The Art of Flexure Mechanism Design

Mechanism constitute the mechanical organs of machines. They are generally composed of rigid segments connected to each other by articulated joints. The function of the joints is to act as bearings, i.e. to constraint the relative motion of the segments it connects, while leaving a freedom of motion in some specific directions. Conventional mechanisms rely on sliding or rolling motions between solid bodies in order to fulfill the bearing function. Consequently, these bearings exhibit friction forcers limiting the motion precision, they require lubrication, they undergo wear, they produce debris and they have a limited lifetime. Flexure mechanisms rely on a radically different physical principle to fulfill the bearing function : the elastic deformation of beams and membranes. This gets around the above-mentioned limitations. The rigid segments of the mechanism are connected to each other via elastically deformable joints called flexures which are springs whose stiffnesses are designed to be very high in the directions where the joint has to constrain relative motion and very flexile in the directions where freedom of motion is required. As a result, mechanisms can be manufactured monolithically and, by proper choice of materials and geometry of the flexures, lead to lifetimes of tens of millions of cycles without any wear or change in the geometry or forces of motion. Thanks to these unique properties flexure mechanisms have become an inescapable technology in all environments where friction, lubrication, wear, debris or mechanical backlash are forbidden : outer space, vacuum, cryogenics, high radiation, ultra-clean environments, etc. This book comes within the scope of this technological evolution. It gathers the knowledge of experts in flexure mechanisms design having worked in the key fields of high precision robotics, aerospace mechanisms, particle accelerators and watch making industry. It is dedicated to engineers, scientists and students working in these fields. The book presents the basic principles underlying flexure mechanism design, the most important flexures and the key formulas for their proper design. It also covers more general aspects of the kinematic design of multi-degrees of freedom mechanism exploiting the state of the art approaches of parallel kinematics. A wide variety of concrete examples of systems designed based on theses approaches are presented in details.

Table of Contents:
Introduction Flexure bearing importance Flexible element classification Book goals Topic delimitation 
 BASIC FLEXURES Underlying theory Basic assumptions Allowable deflections Stiffnesses Flexure joint elements General considerations Leaf springs Rods Torsion bars Circular notch hinges Linear translation bearings Two parallel leaf spring stage Over constrained stage with four parallel leaf springs Four prismatic notch hinge stage Four circular notch hinge stage Conclusion on linear translation bearings Rotational bearings Separate cross spring pivot
 Joined cross spring pivot
 RCC pivot with two leaf springs
 RCC pivot with four notch hinges
 Cross pivot with four notch hinges 
 Comparison of the pivots Radial loads Over constrained pivot with three leaf springs FLEXURE MECHANISMS Flexure structures Kinematics Choice of materials Working envelope Stiffnesses Modular design of flexure mechanisms Introduction Concept of modular kinematics Reduced solution catalogue for ultra-high precision Mechanical design of the building bricks Case study: 5-DOF ultra-high precision robot Ultra-high precision parallel robots family Conclusion Final Note Rectilinear flexure mechanisms Introduction Rectilinear Kinematics Sarrus guiding mechanism 13-hingestage mechanism Analysis and comparison Application to the watt balance Conclusions Examples of planar mechanisms used for out-of-plane functions Introduction Example of design problem of an active cardiac stabilizer Exploiting the vicinity of singularities Optimization of the spherical compliant joint Exploiting the singularities of parallel mechanisms Selection of an actuation mechanism Integration of the three mechanisms in the two planes Conclusions

About the Author :
Simon Henein was born in 1973. He obtained an engineering degree at the Ecole Polytechnique Fédérale de Lausanne (EPFL) in 1996 and went on to complete his doctorate at the EPFL in 2000. In 2001, he published the book "Conception des guidages flexibles" which has become a reference in precision engineering. He then joined the Centre Suisse d'Electronique et Microtechnique (CSEM), Neuchâtel, Switzerland, where he conceived and developed mechanisms for robotic, aerospace, medical and watchmaking applications. He pursued his research career at the Paul Scherrer Institute, Villigen, Switzerland, where he developed instruments for the Swiss Light Source Synchrotron (SLS). Since 2012 he is associate professor in microengineering at the EPFL, holder of an endowed chair in micromechanical and horological design (Instant-Lab). Lennart Rubbert was born in 1984. He studied mechatronics at Institut National des Sciences Appliquées (INSA) in Strasbourg where he got an engineering degree in 2009. He also obtained in 2009 a Master degree in Robotics and Control at the University of Strasbourg. He completed his Ph.D. on the design of compliant mechanisms for surgical robotics in 2012 at the University of Strasbourg. From 2013 to 2015 he performed his postdoc at Instant-Lab (EPFL) with Prof. Simon Henein. In 2015, he became assistant professor at INSA de Strasbourg in the mechanical department and is also a researcher and scientist at ICube in the Control Vision and Robotic team. Florent Cosandier was born in 1984. He obtained his master's degree in engineering from the Ecole Polytechnique Fédérale de Lausanne (EPFL) in 2007, after completing his studies during the master thesis at the Chinese University of Hong Kong (CUHK). In 2013, he obtained his Ph.D. at the EPFL, for which he was awarded the Prix Omega scientific award. He then joined the Swiss Federal Institute of Metrology (METAS) for a postdoctoral position, where he developed precision mechanisms for the new Swiss Watt Balance. In 2014, he joined the Centre Suisse d'Electronique et Microtechnique (CSEM) in Neuchâtel, Switzerland, where he currently develops precision flexure mechanisms for watchmaking, aerospace and metrology applications. Murielle Richard was born in 1984. She obtained her Master of Science in Microengineering at the Ecole Polytechnique Fédérale de Lausanne (EPFL) in 2008, with a special focus on robotics, autonomous systems, machine learning and mechanical design. In 2012, she completed her Ph.D. in Manufacturing Systems and Robotics in the same university. Her research topics covered high-precision and industrial robotics, as well as compliant mechanisms. She presently works at ETA Manufacture Horlogère SA, where she designs high-precision and compliant mechanisms for manufacturing and assembly systems. Her broader activities include industrialization of new products, development of new assembly machines and continuous improvement of production lines.