21 research outputs found
Self-motions of pentapods with linear platform
We give a full classification of all pentapods with linear platform
possessing a self-motion beside the trivial rotation about the platform. Recent
research necessitates a contemporary and accurate re-examination of old results
on this topic given by Darboux, Mannheim, Duporcq and Bricard, which also takes
the coincidence of platform anchor points into account. For our study we use
bond theory with respect to a novel kinematic mapping for pentapods with linear
platform, beside the method of singular-invariant leg-rearrangements. Based on
our results we design pentapods with linear platform, which have a simplified
direct kinematics concerning their number of (real) solutions.Comment: 28 pages, 5 figure
Liaison Linkages
The complete classification of hexapods - also known as Stewart Gough
platforms - of mobility one is still open. To tackle this problem, we can
associate to each hexapod of mobility one an algebraic curve, called the
configuration curve. In this paper we establish an upper bound for the degree
of this curve, assuming the hexapod is general enough. Moreover, we provide a
construction of hexapods with curves of maximal degree, which is based on
liaison, a technique used in the theory of algebraic curves.Comment: 40 pages, 6 figure
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
Mobile Icosapods
Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical joints. It is possible to prove that the maximal number of legs of a mobile pod, when finite, is 20. In 1904, Borel designed a technique to construct examples of such 20-pods, but could not constrain the legs to have base and platform points with real coordinates. We show that Borel’s construction yields all mobile 20-pods, and that it is possible to construct examples where all coordinates are real
Advances in Robot Kinematics : Proceedings of the 15th international conference on Advances in Robot Kinematics
International audienceThe motion of mechanisms, kinematics, is one of the most fundamental aspect of robot design, analysis and control but is also relevant to other scientific domains such as biome- chanics, molecular biology, . . . . The series of books on Advances in Robot Kinematics (ARK) report the latest achievement in this field. ARK has a long history as the first book was published in 1991 and since then new issues have been published every 2 years. Each book is the follow-up of a single-track symposium in which the participants exchange their results and opinions in a meeting that bring together the best of world’s researchers and scientists together with young students. Since 1992 the ARK symposia have come under the patronage of the International Federation for the Promotion of Machine Science-IFToMM.This book is the 13th in the series and is the result of peer-review process intended to select the newest and most original achievements in this field. For the first time the articles of this symposium will be published in a green open-access archive to favor free dissemination of the results. However the book will also be o↵ered as a on-demand printed book.The papers proposed in this book show that robot kinematics is an exciting domain with an immense number of research challenges that go well beyond the field of robotics.The last symposium related with this book was organized by the French National Re- search Institute in Computer Science and Control Theory (INRIA) in Grasse, France