Reconfiguration analysis of a 4-RUU parallel manipulator

Abstract

This paper deals with the characterization of the operation modes of the 4-RUU parallel manipulator with an algebraic approach, namely the Study's kinematic mapping of the Euclidean group SE(3). As the 4-RUU parallel manipulator is an over-constrained manipulator, it can be decomposed into two 2-RUU parallel manipulators. The manipulators are described by a set of constraint equations and the primary decomposition is computed. By combining the results of primary decomposition from two 2-RUU parallel manipulators, it reveals that the 4-RUU parallel manipulator has two Schönflies modes (4-dof) and one lower dimension operation mode (2-dof). The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the constraint equations with respect to the Study parameters in each operation mode. It is shown that there exist singular configurations in which the manipulators may switch from one operation mode to another operation mode. All the singular configurations are mapped onto the joint space, i.e., the actuated joint angles, and are geometrically interpreted. Eventually, the 4-RUU parallel manipulator may switch from the 1st Schönflies mode to the 2nd Schönflies mode, or vice versa, via the 2-dof third mode that contains self-motions.

Kinematics, Workspace, and Singularity Analysis of a Parallel Robot With Five Operation Modes

“…This feature can justify the additional brakes requested to change operation mode by increasing the reachable workspace of one operation mode. This work, together with the literature on the reconfiguration analysis of multi-mode parallel mechanisms [15,[20][21][22][23], provide a comprehensive framework for the analysis of multi-mode parallel robots.…”

“…References [14,15] show 4-DOF 3T1R PMs that have an extra 2-DOF or 3-DOF motion mode in addition to the required 4-DOF 3T1R motion mode. It is noted the metamorphic PMs based on reconfigurable U (universal) or S (spherical) joints [16,17] and the multi-mode PMs with lockable joints [18,19] are in fact kinematically redundant PMs in nature and do not belong to multi-mode PMs that this paper focuses on.…”

“…It is noted the metamorphic PMs based on reconfigurable U (universal) or S (spherical) joints [16,17] and the multi-mode PMs with lockable joints [18,19] are in fact kinematically redundant PMs in nature and do not belong to multi-mode PMs that this paper focuses on. In addition, several methods have been proposed [14,15,[19][20][21][22][23][24][25] to the reconfiguration analysis of multi-mode PMs for identifying all the operation modes and the transition configurations of a PM. However, only a few multi-mode PMs, such as the PM with two 1T1R operation modes used as a novel swivel head for machine tools [2], have been put into use in practice.…”

Algebraic Analysis of a 3-RUU Parallel Manipulator

“…In the foregoing papers, the prismatic joints were considered to be actuated, which makes the analysis inherently algebraic. A more challenging kinematic analysis of an over-constrained 4-RUU PM with square base and moving platform was accomplished by decomposing it into two 2-RUU PMs [7]. The constraint equations of a 3-RUU PM are derived in this paper and its direct kinematics problem is solved.…”

Análisis Cinemático del Manipulador Paralelo 4- P RUR Mediante la Teoría de Tornillos

“…En la literatura se pueden encontrar un amplio número de trabajos dedicados al estudio de manipuladores paralelos tipo 3T1R, por ejemplo su destreza y espacio de trabajo (Altuzarra et al, 2011), el análisis de singularidades de un robot paralelo 4-RUU usando geometría de Grassmann (Amine et al, 2012), el análisis directo de posición medianteálgebra de cuaterniones (Masouleh et al, 2011b), diseñoóptimo basado en el desempeño dinámico (Liu et al, 2012), propuestas de robots con redundancia en su actuación Corves et al, 2016), análisis elastodinámico (Alessandro and Rosario, 2014), diseño de robots de alta velocidad rotacional para operaciones pick-and-place (Xie and Liu, 2015) o con un número reducido de extremidades (Angeles et al, 2006a;Kim et al, 2015), topologías reconfigurables (Nurahmi et al, 2016), síntesis de tipo mediante la teoría de tornillos de manipuladores 3R1T (tres rotaciones y una traslación) desacoplados (Cao et al, 2016), análisis del espacio de trabajo y de singularidades basados en la cinemática inversa (Cervantes-Sánchez et al, 2016). Sin embargo, entre los manipuladores paralelos que desarrollan movimiento de Schönflies destaca uno por su particularmente complicada cinemática: el robot paralelo 3T1R (tres traslaciones y una rotación) con extremidades tipo PRUR (cadena cinemática Prismática-Revoluta-Universal-Revoluta).…”