CLASSIFICATION OF A CLASS OF 3-RER PARALLEL MANIPULATORS USING GROBNER COVER AND PRIMARY DECOMPOSITION OF IDEALS

ecent studies have revealed that the type/number of operation odes of a parallel manipulator (PM) may vary with the link paameters of the PM. However, current research on the impact of ink parameters on the type/number of operation modes of a PM s usually based on intuition. This paper deals with the systemtic classification of a 3-RER PM. The 3-RER PM is composed "f a base and a moving platform connected by three RER legs, ach of which is a serial kinematic chain composed of a revoute (R) joint, a planar (E) joint and an R joint in sequence. The xes of the R joints on the base (or moving platform) are all parllel. At first, a set of constraint equations of the 3-RER PM s first derived. Then using a method called Grobner cover to alculate the comprehensive Gr6bner system of parametric polyomial systems, the 3-RER PM is classified into 21 types. The peration modes of all the types of 3-RER PMs are determined sing 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 -DOF operation modes. This work is the first systematic study on the impact of link parameters on the operation modes of the 3RER PM and will contribute to the design and control of 3-RER PMs and research on multi -mode (or reconfigurable) PMs.