A design oriented study for 3R Orthogonal Manipulators With Geometric Simplifications

This paper proposes a method to calculate the largest Regular Dextrous Workspace (RDW) of some types of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. Then a new performance index based on the RDW is introduced, the isocontours of this index are plotted in the parameter space of the interesting types of manipulators and finally an inspection of the domains of the parameter spaces is conducted in order to identify the better manipulator architectures. The RDW is a part of the workspace whose shape is regular (cube, cylinder) and the performances (conditioning index) are bounded inside. The groups of 3R orthogonal manipulators studied have interesting kinematic properties such as, a well-connected workspace that is fully reachable with four inverse kinematic solutions and that does not contain any void. This study is of high interest for the design of alternative manipulator geometries

An Algorithm for Computing Cusp Points in the Joint Space of 3-RPR Parallel Manipulators

This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the manipulators. The nonsingular change of assembly mode of 3-RPR parallel manipulators was shown to be associated with the existence of cusp points. At each of these points, three direct kinematic solutions coincide. In the literature, a condition for the existence of three coincident direct kinematic solutions was established, but has never been exploited, because the algebra involved was too complicated to be solved. The algorithm presented in this paper solves this equation and detects all the cusp points in the joint space of these manipulators

An Exhaustive Study of the Workspaces Tolopogies of all 3R Orthogonal Manipulators with Geometric Simplifications

International audienceThis paper proposes a classification of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The manipulators are classified into different types with similar kinematic properties. Each type is evaluated according to interesting kinematic properties such as, whether the workspace is fully reachable with four inverse kinematic solutions or not, the existence of voids, and the feasibility of continuous trajectories in the workspace. It is found that several orthogonal manipulators have a "well-connected" workspace, that is, their workspace is fully accessible with four inverse kinematic solutions and any continuous trajectory is feasible. This result is of interest for the design of alternative manipulator geometries

Degeneracy study of the forward kinematics of planar 3-RPR parallel manipulators

This paper investigates two situations in which the forward kinematics of planar 3-RPR parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables r1, r2 and r3 satisfy a certain relationship. This degeneracy yields a double root of the characteristic polynomial in t, which could be erroneously interpreted as two coalesce assembly modes. But, unlike what arises in non-degenerate cases, this double root yields two sets of solutions for the position coordinates (x, y) of the platform. In the second situation, we show that the forward kinematics degenerates over the whole joint space if the base and platform triangles are congruent and the platform triangle is rotated by 180 deg about one of its sides. For these "degenerate" manipulators, which are defined here for the first time, the forward kinematics is reduced to the solution of a 3rd-degree polynomial and a quadratics in sequence. Such manipulators constitute, in turn, a new family of analytic planar manipulators that would be more suitable for industrial applications

An Exhaustive Study of the Workspace Topologies of all 3R Orthogonal Manipulators with Geometric Simplifications

International audienceThis paper analyses the workspace of the three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. These manipulators are classified into different groups with similar kinematic properties. The classification criteria are based on the topology of the workspace. Each group is evaluated according to interesting kinematic properties such as the size of the workspace subregion reachable with four inverse kinematic solutions, the existence and the size of voids, and the size of the regions of feasible paths in the workspace

Singularity Surfaces and Maximal Singularity-Free Boxes in the Joint Space of Planar 3-RPR Parallel Manipulators

In this paper, a method to compute joint space singularity surfaces of 3-RPR planar parallel manipulators is first presented. Then, a procedure to determine maximal joint space singularity-free boxes is introduced. Numerical examples are given in order to illustrate graphically the results. This study is of high interest for planning trajectories in the joint space of 3-RPR parallel manipulators and for manipulators design as it may constitute a tool for choosing appropriate joint limits and thus for sizing the link lengths of the manipulator

Analyse cinématique des manipulateurs sériels 3R orthogonaux et des manipulateurs parallèles plan

The variety of tasks in industry necessitates implementation of new manipulators. A behaviour analysis of thesemanipulators is necessary to compare their performances. The work presented in this thesis deals with the studyof kinematical properties and of the performances comparison of two types of manipulators: 3-revolute (3R)serial orthogonal manipulators and 3-RPR planar parallel manipulators. First, a state of the art on importantnotions on kinematics and design of manipulators is presented. Then, in the 2nd section of this thesis, anexhaustive classification of 3R serial orthogonal manipulators with geometric simplifications is established. Theclassification criterion is the singularities topology in the workspace. Twenty-two different manipulators typesare found. In the 3rd section, the twenty-two types are compared first according to the topology of theirworkspace, then according to a new performance index that we have introduced. In the 4th section, thesingularities in the joint space of 3-RPR planar parallel manipulators are determined and analysed. An algorithmfor the detection of cusp points is established. In the 5th section, two new forward kinematics degeneracyconditions for these manipulators are found. A new class of these manipulators is discovered: the degeneratemanipulators. These degenerate manipulators have always a degenerate forward kinematic model and interestingkinematic properties. Finally, two methods for avoiding the singularities of the 3-RPR parallel manipulators areproposed: the planning of non singular assembly mode changing trajectories and the determination of maximalsingularity free regions in the workspace and in the joint space of these manipulators. Results presented in thisthesis can serve as an efficient help tool for the design of new manipulators.Mots-clés : Serial orthogonal manipulator, planar parallel manipulator, singularitiesLa diversité des tâches dans l’industrie entraîne un besoin de mise en place de nouveaux manipulateurs. Uneanalyse de comportement de ces manipulateurs est nécessaire afin de comparer leurs performances. Les travauxprésentés dans cette thèse portent sur l’étude cinématique et la comparaison de performances de deux types demanipulateurs : les manipulateurs 3R sériels à axes orthogonaux et les manipulateurs 3-RPR parallèles plans.Tout d’abord des notions importantes liées à la cinématique et à la conception de manipulateurs sont présentées.Dans la 2ème partie de cette thèse, une classification exhaustive des manipulateurs 3R sériels orthogonauxparticuliers est établie. Le critère de classification est la topologie des singularités dans l’espace de travail (E.T).Vingt deux types différents de manipulateurs sont trouvés. Dans la 3ème partie, les vingt deux types sontcomparés tout d’abord suivant la topologie de leur E.T, ensuite suivant un nouvel indice de performance. Lesmanipulateurs les plus performants sont mis en évidence. Dans la 4ème partie, les singularités dans l’espacearticulaire des manipulateurs 3-RPR parallèles plans sont déterminées et analysées. Un algorithme pour le calculdes points cusp est établi. Dans la 5ème partie, deux nouvelles conditions de dégénérescence du modèlegéométrique direct (MGD) des ces mêmes manipulateurs sont établies. Une nouvelle classe de ces manipulateursa été découverte : les manipulateurs dégénérés. Ces manipulateurs ont leur MGD toujours dégénéré et despropriétés cinématiques intéressantes. Enfin, deux méthodes pour éviter les singularités de ces manipulateurssont proposées : la planification de trajectoires non singulières de changement de mode d’assemblage, larecherche de zones non singulières dans les espaces de travail et articulaire. Les résultats présentés dans cetravail constituent un outil intéressant d’aide à la conception de nouveaux manipulateurs

Analyse cinématique des manipulateurs sériels 3R orthogonaux et des manipulateurs parallèles plans

La diversité des tâches dans l industrie entraîne un besoin de mise en place de nouveaux manipulateurs. Une analyse de comportement de ces manipulateurs est nécessaire afin de comparer leurs performances. Les travaux présentés dans cette thèse portent sur l étude cinématique et la comparaison de performances de deux types de manipulateurs: les manipulateurs 3R sériels à axes orthogonaux et les manipulateurs 3-RPR parallèles plans. Tout d abord des notions importantes liées à la cinématique et à la conception de manipulateurs sont présente es. Dans la 2ème partie de cette thèse, une classification exhaustive des manipulateurs 3R sériels orthogonaux particuliers est établie. Le critère de classification est la topologie des singularités dans l espace de travail (E.T). Vingt deux types différents de manipulateurs sont trouvés. Dans la 3ème partie, les vingt deux types sont comparés tout d abord suivant la topologie de leur E.T, ensuite suivant un nouvel indice de performance. Les manipulateurs les plus performants sont mis en évidence. Dans la 4ème partie, les singularités dans l espace articulaire des manipulateurs 3-RPR parallèles plans sont déterminées et analysées. Un algorithme pour le calcul des points cusp est établi. Dans la 5ème partie, deux nouvelles conditions de dégénérescence du modèle géométrique direct (MGD) des ces mêmes manipulateurs sont établies. Une nouvelle classe de ces manipulateurs a été découverte: les manipulateurs dégénérés. Ces manipulateurs ont leur MGD toujours dégénéré et des propriétés cinématiques intéressantes. Enfin, deux méthodes pour éviter les singularités de ces manipulateurs sont proposées: la planification de trajectoires non singulières de changement de mode d assemblage, la recherche de zones non singulières dans les espaces de travail et articulaire. Les résultats présentés dans ce travail constituent un outil intéressant d aide à la conception de nouveaux manipulateurs.The variety of tasks in industry necessitates implementation of new manipulators. A behaviour analysis of these manipulators is necessary to compare their performances. The work presented in this thesis deals with the study of kinematical properties and of the performances comparison of two types of manipulators: 3-revolute (3R) serial orthogonal manipulators and 3-RPR planar parallel manipulators. First, a state of the art on important notions on kinematics and design of manipulators is presented. Then, in the 2nd section of this thesis, an exhaustive classification of 3R serial orthogonal manipulators with geometric simplifications is established. The classification criterion is the singularities topology in the workspace. Twenty-two different manipulators types are found. In the 3rd section, the twenty-two types are compared first according to the topology of their workspace, then according to a new performance index that we have introduced. In the 4th section, the singularities in the joint space of 3-RPR planar parallel manipulators are determined and analysed. An algorithm for the detection of cusp points is established. In the 5th section, two new forward kinematics degeneracy conditions for these manipulators are found. A new class of these manipulators is discovered: the degenerate manipulators. These degenerate manipulators have always a degenerate forward kinematic model and interesting kinematic properties. Finally, two methods for avoiding the singularities of the 3-RPR parallel manipulators are proposed: the planning of non singular assembly mode changing trajectories and the determination of maximal singularity free regions in the workspace and in the joint space of these manipulators. Results presented in this thesis can serve as an efficient help tool for the design of new manipulators.NANTES-BU Sciences (441092104) / SudocNANTES-Ecole Centrale (441092306) / SudocSudocFranceF