Active contacts create controllable friction

Nick Gravish; Rohan Shah

REVIEW 3 major objections 5 minor 36 references

Active contacts create controllable friction

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Multiple active contacts with speed-independent friction can together produce a controllable, speed-dependent sliding friction law.

desk verdict A clean experimental demonstration that active contacts can shape the force-speed curve of dry sliding friction; the equal-normal-force assumption is the main soft spot, but it does not break the central claim. read the letter →

arxiv 2501.09746 v1 pith:64JGTISB submitted 2025-01-16 cond-mat.soft physics.bio-ph

Rohan Shah , Nick Gravish This is my paper · ORCID

classification cond-mat.softphysics.bio-ph

keywords activecontactsAmonton-Coulombfrictionforce-speedcurvemedianspeedcontroleffectiveviscosityslidinglocomotiondry

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Sliding friction between dry surfaces is usually taken as a speed-independent force set by the materials and normal load. This paper argues that when a surface has many 'active' contacts—points that move at their own controllable speeds, like wheels or robot feet—the collective friction becomes speed-dependent even though every individual contact obeys the speed-independent Amonton-Coulomb law. The net force-speed curve is then shaped by the distribution of contact speeds: it is a staircase that passes through zero at the median contact speed, so the system's equilibrium sliding speed is that median. The authors verify this with a ten-wheel rotating carousel and show that programming the contact speeds can set an effective viscosity, adjust the sliding friction coefficient in real time, and even produce near-frictionless sliding. If the result holds, contact-speed distribution, not just material and load, becomes a design handle for dry friction.

What carries the argument

The load-bearing object is the sign-sum identity $F(V)=\frac{1}{N}\mu mg\sum_i\frac{v_i-V}{|v_i-V|}$, which converts each contact's speed-independent Amonton-Coulomb force $\mu mg/N$ into a $\pm$ contribution whose sign flips when the system speed $V$ crosses the contact's commanded speed $v_i$. Ordering the $v_i$ makes the net force a staircase between $+\mu mg$ and $-\mu mg$, crossing zero at the median speed; with an even number of contacts the two middle speeds produce a flat zero-force plateau. The equivalent cumulative-distribution form $F(V)=\mu mg(1-2\,\mathrm{CDF}(V))$ turns the distribution of contact speeds into the design parameter. Experimentally, the machinery is a ten-wheel 'carousel' with independently speed-controlled motors, hinge-mounted spokes intended to equalize normal forces, and encoders on every wheel and on the central rotation.

What would settle it

Place an individual load cell under each wheel mount (or otherwise measure per-contact normal force) while the carousel slides through its commanded speed range; if the per-wheel loads differ measurably, the equilibrium speed should follow a weighted median of the contact speeds and the measured force-speed staircase should deviate from Eq. (1) in the direction of the weighted sum. The paper reports no such per-contact load measurement.

Watch

Extended reading notes

Core claim

The central claim is that the force-speed law of a multi-contact sliding system is a property of the set of contact speeds, not of the contacts' individual friction laws. For $N$ contacts with equal friction magnitude $\mu mg/N$ and commanded speeds $v_i$, the net friction is $F(V)=\frac{1}{N}\mu mg\sum_i \frac{v_i-V}{|v_i-V|}$; each term is $\pm 1$, so the curve is a descending staircase with a drop at each $v_i$. The equilibrium sliding speed, where $F=0$, is the median of the $v_i$, independent of the friction coefficient and of the mean contact speed, and robust to outliers. The paper verifies this with a ten-wheel carousel whose wheels have independent motor speeds: 660 random-speed trials confirm median equilibrium, direct ground-reaction measurements match the commanded staircases, uniformly spaced speeds create linear force-speed curves with controllable effective viscosity, and opposing equal-speed contact pairs reduce the measured sliding friction coefficient by $91\pm4\%$ and can make the system nearly frictionless. The discrete law is recast as $F(V)=\mu mg\,(1-2\,\mathrm{CDF}(V))$, which the paper proposes as an analytic route to force-speed curves for continuous active-contact systems such as spinning disks and slithering snakes.

Load-bearing premise

The load-bearing premise is that all ten contacts press on the ground with equal normal force, so each contributes the same friction magnitude $\mu mg/N$; the hinge suspension is meant to enforce this, but per-contact normal forces are never measured.

Editorial extensions

If this is right

The steady sliding speed of an equal-force active-contact system is the median of the contact speeds, so uniform changes in the friction coefficient or in the mean contact speed leave the equilibrium speed unchanged.
The slope of a programmed force-speed curve behaves like a viscosity: the time constant for approaching steady state scales inversely with the slope, matching exponential-relaxation predictions across 490 trials.
Pairing contacts at opposite speeds effectively deactivates them within the speed band, so the sliding friction coefficient can be lowered in real time; at maximum cancellation the measured reduction is $91\pm4\%$ and the sliding is nearly frictionless.
Through the cumulative-distribution formulation, the discrete result gives an analytic force-speed curve for any continuous distribution of contact speeds, which the paper proposes for spinning disks, slithering snakes, and slow granular drag.
Because the force-speed curve is controlled by the speed distribution alone, a single material pair can implement a family of friction laws—step, viscous, near-zero—by reprogramming contact speeds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the cumulative-distribution rule holds generally, a surface with many small counter-rotating rollers could present a programmable friction landscape: adjusting the roller-speed distribution would shape the in-plane force-speed curve, including zero net sliding friction without lifting the load; the paper does not test this engineered-surface application.
The median's robustness to outliers implies that in legged locomotion with many slipping contacts, an outlier limb speed would not shift steady locomotion speed, so a malfunctioning or freely spinning leg might be masked as long as it stays on one side of the median; this is a testable extension to robots.
For even numbers of contacts, the flat zero-force plateau creates a speed-selective mechanical response: nearly frictionless inside the band between the two middle speeds and strongly braking outside it, which could serve as a speed-selective brake or clutch.
Extending the authors' weighted-median remark, deliberately imposing unequal normal loads or per-contact friction coefficients would turn the force-speed curve into a weighted sum and the equilibrium into a weighted median, providing a direct experimental bridge to biological and granular contacts where loads are inherently uneven.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing to know: this paper builds a ten-wheel carousel with independently speed-controlled contacts and shows, convincingly, that the net friction force is the sum of individual Amonton-Coulomb terms, producing programmable force-speed curves—including near-zero friction. The data are plentiful (660 equilibrium trials, 490 viscosity trials) and the simple model matches them well. The median equilibrium result is not brand new, and the authors credit prior work for it; what is new is the direct force-speed measurement and the real-time friction coefficient control, which are neatly done.

The soft spots are real but not disabling. The biggest is the equal-normal-force assumption. Each spoke hangs from a closet hinge, but no per-wheel normal force is measured. The two residuals you'd expect from load imbalance are present: the near-frictionless state reduces force by 91±4%, not 100%, and the median fit slope is 1.065±0.01, not 1. The authors themselves note in the Discussion that with unequal forces you get a weighted median and a weighted CDF, so they are aware of the generalization. Still, the headline quantitative claims are stated in unweighted terms, and the paper should either measure per-wheel loads or explicitly characterize how much imbalance the hinge allows. The qualitative message—active contacts can control friction—survives either way.

Two smaller issues. Figure 4 shows force-speed curves without error bars or repeated trials; given that this is the core measurement, a few repeats would help. And "near frictionless sliding" overstates a 91% reduction; it is a large reduction, but not near frictionless, and the phrasing invites hype.

I disagree with the stress-test's implicit worry that the concept collapses under load imbalance. It doesn't; the model simply becomes weighted. The paper is honest about the equations, uses the right citations, and the experiments are substantial. The main deficiencies are presentation and a missing control, not a fatal flaw.

Who is this for: robophysics, biomechanics, and tribology readers interested in active friction control. It deserves a serious referee, with requests for repeated force-curve measurements and a direct or indirect test of the equal-normal-force assumption. I would engage with it and probably cite it if I worked on active friction or multi-legged locomotion.

Referee Report

3 major / 5 minor

Summary. This paper studies sliding friction of a carousel with ten independently motor-driven wheels in frictional contact with an acrylic ground. The authors model each contact as a speed-independent Coulomb friction element and show that the net force-speed curve obeys Eq. (1), so the equilibrium system speed equals the median of the wheel speeds. Experiments on 660 random speed configurations support the median prediction, force-speed measurements reproduce step-like and programmed linear curves, and measurements of startup time and transients demonstrate controllable effective viscosity and friction coefficient. The paper claims that opposing contact pairs can create near-frictionless sliding.

Significance. If correct, the work establishes that the statistical distribution of active-contact speeds, rather than material properties alone, can shape macroscopic sliding friction, with implications for legged locomotion and engineered surfaces. The model is simple and falsifiable, and the experiments are extensive: 660 equilibrium trials, 490 viscosity trials, and independent mean-vs-median tests. The main quantitative claims rest on the equal-normal-force assumption, which is plausible from the hinge design but not directly measured; this is the central weakness. The paper's proposed CDF formulation in Eq. (2) is a restatement of Eq. (1), but it may be useful for continuous contact distributions.

major comments (3)

[Equilibrium properties of multi-contact friction, Fig. 3b] The equal-normal-force assumption is load-bearing but unverified. Eq. (1) and the median prediction assume each contact contributes the same friction magnitude µmg/N; the only evidence is the hinge design statement. The fitted slope m = 1.065 ± 0.01 in Fig. 3b and the 91 ± 4% reduction in Fig. 6 are both consistent with unequal normal forces, which the authors themselves note would replace the unweighted median with a weighted median. Please either measure per-contact normal forces directly, add a calibration showing equal loads, or explicitly reframe the quantitative claims as approximate.
[Measurement of force-speed curves, Fig. 4] The agreement with the programmed force-speed curves is a central demonstration, but the plotted data appear to be single trials without error bars or repeated runs. Without a measure of trial-to-trial variability, the reader cannot judge whether the deviations at the step transitions (attributed to backlash) are representative or whether the claimed linear viscosity curves are within noise. Please add statistics over repeated force-speed measurements or clearly label representative traces.
[Abstract and Sliding friction coefficient control, Fig. 6] The abstract and the final experimental section describe the result as near-frictionless, but the measured reduction is 91 ± 4%, leaving a residual friction force of about 9% of the braked value. This is a good result but not 'near frictionless'; the wording should be qualified, and the residual mechanism should be discussed.

minor comments (5)

[Throughout] There are several typographical errors: 'counter-exmaples', 'equilirium', 'whe', 'probabiltiy', 'subsitution', 'combing', and 'Communincations' in Ref. [6].
[Fig. 2] The caption labels subfigures a), c), d) but the text refers to 'Fig. 2a,b'; subfigure b appears to be missing or mislabeled.
[Equilibrium properties section] The text refers to 'Fig. 1b' and 'Fig. 1c' when discussing the median and mean experiments; these cross-references should be to Fig. 3.
[Eq. (2)] The CDF definition should specify the integration variable explicitly; the current expression CDF(V) = ∫ P(V) is ambiguous because the dummy variable equals the argument.
[Fig. 4 caption] The text says the commanded force-speed profile is shown in red in Fig. 4a, while the caption says the programmed curves are black lines; please reconcile these color descriptions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central force-speed model is an assumed contact-level law, and the paper tests its aggregate consequences against independent force and speed measurements.

full rationale

The derivation chain starts from the stated per-contact Amonton-Coulomb law, F_i = (µmg/N) sign(v_i - V), and sums these independent contact forces to obtain Eq. (1). This is a model assumption, not a fitted result. The paper then tests the aggregate consequences against independent measurements: the median equilibrium speed is compared to 660 experiments, the force-speed curves are compared directly to load-cell measurements, and the friction-coefficient reduction is compared to ground-reaction forces. Equation (2) is explicitly derived as an algebraic restatement of Eq. (1), and the paper does not use Eq. (2) as evidence for Eq. (1); it is a reformulation rather than a circular input. The viscosity and friction-control measurements involve fitting time constants or normalizing by independently measured brake forces, but the predicted scaling laws are not constructed from the fitted values. Self-citations are incidental and not load-bearing for the central claim. Overall, the aggregate predictions are distinct from and falsifiable against the contact-speed inputs and measured forces, so no circular step is present.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters were fitted to the force-speed data; µmg is measured directly via load cell, and the contact speeds are commanded inputs. The central model rests on four domain assumptions about the apparatus and the friction law, not on invented entities.

assumptions (4)

domain assumption Each contact obeys Amonton-Coulomb friction: F_i = -(µmg/N)(vi - V)/|vi - V|, speed-independent and opposing relative motion.
Invoked in Eq. 1 and the motivating thought experiment; the paper verifies speed independence for the carousel in Fig. 2c but does not derive the law.
domain assumption All ten contacts carry equal normal force, so each friction magnitude is µmg/N.
Required for the unweighted median and unweighted sum; the hinge suspension is intended to equalize load but per-wheel normal force is not measured.
domain assumption Contact speed vi equals the commanded motor speed; wheel-ground slip and gear backlash are small.
The paper measures motor speed change under load as 4.6 +/- 2.0%, supporting but not fully eliminating slip or backlash.
domain assumption The lazy-susan bearing and hinges contribute negligible friction compared with the wheel-ground contacts.
The bearing is described as low-resistance, but no direct subtraction or error analysis is provided.

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Cite this review

Pith. "Pith review of Active contacts create controllable friction." pith.science (2026). https://pith.science/paper/64JGTISB

@misc{pith2026250109746,
  author       = {Pith},
  title        = {Pith review of: Active contacts create controllable friction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/64JGTISB}},
  note         = {Machine review of arXiv:2501.09746}
}

read the original abstract

Sliding friction between two dry surfaces is reasonably described by the speed-independent Amonton-Coulomb friction force law. However, there are many situations where the frictional contact points between two surfaces are "active" and may not all be moving at the same relative speed. In this work we study the sliding friction properties of a system with multiple active contacts each with independent and controllable speed. We demonstrate that multiple active contacts can produce controllable speed-dependent sliding friction forces, despite each individual contact exhibiting a speed-independent friction. We study in experiment a rotating carousel with ten speed-controlled wheels in frictional contact with the ground. We first vary the contact speeds and demonstrate that the equilibrium system speed is the median of the active contact speeds. Next we directly measure the ground reaction forces and observe how the contact speeds can control the force-speed curve of the system. In the final experiments we demonstrate how control of the force-speed curve can create sliding friction with a controllable effective viscosity and controllable sliding friction coefficient. Surprisingly, we are able to demonstrate that frictional contacts can create near frictionless sliding with appropriate force-speed control. By revealing how active contacts can shape the force-speed behavior of dry sliding friction systems we can better understand animal and robot locomotion, and furthermore open up opportunities for new engineered surfaces to control sliding friction.

Figures

Figures reproduced from arXiv: 2501.09746 by the authors.

**Figure 2.** FIG. 2. System design and friction properties. a) Schematic of multi-contact friction rotational “carousel”. An array of ten [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Equilibrium behavior of multi-contact frictional systems. a) Speed versus time of the individual active contacts ( [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. Ground reaction force measurements from active contacts with programmed force-speed curves (black lines). In the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5. Experiment to measure the time to reach [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6. Demonstration of friction control from active con [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Popova and V

E. Popova and V. L. Popov, The research works of coulomb and amontons and generalized laws of friction, Friction 3, 183 (2015)

work page 2015

[2] [2]

N. S. Tambe and B. Bhushan, Friction model for the ve- locity dependence of nanoscale friction, Nanotechnology 16, 2309 (2005)

work page 2005

[3] [3]

A. Ward, F. Hilitski, W. Schwenger, D. Welch, A. W. C. Lau, V. Vitelli, L. Mahadevan, and Z. Dogic, Solid fric- tion between soft filaments, Nat. Mater. 14, 583 (2015)

work page 2015

[4] [4]

M. H. M¨ user, Velocity dependence of kinetic friction in the prandtl-tomlinson model, Phys. Rev. B 84, 125419 (2011)

work page 2011

[5] [5]

Vanossi, C

A. Vanossi, C. Bechinger, and M. Urbakh, Structural lu- bricity in soft and hard matter systems, Nature Com- munincations 11, 4657 (2020)

work page 2020

[6] [6]

Menga, F

N. Menga, F. Bottiglione, and G. Carbone, Dynamically induced friction reduction in micro-structured interfaces, Sci. Rep. 11, 8094 (2021)

work page 2021

[7] [7]

J. Li, F. Zhou, and X. Wang, Modify the friction be- tween steel ball and PDMS disk under water lubrication by surface texturing, Meccanica 46, 499 (2011)

work page 2011

[8] [8]

Menga, F

N. Menga, F. Bottiglione, and G. Carbone, Exploiting surface textures dynamics for dry friction control, Non- linear Dyn. 111, 3099 (2023)

work page 2023