A network approach to mechanisms and machines: some lessons learned

This is essentially a review paper describing progress made in treating mechanisms and machines as networks. Some of the terminology that is helpful to this approach is explained. Relevant elements of graph theory are mentioned. The original aim was to find a robust procedure for finding the instantaneous relative motion of all pairs of bodies within a kinematic chain. The manner in which this was achieved produced several other results that have found unanticipated applications. These are mentioned and publications are cited. Lessons have been learned and these are discussed in Section 11

A technique based on adaptive extended jacobians for improving the robustness of the inverse numerical kinematics of redundant robots

The extended Jacobian is a technique for solving the redundancy of redundant robots. It is based on the definition of secondary tasks, through constraint functions that are added to the mapping between joint rates and end-effector's twist. Several approaches showed its potential, applications, and limitations. In general, the constraint functions are a linear combination of basic functions with constant coefficients. This paper proposes the use of adaptive coefficients in such functions by using the conditioning index of the extended Jacobian as a quality measure. A good conditioning index of the extended Jacobian keeps the robot far from singularities and contributes to the solution of the inverse kinematics. In this paper, initially, the extended Jacobian and the proposed algorithm are discussed, and then, two tests in different circumstances are presented in order to validate the proposal

Kinematic and dynamic analysis of spatial six degree of freedom parallel structure manipulator

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2003Includes bibliographical references (leaves: 63-69)Text in English; Abstract: Turkish and Englishviii, 86 leavesThis thesis covers a study on kinematic and dynamic analysis of a new type of spatial six degree of freedom parallel manipulator. The background for structural synthesis of parallel manipulators is also given. The structure of the said manipulator is especially designed to cover a larger workspace then well-known Stewart Platform and its derivates. The main point of interest for this manipulator is its hybrid actuating system, consisting of three revolute and three linear actuators.Kinematic analysis comprises forward and inverse displacement analysis. Screw Theory and geometric constraint considerations were the main tools used. While it was possible to derive a closed-form solution for the inverse displacement analysis, a numerical approach was used to solve the problem of forward displacement analysis. Based on the results of the kinematic analysis, a rough workspace study of the manipulator is also accomplished. On the dynamics part, attention has been given on inverse dynamics problem using Lagrange-Euler approach.Both high and lower level software were heavily utilized. Also computer software called .CASSoM. and .iMIDAS. are developed to be used for structural synthesis and inverse displacement analysis. The major contribution of the study to the scientific community is the proposal of a new type of parallel manipulator, which has to be studied extensively regarding its other interesting properties

Distance geometry in active structures

The final publication is available at link.springer.comDistance constraints are an emerging formulation that offers intuitive geometrical interpretation of otherwise complex problems. The formulation can be applied in problems such as position and singularity analysis and path planning of mechanisms and structures. This paper reviews the recent advances in distance geometry, providing a unified view of these apparently disparate problems. This survey reviews algebraic and numerical techniques, and is, to the best of our knowledge, the first attempt to summarize the different approaches relating to distance-based formulations.Peer ReviewedPostprint (author's final draft

Industrial Robotics

This book covers a wide range of topics relating to advanced industrial robotics, sensors and automation technologies. Although being highly technical and complex in nature, the papers presented in this book represent some of the latest cutting edge technologies and advancements in industrial robotics technology. This book covers topics such as networking, properties of manipulators, forward and inverse robot arm kinematics, motion path-planning, machine vision and many other practical topics too numerous to list here. The authors and editor of this book wish to inspire people, especially young ones, to get involved with robotic and mechatronic engineering technology and to develop new and exciting practical applications, perhaps using the ideas and concepts presented herein

Numerical computation and avoidance of manipulator singularities

This thesis develops general solutions to two open problems of robot kinematics: the exhaustive computation of the singularity set of a manipulator, and the synthesis of singularity-free paths between given configurations. Obtaining proper solutions to these problems is crucial, because singularities generally pose problems to the normal operation of a robot and, thus, they should be taken into account before the actual construction of a prototype. The ability to compute the whole singularity set also provides rich information on the global motion capabilities of a manipulator. The projections onto the task and joint spaces delimit the working regions in such spaces, may inform on the various assembly modes of the manipulator, and highlight areas where control or dexterity losses can arise, among other anomalous behaviour. These projections also supply a fair view of the feasible movements of the system, but do not reveal all possible singularity-free motions. Automatic motion planners allowing to circumvent problematic singularities should thus be devised to assist the design and programming stages of a manipulator. The key role played by singular configurations has been thoroughly known for several years, but existing methods for singularity computation or avoidance still concentrate on specific classes of manipulators. The absence of methods able to tackle these problems on a sufficiently large class of manipulators is problematic because it hinders the analysis of more complex manipulators or the development of new robot topologies. A main reason for this absence has been the lack of computational tools suitable to the underlying mathematics that such problems conceal. However, recent advances in the field of numerical methods for polynomial system solving now permit to confront these issues with a very general intention in mind. The purpose of this thesis is to take advantage of this progress and to propose general robust methods for the computation and avoidance of singularities on non-redundant manipulators of arbitrary architecture. Overall, the work seeks to contribute to the general understanding on how the motions of complex multibody systems can be predicted, planned, or controlled in an efficient and reliable way.Aquesta tesi desenvolupa solucions generals per dos problemes oberts de la cinemàtica de robots: el càlcul exhaustiu del conjunt singular d'un manipulador, i la síntesi de camins lliures de singularitats entre configuracions donades. Obtenir solucions adequades per aquests problemes és crucial, ja que les singularitats plantegen problemes al funcionament normal del robot i, per tant, haurien de ser completament identificades abans de la construcció d'un prototipus. La habilitat de computar tot el conjunt singular també proporciona informació rica sobre les capacitats globals de moviment d'un manipulador. Les projeccions cap a l'espai de tasques o d'articulacions delimiten les regions de treball en aquests espais, poden informar sobre les diferents maneres de muntar el manipulador, i remarquen les àrees on poden sorgir pèrdues de control o destresa, entre d'altres comportaments anòmals. Aquestes projeccions també proporcionen una imatge fidel dels moviments factibles del sistema, però no revelen tots els possibles moviments lliures de singularitats. Planificadors de moviment automàtics que permetin evitar les singularitats problemàtiques haurien de ser ideats per tal d'assistir les etapes de disseny i programació d'un manipulador. El paper clau que juguen les configuracions singulars ha estat àmpliament conegut durant anys, però els mètodes existents pel càlcul o evitació de singularitats encara es concentren en classes específiques de manipuladors. L'absència de mètodes capaços de tractar aquests problemes en una classe suficientment gran de manipuladors és problemàtica, ja que dificulta l'anàlisi de manipuladors més complexes o el desenvolupament de noves topologies de robots. Una raó principal d'aquesta absència ha estat la manca d'eines computacionals adequades a les matemàtiques subjacents que aquests problemes amaguen. No obstant, avenços recents en el camp de mètodes numèrics per la solució de sistemes polinòmics permeten ara enfrontar-se a aquests temes amb una intenció molt general en ment. El propòsit d'aquesta tesi és aprofitar aquest progrés i proposar mètodes robustos i generals pel càlcul i evitació de singularitats per manipuladors no redundants d'arquitectura arbitrària. En global, el treball busca contribuir a la comprensió general sobre com els moviments de sistemes multicos complexos es poden predir, planificar o controlar d'una manera eficient i segur

Inverse Kinematic Analysis of Robot Manipulators

An important part of industrial robot manipulators is to achieve desired position and orientation of end effector or tool so as to complete the pre-specified task. To achieve the above stated goal one should have the sound knowledge of inverse kinematic problem. The problem of getting inverse kinematic solution has been on the outline of various researchers and is deliberated as thorough researched and mature problem. There are many fields of applications of robot manipulators to execute the given tasks such as material handling, pick-n-place, planetary and undersea explorations, space manipulation, and hazardous field etc. Moreover, medical field robotics catches applications in rehabilitation and surgery that involve kinematic, dynamic and control operations. Therefore, industrial robot manipulators are required to have proper knowledge of its joint variables as well as understanding of kinematic parameters. The motion of the end effector or manipulator is controlled by their joint actuator and this produces the required motion in each joints. Therefore, the controller should always supply an accurate value of joint variables analogous to the end effector position. Even though industrial robots are in the advanced stage, some of the basic problems in kinematics are still unsolved and constitute an active focus for research. Among these unsolved problems, the direct kinematics problem for parallel mechanism and inverse kinematics for serial chains constitute a decent share of research domain. The forward kinematics of robot manipulator is simpler problem and it has unique or closed form solution. The forward kinematics can be given by the conversion of joint space to Cartesian space of the manipulator. On the other hand inverse kinematics can be determined by the conversion of Cartesian space to joint space. The inverse kinematic of the robot manipulator does not provide the closed form solution. Hence, industrial manipulator can achieve a desired task or end effector position in more than one configuration. Therefore, to achieve exact solution of the joint variables has been the main concern to the researchers. A brief introduction of industrial robot manipulators, evolution and classification is presented. The basic configurations of robot manipulator are demonstrated and their benefits and drawbacks are deliberated along with the applications. The difficulties to solve forward and inverse kinematics of robot manipulator are discussed and solution of inverse kinematic is introduced through conventional methods. In order to accomplish the desired objective of the work and attain the solution of inverse kinematic problem an efficient study of the existing tools and techniques has been done. A review of literature survey and various tools used to solve inverse kinematic problem on different aspects is discussed. The various approaches of inverse kinematic solution is categorized in four sections namely structural analysis of mechanism, conventional approaches, intelligence or soft computing approaches and optimization based approaches. A portion of important and more significant literatures are thoroughly discussed and brief investigation is made on conclusions and gaps with respect to the inverse kinematic solution of industrial robot manipulators. Based on the survey of tools and techniques used for the kinematic analysis the broad objective of the present research work is presented as; to carry out the kinematic analyses of different configurations of industrial robot manipulators. The mathematical modelling of selected robot manipulator using existing tools and techniques has to be made for the comparative study of proposed method. On the other hand, development of new algorithm and their mathematical modelling for the solution of inverse kinematic problem has to be made for the analysis of quality and efficiency of the obtained solutions. Therefore, the study of appropriate tools and techniques used for the solution of inverse kinematic problems and comparison with proposed method is considered. Moreover, recommendation of the appropriate method for the solution of inverse kinematic problem is presented in the work. Apart from the forward kinematic analysis, the inverse kinematic analysis is quite complex, due to its non-linear formulations and having multiple solutions. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Artificial neural network (ANN) can be gainfully used to yield the desired results. Therefore, in the present work several models of artificial neural network (ANN) are used for the solution of the inverse kinematic problem. This model of ANN does not rely on higher mathematical formulations and are adept to solve NP-hard, non-linear and higher degree of polynomial equations. Although intelligent approaches are not new in this field but some selected models of ANN and their hybridization has been presented for the comparative evaluation of inverse kinematic. The hybridization scheme of ANN and an investigation has been made on accuracies of adopted algorithms. On the other hand, any Optimization algorithms which are capable of solving various multimodal functions can be implemented to solve the inverse kinematic problem. To overcome the problem of conventional tool and intelligent based method the optimization based approach can be implemented. In general, the optimization based approaches are more stable and often converge to the global solution. The major problem of ANN based approaches are its slow convergence and often stuck in local optimum point. Therefore, in present work different optimization based approaches are considered. The formulation of the objective function and associated constrained are discussed thoroughly. The comparison of all adopted algorithms on the basis of number of solutions, mathematical operations and computational time has been presented. The thesis concludes the summary with contributions and scope of the future research work

Contribuições para a enumeração e para a análise de mecanismos e manipuladores paralelos

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2010A fase de projeto conceitual demecanismos emanipuladores paralelos, i.e. estruturas cinematicas, destina-se ao desenvolvimento da concepçao da cadeia cinematica. As etapas fundamentais para o desenvolvimento da concepao da cadeia cinematica sao sintese e analise. A sintese corresponde à enumeraçao de concepcoes e a analise corresponde `a seleçao das concepçoes mais promissoras considerando os requisitos de projeto. O objetivo deste trabalho é aplicar ferramentas da teoria de grupos e teoria de grafos para a enumeraçao e para a analise de estruturas cinematicas. A enumeraçao sera desenvolvida de forma sistematica em tres niveis: enumeraçao de cadeias cinematicas, enumeraçao de mecanismos e enumeraçao de manipuladores paralelos. A aplicaçao de ferramentas da teoria de grafos e grupos permite desenvolver novos metodos para enumeraçao e, consequentemente, obter novos resultados. A analise sera simplificada considerando um novo metodo que avalia as simetrias das cadeias cinematicas. Uma cadeia cinematica é representada de forma univoca atraves de um grafo. A representaçao atraves do grafo permite a manipulaçao computacional do problema de enumeraçao de cadeias cinematicas. A aplicaçao de ferramentas integradas da teoria de grafos e teoria de grupos permite identificar as simetrias das cadeias cinematicas atraves do grupo de automorfismos do grafo e, assim, é possivel identificar quais são as possiveis escolhas de base para novos mecanismos e avaliar quais sao as possiveis escolhas de base e efetuador final para manipuladores paralelos. O primeiro nivel da sintese corresponde à enumeraçao de cadeias cinematicas com determinada mobilidade, numero de elos, numero de juntas que operam num determinado sistema de helicoides. O segundo nivel da sintese corresponde a enumeraçao de mecanismos. Um mecanismo é uma cadeia cinematica com um elo escolhido para ser a base. Assim, a enumeraçao de mecanismos consiste em determinar todas as possiveis escolhas de bases para uma determinada cadeia cinematica. O principal conceito empregado neste nivel é o de simetria de grafos não coloridos e orbitas do grupo de automorfismos. O terceiro nivel da sintese corresponde `a enumeraçao de manipuladores paralelos. Um manipulador paralelo é uma cadeia cinematica com um elo escolhido para ser a base e outro para ser o efetuador final. Em outras palavras, um manipulador paralelo é um mecanismo com um elo escolhido para ser o efetuador final. Assim, a enumeraçao de manipuladores paralelos consiste em determinar todas as possiveis escolhas de efetuador final para um determinado mecanismo. O principal conceito empregado neste nivel é a simetria de grafos coloridos e orbitas do grupo de automorfismos de grafos coloridos. Na etapa de analise das concepcoes enumeradas serao abordadas propriedades bem estabelecidas na literatura: mobilidade, variedade, conectividade, grau de controle, redundancia e simetria. Mobilidade e variedade sao propriedades globais das estruturas cinematicas. Conectividade, grau de controle e redundancia sao propriedades locais, i.e. entre dois elos da estrutura cinematica e sao dadas por matrizes n×n, onde n é o número de elos da cadeia. A simetria pode ser considerada uma propriedade global e/ou local da estrutura cinem´atica. A aplicaçao de ferramentas integradas da teoria de grafos e teoria de grupos permite demonstrar que as propriedades locais sao invariantes pela acao do grupo de automorfismos do grafo, i.e. elas sao propriedades simetricas. Desta forma, a representaçao matricial é reduzida de n×n para o×n, onde o é o numero de orbitas do grupo de automorfismos do grafo aassociado à estrutura cinematica. Essa abordagem permite simplificar a analise de estruturas cinematicas apenas considerando as simetrias das cadeia associadas