Bulletin of the JSME

Vol.18, No.2, 2024

Journal of Advanced Mechanical Design, Systems, and Manufacturing

Optimal design of a haptic popping toy using response surface
Sayaka YAMADA*, Shogo OKAMOTO*, Yumeka OGURA* and Yuki KOSUGE** Tokyo Metropolitan University
6-6 Asahigaoka, Hino, Tokyo, 191-0065, Japan
E-mail: okamotos@tmu.ac.jp

Received: 4 October 2023; Revised: 13 December 2023; Accepted: 18 January 2024
Abstract
Mechanical buckling of a switch or button produces an attractive sensation of touch; however, a method to optimize
the haptic pleasantness caused by buckling has not been established and well demonstrated. In this study, we
optimized a popping elastic dome toy that provides pleasant haptic sensations when pushed or buckled. Toys
with diﬀerent physical parameters were manufactured following the Box-Behnken design, and their comfort wasevaluated by the users. The design parameters that maximize haptic pleasantness were determined using the
response surface method. The optimally designed popping toy was equally as comfortable as the best one in theinitial specimen set. Further, haptic pleasantness was found to be largely determined by the ease of pushing andhaptic feel at the moment of buckling. This approach is expected to improve the haptic sensations of various
commercial products such as mechanical switches.
Keywords : Response surface, Buckling, Pleasantness, Stiﬀness, Prototyping

1. Introduction
Humans unconsciously touch many objects and materials in their daily lives (Nagano et al., 2013, 2014; Peck andChilders, 2003, 2006; Ujitoko, 2023), and this may partially be because we ﬁnd tactile experience entertaining. Certain
toys, such as the haptic popping toy shown in Fig. 1, stimulate such psychological aspects. The toy creates an engaging
tactile experience by utilizing the rapid change in the reaction force when the rubber hemispherical dome is pressed andbuckled by a ﬁngertip. In addition to toys, mechanical switches or buttons, such as those used inside automobiles andkeyboards, are associated with haptic sensations that aﬀect user satisfaction (Gaspar et al., 2017; Hatzfeld et al., 2010;
Kim and Lee, 2013; Li et al., 2013; Schütte and Eklund, 2005; Simon and Jörgen, 2005; Stamer et al., 2020; Vieira etal., 2017; Wellings et al., 2010; Zheng et al., 2022). Singular patterns of reaction forces and sounds (Burnett and Irune,
2009; Miyari et al., 2022) caused by the buckling or abrupt restoration of spring systems or mechanical levers determine
the haptic comfort when the switches are pressed.
Haptic pleasantness appeals to both adults and children, and many consumer products are designed to meet theserequirements. However, methods for optimizing the haptic pleasantness of mechanical buckling have not been reported in
the literature. For example, Gaspar et al. (2017) and Vieira et al. (2017) reported that the diﬀerence in the reaction force
immediately before and after buckling primarily determines the haptic pleasantness of switches. Hatzfeld et al. (2010)
reported that this force diﬀerence also inﬂuences the hardness, smoothness, and gentleness of the switches. Kosaka et al.
(2005) proposed a system for designing mechanical switches so that their reaction force produces the desired aﬀective
attributes. Valverde et al. (2019) measured the reaction forces of 18 types of push buttons and deﬁned 20 parameters
calculated from the reaction forces. Therefore, earlier studies have examined the eﬀects of stroke (displacement) andreaction force on the subjective evaluation of pressing performance (Colton et al., 2007a, 2007b; Kim and Lee, 2013;
Kosaka et al., 2005; Valverde et al., 2019; Wu et al., 2016; Wu and Smith, 2015). Although optimizing designs forthe buckling feel based on such an examination may be possible, few studies have demonstrated methods to achieve theoptimal feel.
In this study, we experimentally optimized the haptic sensation associated with buckling. Previous studies investigated the antecedents of haptic pleasantness (Hatzfeld et al., 2010; Kim and Lee, 2013; Schütte and Eklund, 2005; Vieira

Paper No.23-00413[DOI: 10.1299/jamdsm.2024jamdsm0014]© 2024 The Japan Society of Mechanical Engineers. This is an open access article under
the terms of the Creative Commons Attribution-NonCommercial-NoDerivs license(https://creativecommons.org/licenses/by-nc-nd/4.0/).

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Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.18, No.2 (2024)

et al., 2017; Wellings et al., 2010) and simulated haptic buckling stimuli (Breitschaft et al., 2021; Park et al., 2011; Parket al., 2020; Partk et al., 2022; Sadia et al., 2020; Suzuki et al., 2020; Wu et al., 2016; Wu and Smith, 2015). For example,
Park et al. (2011) designed several vibrotactile switch-like stimuli and investigated the preferred vibration patterns. Sadia
et al. (2020) successfully simulated three types of mechanical buttons—latch, toggle, and push buttons—using vibrotactile specimens. However, the optimization of the haptic feel for buckling has yet to be reported. In the study with an aim
closest to ours, Li et al. (2013) speciﬁed the design parameter space of diaphragm-type push-buttons such that the ratio of
local maximum and minimum of reaction forces at the moment of buckling was sustained at high values. Although theyused ﬁnite element models to compute the force ratio, we involve user studies to evaluate the haptic feel, which is formedby the force ratio and other factors.
We employed the response surface method used in quality engineering to optimize the buckling sensation with 3Dprinted popping toys as the target object for optimization. The optimization procedures of haptic feel entail prototyping
and user-evaluation of actual specimens, and the costs required for experiments are a major concern. The response
surface method and related experimental designs are known as cost-eﬀective approaches and save us from conducting
an exhaustive search in the parameter space; however, to our knowledge, such optimal designing methods have not been
employed for pursuing haptic comfort. In contrast to buttons or switches, the popping toy has no practical function andonly its haptic sensations are enjoyed; hence, the popping toy is appropriate for validating the optimization method forbuckling pleasantness. The aim of this study was to conﬁrm that an optimization approach based on response curves isapplicable for haptic sensations. Our demonstration of the optimization will provide insights to industries for the haptic
design of objects such as switches and toys.

Fig. 1

Commercial haptic popping toy. Users enjoy the haptic feel of buckling caused when they press thesilicone spherical dome with a ﬁngertip.

2. Specimen: haptic popping toy
Figure 2 shows photographs of the haptic popping toy and a diagram illustrating the dimensions. Popping toys were
produced using a 3D printer (From3; Formlabs Inc., USA). Elastic 50A resin (Formlabs Inc., USA) was used for all thepopping toys. In this section, the design parameters of the popping toys are described. As regards the haptic sensations ofmechanical switches and buttons, the reaction forces caused by pressing them have been frequently discussed. However,many of the parameters deﬁned from the force proﬁles (Valverde et al., 2019) are not independently controlled. Furthermore, methods to independently control those parameters have yet to be investigated. Hence, we selected the dimensionalparameters of the popping toy as its design parameters. Further, we employed surface response methods for parameter
optimization. This method enables the determination of the parameter sets in a multidimensional space composed of continuous variables so as to achieve the designated best performance. This method is not suitable for dealing with categoricalparameters, and we excluded them as such. For experimental optimization problems involving continuous and categoricalvariables, the Taguchi method (Taguchi, 1995) has been frequently adopted.
We preemptively created prototypes of the popping toys and investigated the design parameters related to the pressing
sensation produced by the toys. Consequently, we selected three parameters: the bottom diameter of the dome, d (mm);the height from the surface of the base to the top of the dome, h (mm); and the ﬁllet, R (mm). The ﬁllet R is the radius of
the rounded edge of the dome. The height and diameter can be common design parameters of spherical diaphragms (Li etal., 2013). The thickness of the dome resin is 0.8 mm. The thickness could be important for determining the haptic feel ofpopping toys; however, we excluded the thickness from the design parameters because of manufacturing problems. For[DOI: 10.1299/jamdsm.2024jamdsm0014]© 2024 The Japan Society of Mechanical Engineers

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Fig. 2

Haptic popping toy. (a) Drawing with dimensions. From left, cross-sectional, top, and side views. (b)Photograph of three out of 13 popping toys. (c) Experimental scene. The center of the dome is pushed
by the ﬁngertip (left picture) until it is buckled (middle picture) and completely turned over, producing apleasant haptic feel.

example, domes with a 0.6–0.7 mm thickness are easily broken during manufacturing and cleaning processes. Domes of
0.9–1.0-mm-thickness are too stiﬀ to be adopted for popping toys. Given that the resolution of manufacturing is 0.1 mm,
we ﬁxed the thickness to be 0.8 mm, considering that this value is the best among feasible values. Notably, because
our objective was not to design commercial products, we did not exhaustively investigate all the potentially eﬀective
parameters and materials. As aforementioned, we aimed to demonstrate the optimal design of haptic sensations by using
the popping toy as an example.
We set the minimum and maximum values of d, h, and R to 15 and 20 mm, 4 and 8 mm, and 0.5 and 8 mm,
respectively. The authors and their ﬁve colleagues evaluated the prototypes in preliminary experiments and agreed thatthese ranges would satisfactorily contain the optimal value set. These values are similar to those found in commerciallyavailable popping toys (e.g., Go Pop! from Foxmind Canada Enterprises LTD., Canada). Nonetheless, the commercial
popping toys employ a hemispherical shape with d = 2h = 2R ∼ 16.5 mm. The parameter space explored in this study
encompasses the parameter set of the commercial popping toys. Further, in our study, R is variable; this allows for the
exploration of shapes except for hemispheres.
We employed the Box-Behnken design for the specimen set. The Box-Behnken design and central composite design
are typical approaches for optimal design in quality engineering. The major diﬀerences between them are the levels ofdesign parameters available and the number of experimental trials. In this study, the number of levels for each parameter
was set to three because the ranges of the parameters were small. In this case, the Box–Behnken design led to fewer initial
specimens, namely, 13. The values of d, h, and R for the 13 popping toys created based on the Box-Behnken design arelisted in Table 1. Specimen 7 cannot be manufactured because the ﬁllet value is larger than the diameter. Therefore, its
ﬁllet was adjusted to 7.5 mm.
Table 1

Parameters of 13 popping toys based on the Box-Behnken design. d: diameter of circle (mm), h: height(mm), R: ﬁllet (mm)Specimen no.
d
h
R

1
20
8
4.25

2
20
4
4.25

3
15
8
4.25

4
15
4
4.25

5
20
6
8

6
20
6
0.5

7
15
6
7.5

8
15
6
0.5

9
17.5
8
8

10
17.5
8
0.5

11
17.5
4
8

12
17.5
4
0.5

13
17.5
6
4.25

3. Experiment 1: optimization of haptic popping toy
3.1. Experimental procedures
The participants pushed the center of the dome of the popping toy in the vertical direction by using the pad of the[DOI: 10.1299/jamdsm.2024jamdsm0014]© 2024 The Japan Society of Mechanical Engineers

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index ﬁnger of their right hand until the dome sank completely, as shown in Fig. 2 (c). Participants were allowed to push
it repeatedly until they had a deﬁnitive opinion. Typically, three to ﬁve iterations were required for each trial. During
the experiment, the participants wore sunglasses with masking tape attached to avoid visual discrimination by restricting
them from fully seeing the specimens. Further, the participants were encouraged to employ similar pressing motions for
all the specimens.
For each specimen, four evaluation items were rated: overall evaluation, ease of pushing, buckling, and stiﬀness.
The overall evaluation was deﬁned as the haptic pleasantness of the entire pushing experience. The ease of pushing refers
to how easy it was for the user to push and sink the dome completely. Buckling was deﬁned as the pleasantness when
the dome buckled. The stiﬀness was deﬁned as the hardness of the dome. Buckling and stiﬀness were adopted froma study by Kosaka et al. (2005), in which seven types of aﬀective attributes were used to evaluate mechanical buttons.
We selected only stiﬀness and buckling, which is referred to as clicking in the study by Kosaka et al. (2005), because
the other ﬁve attributes, such as smoothness and clarity, were inapplicable to popping toys. Similar attributes, including
hardness and crispness, were used by Hatzfeld et al. (2010) and Miyairi et al. (2022) to evaluate the haptic feel of buttons.
Furthermore, we found that some participants with large ﬁngertips could not easily press and sink the dome when its
diameter was small. Hence, we introduced another evaluation item, namely, the: ease of pushing.
Each of the four items was rated on a scale from 1 to 9. For the overall evaluation and buckling, 1 and 9 were labeled
as “non-pleasant” and “pleasant,” respectively. For the ease of pushing, 1 and 9 corresponded to “diﬃcult” and “easy,”
respectively. For the stiﬀness, 1 and 9 corresponded to “soft” and “stiﬀ,” respectively. Considering the relative diﬃcultyof assessment, the rating task was performed referring to a reference. For the overall evaluation, ease of pushing, andbuckling, Specimen 5 was used as the reference, and its scores were set to ﬁve. Each participant tested 13 specimens in arandomized order in a single set. Three sets were performed, totaling 39 trials.
3.2. Participants
Ten university students (four of whom were females) participated in the study after providing written informed
consent. The participants were unaware of the study objectives.
3.3. Ethical statement
The study protocols were approved by the Institutional Review Board of the Hino Campus, Tokyo Metropolitan
University (#22-31).
3.4. Analysis
We normalized (z-score) the scores of each evaluation item for each participant. The mean scores of three repetitions
were used to compute a response surface. The response surface was established in the design parameter space for each
evaluation item. We adopted a stepwise multiple regression analysis method with the explanatory variables d (diameter),h (height), R (ﬁllet), and their quadratic and interaction terms. The initial model was quadratic, with nine explanatory
variables: d, h, R, d2 , h2 , R2 , d × h, d × R, h × R. The least signiﬁcant variable in terms of p-value was removed from themodel at each step until all remaining variables were signiﬁcant at p < 0.05. This process was performed for each of thefour evaluation parameters: overall evaluation, buckling, ease of pushing, and stiﬀness. In addition, we investigated therelationship between the overall evaluation and the three evaluation items using multiple regression analysis.
3.5. Results
Figure 3 shows the means and standard errors of the overall scores of specimens. Specimen 11 was judged mostpleasant, followed by Specimens 13 and 9. Table 2 lists the signiﬁcant explanatory variables for each of the four evaluation
items. The signiﬁcant explanatory variables were d, d × h, d × R, d2 , h2 , and R2 for the overall score; d, d × h, d2 , and h2
for the buckling score; d, h, d × R ,and d2 for the ease of pushing score; and h, d × R, d2 , and h2 for the stiﬀness score.
The adjusted R2 values were 0.35, 0.18, 0.64, and 0.63 for the overall, buckling, ease of pushing, and stiﬀness scores,
respectively. The correlation coeﬃcients between the observations and estimations were moderate at 0.61 and 0.45 for theoverall and buckling scores, respectively, and they were strong at 0.80 for both the ease of pushing and stiﬀness scores.
Table 3 presents the results of the regression analysis to estimate the overall evaluation score, using the scores ofbuckling, ease of pushing, and stiﬀness as explanatory variables. The buckling and ease of pushing scores were themost important for the overall evaluation. The adjusted R2 value was 0.69, and the correlation coeﬃcient between theobservations and estimations was strong at 0.84.
[DOI: 10.1299/jamdsm.2024jamdsm0014]© 2024 The Japan Society of Mechanical Engineers

24Normalized overall score of popping toy

Yamada, Okamoto, Ogura and Kosuge,
Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.18, No.2 (2024)

1.0

1

2

3

6

10

8

0
4

9

5

11

13
12

7

Specimennumberെ1.0
Fig. 3

Mean and standard errors of the overall scores of specimens. Greater values are more pleasant.

Based on Tables 2 and 3, the structure of the overall evaluation was determined, as shown in Fig. 4. The ﬁgure shows
the signiﬁcant links found in the multiple regression analyses.
Table 2

Partial regression coeﬃcients and p-values of the signiﬁcant explanatory variables for each evaluation
item: (a) overall evaluation, (b) buckling, (c) ease of pushing, and (d) stiﬀness. Only statisticallysigniﬁcant coeﬃcients are listed.

(a) Overall evaluation
Parameter Coeﬃcient
d
2.83
d×h
0.042
d×R
0.015
d2
−0.090h2−0.073R2−0.017p-value
5.77 × 10−50.0061
6.0 × 10−4
1.7 × 10−5
1.2 × 10−3
0.046(b) Buckling
Parameter Coeﬃcient
d
2.32
d×h
0.077
d2
−0.081h2−0.12p-value0.0031
1.5 × 10−5
4.0 × 10−4
9.1 × 10−6(c) Ease of pushing
Parameter Coeﬃcient
d
1.30
h
−0.16
d×R
0.011
d2
−0.037p-value
0.013
7.82 × 10−8
0.015
5.5 × 10−26(d) Stiﬀness
Parameter Coeﬃcient
h
1.088
d×R
−0.012d2−0.002h2−0.90p-value
2.0 × 10−4
5.5 × 10−26
1.5 × 10−3
2.0 × 10−4

Table 3

Partial regression coeﬃcients and p-values to estimate the overall evaluation score using the other evaluation variables.
Evaluation item
Buckling
Ease of pushingStiﬀness

Coeﬃcient
0.566
0.507
0.020

p-value
2.55 × 10−19
1.30 × 10−10
0.79

4. Experiment 2: post-hoc experiment4.1. Specimen: optimally designed popping toy
We created another popping toy using the optimized parameters based on the results of Experiment 1. On the basis
of Table 2 (a), the response surface formula for the overall evaluation is expressed as
Overall evaluation = 2.83d + 0.042d × h + 0.015d × R − 0.090d2 − 0.073h2 − 0.017R2 − 23.8.

(1)

At the maximum point of the response surface, the partial derivatives of d, h, and R are zero. The three simultaneous
equations were solved and the optimal parameter set was determined to be d = 17.2 mm, h = 3.3 mm, and R = 7.6 mm.
The values of diameter and ﬁllet are within the parameter space used in Experiment 1. The height is out of the range ofthe initial specimen set (4.0 ≤ h ≤ 8.0). Nonetheless, the diﬀerence between the lower limit of the height (4.0 mm) and3.3 mm is only 0.7 mm; hence, we used h = 3.3 mm. The parameters of the optimally designed popping toy were similar
to those of Specimen 11, for which d = 17.5 mm, h = 4 mm, and R = 8 mm.
[DOI: 10.1299/jamdsm.2024jamdsm0014]© 2024 The Japan Society of Mechanical Engineers

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Overallevaluation
0.507

Ease of pushing

0.566−0.0372.32−0.1641.305−0.116−0.081−0.012−0.0901.09

dFig. 4hR

Stiffness

Buckling

0.077

0.012

−0.002

ଶ

ℎଶ

ଶ

dʹh

hʹR

Rʹd

Structure of the overall evaluation score and other variables based on Tables 2 and 3. The values of thelinks are the partial regression coeﬃcients at p < 0.05. R, R2 , and h × R do not signiﬁcantly inﬂuence thevariables in the middle layer.

4.2. Experimental procedures
We compared the optimized popping toy and Specimen 11, which had the largest overall evaluation score among
those used in Experiment 1. The participants pushed these two popping toys freely while wearing sunglasses with masking
tape. They selected the specimen with the highest overall haptic pleasantness as the popping toy. No time limitations wereset; however, all participants completed the experiment within one 1 minute.
4.3. Participants
We considered 0.75 : 0.25 as a practically meaningful preference bias for the two popping toys and estimated thenumber of participants (n) such that the diﬀerence in proportions between 0.75 and the chance level, 0.5, was found to besigniﬁcant at p < 0.05 following the one-sample proportion test:√(0.75 − 0.5) n
1.96 < √.
(2)(0.5 × (1 − 0.5))
The minimum integral n value required to satisfy this equation is n = 16; hence, we set the number of participants to begreater than 15. Twenty-one university students (in their 20s; six females) participated in the post hoc experiment. The
participants were unaware of the study objectives and provided written informed consent before the experiment.
4.4. Analysis
The proportion of participants who selected the optimally designed popping toy for greater haptic pleasantness wascalculated. We then investigated whether the proportion was signiﬁcantly diﬀerent from chance (i.e., 0.5) using the z-test.
4.5. Results
Twelve of the 21 participants selected the optimally designed popping toy for better haptic pleasantness. The proportion of preferences for the optimally designed popping toy was not signiﬁcantly higher than that for Specimen 11(z = 0.65, p = 0.55), indicating that the optimally designed popping toy was preferred as much as Specimen 11.

5. Discussion
The results of Experiment 2 showed that the optimally designed popping toy was as comfortable as the most haptically pleasant specimen in Experiment 1. In quality engineering, this phenomenon is typical when the parameter spaceis small. For example, certain errors between the set and performance measures of the optimized prototype should be
accepted (Krishnaiah and Shahabudeen, 2012). In this study, the parameters of the optimal popping toy were accidentallyclose to those of Specimen 11, which had the highest overall evaluation score among the initial specimen set. Therefore,
we did not observe any meaningful performance improvement using the optimal design. This does not indicate that the
optimal design used in quality engineering is not applicable to haptic sensations. The optimally designed popping toy was
selected as often as Specimen 11 in Experiment 2, and the eﬀectiveness of an optimization approach was demonstrated.
[DOI: 10.1299/jamdsm.2024jamdsm0014]© 2024 The Japan Society of Mechanical Engineers

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Yamada, Okamoto, Ogura and Kosuge,
Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.18, No.2 (2024)

We found that the overall haptic comfort was determined by the buckling and ease of pushing. It is natural forbuckling to aﬀect the haptic comfort of popping toys because they are made to provide a pleasant tactile sensation whenbuckling. Additionally, it is reasonable for the ease of pushing to determine the overall evaluation. It is more diﬃcult fora dome with a smaller diameter to be pressed and reach the bottom, leading to frustration. The rationale for stiﬀness not
aﬀecting the overall haptic pleasantness is debatable. The tactile pleasantness of a switch is mainly determined by thediﬀerence in the reaction force immediately before and after buckling, and stiﬀness is not the dominant antecedent for
determining it (Veira et al., 2017). Popping toys resemble push switches regarding their haptic feel. Hence, stiﬀness may
be a secondary factor in determining haptic pleasantness.
As in Section 3 and Fig. 4, we analyzed three evaluation items or factors that could potentially lead to haptic pleasantness. Among them, buckling, which is the pleasantness felt at the moment of buckling of the dome, was not well
explained by the set of design parameters, with an R2 value of 0.18. This is attributable to the large individual diﬀerences.
We found that the pooled variance σ2 of the evaluation scores of buckling among the participants was greater than thoseof ease of pushing and stiﬀness. Table 4 lists the ratios of variances, which are F-statistics, and their corresponding pvalues for the two-tailed tests. The hypothesis of the equality of variances for σ2buckle /σ2push and σ2stiﬀ /σ2buckle were rejected,
indicating that the variance of the scores of the buckling was greater than those of ease of pushing and stiﬀness. There
are two potential reasons that the pleasantness of buckling is not well predicted by the design parameters of the popping
toy. First, the pleasantness may depend on the ﬁnger’s pressing motion. In our experiment, the ﬁnger motions of the participants were not measured; however, the analysis on their individual diﬀerences may help understand the pleasantnessof buckling stimuli. In particular, we speculate that the individual diﬀerences in ﬁnger velocity is a potential cause. Whenthe velocity is slow, relatively stiﬀ domes tend not to produce pleasant haptic feel. In our experiment, ﬁnger velocities
were not controlled among the participants; hence, the same specimen might have not been equally rated by diﬀerent
participants. Second, distinction between individual preferences may have been another relevant aspect. A clustering
analysis involving a suﬃcient number of participants may suggest the presence of such individual preferences. Thus far,such diﬀerences have rarely been discussed by prior studies on mechanical switches and buttons. These human factors
should be elucidated in the future.
Table 4

Test of equality of variances between the scores for buckling, ease of pushing, and stiﬀness.
Combination of variances
σ2buckle /σ2push
σ2push /σ2stiﬀ
σ2stiﬀ /σ2buckle

Ratio of variancesF(129, 129) = 1.92
F(129, 129) = 0.881
F(129, 129) = 0.592

p-value
2.5 × 10−4
0.47
3.1 × 10−3

Although this study did not measure the reaction force and displacement of the dome during buckling, the correspondence between the dynamic patterns of the reaction forces and the haptic sensations is important, as indicated in earlier
studies (Gaspar et al., 2017; Hatzfeld et al., 2010; Kosaka et al., 2005; Vieira et al., 2017; Weir et al., 2004). In the future,
optimization must be performed from the viewpoint of the reaction force. However, thus far, a method to independently
control multiple parameters that are deﬁned from the force-displacement proﬁle has not been established. Optimizationof the reaction force may require several more research stages. Furthermore, multi-objective optimization should be pursued because the most important role of switches is to deliver a sense of mechanical transition and prevent the misuse ofhuman-machine interfaces. An appropriate balance among the multiple objectives should be considered when applying
the optimization to mechanical switches.

6. Conclusion
Although previous studies have investigated the cause of the haptic pleasantness of buckling, they have not attempted
to obtain an optimal design. In this study, we realized the optimal design of a popping elastic dome toy by using the
response surface method. The optimized popping toy was as pleasant as the specimen that was judged to be the most
comfortable among the 13 specimens evaluated in the experiment. Furthermore, for popping toys or buckling domes, thehaptic sensation at the moment of buckling and ease of pushing determined the overall haptic evaluation. The optimizationof haptic pleasantness caused by buckling or switch-like mechanical ﬂips is useful in various industries, including theautomotive industry (Colton et al., 2007a; Stamer et al., 2020; Vieira et al., 2017), and the response surface method is
promising for this purpose. To further verify the optimization approach, the same or similar optimization approaches must
be applied to other products, such as buttons and switches.
[DOI: 10.1299/jamdsm.2024jamdsm0014]© 2024 The Japan Society of Mechanical Engineers

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Yamada, Okamoto, Ogura and Kosuge,
Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.18, No.2 (2024)

Acknowledgment
This study was partially supported by MEXT Kakenhi (23H04360). We thank Ms. Suzuna Narutaki for her cooperation in designing the haptic popping toy.

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