Open AccessOn the Robot Singularity: A Novel Geometric Approach
Author(s) -
Man Bok Hong
Publication year - 2012
Publication title -
international journal of advanced robotic systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 46
eISSN - 1729-8814
pISSN - 1729-8806
DOI - 10.5772/53779
Subject(s) - jacobian matrix and determinant , singularity , reciprocal , robot , uniqueness , computer science , measure (data warehouse) , parallel manipulator , invariant (physics) , mathematics , topology (electrical circuits) , control theory (sociology) , mathematical analysis , artificial intelligence , control (management) , combinatorics , data mining , philosophy , linguistics , mathematical physics
This paper addresses a novel geometric analysis method of the singularity and kinestatic characteristics of robots. For non-redundant robots, there exist two uniquely determined Jacobians – the screw-based Jacobian and the reciprocal Jacobian. Here, it is shown that if some of the reciprocal products between the column screws of the two Jacobians are close to zero, the robot is in the vicinity of a singular configuration and the corresponding columns of the Jacobian are involved in the singularity. From this observation, an invariant measure of closeness to a singularity is presented using the reciprocal products. Furthermore, by considering the reciprocal products between the actuated joint screws and column screws of the Jacobian, this measure is extended so that the concept of the kinestatic characterization index is presented for parallel robots. Since it is defined as the ratio of reciprocal products from the uniqueness of the two Jacobians, it represents a unique invariant characteristic of robots. From the singularity analyses of the planar 4-bar linkage and the 3-DOF parallel manipulator with PRS-serial chains, the validity of the proposed index is examined and the concept of a kinestatically balanced configuration is introduced as well