---
kind: concept
slug: stick-slip-friction
title: Stick-slip friction
summary: >-
  Friction that alternates between sticking and sliding, so a small oscillating force can move an object in steps. Vibration on a parallel gripper uses it to rotate a thin object (author-reported: 1.5 vs 3.8 degrees orientation error with duty-cycle vs constant vibration). Main trade-off: the switching threshold depends on friction values that papers often do not state.
tags: [friction, manipulation, vibration, contact-mechanics]
papers: ["2411.16055", "2412.14899"]
related: [in-hand-manipulation, nonprehensile-manipulation]
status: draft
updated_at: 2026-10-25
---

## Overview

At a contact, static friction holds two surfaces together while the tangential
force stays below a limit. Above that limit the surfaces slide, and the
friction force drops to a lower kinetic value [arxiv:2412.14899 eq. 7] [arxiv:2412.14899 eq. 8].
Repeated switching between the two states is the stick-slip effect. In
manipulation it can move an object that a steady force would not move
[arxiv:2412.14899 §1].

Only one of the two cards uses stick-slip as its mechanism. The vibration
paper drives the object through repeated stick and slip phases
[arxiv:2412.14899 §2.2.2]. The tilting paper models contacts with friction
cones and force closure. It uses the sticking condition only in one case: a
contact that must be sticky so that it can push upward [arxiv:2411.16055 §IV-A]
[arxiv:2411.16055 fig. 2c]. Its concept tag is therefore loose. Read it as
contact mechanics, not as a stick-slip model.

## Variants

### Vibration-driven stick-slip on a parallel gripper

An eccentric-mass motor on one finger shakes a thin object held by a parallel
gripper. The contact sticks or slips depending on the vibration force relative
to the normal force [arxiv:2412.14899 eq. 7]. Each cycle moves the centre of
mass, and that moves the object. Steering the vibration direction sets whether
the object rotates or translates [arxiv:2412.14899 §2.2.4]. Card:
[Vibration-based Full State In-Hand Manipulation of Thin Objects](/papers/2412.14899).

The duty-cycle variant turns the motor on and off, so the object can settle
back into sticking between pulses [arxiv:2412.14899 §2.3.3]. On a 100 mm radius
disk, the author-reported orientation error fell from 3.8 ± 1.2 degrees with
constant vibration to 1.5 ± 1.02 degrees with 50% duty cycle [arxiv:2412.14899 tab. 1].
The position error for constant vibration is not reported in the table.

### Friction-cone contact modes in a tilt

A curved palm and two supports hold a large object. Each contact is treated as
a friction contact, with its force limited by a friction cone [arxiv:2411.16055 §III].
Whether the object can be tilted depends on the order of three points on one
edge line. In one order, the object slides on two supports while the palm
holds it [arxiv:2411.16055 §IV-A]. In another order, gravity can be balanced
only if the palm contact is sticky [arxiv:2411.16055 §IV-A]. Card:
[Picking by Tilting: In-Hand Manipulation for Object Picking using Effector with Curved Form](/papers/2411.16055).

The planning map uses a friction coefficient of 0.1 at the two supports and
0.1 or 0.2 at the palm [arxiv:2411.16055 fig. 3]. The paper does not state the
real friction values of its hardware [arxiv:2411.16055 §IV-B].

## When to use which

| Situation | Use | Why |
|---|---|---|
| Thin object in a parallel gripper that must rotate and then translate | Vibration-driven stick-slip, with duty-cycle translation | The duty-cycle run had lower orientation error than constant vibration on the disk and plate [arxiv:2412.14899 tab. 1]. Needs an added vibration motor, a rotary steering actuator and camera tracking at 60 Hz [arxiv:2412.14899 §3.2]. |
| Large object that the gripper cannot close around, on a table | Friction-cone tilt with two supports | The 2-DOF palm and the UR3 both picked objects with this method, but the arm failed on a steel box at a 90-degree support angle (0 of 5) and succeeded at 61 degrees [arxiv:2411.16055 tab. I]. |
| No force or torque sensor available | Either | Both papers run open-loop. The tilting paper uses none [arxiv:2411.16055 §V-A]. The vibration paper uses camera pose feedback, not force [arxiv:2412.14899 §3.2]. |
| Friction values are unknown | Either, with caution | Both results depend on friction, and neither paper states the hardware's friction coefficients [arxiv:2412.14899 §2.2.2] [arxiv:2411.16055 §IV-B]. Measure them before planning. |

The duty-cycle and angle results are author-reported, with small trial counts
in the tilting paper (5 per setting) [arxiv:2411.16055 fig. 6c]. Treat them as
evidence of feasibility, not of reliability.

## Implementation sketch

Vibration-driven stick-slip contact, using the paper's threshold and a duty
cycle. The duty-cycle period is not stated in the paper, so `T` is a value
you choose.

```pseudocode
# Stick or slip at one contact  [eq. 7] [eq. 8]
# Input:  driving force f_v, normal force f_N, static mu_s, kinetic mu_k
# Output: friction force on the object

def contact_friction(f_v, f_N, mu_s, mu_k):
    # Stick while the driving force stays inside the static limit  [eq. 7]
    if abs(f_v) <= mu_s * abs(f_N):
        return f_v               # friction balances the drive
    # Otherwise the contact slips; friction is kinetic  [eq. 8]
    return mu_k * abs(f_N)       # magnitude; opposes the sliding
```

```pseudocode
# Duty-cycle vibration for translation  [§2.3.3] [§3.2]
# Input:  time t, period T (not stated in the paper)
# Output: motor on (True) or off (False)

def duty_cycle_on(t, T):
    # 50% duty cycle: on for half of each period  [§3.2]
    return (t mod T) < T / 2
```

Note: the paper's threshold equation [eq. 9] does not follow from its force
definitions as written [arxiv:2412.14899 eq. 9]. Derive the threshold from
[arxiv:2412.14899 eq. 3]–[arxiv:2412.14899 eq. 5] and check it against your measurements.

## Contradictions

None known between the two papers. They use the term in different senses:
the vibration paper treats stick phases as useful, while the tilting paper
calls a sticky palm contact less desirable because it needs large friction
[arxiv:2411.16055 §IV-A] [arxiv:2412.14899 §2.3.3].

## Papers

- [Vibration-based Full State In-Hand Manipulation of Thin Objects](/papers/2412.14899): models stick and slip at a vibrating finger and uses duty-cycle vibration for accurate translation.
- [Picking by Tilting: In-Hand Manipulation for Object Picking using Effector with Curved Form](/papers/2411.16055): friction-cone contact modes for tilting a large object against supports; stick-slip is not its mechanism.