TY - GEN
T1 - Classification of a class of 3-rer parallel manipulators using Gröbner cover and primary decomposition of ideals
AU - Kong, Xianwen
PY - 2019/11/25
Y1 - 2019/11/25
N2 - Recent studies have revealed that the type/number of operation modes of a parallel manipulator (PM) may vary with the link parameters of the PM. However, current research on the impact of link parameters on the type/number of operation modes of a PM is usually based on intuition. This paper deals with the systematic classification of a 3-RER PM. The 3-RER PM is composed of a base and a moving platform connected by three RER legs, each of which is a serial kinematic chain composed of a revolute (R) joint, a planar (E) joint and an R joint in sequence. The axes of the R joints on the base (or moving platform) are all parallel. At first, a set of constraint equations of the 3-RER PM is first derived. Then using a method called Gröbner cover to calculate the comprehensive Gröbner system of parametric polynomial systems, the 3-RER PM is classified into 21 types. The operation modes of all the types of 3-RER PMs are determined using primary decomposition of ideals. Besides the two 4-DOF (degree-of-freedom) 3T1R operation modes, different types of 3-RER PMs may have up to two more 3-DOF or other types of 4-DOF operation modes. This work is the first systematic study on the impact of link parameters on the operation modes of the 3-RER PM and will contribute to the design and control of 3-RER PMs and research on multi-mode (or reconfigurable) PMs.
AB - Recent studies have revealed that the type/number of operation modes of a parallel manipulator (PM) may vary with the link parameters of the PM. However, current research on the impact of link parameters on the type/number of operation modes of a PM is usually based on intuition. This paper deals with the systematic classification of a 3-RER PM. The 3-RER PM is composed of a base and a moving platform connected by three RER legs, each of which is a serial kinematic chain composed of a revolute (R) joint, a planar (E) joint and an R joint in sequence. The axes of the R joints on the base (or moving platform) are all parallel. At first, a set of constraint equations of the 3-RER PM is first derived. Then using a method called Gröbner cover to calculate the comprehensive Gröbner system of parametric polynomial systems, the 3-RER PM is classified into 21 types. The operation modes of all the types of 3-RER PMs are determined using primary decomposition of ideals. Besides the two 4-DOF (degree-of-freedom) 3T1R operation modes, different types of 3-RER PMs may have up to two more 3-DOF or other types of 4-DOF operation modes. This work is the first systematic study on the impact of link parameters on the operation modes of the 3-RER PM and will contribute to the design and control of 3-RER PMs and research on multi-mode (or reconfigurable) PMs.
KW - Euler parameters
KW - Gröbner Cover
KW - Multi-mode mechanism
KW - Operation mode
KW - Quaternion
UR - http://www.scopus.com/inward/record.url?scp=85076456638&partnerID=8YFLogxK
U2 - 10.1115/DETC2019-98057
DO - 10.1115/DETC2019-98057
M3 - Conference contribution
AN - SCOPUS:85076456638
T3 - Proceedings of the IDETC/CIE Conferences
BT - 43rd Mechanisms and Robotics Conference
PB - American Society of Mechanical Engineers
T2 - 43rd Mechanisms and Robotics Conference 2019
Y2 - 18 August 2019 through 21 August 2019
ER -