TY - JOUR
T1 - Classification of 3-Degree-of-Freedom 3-UPU Translational Parallel Mechanisms Based on Constraint Singularity Loci Using Grobner
̈ Cover
AU - Kong, Xianwen
N1 - Funding Information:
The author would like to thank the Engineering and Physical Sciences Research Council (EPSRC), United Kingdom, for the support (Grant No. EP/T024844/1). For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence (where permitted by UKRI, “Open Government Licence” or “Creative Commons Attribution No-derivatives (CC BY-ND) licence” may be stated instead) to any Author Accepted Manuscript version arising.
Publisher Copyright:
Copyright © 2022 by ASME.
PY - 2022/8
Y1 - 2022/8
N2 - A 3-degree-of-freedom (DOF) 3-UPU translational parallel mechanism (TPM) is one of the typical TPMs. Despite comprehensive studies on 3-UPU TPMs in which the joint axes on the base and the moving platform are coplanar, only a few 3-UPU TPMs with skewed base and moving platform have been proposed, and the impact of link parameters on constraint singularity loci of such TPMs has not been systematically investigated. The advances in computing comprehensive Gröbner system (CGS) or Gröbner cover of parametric polynomial systems provide an efficient tool for solving this problem. This paper presents a systematic classification of 3-UPU TPMs with skewed base and moving platform based on constraint singularity loci. First, the constraint singularity equation of a 3-UPU TPM is derived. Using Gröbner cover, the 3-UPU TPMs are classified into 12 types. Finally, a novel 3-UPU TPM is proposed. Reconfiguration analysis shows that unlike most existing 3-UPU TPMs which can transit from a 3-DOF translational mode to two or more 3-DOF operation modes, the proposed 3-UPU TPM can only transit from a 3-DOF translational mode to one general 3-DOF operation mode. The singularity locus divides the workspace of this 3-UPU TPM into two constraint singularity-free regions. As a by-product, a 3-UPU parallel mechanism that the moving platform can undergo 3-DOF translation and 1-DOF infinitesimal rotation is revealed. This work provides a solid foundation for the design of 3-UPU TPMs and a starting point for the classification of 3-UPU parallel mechanisms.
AB - A 3-degree-of-freedom (DOF) 3-UPU translational parallel mechanism (TPM) is one of the typical TPMs. Despite comprehensive studies on 3-UPU TPMs in which the joint axes on the base and the moving platform are coplanar, only a few 3-UPU TPMs with skewed base and moving platform have been proposed, and the impact of link parameters on constraint singularity loci of such TPMs has not been systematically investigated. The advances in computing comprehensive Gröbner system (CGS) or Gröbner cover of parametric polynomial systems provide an efficient tool for solving this problem. This paper presents a systematic classification of 3-UPU TPMs with skewed base and moving platform based on constraint singularity loci. First, the constraint singularity equation of a 3-UPU TPM is derived. Using Gröbner cover, the 3-UPU TPMs are classified into 12 types. Finally, a novel 3-UPU TPM is proposed. Reconfiguration analysis shows that unlike most existing 3-UPU TPMs which can transit from a 3-DOF translational mode to two or more 3-DOF operation modes, the proposed 3-UPU TPM can only transit from a 3-DOF translational mode to one general 3-DOF operation mode. The singularity locus divides the workspace of this 3-UPU TPM into two constraint singularity-free regions. As a by-product, a 3-UPU parallel mechanism that the moving platform can undergo 3-DOF translation and 1-DOF infinitesimal rotation is revealed. This work provides a solid foundation for the design of 3-UPU TPMs and a starting point for the classification of 3-UPU parallel mechanisms.
KW - Gröbner cover
KW - constraint singularity
KW - operation mode
KW - parallel mechanism
KW - reconfiguration analysis
KW - theoretical kinematics
KW - translational parallel mechanism
UR - http://www.scopus.com/inward/record.url?scp=85140301096&partnerID=8YFLogxK
U2 - 10.1115/1.4054307
DO - 10.1115/1.4054307
M3 - Article
SN - 1942-4302
VL - 14
JO - Journal of Mechanisms and Robotics
JF - Journal of Mechanisms and Robotics
IS - 4
M1 - 041010
ER -