SINGULAB - A Graphical user Interface for the Singularity Analysis of Parallel Robots based on Grassmann-Cayley Algebra

This paper presents SinguLab, a graphical user interface for the singularity analysis of parallel robots. The algorithm is based on Grassmann-Cayley algebra. The proposed tool is interactive and introduces the designer to the singularity analysis performed by this method, showing all the stages along the procedure and eventually showing the solution algebraically and graphically, allowing as well the singularity verification of different robot poses.Comment: Advances in Robot Kinematics, Batz sur Mer : France (2008

Geometric Construction-Based Realization of Spatial Elastic Behaviors in Parallel and Serial Manipulators

This paper addresses the realization of spatial elastic behavior with a parallel or a serial manipulator. Necessary and sufficient conditions for a manipulator (either parallel or serial) to realize a specific elastic behavior are presented and interpreted in terms of the manipulator geometry. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. New construction-based synthesis procedures for spatial elastic behaviors are developed. With these synthesis procedures, one can select each elastic component of a parallel (or serial) mechanism based on the geometry of a restricted space of allowable candidates. With each elastic component selected, the space of allowable candidates is further restricted. For each stage of the selection process, the geometry of the remaining allowable space is described

Singularity Analysis of Limited-dof Parallel Manipulators using Grassmann-Cayley Algebra

This paper characterizes geometrically the singularities of limited DOF parallel manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vector of lines (finite and infinite) constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra. Manipulators under consideration do not need to have a passive spherical joint somewhere in each leg. This study is illustrated with three example robot

Increase of Singularity-Free Zones in the Workspace of Parallel Manipulators Using Mechanisms of Variable Structure

International audienceThis paper is focused on the study of singularity of planar parallel manipulators taking into account the force transmission, i.e. study of singularity of planar manipulator by introducing the force transmission factor. Thus the singularity zones in the workspace of the manipulator are defined not only by kinematic criterions from the theoretical perfect model of the manipulator but also by the quality of force transmission. For this purpose, the pressure angle is used as an indicator of force transmission. The optimal control of the pressure angle for a given trajectory of the manipulator is realized by means of legs with variable structure. The suggested procedure to determination of the optimal structure of the planar parallel manipulator 3-RPR is illustrated by two numerical simulations

Type synthesis of 6-DOF mobile parallel link mechanisms based on screw theory

Mobile parallel mechanisms (MPMs), which are parallel mechanisms with moveable bases, have previously been proposed to resolve the limited workspace of conventional parallel mechanisms. However, most previous studies on the subject focused on the kinematic analysis of some specific MPMs and did not discuss a type synthesis method for MPMs. With this in mind, we propose a screw theory-based type synthesis method to find out possible 6-degrees-of-freedom (DOF) MPM structures. In our proposed method, the 6-DOF mobility is divided into 3-DOF planar motion and 3-DOF spatial motion, both of which are realized by the transmitted planar motions of the driving units. Separately, the type synthesis of the entire MPM is divided into that of the driving unit and connecting chain. To realize 3-DOF spatial motion, two methods, applying singularity configuration and adding an additional chain, are proposed as ways to restrict undesired motions for the synthesis of the connecting chain. The driving unit is synthesized via the same type-synthesis method as the connecting chain by considering the driving unit as a planar mechanism. The method used to integrate the driving unit and the connecting chain was constructed based on whether the end pair of the connecting chain should be connected with the driving unit directly or driven by it through an actuating mechanism. As a result, 284 possible types of MPM structure are suggested and four examples of MPMs with six DOFs were synthesized to verify the feasibility of the proposed method