Flexure mechanism design is an art, and this article provides the theoretical and practical foundation for scientists and engineers to express their creativity in this field. Flexure mechanisms, also known as compliant mechanisms, rely on the elasticity of matter to provide motion to mechanism linkages. Flexure mechanisms eliminate the disadvantages of classical joints: friction, wear, lubrication and play, while permitting monolithic design. Flexure-based mechanisms have gained prominence in a wide variety of fields including robotics, surgical instrumentation, aerospace, astronomy, particle accelerators, metrology and horology.
Since the early 20th century, miniaturisation has been one of the major themes of technological development. Miniaturisation is an efficient way to increase the performance of technological systems, and microtechnology devices such as mobile phones, pacemakers and auditory prosthetics have rapidly decreased in size. The same is true for their components (integrated circuits, optoelectronic components, microsystems, etc.) requiring continually improving production methods for their manufacture. This trend is accelerating, so it is essential to adapt instrumentation and tools allowing perception and intervention at the micrometre or even nanometre scale. When the modification of existing tools no longer addresses the needs of miniaturisation, it becomes necessary to invent new ones.
High precision robotics is one class of tools allowing us to work on matter at the sub-micron scale. They allow us to carry out manipulation, machining and assembly tasks, generally in an automated fashion far surpassing human manual capacity, which, at present, cannot be realised by any other means. These robots have evolved from the first industrial robots where the mechanical structure, actuators, sensors and control of the robots was adapted for high precision tasks. In the case of mechanical structures, this adaptation led to the improvement of plain and rolling bearings used in articulated robots. However, this progression has attained a practical limit of precision for physical reasons such as the presence of friction, the weak rigidity of small bearing components, as well as manufacturing tolerances. These limitations are intrinsic to bearings based on friction or rolling contact between solids. The only way to surpass such limits is to radically change the physical principle underlying such bearings and use other types which are compatible with the increased precision of robotics, not by a few percent but by orders of magnitude. For example, this is the case for contactless bearings such as magnetic, air or hydrostatic bearings, as well as articulated flexure bearings, the subject of this book. Flexure bearings are based on the physical principle of the elasticity of matter where precision is not limited as in contact between solids.
Flexure bearing advantages
Absence of friction: Rolling or sliding contact between solids inevitably produces friction which is generally harmful to the linkage. It dissipates energy, producing heat and mechanical hysteresis. This friction depends in a highly non-linear way on the relative speed between the bodies resulting, at low speed, in a stick & slip motion which limits the movement resolution. Moreover, it is the reason for wear of contact parts. The use of rolling bearings for small amplitude displacements not producing complete rotations of the rolling components leads to fretting which reduces bearing longevity by accelerating their wear and corrosion.
Flexible linkages, however, do not suffer from any solid or rolling friction. The onlyre maining friction is internal material friction produced elastically it is virtually negligible.
Absence of wear: Wear of plain and rolling bearings reduces their precision by modifying their geometry and increasing play. Moreover, it is the principal factor limiting longevity.
Flexure bearing are immune from all wear. Their longevity is limited only by material fatigue and its possible corrosion.
Absence of seizing: Seizing is a severe form of adhesive wear between frictional surfaces, binding or welding them, thereby blocking bearing function. The presence of dust or impurities can lead to seizing.
Flexure bearings eliminate the risk of seizing, conferring them great reliability, even in dirty environments.
Absence of lubrification: Plain and rolling bearings generally require lubrication in order to minimise friction and wear. Maintaining adequate lubrication during the entire lifespan of a mechanism requires regular maintenance. More over, lubricants can hardly be used in clean rooms and in partial vacuum (microscopes, satellites), as they are a source of pollution.
Flexure bearings do not require lubrication, do not release any polluting particles and do not require maintenance.
Large transverse rigidity: It is absolutely necessary to have a very rigid mechanical structure in order to produce precision displacements. Rolling bearings exhibit low rigidity unless they are pre-constrained (Hertzian pressure of a rolling body on a rolling surface), and this increases as the rolling elements decrease in diameter.
Transverse rigidity of flexure bearings can be extremely high if the latter are well designed. The smaller the dimensions, the greater advantage to flexure bearings in terms of rigidity.
Absence of play: When plain and rolling bearings are not pre-constrained, mechanical play occurs, resulting in a number of inconveniences. Bearing play reduces mechanical structure precision in two ways. From a static point of view, it modifies the kinematics of articulated structures in a generally unpredictable way. From a dynamic point of view, it reduces the natural vibration frequencies of structures, making them less precise and susceptible to float which leads to harmful shock. When it is too bothersome, play can be checked by mechanical pre-constraint, but this complicates the mechanism.
Flexure bearings do not have play, by design.
Monolithic components: Plain and rolling bearings are made of several mechanically assembled components. These assemblies generally increase congestion and fabrication tolerances decrease the precision of their construction.
Flexure bearings can be made monolithically, rendering them very compact and precise while avoiding delicate and expensive assembly of small components. Flexure rigidity of beams being inversely proportional to the cube of span, compact construction yields a significant increase in structural rigidity.
To go further : This book establishes a conceptual framework for the design of flexure-based articulated structures. Topics featured deal with the theoretical foundations for the design of translational and rotational flexures, the simple kinematic analysis of flexure-based mechanisms, and advanced kinematic approaches to the design of complex flexure-based mechanisms using modules in parallel or serial arrangements. The book also features detailed examples of long stroke flexure mechanisms used in metrology applications, and a detailed example of planar flexure mechanisms having out of plane functionality and used in surgical applications. This book aims to provide scientists and engineers with a conceptual tool, an analytic methodology and the key references for their precision engineering needs.
Extract of the book The Art of Flexure mechanism Design From Florent Cosandier, Simon Heinen, Murielle Richard and Lennart Robert Collection EPFL Press Published at Presses Polytechniques et Universitaires Romandes (PPUR)