Analysing the singularities of 6-SPS parallel robots using virtual legs

A virtual leg in a 6-SPS parallel robot is defined as a leg whose length is determined by the lengths of a subset of the actual legs of the robot. This necessarily implies that this subset of legs defines a rigid subassembly. In this paper, we consider four different rigid subassemblies, and show how the singularities of a robot containing one or several of these subassemblies are modified when substituting its actual legs by virtual legs.Peer Reviewe

New geometric approaches to the singularity analysis of parallel platforms

In general, rearranging the legs of a Stewart- Gough platform, i.e., changing the locations of its leg attachments, modifies the platform singularity locus in a rather unexpected way. Nevertheless, some leg rearrangements have been recently found to leave singularities invariant. In this work, a summary of the some of such singularity-invariant leg rearrangements are presented, and their practical consequences are illustrated with several examples including well-known architectures.Postprint (author’s final draft

Yet another approach to the Gough-Stewart platform forward kinematics

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The forward kinematics of the Gough-Stewart platform, and their simplified versions in which some leg endpoints coalesce, has been typically solved using variable elimination methods. In this paper, we cast doubts on whether this is the easiest way to solve the problem. We will see how the indirect approach in which the length of some extra virtual legs is first computed leads to important simplifications. In particular, we provide a procedure to solve 30 out of 34 possible topologies for a Gough-Stewart platform without variable elimination.Peer ReviewedPostprint (author's final draft

Optimal design of a 6-DOF 4-4 parallel manipulator with uncoupled singularities

A 6-DOF 4-4 parallel manipulator is presented. Its forward kinematics can be solved by a sequence of three trilaterations and, as a consequence, its singularities can be described in geometric terms as the degeneration of three tetrahedra. Moreover, it is shown how the proposed manipulator belongs to the family of flagged parallel manipulators. This identification is useful because the topology of the singularity locus of flagged manipulators has been fully characterized and, what is more important, the singularities of flagged manipulators correspond to uncoupled translations and/or rotations in the workspace of the manipulator. An optimization of its workspace is carried out using Sequential Quadratic Programming and a virtual prototype of the optimal result has been implemented in SolidWorks.Peer Reviewe

Singularity-invariant leg rearrangements in Stewart-Gough platforms

Postprint (author’s final draft

New geometric approaches to the singularity analysis of parallel platforms

Presentado al Workshop de Robótica Experimental celebrado en Sevilla del 28 al 29 de noviembre de 2011.In general, rearranging the legs of a Stewart-Gough platform, i.e., changing the locations of its leg attachments, modifies the platform singularity locus in a rather unexpected way. Nevertheless, some leg rearrangements have been recently found to leave singularities invariant. In this work, a summary of the some of such singularity-invariant leg rearrangements are presented, and their practical consequences are illustrated with several examples including well-known architectures.Peer Reviewe

New geometric approaches to the analysis and design of Stewart-Gough platforms

In general, rearranging the legs of a Stewart-Gough platform, i.e., changing the locations of its leg attachments, modifies the platform singularity locus in a rather unexpected way. Nevertheless, some leg rearrangements have been recently found to leave singularities invariant. Identification of such rearrangements is useful not only for the kinematic analysis of the platforms, but also as a tool to redesign manipulators avoiding the implementation of multiple spherical joints, which are difficult to construct and have a small motion range. In this study, a summary of these singularity-invariant leg rearrangements is presented, and their practical implications are illustrated with several examples including well-known architectures.The authors gratefully acknowledge funding from the Generalitat de Catalunya through the Robotics group (SRG0155).Peer Reviewe

Kinematics analysis of 6-DOF parallel micro-manipulators with offset u-joints : a case study

This paper analyses the kinematics of a special 6-DOF parallel micro-manipulator with offset RR-joint configuration. Kinematics equations are derived and numerical methodologies to solve the inverse and forward kinematics are presented. The inverse and forward kinematics of such robots compared with those of 6-UCU parallel robots are more complicated due to the existence of offsets between joints of RR-pairs. The characteristics of RR-pairs used in this manipulator are investigated and kinematics constraints of these offset U-joints are mathematically explained in order to find the best initial guesses for the numerical solution. Both inverse and forward kinematics of the case study 6-DOF parallel micro-manipulator are modelled and computational analyses are performed to numerically verify accuracy and effectiveness of the proposed methodologies