Source-linked AI summary
Quasi-static analysis of passive stability in a novel underactuated multi-finger hand
Léonie Plancoulaine, Sylvain Guégan, Franck Plestan, Damien Chablat
TL;DR
Underactuated hands make stable equilibrium poses difficult to predict. The paper introduces a quasi-static analytical framework for a three-finger hand with a differential spring-loaded slider, analyzing cylindrical and spherical grasps. The analysis demonstrates stable equilibria while relating admissible object sizes to hand geometry and finger flexion.
Problem
Predicting the stable equilibrium pose of an object grasped by an underactuated hand remains a significant challenge.
Method
A quasi-static analytical approach evaluates passive stability in a three-finger hand with a differential spring-loaded slider for cylindrical and spherical grasps.
Results
Stability and energy-based criteria demonstrate stable equilibrium for cylindrical and spherical grasp configurations, with object-size ranges influenced by hand geometry and finger flexion.
Takeaways & Limitations
The findings provide a foundation for optimizing grasp performance through analysis of mechanism kinematics and admissible object sizes.
Takeaways & Limitations
The present analysis neglects support-object and fingertip friction and is limited to the studied canonical grasp configurations.
Abstract
from arXiv · showhide
Underactuated robotic hands achieve adaptive and robust grasping with a reduced number of actuators, but predicting the stable equilibrium pose of the grasped object remains a significant challenge. This paper introduces a quasi-static analytical approach to assess passive stability in underactuated multi-finger hands. A novel three-finger hand architecture integrating a differential spring-loaded slider mechanism is introduced, enabling versatile and adaptive grasping. The study focuses on how the differential mechanism influences the overall grasp behavior and analyzes the effect of object size on the stable equilibrium configurations for two canonical grasp types: cylindrical and spherical.
1 Introduction
The paper addresses the challenge of predicting stable equilibrium poses in underactuated hands by analyzing how a differential mechanism affects grasp stability and admissible object sizes for cylindrical and spherical grasps.
- Differential mechanisms redistribute contact forces during grasping, but their impact on grasp stability remains largely unexplored.
- Stability analysis identifies suitable grasp configurations and provides insight into object size limitations and mechanical design choices.
- The hand architecture uses a differential spring-loaded slider to distribute one input actuation force among the fingers with minimal weight.
- The study investigates passive stability, differential-mechanism effects, stable equilibrium positions, and admissible object sizes for cylindrical and spherical grasps.
2 Hand architecture
The proposed hand combines three levels of underactuation in a three-finger architecture: differential force distribution, passive finger rotation, and underactuated finger kinematics.
- Three fingers are arranged on a 50 mm-radius circle with 120° spacing, while underactuation occurs between fingers, at passive finger rotation, and within the fingers.
- A spring-loaded slider distributes actuation between fingers; blocked fingers compress their springs so the other fingers can continue moving.
- Mechanical linkages connect the slider to the fingers, enabling torque transmission through lever-like motion.
- Antagonistic springs passively actuate a revolute joint at each finger base, enabling three-dimensional motion without significantly increasing mechanical complexity.
- Finger kinematics support precision and power grasps through two interlinked closed loops, while this study focuses on precision grasp.
3 Method
The method uses a two-dimensional quasi-static equilibrium analysis of cylindrical and spherical grasps, combining contact-force equations, geometry, and local energy-based stability criteria.
- The analysis neglects table and fingertip friction to isolate kinematic effects and the passive differential mechanism, while assuming single-point midpoint contact and negligible S2i torque.
- Finger actuation torque combines the differential mechanism’s spring forces with a 50 N global actuation force and lever-arm geometry.
- Object geometry determines the distal-phalanx distance from the finger axis using object width, hand radius, finger thickness, and object displacement.
- Static equilibrium is solved from the summed finger forces, determining the stable object position and corresponding finger configuration.
- Cylindrical grasp assumes equal forces from fingers 2 and 3, whereas the two scenarios use geometry-specific finger arrangements and object positions.
- Local stability is assessed through the Hessian of potential energy, requiring positive eigenvalues around equilibrium.
4 Results
The hand reaches stable equilibria for cylindrical and spherical grasps, with object size shaping admissible configurations and contact-force behavior. Local Hessian analysis indicates stability around the reported equilibria.
- Cylindrical grasp: A prism 110 mm wide reaches a stable cylindrical-grasp position at qx = 18.11 mm.The offset reflects the finger arrangement, finger kinematics, and differential mechanism.
- Cylindrical grasp: Cylindrical grasping reaches the joint limit θ21 = -52° at a maximum object width of 116 mm, while thinner objects remain within the minimum limit.The minimum limit θ2i = -140° is never reached, so the hand can grasp objects as thin as a sheet of paper.
- Cylindrical grasp: The maximum cylindrical-grasp contact force occurs at an object width of 70 mm, while force and displacement follow a concave trend with object width.The trend reflects the lever arm and finger geometry.
- Spherical grasp: For spherical grasping, centered alignment gives zero object displacement and spring compression, equal finger forces, and symmetric finger angles.The spherical configuration has θ11 = θ12 = θ13 = 0° and f21 = f22 = f23.
- Spherical grasp: Spherical grasping admits object widths from 18.4 mm to 150 mm, with the lower bound set by finger collisions and the upper bound by finger geometry and flexion range.The minimum-width expression uses finger width n = 31.9 mm; the maximum is linked to l1 and the available flexion range.
5 Conclusions and future work
The study uses stability analysis and energy-based criteria to show stable equilibria for cylindrical and spherical grasps while identifying design factors that affect admissible object sizes.
- The findings provide a foundation for optimizing grasp performance through mechanism-kinematic design.
- Stability analysis and energy-based criteria demonstrate stable equilibrium for cylindrical and spherical grasp configurations.
- Proximal phalanx length, finger flexion range, and phalanx width significantly affect the range of admissible object sizes.
- Future work will incorporate support-object and fingertip friction to study grasping from initial contact through lift-off.
- Planned extensions include enveloping and arbitrary-shape grasps, maximum graspable mass, object-specific hand design, and learning-based controllers.