temperature is controlled by the Peltier elements.

**3. Measurement system** 

In the experiments of the paper, *Ep* is set a constant value of 1.0 and the other values are

To measure the human finger's tactile sensation capability of recognizing fine step-heights using psychophysical experiments, a measurement system that creates step-heights of 0 to 1000 µm and presents several pairs of the step-heights to human subject's fingers according to the PEST algorithm were developed (Fig. 4). In the psychophysical experiments of this paper, the subjects touch fine step-heights in active-touch manner (Fig. 5) and passive-touch manner (Fig. 6). The step-height presentation device has the capability of controlling four parameters of the step-height presentation, i.e., the step-height, presentation velocity, presentation angle, and presentation temperature. The first three parameters are controlled by a computer that drives the wedge-shaped Z stage, the X-table and the rotary table, and

A fine step is formed between two fine finished stainless steel plates, and the height of the step is a stimulus magnitude. The stepping motor-driven Z stage slides one of the stainless

*R R n min* (6)

*Rn* is set twice *Rn*-1.

**Rule #3: Condition of termination** 

twice the previous incremental range.

Fig. 4. Step-height presentation device.

Fig. 5. Scene of psychophysical experiment of active-touch manner.

Fig. 6. Scene of psychophysical experiment of passive-touch manner.

Measurement System of Fine Step-Height

**4. Experimental methods** 

were determined.

standard stimuli.

the upper thresholds.

Discrimination Capability of Human Finger's Tactile Sense 171

To measure the difference thresholds for fine step-heights in the active-touch experiments, five male subjects in their twenties of age touched and discriminated step pairs with the center of their index fingertips in active-touch manner. The subjects were allowed to touch step pairs in the 0-degree finger-motion direction as long as they wanted as choosing the motion velocity of their fingers arbitrarily. In the active-touch experiments, five step-heights

Table 1 shows the initial values of *δc*1, *R*1 and *Rmin* used in the PEST rules for each standard stimulus of *δs*. Each of the comparison step-heights of *δc*1 was the value presented in the first trial block of the discrimination tasks. Also the value of *P* was set at 0.75 to obtain the upper thresholds. During the trials the subjects were required to press the computer-mouse button to input the answers into the computer even if they could not judge the difference between the step pair. The step-heights of the continuous trials were calculated based on the PEST algorithm using the answers and finally the upper thresholds for each standard step-height

*δ<sup>s</sup>* [µm] 10 40 70 100 130 *δc*1 [µm] 20 70 110 150 190 *R*1 [µm] 3 9 12 15 19 *Rmin* [µm] 0.3 0.9 1.2 1.5 1.9

**4.2 Difference thresholds for fine step-heights in passive-touch discrimination task**  To measure the difference thresholds for fine step-heights in the passive-touch experiments, the six male subjects that had participated in the above-mentioned experiments touched and discriminated step pairs with the center of their index fingertips in passive-touch manner. The steps were moved at the reciprocating velocity of 25 mm/s and the 0-degree presentation angle using the presentation device and the subjects were allowed to touch them through the hole of the cover plate with their fingers as long as they wanted. In the passive-touch experiment, five step-heights of 10, 30, 50, 70 and 100 µm were used as the

Table 2 shows the initial values used in the PEST rules for each standard stimulus. Also the value of *P* was set at 0.75 to obtain the upper thresholds. The discrimination tasks in the passive-touch experiment were conducted and as a result, the PEST algorithm determined

*δ<sup>s</sup>* [µm] 10 30 50 70 100 *δ<sup>c</sup>*<sup>1</sup> [µm] 20 50 80 110 150 *R*<sup>1</sup> [µm] 3 6 9 12 15 *Rmin* [µm] 0.3 0.6 0.9 1.2 1.5

Table 2. Standard step-heights and the initial values used in the PEST rules.

Table 1. Standard step-heights and the initial values used in the PEST rules.

**4.1 Difference thresholds for fine step-heights in active-touch discrimination task** 

of 10, 40, 70, 100 and 130 µm were used as the standard stimuli.

plates vertically to control the step-height. The servo motor-driven X-table generates the presentation velocity by its reciprocating movement. The rotary table regulates the presentation angle by rotating the X table placed on it. The Peltier elements maintain, using the Peltier effect to heat or cool, the step plates' temperature by regulating the DC voltage applied to them. Here, the presentation angle of the step plates to a subject's finger is controlled as shown in Fig. 7. The motion direction of the X-table is always perpendicular to the direction of a step edge. Consequently, the presentation device is capable of presenting a fine step-height at the reciprocating velocity of 0 to 60 mm/s and the presentation angle of 0 to 180 degrees. In addition, the step plates' temperature can be controlled within the range of 8 to 50 degrees centigrade.

Fig. 7. Presentation angles of step.

In the psychophysical experiments using the measurement system, when the human subjects are required to judge which step-height of the presented step pair is larger, they press each of the right/left computer-mouse buttons to input the answer into the computer. The step-heights of the next trial are calculated by computer based on the PEST algorithm using the subject's answers.

In the passive-touch experiments of this paper, a cover plate with a hole like fingertip profile was installed to cover the step-height presentation device as Fig. 6 showed and the human subjects touched the step plates through the hole using their top and center of their fingertips as shown in Fig. 8. During the experiments, to prevent the sensitivity of human tactile sensation from declining, the step plates' temperature and the room temperature were kept constant approximately 37 and 26 degrees centigrade, respectively. Before the experiments the human subjects washed their hands with soap to keep them clean

Fig. 8. Fingertip regions.
