The forward kinematics of doubly-planar Gough-Stewart platforms and the position analysis of strips of tetrahedra

The final publication is available at link.springer.comA strip of tetrahedra is a tetrahedron-tetrahedron truss where any tetrahedron has two neighbors except those in the extremes which have only one. The problem of finding all the possible lengths for an edge in the strip compatible with a given distance imposed between the strip end-points has been revealed of relevance due to the large number of possible applications. In this paper, this is applied to solve the forward kinematics of 6-6 Gough-Stewart platforms with planar base and moving platform, a problem which is known to have up to 40 solutions (20 if we do not consider mirror configurations with respect to the base as different solutions).Peer ReviewedPostprint (author's final draft

Closure polynomials for strips of tetrahedra

The final publication is available at link.springer.comA tetrahedral strip is a tetrahedron-tetrahedron truss where any tetrahedron has two neighbors except those in the extremes which have only one. Unless any of the tetrahedra degenerate, such a truss is rigid. In this case, if the distance between the strip endpoints is imposed, any rod length in the truss is constrained by all the others to attain discrete values. In this paper, it is shown how to characterize these values as the roots of a closure polynomial whose derivation requires surprisingly no other tools than elementary algebraic manipulations. As an application of this result, the forward kinematics of two parallel platforms with closure polynomials of degree 16 and 12 is straightforwardly solved.Peer ReviewedPostprint (author's final draft

Closure polynomials for strips of tetrahedra

The final publication is available at link.springer.comA tetrahedral strip is a tetrahedron-tetrahedron truss where any tetrahedron has two neighbors except those in the extremes which have only one. Unless any of the tetrahedra degenerate, such a truss is rigid. In this case, if the distance between the strip endpoints is imposed, any rod length in the truss is constrained by all the others to attain discrete values. In this paper, it is shown how to characterize these values as the roots of a closure polynomial whose derivation requires surprisingly no other tools than elementary algebraic manipulations. As an application of this result, the forward kinematics of two parallel platforms with closure polynomials of degree 16 and 12 is straightforwardly solved.Peer ReviewedPostprint (author's final draft

Closed-form position analysis of variable geometry trusses

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Variable geometry trusses are composed, in general, of unit cells which can be modeled as bars connected by spherical joints. Under mild conditions, it has been shown that the only feasible cells are topologically equivalent to bipyramids. Unfortunately, using standard formulations, the closed-form position analysis of bipyramids is not a trivial task. Actually, it has only been achieved for bipyramids with up to 7 vertices, whose closure polynomial has been shown to be of order 24. In this paper, using a distance-based formulation and a kinematic inversion for fans of tetrahedra, the problem is solved for bipyramids with up to 11 vertices, whose closure polynomial is of degree 896. No other position analysis problem leading to such a high-order closure polynomial has been previously solved.Peer ReviewedPostprint (author's final draft

Design and implementation of 3-RRR spherical parallel robot with three coaxial actuator

This work, entitled “Design and Implementation of 3-RRR Spherical Parallel Robot with Three Coaxial Actuators” has had the scope to analytically study the kinematics (both inverse and forward one) of a coaxial configuration of a spherical manipulator. The complete 3D design of the robot has been realised, building it thanks to a 3D printing process called FDM Technology (fused deposition modelling). Moreover, it has been modelled a Feed-Forward Position Control in order to move the three electrical motors, in Matlab environment. As for the state of the art, this thesis has distanced itself from the literature before [5, 4, 6, 3], not using a Denavith-Hartenberg’s approach or a loop equation process, in order to describe the kinematics, but investigating on new method, that could be more efficient in a computational terms, and exploiting its peculiar characteristics and functioning. For these reasons, it has been chosen a geometric method [20] to realise the analytical model of the manipulator. This approach has involved only constant and variable distances, relative to a set of fundamental points, after defining the parameters of the robot’s architecture. In the end, these choices, mentioned before, lead to obtain, as a results, a clear simulation of the robot, in order to better manage it and to focus on the core of both the kinematics and implementations, instead of the traditional process to obtain them, already investigated in literatureIncomin

The closure condition of the double banana and its application to robot position analysis

A double banana is defined as the bar-and-joint assembly of two bipyramids joined by their apexes. Clearly, the bar lengths of this kind of assembly are not independent as we cannot assign arbitrary values to them. This dependency can be algebraically expressed as a closure condition fully expressed in terms of bar lengths. This paper is devoted to its derivation and to show how its use simplifies the position analysis of many well-known serial and parallel robots thus providing a unifying treatment to apparently disparate problems. This approach permits deriving the univariate polynomials, needed for the closed-form solution of these position analysis problems, without relying on trigonometric substitutions or difficult variable eliminations

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