Static Stability Analysis of a Planar Object Grasped by Multifingers with Three Joints

Abstract

This paper discusses static stability of a planar object grasped by multifingers with three joints. Each individual joint (prismatic joint or revolute joint) is modeled as a linear spring stiffness. The object mass and the link masses are also included. We consider not only pure rolling contact but also frictionless sliding contact. The grasp stability is investigated using the potential energy method. This paper makes the following contributions: (i) Grasp wrench vectors and grasp stiffness matrices are analytically derived not only for the rolling contact but also for the sliding contact; (ii) It is shown in detail that the vectors and the matrices are given by functions of grasp parameters such as the contact conditions (rolling contact and sliding contact), the contact position, the contact force, the local curvature, the link shape, the object mass, the link masses, and so on; (iii) By using positive definiteness of the difference matrix of the grasp stiffness matrices, it is analytically proved that the rolling contact grasp is more stable than the sliding contact grasp. The displacement direction affected by the contact condition deviation is derived; (iv) By using positive definiteness of the differential matrix with respect to the local curvatures, it is analytically proved that the grasp stability increases when the local curvatures decrease. The displacement direction affected by the local curvature deviation is also derived; (v) Effects of the object mass and the joint positions are discussed using numerical examples. The numerical results are reinforced by analytical explanations. The effect of the link masses is also investigated.

Design and stability analysis of bionic end-effector fingers for yarn tube gripping

“…Existing grasping stability analysis is more for two fingers grasping objects in two-dimensional plane, which has limited application, while this study considers fingertip friction in three-dimensional space to investigate the grasping stability factors of the three-finger end-effector. Rolling contact grasping is more stable than sliding contact grasping [8], and the rolling motion of fingertips and grasped objects includes infinitesimal translations and rotations, and they are due to small external disturbances. Static equilibrium is defined as the sum of all contact forces equal to zero.…”

“…The gripping performance of the underdriven end-effector depends largely on the structural design rather than the control method [5][6], therefore, the stability design of the fingertip is a prerequisite for achieving stable fingertip gripping. Funahashi et al [7] considered the curvature and frictional contact between the hand and the object at the contact point, and established the stiffness matrix by using the potential energy of the grasping system to study the grasping stability of fingertips; T Yamada et al [8] used the positive characterization of the difference matrix of the fingertip grasp stiffness matrix to study and prove that rolling contact grasp is more stable than sliding contact grasp. The current research on the stability of fingertip grasping is mostly applied in the two-dimensional plane with limited applicability, while the present study extends it to grasping in three-dimensional space.…”

Quasi-static Stability Analysis of Frictionless Planar Enveloping Grasps (Analysis of curvature effects at contact points)

“…Ref. [1] analyzed grasp stability of pinching grasps. Local curvature effects on the stability were also investigated.…”