Singularity analysis of a kinematically redundant (6+2)-DOF parallel mechanism for zero-torsion configurations

• Published in: Mechanism and machine theory Vol. 170; p. 104682
• Main Authors: Lacombe, Jonathan, Gosselin, Clément
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-04-2022
• Subjects: Gough–Stewart platform; Kinematic redundancy; Parallel mechanism; Path planning; Singularity analysis; Zero-torsion configuration; Zero-torsion configuration; Parallel mechanism; Path planning; Kinematic redundancy; Singularity analysis; Gough–Stewart platform
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2021.104682

The orientational workspace of parallel mechanisms is known to be restricted due to singular configurations of type II. Recently, a (6+3)-degree-of-freedom (DOF) kinematically redundant parallel mechanism was proposed based on the well-known Gough–Stewart platform. It was shown that, for the specific architecture proposed, a minimum of three redundant DOFs is necessary to guarantee the existence of a non-singular configuration for any pose of the platform. This work presents a different architecture with two redundant DOFs instead of three, and has for primary objective to derive the singularity locus for zero-torsion configurations. The results indicate that the mathematically possible singularities are outside of the reachable workspace, suggesting that for zero-torsion trajectories, two kinematically redundant DOFs are sufficient to greatly enhance the orientational workspace of the proposed architecture. An example path with large tilting angle is presented in a multimedia extension of the article in order to demonstrate the capability of the mechanism to reach such orientations without encountering inevitable singularities.
•Linear decomposition of Jacobian matrix determinant leads to system of equations.•The singularity locus was partitioned into two sub-types of singular configurations.•The use of the resultant of polynomials leads to the expressions of singularity.•The singular configurations found were shown to be mechanically unreachable.•The results refer to zero-torsion configurations of the platform.