Singularity Analysis of Limited-dof Parallel Manipulators using Grassmann-Cayley Algebra

This paper characterizes geometrically the singularities of limited DOF parallel manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vector of lines (finite and infinite) constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra. Manipulators under consideration do not need to have a passive spherical joint somewhere in each leg. This study is illustrated with three example robot

Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann-Cayley Algebra

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower-mobility parallel manipulators and parallel manipulators, of which some legs do not have any spherical joint, are such manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley Algebra. Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators

Synthesizing Parallel Flexures That Mimic the Kinematics of Serial Flexures Using Freedom and Constraint Topologies

The principles of the freedom and constraint topologies (FACT) synthesis approach are adapted and applied to the design of parallel flexure systems that mimic degrees of freedom (DOFs) primarily achievable by serial flexure systems. FACT provides designers with a comprehensive library of geometric shapes. These shapes enable designers to visualize the regions wherein compliant flexure elements may be placed for achieving desired DOFs. By displacing these shapes far from the point of interest of the stage of a flexure system, designers can compare a multiplicity of concepts that utilizes the advantages of both parallel and serial systems. A complete list of which FACT shapes mimic which DOFs when displaced far from the point of interest of the flexure system's stage is provided as well as an intuitive approach for verifying the completeness of this list. The proposed work intends to cater to the design of precision motion stages, optical mounts, microscopy stages, and general purpose flexure bearings. Two case studies are provided to demonstrate the application of the developed procedure

Design of flexure-based motion stages for mechatronic systems via FACT

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 191-195).The aim of this thesis is to generate the knowledge required to (i) synthesize serial flexure systems and (ii) optimally place actuators using a comprehensive library of geometric shapes called freedom, actuation, and constraint spaces. These geometric shapes guide designers through the creative process of concept generation without compromising engineering rigor. Each shape rapidly conveys the mathematics of screw theory, projective geometry, and constraint-based design by visually depicting regions where constraints and actuators may be placed for synthesizing optimal flexure concepts. In this way, designers may consider every flexure concept that satisfies the desired functional requirements before selecting the final design. FACT was created to improve the design processes for small-scale flexure systems and precision machines. For instance, there is a need to create multi-axis nanopositioners for emerging three-dimensional nano-scale research/manufacturing. Through this work the following contributions were made: (1) the fifty freedom and constraint space types were found that may be used to synthesize both parallel and serial flexure concepts, (2) intermediate freedom spaces were created that help designers stack conjugated flexure elements to avoid or utilize underconstraint, (3) a twist-wrench stiffness matrix was created to model the elastomechanic behavior of flexure systems, (4) the twenty-six actuation spaces were found that help guide designers in placing actuators that minimize motion errors, and (5) a theory was created that determines the force and displacement actuator outputs for accessing a desired DOF once actuators have been placed. A serially conjugated lead screw flexure was designed using the FACT design process and a parallel flexure system was built to validate the theory of actuation described in this thesis.by Jonathan Brigham Hopkins.Ph.D

Contribution à l'étude cinématique et dynamique des machines parallèles

This thesis deals with the kinematic and dynamic modelling of limited degree-of-freedom parallel robots. These robots with less than six degrees of freedom are able to carry out several industrial tasks. The main reason of using such robots is to reduce the production costs by using less legs and motors. However, in some cases, these structures can produce a complex motion defined as a simultaneous combination of translation and rotation of the moving platform, which is the case of the Verne parallel module having three translation degrees of freedom. The modelling of this type of robots can prove to be complicated. This report includes five chapters. In the first chapter, a classification of parallel architectures is presented and a state of the art on important notions on kinematics and design of manipulators is exposed. The second and the third chapters are devoted to the kinematic modelling, serial singularity analysis and workspace calculation of the Verne machine. The fourth chapter deals with parallel singularity analysis of limited degrees of freedom robots using Grassmann-Cayley algebra. The geometrical conditions of existence of parallel singularities of three classes of parallel manipulators are found. Finally, the fifth chapter covers the dynamic modelling of limited degree-of-freedom parallel manipulators. A general method based on the Newton-Euler algorithm is developed. The proposed method takes in consideration all the dynamics of these robots including the legs dynamics as well as the mobile platform dynamics.Les travaux présentés dans cette thèse portent sur l’étude cinématique et dynamique des robots parallèles à mobilités restreintes. Ces robots à moins de 6 degrés de liberté permettent d’effectuer de multiples tâches demandées par l’industrie. La raison principale de l’utilisation de ces robots est la volonté de réduire le coût en utilisant moins de jambes et moins de moteurs. Cependant, ces structures peuvent dans certains cas produire un mouvement de la plate-forme contraint par un couplage entre la position et l’orientation comme pour le module parallèle de la machine Verne ayant trois degrés de liberté de translation. Dans ce cas, la modélisation peut s’avérer compliquée. Ce mémoire comporte cinq chapitres. Dans le premier chapitre, une classification des architectures parallèles est présentée et des notions importantes liées à la cinématique et à la conception des manipulateurs sont exposées. Les deuxième et troisième chapitres sont consacrés à la modélisation géométrique, à l’étude des singularités sérielles et au calcul de l’espace de travail de la machine Verne. Le quatrième chapitre traite les singularités parallèles des manipulateurs à mobilités restreintes en utilisant l’algèbre de Grassmann-Cayley. Les conditions géométriques d’existence des singularités pour trois classes de manipulateurs sont trouvées. Les chaînes de ces manipulateurs transmettent des forces et/ou couples à la plate-forme mobile. Finalement, le cinquième chapitre concerne la modélisation dynamique des manipulateurs à mobilités restreintes. Une méthode générale basée sur les algorithmes de type Newton-Euler est développée. La méthode proposée prend en compte la dynamique des jambes et de la plate-forme. Nous obtenons ainsi des modèles dynamiques complets de ces robots

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

Terza giornata di studio Ettore Funaioli: 16 luglio 2009

In questo volume sono raccolte le memorie presentate in occasione della “Terza giornata di studio Ettore Funaioli”, che si è tenuta il 16 luglio 2009 presso la Facoltà di Ingegneria dell’Alma Mater Studiorum – Università di Bologna. La giornata è stata organizzata dagli ex allievi del prof. Funaioli con la collaborazione del DIEM, Dipartimento di Ingegneria delle Costruzioni Meccaniche, Nucleari, Aeronautiche e di Metallurgia dell’Alma Mater Studiorum – Università di Bologna, con il patrocinio del GMA – Gruppo di Meccanica Applicata

Terza giornata di studio Ettore Funaioli: 16 luglio 2009

In questo volume sono raccolte le memorie presentate in occasione della “Terza giornata di studio Ettore Funaioli”, che si è tenuta il 16 luglio 2009 presso la Facoltà di Ingegneria dell’Alma Mater Studiorum – Università di Bologna. La giornata è stata organizzata dagli ex allievi del prof. Funaioli con la collaborazione del DIEM, Dipartimento di Ingegneria delle Costruzioni Meccaniche, Nucleari, Aeronautiche e di Metallurgia dell’Alma Mater Studiorum – Università di Bologna, con il patrocinio del GMA – Gruppo di Meccanica Applicata