Reconfiguration analysis of a 3-DOF parallel mechanism using Euler parameter quaternions and algebraic geometry method

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel mechanism (PM) with multiple operation modes – a disassembly-free reconfigurable PM – using the Euler parameter quaternions and algebraic geometry approach. At first, Euler parameter quaternions are classified into 15 cases based on the number of constant zero components and the kinematic interpretation of different cases of Euler parameter quaternions is presented. A set of constraint equations of a 3-RER PM with orthogonal platforms is derived with the orientation of the moving platform represented using a Euler parameter quaternion and then solved using the algebraic geometry method. It is found that this 3-RER PM has 15 3-DOF operation modes, including four translational modes, six planar modes, four zero-torsion-rate motion modes and one spherical mode. The transition configurations, which are singular configurations, among different operation modes are also presented. Especially, the transition configurations in which the PM can switch among eight operation modes are revealed for the first time.