Stick-slip friction

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 2412.14899 eq. 7 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 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 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 2411.16055 §IV-A 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 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 2412.14899 §2.2.4. Card: Vibration-based Full State In-Hand Manipulation of Thin Objects.

The duty-cycle variant turns the motor on and off, so the object can settle back into sticking between pulses 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 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 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 2411.16055 §IV-A. In another order, gravity can be balanced only if the palm contact is sticky 2411.16055 §IV-A. Card: Picking by Tilting: In-Hand Manipulation for Object Picking using Effector with Curved Form.

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

When to use which

The duty-cycle and angle results are author-reported, with small trial counts in the tilting paper (5 per setting) 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.

# 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

# 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 2412.14899 eq. 9. Derive the threshold from 2412.14899 eq. 3–2412.14899 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 2411.16055 §IV-A 2412.14899 §2.3.3.

Papers

• Vibration-based Full State In-Hand Manipulation of Thin Objects: 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: friction-cone contact modes for tilting a large object against supports; stick-slip is not its mechanism.