Compliant Mechanisms Research Articles

The STAGE method for simultaneous design of the stress and geometry of flexure mechanisms

Current design methods for flexure (or compliant) mechanisms regard stress as a secondary, limiting factor. This is remarkable because stress is also known as a useful design parameter. In this paper we propose the Stress And Geometry (STAGE) method, to design the geometry of a flexure mechanism together with a desired stress field. From this design, the stress-free to-be-fabricated geometry is computed using the inverse finite element method. To demonstrate the potential of the method, the geometry of the well-known crossed-flexure pivot is taken as example. We first show how this mechanism can be redesigned for the same functional geometry with various internal stresses. This results for a specific choice of stress field in a design of a crossed-flexure pivot with 23% lower peak stresses during motion as compared to the known designs, for a ±45° rotation. We then present a second example, of a Folded Leaf Spring (FLS). With a parameter sweep the optimal stress field is calculated, showing a peak stress reduction of 28% during motion. This result was validated with an experiment, showing a normalized mean absolute error of 5.5% between experiment and theory. With a second experiment it was verified that the functional geometry of the FLS with internal stresses was equal to the one without internal stresses, with geometric deviations smaller than half the thickness of the flexures.

A Synthesis Approach of XYZ Compliant Parallel Mechanisms Toward Motion Decoupling With Isotropic Property and Simplified Manufacturing

Abstract Decoupled compliant parallel mechanisms with isotropic legs possess many excellent performances, including ease of actuation, control, manufacture and mathematical analysis, as well as effective error compensation. Despite the advent of numerous isotropic compliant parallel mechanisms, their synthesis process predominantly relies on the empirical knowledge of engineers, with an absence of dedicated synthesis methodologies. This paper proposes the constraint algebra method, a novel synthesis method capable of autonomously exploring feasible constraint space for the synthesis. This method involves algebraic formulation of the constraints for the compliant modules, followed by solving constraint equations to find the feasible constraints and orientations, thereby facilitating the synthesis with intended performance characteristics. The multiplicity of solutions to the constraint equations enables the generation of diverse designs, including innovative configurations that are challenging to obtain via other methods and experience. Furthermore, by the consideration of machinability in several steps of synthesis, the optimal configuration can be selected for simplified manufacture. A design case has been monolithically prototyped and experimentally tested. The proposed methodology holds promise for potential extension to the synthesis of other types of compliant mechanisms.

Dimensional and Weight Characterization of 3D Printed PET Specimens Designed for Compliant Mechanisms

Dimensional and Weight Characterization of 3D Printed PET Specimens Designed for Compliant Mechanisms

Design of a Compliant Sternum Prosthesis for Improving Respiratory Dynamics

This study presents a novel approach to sternum prosthesis design, aiming to address the limitations of the current solutions by employing compliant mechanisms. The research focuses on developing a prosthetic design capable of generating lifting movements on ribs during breathing. First, a videogrammetry experimental test and virtual simulations were conducted to ascertain the vertical forces applied to each sternum joint. Subsequently, a compliant mechanism design was initiated, involving optimization and finite element analysis (FEM). A comprehensive kinematic performance analysis was performed to evaluate the prosthetic design. The results indicate that the obtained displacements of each rib closely align with those reported in the existing literature, demonstrating the effectiveness of the proposed solution. In conclusion, the developed sternum prosthesis exhibits the capability to recover approximately 56% of the ribs’ natural movements, highlighting its potential as an innovative and promising solution in the field of chest prosthetics.

Achieving near-zero particle generation by simplicity of design—A compliant-mechanism-based gripper for clean-room environments

Lab Automation facilitates high-throughput processes and improves reproducibility and efficiency while removing human action, primary source of contaminating particles. Handling poses a risk of contamination due to close contact with the objects. We propose a novel gripper (CrocoGrip) relying on compliant mechanisms to reduce the amount of contaminating particles generated by the gripper rather than preventing their emission, the latter being the common approach in current grippers. Our novel gripper is actuated by linear solenoids and purely relies on deformation for its motion. As a result, abrasive behavior and, therefore, the generation of particles is reduced without the need for additional sealing. We experimentally proved that only particles smaller than 3.0µm are emitted by the gripper, with a large proportion of the particles being generated by the actuation. The CrocoGrip fulfills the demands of ISO14644 class 5. The gripping relies on the deformation energy of the compliant mechanism, making the gripping energy-efficient and safe. The maximum gripping force achieved by the CrocoGrip was 5.5N. Because the force transmitted to the handling object depends on the design of the gripping jaws, which are interchangeable, the force can be reduced for more sensible handling objects. Using three different sets of jaws, CrocoGrip was able to handle a microplate in SBS-standard, a 50mL Falcon tube, and a Ø60mm Petri dish using a robotic arm. Due to the monolithic design of the CrocoGrip and, as a result, the need for few components, we achieve a simplicity of design, making cleaning, sterilization and maintenance easy, even for nonexperts. The CrocoGrip exploits the advantages of compliant mechanisms, especially for applications requiring clean-room environments. This approach of compliant-mechanism-based grippers enables an increase in the cleanliness of handling processes without an increase in system complexity of the gripper to facilitate the lab automation of highly sensible processes, such as in tissue engineering.

Gradients of properties increase the morphing and stiffening performance of bioinspired synthetic fin rays

State-of-the-art morphing materials are either very compliant to achieve large shape changes (flexible metamaterials, compliant mechanisms, hydrogels), or very stiff but with infinitesimal changes in shape that require large actuation forces (metallic or composite panels with piezoelectric actuation). Morphing efficiency and structural stiffness are therefore mutually exclusive properties in current engineering morphing materials, which limits the range of their applicability. Interestingly, natural fish fins do not contain muscles, yet they can morph to large amplitudes with minimal muscular actuation forces from the base while producing large hydrodynamic forces without collapsing. This sophisticated mechanical response has already inspired several synthetic fin rays with various applications. However, most ‘synthetic’ fin rays have only considered uniform properties and structures along the rays while in natural fin rays, gradients of properties are prominent. In this study, we designed, modeled, fabricated and tested synthetic fin rays with bioinspired gradients of properties. The rays were composed of two hemitrichs made of a stiff polymer, joined by a much softer core region made of elastomeric ligaments. Using combinations of experiments and nonlinear mechanical models, we found that gradients in both the core region and hemitrichs can increase the morphing and stiffening response of individual rays. Introducing a positive gradient of ligament density in the core region (the density of ligament increases towards the tip of the ray) decreased the actuation force required for morphing and increased overall flexural stiffness. Introducing a gradient of property in the hemitrichs, by tapering them, produced morphing deformations that were distributed over long distances along the length of the ray. These new insights on the interplay between material architecture and properties in nonlinear regimes of deformation can improve the designs of morphing structures that combine high morphing efficiency and high stiffness from external forces, with potential applications in aerospace or robotics.

Topology Design of Compliant Mechanism Design With Multiple Component Modeling Connected by Various Joints

Abstract This study presents a novel framework for the optimal design of compliant mechanisms, specifically addressing the structural drawbacks of conventional single-point or de facto hinges. The hinges often lead to structural instability and stress concentration while deriving maximum motion. To overcome these issues, we introduce a new method that can design stable and elastic domains connected by either revolute or prismatic joints. The new method, called sequential analysis based on the reaction force, can successfully eliminate weak hinge points while optimizing joint locations. The efficiency of developed methodology is validated through several numerical examples, yielding compliant mechanisms with suppressed hinges.

Design of a large stroke compliant gripping mechanism for constant-force applications

Design of a large stroke compliant gripping mechanism for constant-force applications

A compliant constant-force mechanism with sub-Newton force and millimeter stroke output

Force control technology plays a pivotal role in manipulating vulnerable objects. This paper presents a new compliant mechanism with constant-force output characteristics, which can prevent force damage due to displacement overshoot. Due to its unique passive structure, it is exempted from intricate sensors and complicated controllers. The quasi-static constant-force mechanism is obtained by the parallel combination of positive- and negative-stiffness mechanisms. Such a straightforward method facilitates a rapid development and implementation process. The procedures of architectural arrangement selection, theoretical model establishment, parameter sensitivity evaluation, and multi-objective structural optimization are carried out to achieve specified constant-force characteristics. Moreover, the prototype fabrication and performance testing of a constant-force mechanism have been performed. The results demonstrate that the mechanism delivers a constant output force of 339 mN in the motion range of 1.84 mm. The constant-force feature is solely governed by the actuating displacement and is independent of driving speed and acceleration. The promising application of the constant-force mechanism has been demonstrated by manipulating small force-sensitive objects such as biological eggs.

Analytical Modeling and Validation of New Prismatic Compliant Joints Based on Zero Poisson’s Ratio Lattice Structures

Abstract The design and analysis of prismatic compliant joints have received less attention compared to that given to revolute compliant joints, thus limiting their implementation in compliant mechanisms beyond translational stages. Lattice structures have been used effectively to increase flexibility and stiffness ratios in compliant joints. Considering these, new prismatic compliant joints based on zero Poisson’s ratio lattice structures (ZP-PCJ) are proposed. Lattices with three different cell arrangements are considered: single cells, 2×2, and 3×3 lattices. Additionally, unit cells with three different geometries are studied: triangular, chamfer, and cosine. The compliance matrices of the ZP-PCJs are assembled analytically using Castigliano’s second theorem and compliance series–parallel simplification. The compliance ratios along the three orthogonal axes of the ZP-PCJs are computed varying their geometric parameters. Finite element models are constructed to validate the analytical results. Experimental tests are performed on additively manufactured ZP-PCJs to corroborate the compliance coefficients. Results showed that analytical models can predict the ZP-PCJ’s elastic properties accurately, differences less than 3% and 12% were obtained when compared to computational and experiments, respectively. Based on the compliance ratios obtained, the ZP-PCJs are suitable for two-dimensional applications. Finally, the ZP-PCJs are implemented in a compliant mechanism to evaluate their behavior, analytically and computationally. The ZP-PCJs have advantages such as eliminating axis drift and high flexibility in motion-direction while maintaining stiffness in other directions. The differences observed when comparing the analytically obtained estimations with simulations and experimental data suggest that ZP-PCJ analytical models are reliable for estimating their performance in compliant systems.

Expanding research impact through engaging the maker community and collaborating with digital content creators.

This paper proposes a method for increasing the impact of academic research by providing materials for public use, thus engaging the maker community, and by collaborating with internet content creators to extend the reach. We propose a framework for engagement and report a multi-year study that evaluates short, intermediate, and long-term outcomes, with a second effort to demonstrate repeatability of the short-term outcomes. In the first study, we posted forty-one 3D printable compliant mechanisms on public repositories and collaborated with physicist and content creator Derek Muller (Veritasium YouTube channel). Outputs and outcomes from this interaction were measured over 3 years. The framework was exercised again with four new 3D printable mechanisms in collaboration with engineer and STEM influencer Mark Rober. The proposed methods aim to help researchers extend the reach of their work to broader audiences, including professional engineers, hardware designers, educators, students, researchers, and hobbyists. This work demonstrates promising impacts of the framework, including (1) extending public awareness of research findings to broader audiences by engaging the maker community and collaborating with content creators, (2) accelerating the pace of innovation and further hardware-based research through public application of research findings, (3) fostering a culture of open-source design and collaboration among other researchers, engineers, educators, and makers, and (4) increasing utilization of peer-reviewed published content. These outreach practices can be valuable tools for researchers to increase impact of and excitement for their research.

A spatial 3-DOF piezoelectric robot and its speed-up trajectory based on improved stick-slip principle

Piezoelectric robots have been proven to be suitable for high-precision, cross-scale micro-nano manipulation due to their nanometre resolution and high flexibility. To make up for the limited stroke of micro-nano positioning platforms, a spatial three-degrees-of-freedom (3-DOF) piezoelectric robot is proposed in this study to enable three-dimensional micro-nano manipulation of objects. The robot utilizes the deformation of the piezoelectric stack as the source of displacement. It is comprised of a parallel compliant mechanism and a guided compliant mechanism in series, resulting in a compact robot body. The robot is capable of linear displacement in x-, y- and z-axes. The stiffness of the guided compliant mechanism is calculated using theoretical modeling and compared with the finite element simulation results, with a deviation of less than 5.6% verifying the accuracy of the model. The robot operates using two motion principles: the direct drive principle, which has a resolution of 16, 15, and 11 nm in x-, y- and z-axes, and a motion space of 13×11×7 μm3; and the improved stick-slip principle, which has a theoretical infinite stroke and a maximum speed of 4.2 and 3.9 mm/s in x- and y-axes. The speed of the improved stick-slip principle is 42% higher than that of the traditional stick-slip principle in x- and y-axes. The robot has a spatial 3-DOF, nanometre resolution, millimeter speed, and can carry more than 500 g.

Analysis of compliant mechanisms with series and parallel substructures through the ellipse of elasticity theory

Compliant mechanisms with complex hybrid configurations have been designed to meet the requirements of specific applications demanding high performance. Kinetostatic analysis, fundamental at the early stage of design, can become difficult for compliant systems characterized by series and parallel substructures. In the present paper, the ellipse of elasticity method is implemented for the analysis of a compliant mechanism with hybrid topology. Firstly, the ellipses associated to the different flexure hinges, characterized by uniform or non-uniform cross-sections, and by constant or variable initial curvature, are determined. Then, the unique ellipse representing the compliant mechanism is obtained by means of series and parallel compositions. By exploiting the antiprojective polarity properties of the ellipse, the kinetostatic analysis of the compliant system is reduced to a geometric problem with a straightforward solution. Linear and nonlinear finite element analyses and experimental tests are performed to verify the theoretical results.

Compliant mechanism design of combined aircraft wing for stable separation

Abstract Stable separation is a crucial condition that must be met in order for combined aircraft to successfully engage in cooperative flight. In order to achieve the desired fast and controlled separation, this paper proposes a novel design for a torque-driven compliant separation mechanism. By taking into account the compliance characteristics of a sinusoidal acceleration function curve, a mechanical model for the separation mechanism is developed. By utilising the Coulomb friction law, an accurate determination of the aerodynamic load distribution under various conditions is achieved. Subsequently, the relationship between the unlocking moment and the aerodynamic load is derived based on these findings. Through the utilisation of the finite element method, a model of the separation mechanism is generated. To ensure the safety and reliability of the compliant separation mechanism, the mechanical properties of the structural materials are thoroughly analysed under the maximum aerodynamic load. Subsequently, the separation mechanism structure is constructed and subjected to testing in order to showcase the compliance characteristics. In addition, this paper conducts a simulation to analyse the impact of flight speed and angle-of-attack on the separation process. By doing so, the optimal conditions for separation are determined. The methods and findings presented in this study have the potential to contribute valuable insights to the design of combined aircraft.

Modeling compliant bistable mechanisms: An energy method based on the high-order smooth curvature model

This paper applies an energy method based on the high-order smooth curvature model to address the challenges of kinetostatically modeling the complicated nonlinear post-buckling behavior of inclined compliant beams. The proposed energy method is grounded in the principle of minimum strain energy, implying that the total strain energy is minimized at the equilibrium configuration. In this work, the high-order smooth curvature model is adopted to accurately model the bending strain energy of large deformation beams. Subsequently, the Lagrange multiplier method is employed to ascertain the minimum of strain energy while concurrently determining the corresponding tip loads. Additionally, the deformation shape and maximum stress are determined via the smooth curvature model. The proposed method is introduced for the first time in modeling compliant bistable mechanisms, and it is proven that the method can be used for modeling compliant beams with inclined angles ranging from 0 to 90 degrees. Following the modeling, finite element analysis and experimental tests are conducted to verify the accuracy of the proposed energy method. A comprehensive comparative analysis between proposed method and existing methods is conducted. The comparison results prove that the model is more computationally efficient without compromising modeling accuracy The proposed modeling method can not only be used for modeling compliant bistable mechanisms but also has extendable applications in modeling initially-curved compliant beams, contact-aid design problems, and distributed load problems.The present work not only advances the practical application of the proposed energy method but also lays the foundation for future research in modeling compliant mechanisms.

Bistable Aerial Transformer: A Quadrotor Fixed-Wing Hybrid That Morphs Dynamically Via Passive Soft Mechanism

Abstract Aerial vehicle missions require navigating trade-offs during design, such as the range, speed, maneuverability, and size. Multi-modal aerial vehicles enable this trade-off to be negotiated during flight. This paper presents a Bistable Aerial Transformer (BAT) robot, a novel morphing hybrid aerial vehicle that switches between quadrotor and fixed-wing modes via rapid acceleration and without any additional actuation beyond those required for normal flight. The design features a compliant bistable mechanism made of thermoplastic polyurethane (TPU) that bears a large mass at the center of the robot’s body. When accelerating, inertial forces transition the vehicle between its stable modes, and a four-bar linkage connected to the bistable mechanism folds the vehicle’s wings in and out. The paper includes the full robot design and a comparison of the fabricated system to the elastodynamic simulation. Successful transitions between the two modes in mid-flight, as well as sustained flight in each mode indicate that the vehicle experiences higher agility in the quadrotor mode and higher flight efficiency in the fixed-wing mode, at an energy equivalent cost of only 2 s of flight time per pair of transitions. The vehicle demonstrates how compliant and bistable mechanisms can be integrated into future aerial vehicles for controllable self-reconfiguration for tasks such as surveillance and sampling that require a combination of maneuverability and long-distance flight.

Design and Analysis of a Symmetric Overconstrained Compliant Tilt/Tip Stage Based on a Hybrid Transmission Ratio Model

Abstract Developing a compliant mechanism that have potential in parasitism suppression and cross-axis decoupling is a major challenge to meet the requirement of spatial micro-/nano positioning. This work introduces a compliant tilt/tip stage design with a symmetric and overconstrained configuration that is equipped with four reverse bridge notch flexure amplifiers (RBNFAs) and five revolute notch flexure hinges as multiaxis decoupled structures. A hybrid transmission ratio model is developed to describe the mechanical behavior of this stage using elastic beam and pseudo-rigid-body theories. Finite element analysis (FEA) confirmed the analytical model results. A comprehensive study is performed based on FEA model to validate the influence of a particular configuration on parasitic motion and decoupling effect. A prototype stage is 3D printed and experimentally tested, which confirmed the predictions of the analytical hybrid model. In addition, further analysis was conducted to examine the static mechanical characteristics and parasitic behavior of the stage.

Topology Optimization of a Compliant Constant-Force End Effector for Robotic Operations Over Uneven Surfaces

Abstract A compliant constant-force mechanism (CCFM) is a specific type of compliant mechanism that serves as a passive force regulation device. When subjected to a load, it undergoes deformation, resulting in an almost consistent output force regardless of changes in input displacement. Traditional methods used to design CCFMs typically rely on either stiffness combination or parametric optimization based on existing design configurations. To enable the direct synthesis of CCFMs according to desired boundary conditions, this study proposes a systematic topology optimization method. This method includes a new morphology-based scheme designed to ensure the connectivity of the topological results, thereby achieving this objective. Using this approach, a CCFM suitable for end effector applications is designed and manufactured through 3D printing. Four of these CCFMs are then utilized to create an innovative compliant constant-force end effector for robotic operations on uneven surfaces. The experimental results demonstrate that the presented design achieves output force modulation through elastic deformation, eliminating the need for additional sensors and controllers to regulate the output force. The presented design can be mounted on a robotic arm to provide overload protection and maintain a consistent force output during operation when encountering irregular and uneven surfaces.

Dynamic modeling and optimization of mechanical drift for compliant parallel micromanipulation driven by V-shape linear ultrasonic motors

Designing micro-mechanisms that satisfy large strokes, high precision, and multiple degrees of freedom has consistently been a research focus and challenge in the field of micromanipulation systems. Linear ultrasonic motors (LUMs), with advantages such as millimeter-level travel, nanometer-level motion resolution, and power-off self-locking, significantly contribute to the advancement in the mechanism design of micromanipulation systems. However, the challenge of mechanical drift lacks a comprehensive theoretical analysis to explain its cause and limits its application. This paper presents a mechanical drift modeling method for a compliant parallel micromanipulation (CPM) driven by a LUM. The model primarily focuses on the creep characteristics of the flexure clamp element in the LUM. Based on the stiffness matrix analysis method of the compliant parallel mechanism kinematics, the mechanical drift dynamics model of the CPM is established. The influence of the main structural parameters on the CPM mechanical drift is investigated. The research indicates that the creep of flexure clamps in the CPM is the main factor leading to the mechanical drift. Optimization of mechanical drift is achieved by choosing flexure clamps with higher tangential stiffness for LUM and flexure hinge joints with greater flexibility for CPM. Finally, experimental studies reveal that under equivalent conditions, the mechanical drift of the optimized CPM was significantly reduced than before, proving the rationality of the theoretical model and optimization method.

Ultra-Compact Orthoplanar Spring via Euler-Spiral Flexures

Orthoplanar springs are single-component compliant mechanisms that can be fabricated from sheet material and undergo deflection orthogonal to the plane of the mechanism. They are useful in applications where spatial constraints are significant. An Euler spiral is a curve whose curvature is linearly proportional to the arc length allowing for the curve to assume a flat position under a load. In this work, orthoplanar spring and Euler-spiral concepts are synthesized to create a single-component spring mechanism that lies flat under a load. Where traditional planar springs under a load will take on an out-of-plane contour, the Euler-spiral orthoplanar spring lies completely flat under a load. The relationship between the load needed to flatten the orthoplanar Euler-spiral spring and its physical geometry is examined. A use case where the Euler-spiral orthoplanar spring is utilized as a deployment mechanism for a mid-flight emerging antenna on the surface of a flight body is presented.