Design and Experimental Characterization of a Vacuum-Actuated Granular-Jamming Actuator for Stiffness Modulation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the authors report on a kind of variable-stiffness tactile interface for soft robotic actuator with granural jamming manner. The as-presented prototype design is simple in both structure and control, and it can be of interest in the community of soft robotics. Overall, this manuscript is well organized and can be accepted upon revision by addressing the following questions.

1. The authors provide detailed global stiffness plots (Figure 4) and local stiffness heatmaps (Figure 5), which are highly useful for engineering design. However, the current discussion remains largely qualitative (e.g., "nonlinear," "progressive"). To enhance the engineering significance of the paper, I recommend fitting a bivariate empirical stiffness model that incorporates both indentation displacement and vacuum pressure. Providing a mathematical relationship would allow other researchers to directly simulate or pre-estimate parameters for similar designs.

2. Haptic feedback and palpation are inherently dynamic processes involving both pressing and releasing cycles. The current experiments only report the quasi-static loading (compression) phase. I recommend adding the unloading force-displacement curves and calculating the hysteresis loss. This will provide a more comprehensive mechanical characterization and serve as essential baseline data for future high-frequency dynamic control.

Author Response

Comment 1:

The authors provide detailed global stiffness plots (Figure 4) and local stiffness heatmaps (Figure 5), which are highly useful for engineering design. However, the current discussion remains largely qualitative (e.g., "nonlinear," "progressive"). To enhance the engineering significance of the paper, I recommend fitting a bivariate empirical stiffness model that incorporates both indentation displacement and vacuum pressure. Providing a mathematical relationship would allow other researchers to directly simulate or pre-estimate parameters for similar designs.

Response:

We thank the reviewer for this valuable suggestion. To provide a quantitative representation of the coupled effects of vacuum pressure and indentation depth, we fitted the mean local-stiffness data using a second-order bivariate polynomial as a function of vacuum-pressure magnitude and indentation displacement. The resulting empirical model achieved an of 0.964 and an RMSE of 0.756 N/mm over the experimentally evaluated range. The model and its applicable ranges have been added to the manuscript. We also clarify that the relationship is an empirical representation of the present prototype and is not intended as a generalized constitutive model for granular-jamming systems.

 

Comment 2:

Haptic feedback and palpation are inherently dynamic processes involving both pressing and releasing cycles. The current experiments only report the quasi-static loading (compression) phase. I recommend adding the unloading force-displacement curves and calculating the hysteresis loss. This will provide a more comprehensive mechanical characterization and serve as essential baseline data for future high-frequency dynamic control.

Response:

We agree to reviewer’s concern towards addition of onloading curves and hysteresis phases to the data. Unfortunately, we are unable to perform any more experiments. We have mentioned it in our limitations, and we further clarified that the given procedure characterized the whole nodule system as a one coupled system.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript, “Design and Experimental Characterization of a Vacuum-Actuated Granular-Jamming Actuator for Stiffness Modulation,” presents the design and quasi-static experimental characterization of a 25-mm granular-jamming tactile nodule containing 8 g of PET microbeads. 

I do not recommend acceptance in its current form because the paper currently presents the work more strongly than the experimental evidence supports. 

1. The novelty and literature gap need to be substantially strengthened

The manuscript states that relatively few studies have quantitatively characterized a fingertip-scale granular-jamming tactile element over multiple vacuum levels.

This claim requires a much more convincing literature comparison.

There is already prior work specifically combining granular jamming, pneumatic actuation, indentation testing, and haptic palpation. For example, Li et al. reported granular-jamming stiffness-feedback actuators for multi-fingered haptic palpation and evaluated them through indentation testing and human stiffness-discrimination experiments. There is also published work on a palpation-display nodule using pneumatic control and granular jamming. Furthermore, recent work has demonstrated wearable stiffness-rendering haptic devices using jamming mechanisms, including a 2025 honeycomb-jamming haptic device with experimentally characterized stiffness modulation.

Therefore, the authors should not frame the contribution simply as demonstrating that granular jamming can produce variable stiffness in a tactile nodule.

2. The haptic/palpation claims are stronger than the experiments support

The manuscript appropriately states that human-subject studies are future work.

Nevertheless, several passages imply that the measured nonlinear stiffness is advantageous for realistic palpation and that it can reproduce biological tissue behavior. For example, the manuscript argues that the progressive increase in local stiffness resembles the resistance encountered during biological palpation.

This is an interesting hypothesis, but it has not been experimentally validated.

The authors should distinguish between:

“mechanically compatible with a potential palpation application”

and

“demonstrated to reproduce realistic biological tissue palpation.”

The latter requires tissue-equivalent mechanical targets and/or human perceptual experiments.

Similarly, the conclusion should avoid implying that realistic tactile feedback has been demonstrated when the current work only establishes mechanical characterization.

3. The “repeatability” claim should be quantified

The paper states that the stiffness modulation is “large and repeatable,” but only SD error bars are presented.

Please report a quantitative repeatability metric, such as:

• coefficient of variation,
• intraclass correlation coefficient,
• maximum percentage deviation,
• or another appropriate measure.

If only one physical nodule was tested, the authors should explicitly call this within-device repeatability rather than general repeatability of the actuator design.

Testing multiple independently fabricated nodules would greatly strengthen the study.

 

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Minor comments:

1. Table 1 contains an obvious formatting/incomplete-text error

The final row currently reads:

“Analyzed compression window m post-contact displacement”

instead of specifying the intended value, presumably 2.00 mm post-contact displacement.

This must be corrected.

2. Figure 5 needs a clearer caption and axis description

The Figure 5 caption reads:

“Local stiffness behavior Heatmap of local stiffness…”

This should be grammatically corrected.

The heatmap is potentially one of the most useful figures in the manuscript, so the authors should clearly identify:

• pressure units,
• indentation-depth units,
• stiffness units,
• interpolation method, if any,
• and whether the values are means across five trials.

3. Figure 3 would benefit from uncertainty representation

The force–displacement curves are shown as mean curves, but the variability is not visually represented.

Consider adding:

• shaded ±SD bands, or
• 95% confidence bands.

This would make the repeatability assessment much stronger.

4. Reference [15] appears incorrectly formatted

Reference [15] is listed as:

“H. H., ‘On the Contact of Elastic Solids,’ J. Reine Angew Math., vol. 92…”

This should be checked carefully and corrected to the proper bibliographic information for Hertz's classical contact-mechanics paper.

Author Response

The manuscript, “Design and Experimental Characterization of a Vacuum-Actuated Granular-Jamming Actuator for Stiffness Modulation,” presents the design and quasi-static experimental characterization of a 25-mm granular-jamming tactile nodule containing 8 g of PET microbeads. 

I do not recommend acceptance in its current form because the paper currently presents the work more strongly than the experimental evidence supports.

 

Comment 1:

The novelty and literature gap need to be substantially strengthened

The manuscript states that relatively few studies have quantitatively characterized a fingertip-scale granular-jamming tactile element over multiple vacuum level. This claim requires a much more convincing literature comparison. There is already prior work specifically combining granular jamming, pneumatic actuation, indentation testing, and haptic palpation. For example, Li et al. reported granular-jamming stiffness-feedback actuators for multi-fingered haptic palpation and evaluated them through indentation testing and human stiffness-discrimination experiments. There is also published work on a palpation-display nodule using pneumatic control and granular jamming. Furthermore, recent work has demonstrated wearable stiffness-rendering haptic devices using jamming mechanisms, including a 2025 honeycomb-jamming haptic device with experimentally characterized stiffness modulation.

Therefore, the authors should not frame the contribution simply as demonstrating that granular jamming can produce variable stiffness in a tactile nodule.

 

Response:

We thank the reviewer for this important comment. We agree that granular-jamming tactile and palpation interfaces have been demonstrated previously and that the novelty of the present study should not be framed as the use of granular jamming itself. We have revised the Introduction to better acknowledge prior granular-jamming haptic studies, including indentation-based stiffness-feedback actuators, and to more precisely define the contribution of the present work. The revised manuscript now emphasizes the systematic characterization of a fingertip-scale tactile element across eleven vacuum levels, including both global stiffness and depth-dependent local stiffness. In addition, following another reviewer’s suggestion, we have added an empirical bivariate model describing local stiffness as a function of vacuum pressure and indentation depth. The novelty and scope of the study have been revised accordingly.

 

 

Comment 2:

The haptic/palpation claims are stronger than the experiments support

The manuscript appropriately states that human-subject studies are future work.

Nevertheless, several passages imply that the measured nonlinear stiffness is advantageous for realistic palpation and that it can reproduce biological tissue behavior. For example, the manuscript argues that the progressive increase in local stiffness resembles the resistance encountered during biological palpation.

This is an interesting hypothesis, but it has not been experimentally validated.

The authors should distinguish between:

“mechanically compatible with a potential palpation application”

and

“demonstrated to reproduce realistic biological tissue palpation.”

The latter requires tissue-equivalent mechanical targets and/or human perceptual experiments.

Similarly, the conclusion should avoid implying that realistic tactile feedback has been demonstrated when the current work only establishes mechanical characterization.

Response

We agree with the reviewer that the present mechanical characterization does not demonstrate reproduction of biological tissue mechanics or perceptual realism. We have therefore revised the manuscript to distinguish the measured mechanical capability of the device from its potential application to palpation. Specifically, we now clarify that no tissue-specific mechanical comparison or human-subject perceptual evaluation was performed and that these evaluations are required before claims regarding realistic biological palpation can be made.

 

Comment 3:

The “repeatability” claim should be quantified

The paper states that the stiffness modulation is “large and repeatable,” but only SD error bars are presented.

Please report a quantitative repeatability metric, such as:

• coefficient of variation,
• intraclass correlation coefficient,
• maximum percentage deviation,
• or another appropriate measure.

If only one physical nodule was tested, the authors should explicitly call this within-device repeatability rather than general repeatability of the actuator design.

Testing multiple independently fabricated nodules would greatly strengthen the study.

Response:

We thank the reviewer for this suggestion. Because the repeated measurements were obtained from a single fabricated nodule, we have revised the manuscript to describe the results specifically as within-device repeatability. We also quantified repeatability using the coefficient of variation (CV) of global stiffness across the five trials at each vacuum level. The CV ranged from 1.7% to 17.3%, with a mean of 7.8% across the eleven pressure conditions. These quantitative repeatability results have been added to the manuscript. We also clarify that repeatability across independently fabricated nodules was not evaluated and remains an important subject for future work.

 

Minor Comment 1:

Table 1 contains an obvious formatting/incomplete-text error

The final row currently reads:

“Analyzed compression window m post-contact displacement”

instead of specifying the intended value, presumably 2.00 mm post-contact displacement.

This must be corrected.

Response:

Thank you for identifying this formatting error. The incomplete entry in Table 1 has been corrected. For clarity, the original row has been replaced with two entries specifying the 0–2.00 mm post-contact compression range and the 0.10–1.80 mm post-contact displacement range used for global stiffness regression..

 

Minor Comment 2:

The Figure 5 caption reads:

“Local stiffness behavior Heatmap of local stiffness…”

This should be grammatically corrected.

The heatmap is potentially one of the most useful figures in the manuscript, so the authors should clearly identify:

• pressure units,
• indentation-depth units,
• stiffness units,
• interpolation method, if any,
• and whether the values are means across five trials.

Response:

Thank you for identifying the ambiguity in the Figure 5 caption. The caption has been revised to clearly specify vacuum pressure (kPa), indentation depth (mm), and local stiffness (N/mm), and to clarify that the displayed values represent mean local stiffness across five trials at each vacuum-pressure condition. We have also clarified that no interpolation was applied between the displayed values.

 

Minor Comment 3

 Figure 3 would benefit from uncertainty representation

The force–displacement curves are shown as mean curves, but the variability is not visually represented.

Consider adding:

• shaded ±SD bands, or
• 95% confidence bands.

This would make the repeatability assessment much stronger.

Response:

Thank you for this suggestion. Figure 3 has been revised to include shaded ±1 standard deviation bands around the mean force–displacement curves, providing a clearer representation of trial-to-trial variability across the five repeated measurements at each vacuum-pressure condition.

 

Minor Comment 4

 Reference [15] appears incorrectly formatted

Reference [15] is listed as:

“H. H., ‘On the Contact of Elastic Solids,’ J. Reine Angew Math., vol. 92…”

This should be checked carefully and corrected to the proper bibliographic information for Hertz's classical contact-mechanics paper.

Response:

Thank you for identifying this bibliographic error. The reference to Hertz’s classical contact-mechanics paper has been corrected with the proper author information and bibliographic details.

 

Reviewer 3 Report

Comments and Suggestions for Authors

The study presents the design, fabrication, and experimental characterization of a vacuum-controlled granular-jamming tactile nodule for palpation-based haptic feedback. Despite the use of manually controlled system as a low-cost proof-of-concept platform, the results obtained seem to be quite interesting.

Comments and Questions:

1. References to literature should be before the period at the end of the sentence, not after it. As for example "..., and human-machine interfaces [1], [2]."

2. The equations should be numbered.

3. The variables in the text should be italicized similarly to equations, for example on page 5.

4. The variables "𝒌𝒈" and "𝒌𝒍𝒐𝒄𝒂𝒍" should not be in bold in the text on page 5 (they are not vectors).

5. What does mean  "d" in the numerator of the last equation on page 5?

6. Page 6, Lines 258-260: Please explain more clearly "...and is attributed to normal experimental variability rather than a reduction in jamming performance." What do you mean "normal experimental variability"?

 

 

 

Author Response

The study presents the design, fabrication, and experimental characterization of a vacuum-controlled granular-jamming tactile nodule for palpation-based haptic feedback. Despite the use of manually controlled system as a low-cost proof-of-concept platform, the results obtained seem to be quite interesting.

Comment 1:

References to literature should be before the period at the end of the sentence, not after it. As for example "..., and human-machine interfaces [1], [2]."

Response:

Thank you for identifying this formatting issue. In-text citations have been revised throughout the manuscript so that references appear before the punctuation at the end of each sentence.

 

Comment 2

The equations should be numbered.

Response:

Equations are now numbered.

 

Comment 3

The variables in the text should be italicized similarly to equations, for example on page 5.

Response:
Thank you for identifying this formatting issue. Mathematical variables have been italicized consistently in the text to match their notation in the equations.

 

Comment 4

The variables "??" and "??????" should not be in bold in the text on page 5 (they are not vectors).

Response:

The variables are now in normal font.

 

Comment 5

What does mean  "d" in the numerator of the last equation on page 5?

Response:
Thank you for pointing out this ambiguity. The notation in the local-stiffness equation has been clarified. The variable represents the contact-relative indentation displacement, and  represents the local slope of the force–displacement curve. The variable definition has been revised accordingly in the manuscript.

 

Comment 6

Page 6, Lines 258-260: Please explain more clearly "...and is attributed to normal experimental variability rather than a reduction in jamming performance." What do you mean "normal experimental variability"?

Response:

Thank you for this comment. We have clarified this statement in the revised manuscript. The decrease in mean global stiffness from 9.808 N/mm at −62.1 kPa to 9.562 N/mm at −68.9 kPa was approximately 2.6%. This difference is small relative to the trial-to-trial variability observed in the repeated measurements and therefore does not provide evidence of a systematic reduction in jamming performance at the highest vacuum level.

 

Reviewer 4 Report

Comments and Suggestions for Authors

This paper covers the manufacturing and testing of a granular jammed actuator for haptics applications. The test system is relatively simple but functional, and a quantitative description of relative stiffness at different vacuum pressures has been tested. It is this variable vacuum pressure versus effective stiffness that seems to be the most novel aspect of the work, and the authors discover that, in their specific setup, the stiffness can change in a gradual fashion with increasing vacuum rather than as a simple on/off stiffness switch. This paper can be published eventually, but it does have some missing content that is critical for the reviewers and readers to understand before it can be published in Actuators.

For example, what exactly was the balloon-grade elastomer, and where did it come from? This is a very critical component because it may, in fact, provide a lower limit on the overall stiffness. For example, if it was extraordinarily soft, it would simply allow all the grains to push through despite vacuum jamming. In fact, one of the most difficult parts of the paper to understand is what contribution is coming from the overall stiffness of the membranes and what is coming from the granular jamming itself. Not only is there physical support from the top printed membrane and the bottom elastomer membrane, but presumably there is also friction between the rigid frame and the grains. Have the authors considered all of the contributions to the stiffness measurements?

Can you provide a purchasing source for the beads used in the jamming membrane, and explain why they were used in the first place? There are, of course, many possibilities for granular jamming media, including beads, sand, coffee grounds, etc., but in general, spherical components will have a lower overall jamming strength than irregularly shaped grains due to the higher incidence of slipping between particles. What factors went into the design decisions for this choice of granular media?

The beads are listed as an 8 g component, but would it be better to list this as a volume fraction of the designed membrane size? Is there some other, better way of characterizing this so that, if a material with a different density were used, others could better reproduce the work?

It is unclear during the compression test exactly how the bottom membrane is supported by the underlying immovable base. Is it freely deformable in all directions, or is there a support around which the bottom membrane deforms? It seems like the support design might have a significant influence on the overall data collected. Were the beads repositioned or relaxed between trials, or were they left in the previously deformed configuration after each compressive test?

Finally what is the actual stiffness of the Mark 10 G1011 rubber tip?  the measured indentation curves are effectively the stiffness of this tip and the granular jamming actuator in series.  how was the influence of the tip removed from your experimental results?

Author Response

This paper covers the manufacturing and testing of a granular jammed actuator for haptics applications. The test system is relatively simple but functional, and a quantitative description of relative stiffness at different vacuum pressures has been tested. It is this variable vacuum pressure versus effective stiffness that seems to be the most novel aspect of the work, and the authors discover that, in their specific setup, the stiffness can change in a gradual fashion with increasing vacuum rather than as a simple on/off stiffness switch. This paper can be published eventually, but it does have some missing content that is critical for the reviewers and readers to understand before it can be published in Actuators.

 

Comment 1:

For example, what exactly was the balloon-grade elastomer, and where did it come from? This is a very critical component because it may, in fact, provide a lower limit on the overall stiffness. For example, if it was extraordinarily soft, it would simply allow all the grains to push through despite vacuum jamming. In fact, one of the most difficult parts of the paper to understand is what contribution is coming from the overall stiffness of the membranes and what is coming from the granular jamming itself. Not only is there physical support from the top printed membrane and the bottom elastomer membrane, but presumably there is also friction between the rigid frame and the grains. Have the authors considered all of the contributions to the stiffness measurements?

Response:

Thank you for this comment. The bottom membrane was fabricated from a thin elastomeric membrane obtained from a commercially available balloon, and this description has been clarified in the revised manuscript. We agree that the top membrane, bottom membrane, and granular medium each contribute to the measured mechanical response. These contributions were not characterized independently in the present study. Accordingly, we have clarified that the reported stiffness represents the effective stiffness of the assembled tactile nodule rather than the stiffness of the granular medium alone. Component-level characterization is identified as an important direction for future work.

 

Comment 2

Can you provide a purchasing source for the beads used in the jamming membrane, and explain why they were used in the first place? There are, of course, many possibilities for granular jamming media, including beads, sand, coffee grounds, etc., but in general, spherical components will have a lower overall jamming strength than irregularly shaped grains due to the higher incidence of slipping between particles. What factors went into the design decisions for this choice of granular media?

Response:

T Thank you for this comment. The microbeads were purchased from ArtBeeCrafts through eBay as commercially available spherical plastic microbeads with a nominal diameter of 0.6–0.8 mm. Although the original packaging included a notation indicating PET, we were unable to confirm the specific polymer composition from the available product specifications or other documentation. We have therefore conservatively revised the manuscript to refer to the material as “plastic microbeads” rather than “PET microbeads.” Spherical microbeads were selected because preliminary testing showed more consistent particle rearrangement and recovery after vacuum release compared with irregular granular materials such as sand and coffee grounds. Although irregular particles may provide greater interlocking, repeatable transition between the jammed and unjammed states was prioritized for the present tactile application.

 

Comment 3

The beads are listed as an 8 g component, but would it be better to list this as a volume fraction of the designed membrane size? Is there some other, better way of characterizing this so that, if a material with a different density were used, others could better reproduce the work?

Response:

Thank you for this comment. A fixed bead mass of 8 g was used for all experiments because the present study evaluated a single nodule geometry and granular fill condition rather than investigating packing fraction as an independent design variable. The bead mass was selected during prototype development to provide sufficient particle mobility in the unjammed state while allowing effective jamming under vacuum. We agree that volume fraction is an important parameter for more general characterization of granular-jamming behavior, and systematic evaluation of fill fraction should be considered in future design studies..

 

Comment 4

It is unclear during the compression test exactly how the bottom membrane is supported by the underlying immovable base. Is it freely deformable in all directions, or is there a support around which the bottom membrane deforms? It seems like the support design might have a significant influence on the overall data collected. Were the beads repositioned or relaxed between trials, or were they left in the previously deformed configuration after each compressive test?

Response:

Thank you for this comment. During compression testing, the bottom membrane of the nodule rested directly on the rigid base of the test frame, providing a fixed support condition. Between successive trials, the nodule was vented to atmospheric pressure and gently agitated to redistribute the particles before the next vacuum level was established. These experimental conditions have been clarified in the revised manuscript.

Comment 5

Finally what is the actual stiffness of the Mark 10 G1011 rubber tip?  the measured indentation curves are effectively the stiffness of this tip and the granular jamming actuator in series.  how was the influence of the tip removed from your experimental results?

Response:

Thank you for this comment. We agree that the compliance of the rubber indenter contributes to the measured force–displacement response. Because the indenter compliance was not characterized independently, its contribution cannot be separated from those of the membrane and granular medium. We have therefore clarified that the reported values represent the effective stiffness of the complete nodule–indenter contact system rather than an intrinsic material property of the granular medium. The rubber tip was intentionally used to provide a compliant, finger-like contact interface representative of the intended tactile interaction.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Authors have addressed all comments successfully.

Reviewer 3 Report

Comments and Suggestions for Authors

Dears Authors,

Equations are now numbered., but not according to Actuators template file.

Reviewer

Reviewer 4 Report

Comments and Suggestions for Authors

My comments have been mostly addressed, although I still think details on the manufacturing and materials are missing (material sources, mechanical characterization etc.)