A Geometric Constructive Approach for the Workspace Analysis of Symmetrical 5-PRUR Parallel Mechanisms (3T2R)

Abstract

This paper investigates an important kinematic property, the constant-orientation workspace, of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical limbs of the PRUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, the emphasis is placed on the determination of constant-orientation workspace using geometrical interpretation of the so-called vertex space, i.e., motion generated by a limb for a given orientation, rather than relying on classical recipes, such as discretization methods. For the sake of better understanding a CAD model is also provided for the vertex space. The constructive geometric approach presented in this paper provides some insight into the architecture optimization. Moreover, this approach facilitates the computation of the evolution of the volume of the constant-orientation workspace for different orientations of the end-effector.

Singularity analysis of 3T2R parallel mechanisms using Grassmann–Cayley algebra and Grassmann geometry

“…This mechanical simplification leads to a 5-RPUR type mechanism. Further results regarding the kinematic properties such as the solution of the IKP, the FKP and the determination of the constant orientation workspace can be found in [18,19,[31][32][33][34]. It should be noted that the origin of this research work is based on the results obtained for their FKP, with 1680 finite solutions [18], and the constant-orientation workspace where Bohemian domes [46] come up for the vertex space [33].…”

“…Due to the short history of symmetric 5-DOF PMs, more precisely the ones performing a 3T2R motion pattern, their kinematic properties are still not well understood. In some recent studies, the Inverse Kinematic Problem (IKP), Forward Kinematic Problem (FKP), workspace and singularities were investigated [18,19,[31][32][33][34]. The singularities were investigated upon a different perspective based on GG [32].…”

Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles

“…Members of class IV have been found by systematic structural synthesis with screw theory, which has been performed in [31] for symmetric 3T2R mechanisms. The resulting 5RPUR of Figure 1d and 5PRUR are analyzed in [10,32]. In a practical application with competing requirements on workspace, stiffness, costs and precision, each of the existing systems has its legitimization.…”

“…The parallel robots with five DoF presented above have a kinematic structure which allows for an analytic model of the inverse kinematics. All references define the end-effector orientation with two consecutive elementary rotations, i.e., define two Euler angles to represent the tool axis orientation in minimal coordinates [10,13,[19][20][21][22]26,28,32,33], which is called "partial pose" in [13]. The inverse kinematics problem (IKP) is first solved for the first chain, which is called "leading chain" in this paper.…”

Forward kinematic problem of 5-RPUR parallel mechanisms (3T2R) with identical limb structures

“…To the best of the knowledge of the authors, up to now, very few kinematic studies have been conducted on 5-DOF parallel mechanisms with identical limb structures [24][25][26][27][28][29][30]. This is probably due to their short history.…”