Half-turns and line symmetric motions

A line symmetric motion is the motion obtained by reflecting a rigid body in the successive generator lines of a ruled surface. In this work we review the dual quaternion approach to rigid body displacements, in particular the representation of the group SE(3) by the Study quadric. Then some classical work on reflections in lines or half-turns is reviewed. Next two new characterisations of line symmetric motions are presented. These are used to study a number of examples one of which is a novel line symmetric motion given by a rational degree five curve in the Study quadric. The rest of the paper investigates the connection between sets of half-turns and linear subspaces of the Study quadric. Line symmetric motions produced by some degenerate ruled surfaces are shown to be restricted to certain 2-planes in the Study quadric. Reflections in the lines of a linear line complex lie in the intersection of the Study quadric with a 4-plane. © 2010 Elsevier Ltd. All rights reserved

Workspace topologies of industrial 3R manipulators

A mathematical analysis is used to characterize workspace topologies of industrial 3R manipulators. A level-set reconstruction of the workspace is formulated to identify characteristic points with fairly simple algebraic expressions. Thus, industrial 3R manipulators are classified as functions of workspace kinematic properties. Examples are illustrated to show practical usefulness of the proposed workspace characterization

Nonsingular change of assembly mode without any cusp

International audienceThis paper shows for the first time a parallel manipulator that can execute nonsingular changes of assembly modes while its joint space is free of cusp points and cuspidal edges. The manipulator at hand has two degrees of freedom and is derived from a 3-RPR manipulator; the shape of its joint space is a thickening of a figure-eight curve. A few explanations concerning the relationship between cusps and alpha curves are given

Pose, posture, formation and contortion in kinematic systems

The concepts of pose, posture, formation and contortion are defined for serial, parallel and hybrid kinematic systems. Workspace and jointspace structure is examined in terms of these concepts. The inter-relationships of pose, posture, formation and contortion are explored for a range of robot workspace and jointspace types

A fast branch-and-prune algorithm for the position analysis of spherical mechanisms

The final publication is available at link.springer.comDifferent branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.Peer ReviewedPostprint (author's final draft

Improving the forward kinematics of cable-driven parallel robots through cable angle sensors

This paper presents a sensor fusion method that aims at improving the accuracy of cable-driven planar parallel mechanisms (CDPMs) and simplifying the kinematic resolution. While the end-effector pose of the CDPM is usually obtained with the cable lengths, the proposed method combines the cable length measurement with the cable angle by using a data fusion algorithm. This allows for a resolution based on the loop closure equations and a weighted least squares method. The paper first presents the resolution of the forward kinematics for planar parallel mechanisms using cable angle only. Then, the proposed sensor fusion scheme is detailed. Finally, an experiment comparing the different procedures for obtaining the pose of the CDPM is carried out, in order to demonstrate the efficiency of the proposed fusion method

Asymptotic singularities of planar parallel 3-RPR manipulators

We study the limits of singularities of planar parallel 3-RPR manipulators as the lengths of their legs tend to infinity, paying special attention to the presence of cusps. These asymptotic singularities govern the kinematic behavior of the manipulator in a rather large portion of its workspace

Singularity-invariant leg rearrangements in Stewart-Gough platforms

Postprint (author’s final draft