Some Mobile Overconstrained Parallel Mechanisms

The Griffis-Duffy platform is an example of an overconstrained parallel mechanism. Although it has 6 SS legs joining its platform to its base it is still mobile. In this work similar structures are found but with different types of legs. The key to finding these structures is a pair of theorems concerning 3 degree-of-freedom mechanisms subjected to a translation or a half-turn. Although these results are not new concise statements and proofs are given. These constructions are then applied to parallel mechanisms consisting of 3 RPS legs and 3UPU legs. Some details of the rigid-body motions that the platform of these mechanisms can execute are found. This is facilitated by the observations that rigid displacements permitted by an RPS leg are the displacements which constrain a point to a fixed plane, while the displacements of a UPU leg constrain a line to be coplanar to a fixed line

Parametric stiffness analysis of the Orthoglide

This paper presents a parametric stiffness analysis of the Orthoglide. A compliant modeling and a symbolic expression of the stiffness matrix are conducted. This allows a simple systematic analysis of the influence of the geometric design parameters and to quickly identify the critical link parameters. Our symbolic model is used to display the stiffest areas of the workspace for a specific machining task. Our approach can be applied to any parallel manipulator for which stiffness is a critical issue

Robotization of hand woven carpet technology process

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2008Includes bibliographical references (leaves: 85-91)Text in English; Abstract: Turkish and Englishxi, 96 leavesThis thesis covers a study on the structural design of new overconstrained mechanisms and manipulators and their application to the robotization of hand woven carpet technology process.Moreover, recurrent vector equations are investigated for the synthesis of linkages, and used for the design of new mechanisms with linear-angular conditions in the subspace with general constraint one. These conditions are generalized for defining the structural groups of subspace ..5 and these structural groups are used both for the creation of new parallel manipulators and new serial-parallel platform manipulators.After investigating hand woven carpets, the knowledge gained during the structural design of mechanisms is applied to the robotization of hand woven carpet technology process. Finally, design of carpet weaving robot is introduced

Type synthesis of 6-DOF mobile parallel link mechanisms based on screw theory

Mobile parallel mechanisms (MPMs), which are parallel mechanisms with moveable bases, have previously been proposed to resolve the limited workspace of conventional parallel mechanisms. However, most previous studies on the subject focused on the kinematic analysis of some specific MPMs and did not discuss a type synthesis method for MPMs. With this in mind, we propose a screw theory-based type synthesis method to find out possible 6-degrees-of-freedom (DOF) MPM structures. In our proposed method, the 6-DOF mobility is divided into 3-DOF planar motion and 3-DOF spatial motion, both of which are realized by the transmitted planar motions of the driving units. Separately, the type synthesis of the entire MPM is divided into that of the driving unit and connecting chain. To realize 3-DOF spatial motion, two methods, applying singularity configuration and adding an additional chain, are proposed as ways to restrict undesired motions for the synthesis of the connecting chain. The driving unit is synthesized via the same type-synthesis method as the connecting chain by considering the driving unit as a planar mechanism. The method used to integrate the driving unit and the connecting chain was constructed based on whether the end pair of the connecting chain should be connected with the driving unit directly or driven by it through an actuating mechanism. As a result, 284 possible types of MPM structure are suggested and four examples of MPMs with six DOFs were synthesized to verify the feasibility of the proposed method

Stiffness Analysis of Overconstrained Parallel Manipulators

The paper presents a new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations for the unloaded manipulator configuration, which allows computing the stiffness matrix for the overconstrained architectures, including singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators of 3-PUU and 3-PRPaR architectures. Accuracy of the proposed approach was evaluated for a case study, which focuses on stiffness analysis of Orthoglide parallel manipulator

Stiffness Analysis Of Multi-Chain Parallel Robotic Systems

The paper presents a new stiffness modelling method for multi-chain parallel robotic manipulators with flexible links and compliant actuating joints. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations, which allows computing the stiffness matrix for singular postures and to take into account influence of the external forces. The advantages of the developed technique are confirmed by application examples, which deal with stiffness analysis of a parallel manipulator of the Orthoglide famil

Critically Twisted Kinematic Chains

Els caleidocicles de Möbius són una família nova de mecanismes amb un grau de llibertat. Presentem cadenes quinemàtiques noves amb propietats similars i busquem casos especials. Donem un argument de plausibilitat per la mobilitat de les cadenes basat en un teorema nou sobre la transposició d'elements adjacents. Finalment, discutim la relació entre els nostres sistemes i el camp emergent de la geometria diferencial discreta.Los caleidociclos de Möbius son una familia nueva de mecanismos con un grado de libertad. Presentamos cadenas quinemáticas nuevas con propiedades similares y buscamos casos especiales. Damos un argumento de plausibilidad para la mobilidad de las cadenas basado en un teorema nuevo sobre la transposición de elementos adyacentes. Finalmente, discutimos la relación entre nuestros sistemas y el campo emergente de la geometría diferencial discreta.Möbius kaleidocycles are a newly discovered family of underconstrained linkages with one degree of freedom. We present many new kinematic chains with similar properties and look for special cases. We give a plausibility argument for the mobility of our chains based on a new theorem on the transposition of adjacent links. Finally, we discuss the relationship between our systems and the emerging field of discrete differential geometry.Outgoin

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