Four-bar linkages can transmit angular motion between two rigid links, but their transmission ratio is generally not constant due to kinematic nonlinearities. When such linkages are implemented with flexures-replacing joints with elastic elements to eliminate friction, backlash, and wear-additional parasitic motions are introduced. This article demonstrates that nonlinearities arising from both rigid-body kinematics and flexure deformations can be harnessed to compensate for one another, leading to optimized flexure-based couplers, inversors, reducers, and amplifiers. The analytical model merges Euler-Bernoulli beam theory with loop-closure kinematics, providing geometric design rules that exploit these nonlinear effects to improve transmission constancy. Finite element modeling and experiments on polymer prototypes confirm the validity of the approach, showing that optimized flexure couplers can match or even surpass the performance of ideal four-bar linkages. For instance, in a flexure mechanism with a 1:-1 transmission ratio, the error is reduced from 23% to below 1% for angular displacements up to +/- 20 degrees. These results establish flexure-based transmission mechanisms as a new class of kinematic building blocks for the design of purely rectilinear and purely circular flexures.

Compliant mechanisms achieve motion through elastic deformation rather than contact surfaces, eliminating friction, wear, and lubrication requirements. Historically, conventional manufacturing processes have constrained both the design and adoption of these mechanisms in cryogenic and space applications. This work exploits the design freedom of Laser Powder Bed Fusion (LPBF) to propose a streamlined Design for Additive Manufacturing (DfAM) workflow for optimizing and customizing a flexure pivot operating at 4.2 K within the Mode Selector Mechanism (MSM). The methodology comprises three stages: (i) material selection and post-processing—316L stainless steel combined with stress annealing and HIP—to ensure cryogenic compatibility and fatigue strength; (ii) optimization of the Interlocked Lattice Flexure (ILF) geometry considering performance metrics (stroke, stiffness, guiding accuracy) and AM constraints (overhang, minimum feature size); and (iii) flexure thickness tuning to meet project-specific requirements while mitigating AM-induced variability, enabling rapid customization. Numerical and experimental validation confirmed compliance with design targets: ± 3.5^∘ stroke, stiffness of 3.97 mN m/ ^∘ , and fatigue life exceeding 10^6 cycles under over-testing conditions (115

Residual stresses can be advantageously used to permanently preload flexure micro-mechanisms in order to modify their deflection and stiffness. This paper presents a new preloading chevron mechanism (PCM) used to amplify the preloading effect of thin film residual stress. To evaluate the preloading performances of this structure, the deflection characteristics of buckled beams and flexure linear stages preloaded by a PCM is investigated experimentally. All the mechanisms are manufactured from a monocrystalline silicon substrate using deep reactive ion etching and residual stress is provided by wet thermal oxidation. Measurements show that the deflection magnitude of fixed-fixed oxidized silicon buckled beams can be increased by up to 5 times when a PCM is integrated. The flexure linear stages studied in this research are composed of a parallel leaf spring stage connected to two fixed-guided buckled beams preloaded by a PCM. Depending on the beam dimensions, the stage translational stiffness can be set to a specific value. We designed a near-zero positive stiffness linear stage revealing a measured stiffness reduction of 98%, and a bistable linear stage with a constant negative stiffness region. Thanks to the elevated preloading displacement supplied by the PCM, the operating stroke (actuation region where the stiffness remains constant) is relatively large (more than 0.4 mm travel for 2.59 mm leaf spring length). The analytical and numerical models carried out to design the mechanisms are in good agreement with the experimental data. The results show that the fixed frame stiffness has a significant effect on the preloading performances due to the substantial forces exerted by the PCM. Furthermore, the presented preloading concept, modeling and sizing method could be applied to other compliant mechanism designs, scales and materials, enabling applications in microelectromechanical systems and watchmaking.

Mechanical watches are generally regulated by a balance and a spring constituting a harmonic oscillator. This mechanism is intrinsically force-balanced, which makes it essentially insensitive to gravity as well as to the linear accelerations of the watch. Nevertheless, this mechanism is not dynamically balanced, i.e., its motion is affected by the angular accelerations of the watch around axes parallel to the pivoting axis of the balance. This phenomenon degrades the chronometric precision of the watch when worn on the wrist. This article presents a novel dynamically-balanced oscillator mechanism dedicated to mechanical watches, which solves this issue: a 1-DOF mechanism relying on a flexure-based Watt's linkage equipped with two balances rotating in opposite directions. The use of flexures brings additional advantages: absence of friction, no need for lubrication, increased quality factor, and monolithic design. The mechanism is presented with its Pseudo- Rigid-Body-Model and the numerical model used to predict force and dynamic-balancing residual defects: this includes sag and frequency variations under in-plane gravitational loads and pose sensitivity to in-plane angular accelerations. Experimental results from a 2:1 scale titanium prototype, compared to a watch-scale prototype, validated both the analytical and numerical models for large force and dynamic-balancing defects. An iterative tuning method achieved a sag variation below 5 mu m, a daily rate variation of less than 18 seconds per day for all in-plane gravity orientations, and sensitivity to angular accelerations 250 times lower than its single-balance version.

This article presents a novel family of exactly-rectilinear translation mechanisms, called the "QUADRISTAGE family", based on one-degree-of-freedom planar kinematics exclusively using pivot joints and rigid segments. Several variants are presented, some providing exactly rectilinear motions and other nearly-rectilinear motions. These kinematic architectures can advantageously be physically implemented using flexure-joints, to achieve accurate and repeatable motion, as well as to overcome the conventional trade-offs in flexure mechanism design, enabling higher mechanical performance. This leads to large-stroke highly rectilinear mechanisms with highly linear force vs displacement characteristics, high load capacity and high support stiffness. Theses mechanisms can be machined monolithically at centimeter or milliliter scale for a broad range of high precision engineering applications or for MEMS devices.

Flexure-based linear stages have become prevalent in precision engineering; however, most designs suffer from parasitic shifts that degrade positioning accuracy. Conventional solutions to mitigate these parasitic motions often compromise support stiffness, reduce motion range, and increase structural complexity. This study presents a novel family of flexure-based rectilinear-motion stages using coupled n-RRR planar parallel mechanisms, achieving extremely low parasitic shifts while addressing the forementioned limitations. Four design variants are selected and analyzed via Finite Element Method (FEM) simulations, evaluating parasitic shifts, stroke, and support stiffness. The most precise configuration, a 4-RRR rectilinear stage having kinematic chains coupled via two Watt linkages, exhibits a lateral shift smaller than 0.258 µm and an in-plane parasitic rotation smaller than 12.6 µrad over a 12 mm stroke. Experimental validation using a POM prototype confirms the high positioning precision and support stiffness properties. In addition, a silicon prototype incorporating thermally preloaded buckling beams is investigated to reduce its translational stiffness. Experimental results show a translational stiffness reduction of 98% in the monostable configuration and 112% in the bistable configuration (i.e., negative stiffness), without support stiffness reduction. These results highlight the potential of the proposed mechanisms for a wide range of precision applications, offering a scalable and high-accuracy solution for micro- and nano-positioning systems.

The balancing of mechanisms consists in distributing their moving masses, inertias, and elastic components in order to achieve key mechanical properties, such as the elimination of the shaking forces and moments exported onto their supporting structure or the insensitivity of the mechanism to gravity and to the motions of its chassis. This article introduces a new refined systematic taxonomy for the classification of multi-degree-of-freedom (DoF) 3-dimensional passively balanced mechanisms. The taxonomy is composed of 15 distinct types – compared to only 4 types described in the literature. Each type is provided with its definition, the necessary conditions to be satisfied, the list of resulting mechanical properties, and a 1-DoF mechanism example. This taxonomy applies to mechanisms subject to gravity and mounted onto fixed or mobile chassis undergoing linear and angular accelerations, and, newly, also angular velocities. It is represented as a 4-set Venn diagram built on 4 primary balancing types: static, force, moment, and a newly introduced inertial invariance. This theoretical work allows for a refined categorization of the broad spectrum of balanced mechanisms while alleviating some inconsistencies observed in the existing literature.

Future space applications require the assembly of large structures in orbit. This can only be achieved by using autonomous robotic systems able to handle repetitive tasks with heavy and large parts in such challenging environment. This paper provides an overview of a system designed to perform autonomous assembly of segmented mirror tiles, as a proof of feasibility for assembling large structures in space using robotic technologies. We describe the hardware components of the system, and present the software layer, including assembly planning, and skill engine. An experimental evaluation of the assembly process is carried out, thus showing the performance achieved with the system.

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wear. This paper presents an alternative mechanism that is functionally equivalent to a classical flywheel while relying exclusively on limited-stroke flexure joints. This novel one-degree-of-freedom zero-force mechanism has no wear and requires no lubrication: it is thus compatible with extreme environments, such as vacuum, cryogenics, or ionizing radiation. The mechanism is composed of two coupled pivoting rigid bodies whose individual angular momenta vary during motion but whose sum is constant at all times when the pivoting rate is constant. The quantitative comparison of the flexure-based flywheel to classical ones based on a hollow cylinder as inertia shows that the former typically stores 6 times less angular momentum and kinetic energy for the same mass while typically occupying 10 times more volume. The freedom of design of the shape of the rigid bodies offers the possibility of modifying the ratio of the stored kinetic energy versus angular momentum, which is not possible with classical flywheels. For example, a flexure-based flywheel with rigid pivoting bodies in the shape of thin discs stores 100 times more kinetic energy than a classical flywheel with the same angular momentum. A proof-of-concept prototype was successfully built and characterized in terms of reaction moment generation, which validates the presented analytical model.

Flexure pivots, which are widely used for precision mechanisms, generally have the drawback of presenting parasitic shifts accompanying their rotation. The known solutions for canceling these undesirable parasitic translations usually induce a loss in radial stiffness, a reduction of the angular stroke, and nonlinear moment-angle characteristics. This article introduces a novel family of kinematic structures based on coupled n-RRR planar parallel mechanisms, which presents exact zero parasitic shifts while alleviating the drawbacks of some known pivoting structures. Based on this invention, three symmetrical architectures have been designed and implemented as flexure-based pivots. The performance of the newly introduced pivots has been compared with two known planar flexure pivots having theoretically zero parasitic shift via Finite Element models and experiments performed on plastic mockups. The results show that the newly introduced flexure pivots are an order of magnitude radially stiffer than the considered pivots from the state-of-the-art while having equivalent angular strokes. To experimentally evaluate the parasitic shift of the novel pivots, one of the architectures was manufactured in titanium alloy using wire-cut electrical discharge machining. This prototype exhibits a parasitic shift under 1.5 mu m over a rotation stroke of +/- 15 deg, validating the near-zero parasitic shift properties of the presented designs. These advantages are key to applications such as mechanical time bases, surgical robotics, or optomechanical mechanisms.

An ultraquiet environment is required for space missions contingent on high-precision pointing instruments. Hexapod platforms represent a promising solution for isolating primary sources of microvibration, such as reaction wheels and cryocoolers, from sensitive payloads. This paper addresses the mechanical design and verification aspects of a semi-active system relying on electromagnetic shunt dampers (EMSDs) and alternative strut joints. The comparatively simple architecture is beneficial in terms of mass, power consumption and disturbance attenuation across a wide frequency range, but ensuring launch survivability presents unique challenges. Here, preliminary analyses driving design choices are discussed and results from the current stage of manufacturing, integration and testing of the hexapod are presented.

Flexure pivots, which are widely used for precision mechanisms, generally have the drawback of presenting parasitic shifts accompanying their rotation. The known solutions for canceling these undesirable parasitic translations usually induce a loss in radial stiffness, a reduction of the angular stoke, and a nonlinear moment-angle characteristics. This article introduces a novel family of kinematic structures based on coupled n-RRR planar parallel mechanisms which presents exact zero parasitic shifts, while alleviating the drawbacks of some known pivoting structures. Based on this invention, three symmetrical architectures have been designed and implemented as flexure-based pivots. The performance of the newly introduced pivots has been compared via Finite Element models with that of two known planar flexure pivots having theoretically zero parasitic shift. The results show that the newly introduced flexure pivots are an order of magnitude radially stiffer than the considered pivots from the state of the art, while having zero parasitic shift properties and equivalent angular strokes. These advantages are key to applications such as mechanical time bases, surgical robotics, or optomechanical mechanisms. Polymer mockups and a titanium alloy prototype have been manufactured for future experimental validation.

Recent developments of compliant mechanisms built by additive manufacturing confirm their potential for highprecision applications in harsh environments. Several projects are presented, from simple flexure pivots to complex 3D compliant mechanisms designs, to show the advantages and challenges of the design, manufacturing and testing of such systems. Focus is put on the specific design methodology, the integration of electrical functions, the guiding and lifetime performance results to highlight the potential for future high-precision applications such as high-precision, cryogenic or space. First, the redesign of simple flexure blades and crossed-blade pivots has been performed. The guiding performances have been compared to simulations. Then, more complex architectures of compliant mechanisms have been designed, manufactured and tested. For example, the European Space Agency (ESA) project Compliant Mechanisms based on Additive Manufacturing (COMAM) and the European H2020 project Prototype for Ultra Large Structure Assembly Robot (PULSAR). This project validates the positioning of tiles integrated on 3D printed flexible pivots and gimbals with a repeatability better than 1 μm. ESA selected CSEM for a new project, the development of a new compliant mechanism with a rotary to linear motion transformation. It is presented here with a novel 3D printed monolithic architecture made of stainless steel.

An innovative concept of building compliant mechanisms by additive manufacturing (AM) developed at CSEM is presented. Bringing together CSEM’s experience in the design and development of high-performance flexural elements and mechanisms for more than 30 years has opened the doors to new opportunities. The complete development of compliant structures for AM enables CSEM to develop innovative concepts to drastically reduce the need of machining after AM. Support structures under flexure blades are integrated to the flexures with no need for removal, which makes the overall process becomes more streamlined. Thanks to this concept, CSEM has developed new architectures of compliant mechanisms based on additive manufacturing (COMAM) for the European Space Agency (ESA). These demonstrators will be used as use-case for future high-precision and harsh environment applications such as cryogenic and space. The complete development workflow, starting with the design, topology optimization, manufacturing, post-processes, validation, up to performance and environmental testing will be presented.

Based on a new concept to build flexible structures by metallic 3D printing that has been developed at CSEM, several compliant mechanisms have been redesigned for Additive Manufacturing (AM). In addition to the new geometric possibilities offered by AM, the needs for machining and assembly after printing are drastically reduced. Support structures under flexure blades are thus minimized and the overall process becomes more streamlined. Moreover, this idea allows us to advantageously design and produce monolithic cross blade flexure pivots with interlocked flexures. Thanks to this concept, CSEM is now developing and testing new architectures of Compliant Mechanisms based on Additive Manufacturing (COMAM) for the European Space Agency (ESA) in the frame of a GSTP research project.

The H2020 project PULSAR (Prototype for an Ultra Large Structure Assembly Robot) development objective is to create three demonstrators that that will pave the way for the construction of large structures in orbit. The study case considered in PULSAR is the assembly of a segmented primary mirror for next generation 35m space-based telescope. In the frame of this project, CSEM is developing Single Mirror Tile demonstrators (SMT) that host a positioning mechanism capable of adjusting the position of the hexagonal mirror in order to compensate for inaccuracies generated by the robotic assembly. This mechanism has a tripod architecture. It is composed of three linear actuators and of transmission stages, each made of a flexible pivot and of a gimbal. This mechanism allows for controlling the mirror position along three degrees of freedom (piston translation and tip and tilt rotations). The piston stroke is required to be ±3 mm with a resolution of 1 μm and a repeatability better than 5 μm while the tip/tilt strokes are ±1° with 4 μrad of resolution and 20 μrad of repeatability. The design of the tiles benefits from CSEM extensive experience in compliant mechanisms and additive manufacturing applied to the domain of scientific instrumentations for space applications.

An innovative design of a Large Angle Flexure Pivot (LAFP) is described. It combines the advantages of flexure mechanisms while surpassing one of their few flaws, small displacement strokes. The LAFP design exceeds these angular limitations to reach a deflection of 180° (±90°). The centre shifts laterally by less than ±35 μm throughout the full rotation range. The LAFP is meant to be mounted in pairs, coaxially and with the payload between them. The intended application of the LAFP is to angularly guide an optical component in a space environment for future science missions operating in a cryogenic environment. A dedicated performance test bench was developed and manufactured to test the pivot characteristics notably the lateral shift using Eddy current sensors. The test bench incorporates a representative dummy payload for mass and inertia. Extensive FEM analysis has been performed to validate the design at component level and further analysis with the pivots mounted with a representative payload on a test bench for random vibration, shock and thermal cycling environment. The second test bench for the vibration and shock tests has been manufactured incorporating a simplified launch locking device. The performance tests have confirmed a lateral shift of less than ±35 μm over an angular range of ±90°. The pivots have been successfully tested and survived vibration loads for high level sine at 24 g and random vibration at 12 grms in all three directions.

The new geometric possibilities offered by Additive Manufacturing (AM) combined with a complete redesign of compliant mechanisms have allowed CSEM to develop innovative concepts (patent pending) to drastically reduce the need of machining and assembly after additive manufacturing. Support structures under flexure blades are thus minimised and the overall process becomes more streamlined. Moreover, this idea allows us to easily design and produce monolithic cross blade flexure pivots with interlocked flexible blades. Thanks to this concept, CSEM is now developing new architectures of Compliant Mechanisms based on Additive Manufacturing (COMAM) for the European Space Agency (ESA) in the frame of a GSTP research project.

This work discusses 6 design principles useful to optimise compliant mechanisms for Additive Manufacturing (AM) and more specifically Selective Laser Melting (SLM). The design principles are: 1) lattice flexures, 2) interlocking flexures, 3) embedded support structures, 4) flexure shape optimization, 5) structural topology optimization and 6) thermal warpage compensation. These six design principles are first illustrated with the example of a simple pivot. Lastly, they are applied to a compliant rotation reduction mechanism. Structural topology optimization, Lattice flexures, Selective Laser Melting (SLM), Support structures, Interlocked flexures, Compliant mechanisms.