Design and Characterization of Curved and Spherical Flexure Hinges for Planar and Spatial Compliant Mechanisms

A flexure hinge is a flexible connector that can provide a limited rotational motion between two rigid parts by means of material deformation. These connectors can be used to substitute traditional kinematic pairs (like bearing couplings) in rigid-body mechanisms. When compared to their rigid-body counterpart, flexure hinges are characterized by reduced weight, absence of backlash and friction, part-count reduction, but restricted range of motion. There are several types of flexure hinges in the literature that have been studied and characterized for different applications. In our study, we have introduced new types of flexures with curved structures i.e. circularly curved-beam flexures and spherical flexures. These flexures have been utilized for both planar applications (e.g. articulated robotic fingers) and spatial applications (e.g. spherical compliant mechanisms). We have derived closed-form compliance equations for both circularly curved-beam flexures and spherical flexures. Each element of the spatial compliance matrix is analytically computed as a function of hinge dimensions and employed material. The theoretical model is then validated by comparing analytical data with the results obtained through Finite Element Analysis. A case study is also presented for each class of flexures, concerning the potential applications in the optimal design of planar and spatial compliant mechanisms. Each case study is followed by comparing the performance of these novel flexures with the performance of commonly used geometries in terms of principle compliance factors, parasitic motions and maximum stress demands. Furthermore, we have extended our study to the design and analysis of serial and parallel compliant mechanisms, where the proposed flexures have been employed to achieve spatial motions e.g. compliant spherical joints

Modeling of the elastic mechanical behavior of thin compliant joints under load for highest-precision applications

For the most demanding measurement tasks in force metrology flexure hinges in compliant mechanisms represent a key component. To enhance the mechanical properties of devices like weighing cells, the ability of precise modeling of flexure hinges is essential. The present scientific work focuses on the modeling of the mechanical behavior of a single flexure hinge subjected to geometric deviations and non-ideal loading conditions as those encountered in weighing cells. The considered hinge has a semi-circular contour and a large width compared to its minimum notch height. This geometry is modeled using the finite element method. Requirements for a trustworthy and efficient computation are elaborated under the consideration of geometric deviations for later parametric studies. Analytical expressions found in the literature are compared to numerical results to prove the validity of their assumptions for thin hinges. The model is used for studying the deviation of the stiffness in non-ideal flexure hinges. Sources of deviation are identified and described by parameters. The range of values for each parameter is chosen on the basis of available manufacturing technology. Influential parameters are identified through a sensitivity analysis. The effect of loading conditions is studied in the context of the application in weighing cells. For the enhancement of the overall sensitivity, the stiffness of the flexure hinges can be reduced. One option, the alteration of the geometry by adding a flexure strip in the center of the semi-circular flexure hinge is studied in comparison to existing analytical equations. The effects of ground tilts for a single loaded flexure hinge are investigated as a foundation for future modeling of a tilt insensitive state of a weighing cell mechanism (autostatic state). By adjusting the vertical position of the center of mass of the lever, the tilt sensitivity can be reduced to zero. An approach to find the position for this state is presented considering the numerical limitations of finite element modeling. Using this approach, the variation of the sought position is evaluated for different values of the design parameters.Tesi

A Generic Compliance Modeling Method for Two-Axis Elliptical-Arc-Filleted Flexure Hinges

As a kind of important flexible joint, two-axis flexure hinges can realize in-plane and out-of-plane motions and can be used for constructing flexure-based spatial compliant mechanisms. The paper introduces a common two-axis elliptical-arc-filleted flexure hinge that is generated by two different elliptical-arc-filleted cutout profiles and that provides some new hinge types. The analytical compliance equations of both half-segments of the two-axis elliptical-arc flexure hinges are firstly formulated, and then, based on a generic compliance modeling method of a flexure serial chain, the closed-form compliance and precision matrices of two-axis elliptical-arc-filleted flexure hinges are established and validated by the finite element method. Some numerical simulations are conducted to compare the effect of different design geometric parameters on the performance of the two-axis flexure hinges

Ein Beitrag zur geometrischen Gestaltung und Optimierung prismatischer Festkörpergelenke in nachgiebigen Koppelmechanismen

Wesentlicher Aspekt bei der Synthese eines nachgiebigen Koppelmechanismus ist die geometrische Gestaltung und Optimierung der prismatischen Festkörpergelenke hinsichtlich geforderter Mechanismuseigenschaften. In der vorliegenden Arbeit erfolgt eine ganzheitliche, d. h. vom Einzelgelenk auf den Mechanismus übertragbare Untersuchung unter Berücksichtigung der Drehachsenverlagerung. Es wird eine allgemein anwendbare Synthesemethode nachgiebiger Mechanismen abgeleitet, die ausgehend vom Starrkörpermechanismus eine gezielte Gestaltung sowie beschleunigte FEM-basierte Optimierung ermöglicht. Hiermit lassen sich der Bewegungsbereich vergrößern und die Bahngenauigkeit erhöhen. Die Besonderheit der Synthesemethode besteht in der Verwendung identischer oder unterschiedlicher Festkörpergelenke mit Standard- oder Polynomkonturen. Hierfür werden grundlegende Hinweise sowie drei neue Ansätze zur Bestimmung der geometrischen Gelenkparameter mittels Umsetzungstabelle, Kurventafel oder computergestützter Konturoptimierung vorgestellt. Das Potenzial der Synthesemethode für die Präzisionstechnik wird an einer Schubkurbel zur Realisierung einer Punktgeradführung aufgezeigt.For the realization of high precise motion, often compliant mechanisms are used instead of rigid-body mechanisms. In these solid-state mechanisms, the flexibility is achieved by material coherent revolute joints. In compliant linkage mechanisms, mostly prismatic flexure hinges with basic cut-out geometries are used. In contrast to form- and force-closed joints the angular deflection of flexure hinges is limited. Thus, the motion range of the mechanism is limited too. In addition, no exact relative rotation of two rigid links is possible with a flexure hinge, as always a shift of its axis of rotation occurs. In turn, this leads to path deviations of the compliant mechanism compared to the rigid-body mechanism. Regarding the required mechanism properties, the step of the geometric design of the prismatic flexure hinges is a key aspect in the synthesis of a compliant linkage mechanism, which is investigated in this thesis. Hence, a holistic consideration is carried out, which can be transferred from a hinge to a mechanism. For the investigation of a single flexure hinge a suitable approach for modeling the rotational axis is crucial. After this, the multi-criteria optimization of the hinge contour is investigated for a single hinge and in the mechanism. Based on known rigid-body replacement approaches, this thesis presents a general method for the synthesis of compliant linkage mechanisms. The synthesis method allows a specific design and accelerated FEM-based optimization with identical or different hinges. This can be used to increase the motion range and to improve the path accuracy. The contribution of the synthesis method results due to the consideration of the design of the prismatic flexure hinges with standard or polynomial contours. For this, basic hints and three new approaches for determining the geometric parameters of the hinge contour and dimensions using a look-up table, nomogram or computer-aided contour optimization are proposed. Such designed mechanisms are particularly suitable for use in precision engineering. The potential of the synthesis method is exemplified for a compliant slider-crank mechanism for realizing a rectilinear guiding of a coupler point.Zur Realisierung von Bewegungen mit hohen Anforderungen an die Präzision werden Starrkörpermechanismen zunehmend durch nachgiebige Mechanismen ersetzt, in denen die Beweglichkeit durch stoffgekoppelte Drehgelenke realisiert wird. In diesen nachgiebigen Koppelmechanismen kommen überwiegend prismatische Festkörpergelenke mit einfachen geometrischen Aussparungen zum Einsatz. Im Gegensatz zu form- und kraftgekoppelten Gelenken ist der Auslenkwinkel eines Festkörpergelenkes begrenzt, wodurch der Bewegungsbereich des Mechanismus eingeschränkt wird. Zudem lässt sich mit einem Festkörpergelenk keine exakte relative Drehung zweier starrer Glieder realisieren, da grundsätzlich eine Drehachsenverlagerung stattfindet. Dadurch ergeben sich Bahnabweichungen des nachgiebigen Mechanismus im Vergleich zum Starrkörpermechanismus. Wesentlicher Aspekt bei der Synthese eines nachgiebigen Koppelmechanismus ist die in dieser Arbeit untersuchte Phase der geometrischen Gestaltung und Optimierung der prismatischen Festkörpergelenke hinsichtlich geforderter Mechanismuseigenschaften. Hierzu erfolgt eine ganzheitliche, d. h. vom Gelenk auf den Mechanismus übertragbare Betrachtung. Für die durchgeführte Untersuchung von Einzelgelenken ist ein geeigneter Ansatz zur Drehachsenmodellierung von entscheidender Bedeutung. Die anschließende mehrkriterielle Optimierung der Gelenkkontur findet für ein Einzelgelenk und im Mechanismus statt. Als Ergebnis der Arbeit wird eine allgemein anwendbare Synthesemethode nachgiebiger Koppelmechanismen abgeleitet, die ausgehend vom Starrkörpermechanismus eine gezielte Gestaltung sowie beschleunigte FEM-basierte Optimierung mit identischen oder unterschiedlichen Gelenken ermöglicht. Hiermit lassen sich der Bewegungsbereich vergrößern und die Bahngenauigkeit erhöhen. Die Besonderheit der Synthesemethode besteht in der Berücksichtigung der Gestaltung prismatischer Festkörpergelenke mit Standard- oder Polynomkonturen. Hierfür werden grundlegende Hinweise sowie drei neue Ansätze zur Bestimmung der geometrischen Parameter der Gelenkkontur und -abmessungen mittels Umsetzungstabelle, Kurventafel oder computergestützter Konturoptimierung vorgestellt. Auf diese Weise gestaltete Mechanismen eignen sich besonders für die Präzisionstechnik. Das Potenzial der Synthesemethode wird am Beispiel einer nachgiebigen Schubkurbel zur Realisierung einer Punktgeradführung aufgezeigt

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

Analysis of plane problems with defects of different geometric shapes

This thesis presents research on a plate with defects of various geometric shapes, including a circular hole, a 'finite-height crack,' a notch, and a parabolic notch. The primary focus of the entire work is to produce analytical solutions for the stress state of a plate containing one of these defects, subjected to different loading modes. Additionally, the thesis explores the unique situation where the plane problem extends into the third dimension, forming a 3D body, and examines the end effects. While the stress state within a plate with a circular hole is a classical problem with a fully solved solution, this thesis delves into the shakedown phenomenon under cyclic loading, offering insights of practical importance. Defects containing one or more singular features are also worth investigating. Singular features are defined as areas where stress is concentrated and tends to infinity in elastic analysis, such as cracks or sharp notches. The general approach to these problems typically involves using asymptotic or approximate solutions, like Williams’ solution. However, this thesis aims to produce a non-approximated, closed-form solution for the stress field of a wedge (with angles ranging from zero to 2π) interacting with a singularity (singular force or dislocation) under the anti-plane loading. This methodology can be extended to a parabolic notch, which is also discussed. The 'finite-height crack' is another example involving singular features, but it has two singularities at a 'short' distance apart. Therefore, the thesis discusses the interaction of the stress state around the two singularities and predicts the location of fracture initiation in a 'finite-height' crack case. Finally, the thesis explores a scenario where a plane problem extends into the third dimension, becoming a 3D problem. An example is presented using plane contact as a reference, employing numerical methods to analyse the 3D end effect. This work provides a clear explanation of how the end effect generalizes at the free end and the distance it propagates in terms of the geometric feature length

Proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress

Published proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress, hosted by York University, 27-30 May 2018