1-DOF Underactuated Robotic Hand with Adaptive Grasping via Torsional Springs

Adrian — Northeastern University, EECE5554

A four-finger underactuated robotic gripper inspired by the SDM Hand (Dollar & Howe), designed and simulated in SolidWorks. The gripper achieves adaptive grasping across varied object geometries using a single actuator per finger and passive torsional springs.

How to Run

Requirements: SolidWorks with the Motion Analysis add-in enabled.

1. Open cad/assemblies/final_assem.SLDASM in SolidWorks. If prompted to locate missing references, point each part to the corresponding .SLDPRT file in cad/parts/.
2. In the bottom panel, select the Motion Study tab.
3. Click Calculate (or Play) to run the simulation.
4. To test a different object geometry, suppress the current object body in the assembly tree and unsuppress the desired one, then recalculate.

Overview

Fully actuated robotic hands offer dexterity but are mechanically complex. Simple grippers lack versatility. This design occupies the middle ground: a 1-DOF-per-finger underactuated hand that uses torsional springs at passive joints to conform to object geometry without additional actuation.

Each finger has 3 DOF (proximal, middle, distal) but only 1 actuated DOF — a tendon force applied at the distal link tip directed radially inward. The remaining 2 DOF per finger are governed by torsional springs, giving the full 4-finger hand 12 total DOF with only 4 actuated.

Mechanism Design

Finger Structure

Each finger is a planar serial chain of three rigid links connected by revolute joints:

Link	Length (mm)	Joint Angle	Type
Proximal	100	θ₁ ∈ [0°, −47°]	Actuated
Middle	180	θ₂ = 30°	Passive
Distal	194	θ₃ = 30°	Passive

The four fingers are arranged symmetrically around a central palm structure.

Spring Configuration

Torsional springs at each revolute joint bias the fingers toward closure:

• Proximal & middle joints: k = 18 N·mm/deg
• Distal joint: k = 5 N·mm/deg (greater fingertip compliance)
• Damping: C = 15 N·mm/(deg/s), linear type

Springs are wound inward (counter-clockwise on left fingers, clockwise on right), maintaining a non-zero passive joint angle at rest and keeping fingers away from kinematic singularities.

Mobility & DOF Analysis

Using the planar Grübler formula for a single finger (n = 4 links, j₁ = 3 revolute joints):

M_finger = 3(4 − 1) − 2(3) = 3
M_hand   = 4 × 3 = 12  (4 actuated, 8 passive)

Forward Kinematics

End-effector position for a single finger (passive joints fixed at spring-free angle):

x = l₁cos(θ₁) + l₂cos(θ₁+θ₂) + l₃cos(θ₁+θ₂+θ₃)
y = l₁sin(θ₁) + l₂sin(θ₁+θ₂) + l₃sin(θ₁+θ₂+θ₃)

Sweeping θ₁ across its full ~47° range traces the end-effector workspace. In practice, passive joints rotate freely in response to contact, extending the effective reachable configurations.

SolidWorks Motion Study

Simulation Setup

• Actuation: 1 N force applied at the distal link tip, directed radially inward (force vector rotates with the finger)
• Material: Rubber (dry) on arms and objects to simulate soft finger pads and increase friction
• Objects tested: Box, cylinder, oblate spheroid, thin rectangle

Results

Object	Outcome
Box	Stable, uniform contact distribution
Cylinder	Best demonstrated adaptive wrapping behavior
Oblate Spheroid	Each finger found stable configuration despite curved profile
Thin Rectangle	Least uniform — inconsistent closure rate caused object to shift before stabilizing

Angular displacement plots confirm that the actuated base joint θ₁ shows a transient spike (force overcoming static spring resistance), while passive joints θ₂ and θ₃ demonstrate smooth independent rotation — validating that the torsional springs successfully transmit closure through the kinematic chain.

CAD Files

All parts modeled in SolidWorks (.SLDPRT), assembled in cad/assemblies/final_assem.SLDASM.

Assemblies (cad/assemblies/)

File	Description
final_assem.SLDASM	Main assembly
final_assem_backup.SLDASM	Backup assembly

Parts (cad/parts/)

File	Description
final_base.SLDPRT	Palm/base structure
distal_link_final.SLDPRT	Distal phalanx
middle_final_link.SLDPRT	Middle phalanx
pin.SLDPRT	Revolute joint pin
sphere.SLDPRT	Spherical test object
final_bottle.SLDPRT	Bottle-shaped passive element
final box.SLDPRT	Box test object

Media

Simulation videos are in the media/ folder:

File	Description
final_assem.mp4	Primary assembly demonstration
final_assem_sq.mp4	Box/square object grasping
final_assem_bigger_cir.mp4	Larger cylinder grasping
final_assem_oblate.mp4	Oblate spheroid grasping
sphere_vid.mp4	Spherical object grasping

References

1. A. M. Dollar and R. D. Howe, "The highly adaptive SDM hand: Design and performance evaluation," IJRR, vol. 29, no. 5, pp. 585–597, 2010.
2. M. Ciocarlie and P. Allen, "Hand posture subspaces for dexterous robotic grasping," IJRR, vol. 28, no. 7, pp. 851–867, 2009.
3. C. Gosselin, F. Pelletier, and T. Laliberte, "An anthropomorphic underactuated robotic hand with 15 dofs and a single actuator," pp. 749–754, 2008.
4. R. R. Ma and A. M. Dollar, "An underactuated hand for efficient finger-gaiting-based dexterous manipulation," IEEE ROBIO, 2014, pp. 2214–2219.