Abstract
Abstract The type/number of operation modes of a parallel manipulator (PM) may vary with the link parameters of the PM. This paper presents a systematic classification of a 3-RER PM based on the type/number of operation modes. Here, R and E denote revolute joint and planar joint, respectively. The 3-RER PM was proposed as a 4-degree-of-freedom (DOF) 3T1R PM in the literature. Using the proposed method, classification of a PM based on the type/number of operation modes can be carried out in four steps, including formulation of constraint equations of the PM, preliminary classification of the PM using Gröbner cover, operation mode analysis of all the types of PMs using primary decomposition of ideals, and identification of redundant types of PMs. The classification of the 3-RER PM shows that it has 13 types. Besides the two 4-DOF 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. Motion characteristics of the moving platform of 3-RER PMs are also identified using Euler parameter quaternions. This work is the first systematic study on the impact of link parameters on the operation modes of the 3-RER PM and provides a solid foundation for further research on the design and control of 3-RER PMs and other multi-mode (or reconfigurable) PMs.
Highlights
The impacts of link parameters on the degree of characteristic univariate polynomial equations for the forward kinematics of parallel manipulators (PMs) have been well studied
Considering the scale of parametric polynomial systems that the current algorithms [13–15] can solve, this paper is to investigate the classification of a 3-RER PM, which was originally proposed as a 3T1R PM [17–19]
The 3-RER PM has been classified into 13 types using the Gröbner cover and primary decomposition of ideals
Summary
The impacts of link parameters on the degree of characteristic univariate polynomial equations for the forward kinematics of parallel manipulators (PMs) have been well studied (see for instance Refs. [1–4]). It has been shown [5–7] that the type/ number of operation modes of a PM may vary with the link parameters of the PM. And throughout this paper, R, P, U, and E denote revolute joint, prismatic joint, universal joint, and planar joint, respectively Both the 4-UPU PM with congruent square base and platform [6] and the 3-RER PM with congruent triangular base and platform [7] have two types of 4-DOF operation modes. The advances in computing CGS or Gröbner cover of parametric polynomial systems provide an efficient tool for the classification of the above 3-RER PM.
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