Closed-form solutions of the kinetostatics of a 2limbs 6 dof parallel mechanism with kinematic and actuation redundancies

Abstract

A novel two-limb six-degrees-of-freedom (dof) parallel robot redundantly driven by eight actuators is proposed. The proposed robot was named Atarigi Carrier or ATARIGI for short. An atarigi is a long wooden pestle, an instrument used in Japanese cooking. A chef holds an atarigi with his two hands and grinds sesame and miso paste in a large mortar bowl. The precessional motion of the robot is similar to that of a Japanese chef using an atarigi. The mechanism of ATARIGI has a two-layer structure in which the eight-dof actuators control six-dof hand via seven-dof internal mechanism. The first part of the hierarchy from the eight-dof actuators to the seven-dof internal mechanism has actuation redundancy, and the second part of the hierarchy from the seven-dof internal mechanism to the 6-dof hand has kinematic redundancy. ATARIGI is a novel parallel mechanism which simultaneously has kinematic redundancy and actuation redundancy. The kinematic redundancy contributes to singularity avoidance, while the actuation redundancy contributes to backlash removal by acting on the internal forces of the mechanism. These redundancies enable the proposed parallel robot to have a large workspace by avoiding the singularity and high accuracy by removing the backlashes. Closed-form solutions for forward and inverse displacement analysis, and forward and inverse kinetostatic analysis were derived. The derived solution was implemented using MATLAB and Mathematica, and the validity was verified by numerical calculations.