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

Generation of dynamic structures in nonequilibrium reactive bilayers

We present a nonequlibrium approach for the study of a flexible bilayer whose two components induce distinct curvatures. In turn, the two components are interconverted by an externally promoted reaction. Phase separation of the two species in the surface results in the growth of domains characterized by different local composition and curvature modulations. This domain growth is limited by the effective mixing due to the interconversion reaction, leading to a finite characteristic domain size. In addition to these effects, first introduced in our earlier work [Phys. Rev. E {\bf 71}, 051906 (2005)], the important new feature is the assumption that the reactive process actively affects the local curvature of the bilayer. Specifically, we suggest that a force energetically activated by external sources causes a modification of the shape of the membrane at the reaction site. Our results show the appearance of a rich and robust dynamical phenomenology that includes the generation of traveling and/or oscillatory patterns. Linear stability analysis, amplitude equations and numerical simulations of the model kinetic equations confirm the occurrence of these spatiotemporal behaviors in nonequilibrium reactive bilayers.Comment: To appear in Phys. Rev.

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

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

Advances in Robot Kinematics : Proceedings of the 15th international conference on Advances in Robot Kinematics

International audienceThe motion of mechanisms, kinematics, is one of the most fundamental aspect of robot design, analysis and control but is also relevant to other scientific domains such as biome- chanics, molecular biology, . . . . The series of books on Advances in Robot Kinematics (ARK) report the latest achievement in this field. ARK has a long history as the first book was published in 1991 and since then new issues have been published every 2 years. Each book is the follow-up of a single-track symposium in which the participants exchange their results and opinions in a meeting that bring together the best of world’s researchers and scientists together with young students. Since 1992 the ARK symposia have come under the patronage of the International Federation for the Promotion of Machine Science-IFToMM.This book is the 13th in the series and is the result of peer-review process intended to select the newest and most original achievements in this field. For the first time the articles of this symposium will be published in a green open-access archive to favor free dissemination of the results. However the book will also be o↵ered as a on-demand printed book.The papers proposed in this book show that robot kinematics is an exciting domain with an immense number of research challenges that go well beyond the field of robotics.The last symposium related with this book was organized by the French National Re- search Institute in Computer Science and Control Theory (INRIA) in Grasse, France

Finite strain chemo-thermo-electro-mechanics with applications in mechanobiology

La tesi proposta nasce da ben definite motivazioni biologiche, con lo scopo di fornire una caratterizzazione del comportamento delle cellule endoteliali nel processo di angiogenesi tumorale. Diversi framework multi-fisici vengono introdotti per applicazioni nel campo della meccanobiologia, così come in altre aree di ricerca. L’angiogenesi è un noto processo progressivo, fisiologico o patologico, caratterizzato dalla formazione di nuovi vasi sanguigni che si originano da quelli pre-esistenti. Le cellule endoteliali, le quali rivestono le pareti interne dei vasi sanguigni, vengono influenzate da stimuli extra-cellulari rilasciati dalle cellule tumorali, e rispondono tramite rilocazione di recettori (proteine) sulla loro membrana, migrazione cellulare collettiva e riorganizzazione in nuovi vasi sanguigni. Il ruolo della dinamica recettoriale e della meccanica cellulare in risposta agli stimuli extra-cellulari è dunque oggetto di grande interesse, in quanto processi cruciali nelle fasi iniziali dell’angiogenesi. Le funzioni strutturali della cellula, le quali permettono l’avvenimento di processi ben noti come l’adesione e l’accasciamento cellulare, la motilità e la migrazione, sono attribuite alla generazione e la riorganizzazione della macchina contrattile citoscheletrica. Il citoscheletro è una rete interconnessa di proteine e polimeri filamentosi, soggetto ad un imponente riarrangiamento che permette la generazione di diverse strutture polimeriche, fornendo le forze e il supporto strutturale necessari per il movimento cellulare. Il ruolo della meccanica nei processi biologici è dunque di inconfutabile rilevanza, così come la responsabilità della meccanobiologia di fornire un supporto ad una caratterizzazione esaustiva dei sistemi viventi. Modell multi-fisici con applicazioni in meccanobiologia richiedono di tener conto degli svariati fenomeni coinvolti nel processo sotto investigazione. La teoria della meccanica del continuo in grandi deformazioni rappresenta certamente il miglior candidato per descrivere la risposta strutturale delle cellule soggette a massicce deformazioni durante i processi di adesione cellulare, accasciamento e migrazione. Ciononostante, la sola meccanica è evidentemente insufficiente. Nonostante l’accoppiamento tra la meccanica in grandi deformazioni e la termodinamica sia alla base di innumerevoli modelli multi-fisici, è indubbia la necessità di considerare altri processi quali il trasporto di massa con appropriate leggi di diffusione, e di tenere conto delle reazioni chimiche. L’accoppiamento tra termodinamica, meccanica e chemo-diffusione conduce alla realizzazione dei così definiti chemo-transport-mechanical frameworks. Inoltre, e così come ben noto nel campo della termodinamica, la necessità di fornire una caratterizzazione statisticamente basata di alcuni fenomeni è frequente. È il caso della modellazione dei reticoli polimerici nel campo della fisica dei polimeri. Si presentano di conseguenza sfide aggiuntive nel tener conto di eventi multi-fisici a differenti scale spazio-temporali. In questa tesi, i modelli teorici multi-fisici proposti trovano applicazioni che non sono puramente ristrette al campo della meccanobiologia. Termodinamica e meccanica in grandi deformazioni, meccanica dei continui statisticamente basata, e la teoria dell’elettromagnetismo Galileiano, rappresentano i principali temi investigati nella tesi e adottati per la realizzazione di diverse formulazioni multi-fisiche.The proposed thesis comes from well-defined biological motivations, aiming at providing a characterization of endothelial cell behavior in tumor angiogenesis. Several multi-physics frameworks are introduced for applications in the realm of mechanobiology, as well as in many other research areas. Angiogenesis is a well known physiological or pathological multistep process that consists in the formation of new blood vessels from preexisting ones. Covering the inner walls of blood vessels, endothelial cells are affected by extracellular stimuli released by tumor cells, and respond via relocation of receptor proteins along their membrane, collective migration and reorganization in novel vessels. The role of receptor dynamics and cell mechanics in response to extracellular stimuli is therefore object of great interest, as they are pivotal processes at the early stages of angiogenesis. Cell structural functions, allowing the occurrence of well known processes such as cell adhesion and spreading, motility and migration, are ascribed to the generation and reorganization of the cytoskeletal contractile machinery. The cytoskeleton is an interconnected network of regulatory proteins and filamentous polymers that undergoes massive rearrangements to generate different biopolymer structures, providing the necessary forces and structural support for cell movements. It is therefore of unquestionable relevance the role of mechanics in biological processes, as well as the responsibility of mechanobiology to provide a support for an exhaustive characterization of alive systems. Multi-physics models with applications in mechanobiology require to account for several phenomena involved in the process under investigation. The finite strain theory in continuum mechanics certainly represents the best candidate to describe the structural response of cells undergoing massive deformations during cell adhesion, spreading, and migration. However, mechanics itself is evidently not sufficient. Despite the coupling between finite strain mechanics and thermodynamics stands for the basis of a countless amount of multi-physics models, the necessity to consider other processes such as mass transport with proper diffusion laws, and to account for chemical reactions, is beyond doubt. The coupling between thermo-mechanics and chemo-transport phenomena leads thus to design the so-termed chemo-transport-mechanical frameworks. Furthermore, and as well known in the realm of thermodynamics, insightful models often need to provide a statistically-based characterization of phenomena. It is the case of cross-linked polymer networks modeling in the field of polymer physics. Additional challenges therefore arise in accounting for multi-physics events that occur at different space-time scales. In this thesis, general and theoretical multi-physics models are proposed for applications that are not only restricted to the realm of mechanobiology. Finite strain continuum thermo-mechanics, diffusion laws and phase segregation, chemical reactions with trapping, statistically-based continuum mechanics, and the Galilean electromagnetic theory, represent the main topics investigated in this thesis and adopted for designing several multi-physics formulations