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

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

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

Passive Compliance Control of Redundant Serial Manipulators

Current industrial robotic manipulators, and even state of the art robotic manipulators, are slower and less reliable than humans at executing constrained manipulation tasks, tasks where motion is constrained in some direction (e.g., opening a door, turning a crank, polishing a surface, or assembling parts). Many constrained manipulation tasks are still performed by people because robots do not have the manipulation ability to reliably interact with a stiff environment, for which even small commanded position error yields very high contact forces in the constrained directions. Contact forces can be regulated using compliance control, in which the multi-directional elastic behavior (force-displacement relationship) of the end-effector is controlled along with its position. Some state of the art manipulators can directly control the end-effector\u27s elastic behavior using kinematic redundancy (when the robot has more than the necessary number of joints to realize a desired end-effector position) and using variable stiffness actuators (actuators that adjust the physical joint stiffness in real time). Although redundant manipulators with variable stiffness actuators are capable of tracking a time-varying elastic behavior and position of the end-effector, no prior work addresses how to control the robot actuators to do so. This work frames this passive compliance control problem as a redundant inverse kinematics path planning problem extended to include compliance. The problem is to find a joint manipulation path (a continuous sequence of joint positions and joint compliances) to realize a task manipulation path (a continuous sequence of end-effector positions and compliances). This work resolves the joint manipulation path at two levels of quality: 1) instantaneously optimal and 2) globally optimal. An instantaneously optimal path is generated by integrating the optimal joint velocity (according to an instantaneous cost function) that yields the desired task velocity. A globally optimal path is obtained by deforming an instantaneously generated path into one that minimizes a global cost function (integral of the instantaneous cost function). This work shows the existence of multiple local minima of the global cost function and provides an algorithm for finding the global minimum

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

Modeling and simulation of a Stewart platform type parallel structure robot

The kinematics and dynamics of a Stewart Platform type parallel structure robot (NASA's Dynamic Docking Test System) were modeled using the method of kinematic influence coefficients (KIC) and isomorphic transformations of system dependence from one set of generalized coordinates to another. By specifying the end-effector (platform) time trajectory, the required generalized input forces which would theoretically yield the desired motion were determined. It was found that the relationship between the platform motion and the actuators motion was nonlinear. In addition, the contribution to the total generalized forces, required at the actuators, from the acceleration related terms were found to be more significant than the velocity related terms. Hence, the curve representing the total required actuator force generally resembled the curve for the acceleration related force. Another observation revealed that the acceleration related effective inertia matrix I sub dd had the tendency to decouple, with the elements on the main diagonal of I sub dd being larger than the off-diagonal elements, while the velocity related inertia power array P sub ddd did not show such tendency. This tendency results in the acceleration related force curve of a given actuator resembling the acceleration profile of that particular actuator. Furthermore, it was indicated that the effective inertia matrix for the legs is more decoupled than that for the platform. These observations provide essential information for further research to develop an effective control strategy for real-time control of the Dynamic Docking Test System

Position analysis based on multi-affine formulations

Aplicat embargament des de la data de defensa fins el 31/5/2022The position analysis problem is a fundamental issue that underlies many problems in Robotics such as the inverse kinematics of serial robots, the forward kinematics of parallel robots, the coordinated manipulation of objects, the generation of valid grasps, the constraint-based object positioning, the simultaneous localization and map building, and the analysis of complex deployable structures. It also arises in other fields, such as in computer aided design, when the location of objects in a design is given in terms of geometric constrains, or in the conformational analysis of biomolecules. The ubiquity of this problem, has motivated an intense quest for methods able of tackling it. Up to now, efficient algorithms for the general problem have remained elusive and they are only available for particular cases. Moreover, the complexity of the problem has typically led to methods difficult to be implemented. Position analysis can be decomposed into two equally important steps: obtaining a set of closure equations, and solving them. This thesis deals with both of them to obtain a general, simple, and yet efficient solution method that we call the trapezoid method. The first step is addressed relying on dual quaternions. Although it has not been properly highlighted in the past, the use of dual quaternions permits expressing the closure condition of a kinematic loop involving only lower pairs as a system of multi-affine equations. In this thesis, this property is leveraged to introduce an interval-based method specially tailored for solving multi-affine systems. The proposed method is objectively simpler (in the sense that it is easier to understand and to implement) than previous methods based on general techniques such as interval Newton methods, conversions to Bernstein basis, or linear relaxations. Moreover, it relies on two simple operations, namely, linear interpolations and projections on coordinate planes, which can be executed with a high performance. The result is a method that accurately and efficiently bounds the valid solutions of the problem at hand. To further improve the accuracy, we propose the use of redundant, multi affine equations that are derived from the minimal set of equations describing the problem. To improve the efficiency, we introduce a variable elimination methodology that preserves the multi-affinity of the system of equations. The generality and the performance of the proposed trapezoid method are extensively evaluated on different kind of mechanisms, including spherical mechanisms, generic 6R and 7R loops, over-constrained systems, and multi-loop mechanisms. The proposed method is, in all cases, significantly faster than state of the art alternatives.El problema de l'anàlisi de posició és un tema fonamental que subjau a molts problemes de la robòtica, com ara la cinemàtica inversa de robots sèrie, la cinemàtica directa de robots paral·lels, la manipulació coordinada d'objectes, la generació de prensions vàlides amb mans robòtiques, el posicionament d'objectes basat en restriccions, la localització i la creació de mapes de forma simultània, i l'anàlisi d'estructures desplegables complexes. També sorgeix en altres camps, com ara en el disseny assistit per ordinador, quan la ubicació dels objectes en un disseny es dóna en termes de restriccions geomètriques o en l'anàlisi conformacional de biomolècules. La omnipresència d'aquest problema ha motivat una intensa recerca de mètodes capaços d'afrontar-lo. Fins al moment, els algoritmes eficients per al problema general han estat esquius i només estan disponibles per a casos particulars. A més, la complexitat del problema normalment ha conduït a mètodes difícils d'implementar. L'anàlisi de posició es pot descompondre en dos passos igualment importants: l'obtenció d'un sistema d'equacions de tancament i la resolució d'aquest sistema. Aquesta tesi tracta de tots dos passos per tal d'obtenir un mètode de solució general, senzill i alhora eficient que anomenem el mètode del trapezoide. El primer pas s'aborda utilitzant quaternions duals. Tot i que no ha estat suficientment destacat en el passat, l'ús de quaternions duals permet expressar la condició de tancament d'un bucle cinemàtic que impliqui només parells inferiors com a un sistema d'equacions multi-afins. En aquesta tesi s'aprofita aquesta propietat per introduir un mètode especialment dissenyat per resoldre sistemes multi-afins. El mètode proposat és objectivament més senzill (en el sentit que és més fàcil d'entendre i d'implementar) que els mètodes anteriors que utilitzen tècniques generals com ara els mètodes de Newton basats en intervals, les conversions a la base de Bernstein o les relaxacions lineals. A més, el mètode es basa en dues operacions simples, a saber, les interpolacions lineals i les projeccions en plans de coordenades, que es poden executar de forma molt eficient. El resultat és un mètode que acota amb precisió i eficiència les solucions vàlides del problema. Per millorar encara més la precisió, proposem l'ús d'equacions multi-afins redundants derivades del conjunt mínim d'equacions que descriuen el problema. Per altra banda, per millorar l'eficiència, introduïm un metodologia d'eliminació de variables que preserva la multi-afinitat del sistema d'equacions. La generalitat i el rendiment del mètode del trapezoide s'avalua extensivament en diferents tipus de mecanismes, inclosos els mecanismes esfèrics, bucles 6R i 7R genèrics, sistemes sobre-restringits i mecanismes de múltiples bucles. El mètode proposat és, en tots els casos, significativament més ràpid que els mètodes alternatius descrits en la literatura fins al moment.Postprint (published version

Kinematics and Robot Design II (KaRD2019) and III (KaRD2020)

This volume collects papers published in two Special Issues “Kinematics and Robot Design II, KaRD2019” (https://www.mdpi.com/journal/robotics/special_issues/KRD2019) and “Kinematics and Robot Design III, KaRD2020” (https://www.mdpi.com/journal/robotics/special_issues/KaRD2020), which are the second and third issues of the KaRD Special Issue series hosted by the open access journal robotics.The KaRD series is an open environment where researchers present their works and discuss all topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. It aims at being an established reference for researchers in the field as other serial international conferences/publications are. Even though the KaRD series publishes one Special Issue per year, all the received papers are peer-reviewed as soon as they are submitted and, if accepted, they are immediately published in MDPI Robotics. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”.KaRD2019 together with KaRD2020 received 22 papers and, after the peer-review process, accepted only 17 papers. The accepted papers cover problems related to theoretical/computational kinematics, to biomedical engineering and to other design/applicative aspects

A general method for the numerical computation of manipulator singularity sets

The analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness under contract DPI2010-18449, and by a Juan de la Cierva contract supporting the fourth author.Peer Reviewe