Adaptive Compliant Gripper — Underactuated Fingers (2D)

Object

Tendon & Compliance

Tendon tension 0%

Joint spring stiffness 6

Grasp readout

Total contact force

0.0

Contact points

Grasp state

Open

Force balance (σ)

–

Finger link (rigid) Torsional-spring joint Active contact (force ∝ glow)

How this differs from the 3D model

The 3D Adaptive Compliant Gripper compares one preset closing force against a slip-triggered adaptive one. This 2D companion opens the gripper's own mechanism up: each of the three fingers is an underactuated chain — one tendon per finger, two joints, no per-joint motor. Every joint is a torsional spring:

joint torque:  I·θ̈ = τ_tendon − k·θ − c·θ̇ + τ_contact
contact→joint: τ_contact = Σ F_contact · (P_contact − P_pivot)⊥   (virtual-work / Jacobian-transpose coupling)

τ_tendon is identical for every joint on a finger — one pull, many joints. That's underactuation: 3 tendons drive 6 joints.
Before any contact, the softer-feeling joint (lower effective resistance) closes first, exactly like a real underactuated finger.
The instant a link touches the object, the contact's reaction torque at that joint rises to balance the tendon torque there — that joint stops advancing while the same tendon keeps closing the other joint, so the finger keeps wrapping past the contact point.
No sensor ever measures the object's shape — the differing torques at each spring joint are the only thing doing the adapting. That's why a circle, a square and an irregular blob each end up held by a different, unprogrammed finger posture.

The lower chart sums the penetration-based contact force per finger in real time — the force-distribution readout is a side-effect of the mechanics, never an input to them.

Palm / hub Finger links Object

Radial view — 3 underactuated fingers

Open

Contact-force distribution (per finger)