Workspace of Multifingered Hands Using Monte Carlo Method

Multifingered hands have the capability of dexterous manipulation of grasped objects and thus significantly increase the capabilities of a robot equipped with multifingered hands. Inspired by a multijointed human finger and the hand, we propose a six degree-of-freedom (DOF) model of a three-fingered robotic hand as a parallel manipulator. Two kinds of contact, namely point contact with friction and rolling without slipping between the fingertips and the grasped object, are considered. The point contact with friction is modeled as a three DOF spherical joint, and for rolling without slipping, we use the resultant nonholonomic constraints between the grasped object and the fingers. With realistic limits on the joints in the fingers and dimensions of finger segments, we obtain the well-conditioned manipulation workspace of the parallel manipulator using a Monte Carlo-based method. Additionally, we present two new general results—it is shown that maximum position and orientation workspace is obtained when the cross-sectional area of the grasped object is approximately equal to the area of the palm of the hand and when rolling without slipping is ensured the size of the well-conditioned workspace is significantly larger (⁠$∼1.2–1.5$ times). We also present representative experiments of manipulation by a human hand and show that the experimental results are in reasonable agreement with those obtained from simulations.