Compliant Mechanisms Research Articles

Concept design of a monolithic compliant series-elastic actuator with integrated position and two-level force sensing

Safe physical interaction is significant for the protection of the operated target during delicate micromanipulation tasks. This paper proposes the concept design of a series-elastic actuator mainly constructed by a fully compliant mechanism. It can reduce the transient contact force when the tip touches an object and monitor the interaction force in real time for safe handling. The rear end of the actuator is a flexible linear guide connected with a voice coil motor to offer a bidirectional displacement. The actuator’s front end features a stiffness-switchable mechanism based on folding flexure beams, which provides two-level force buffering and sensing to accommodate varying degrees of contact status. Three strain gauges are integrated into the flexible beam of the mechanism, one of which is used for displacement sensing and the others for monitoring interactive force. After the structural design of the actuator, an analytical model is developed to assess its kinematic performance, which is further verified by finite-element simulation and experimental testing. The experimental results agree with the model and simulation, confirming the effectiveness and reliability of the actuator. The compliant actuator can be applied to some micromanipulation scenarios requiring precision positioning, contact, and interaction at the operating end.

Adaptive passive admittance control of a compliant collaborative robot

Compliance of the collaborative robots plays an important role in human-robot interaction. Due to the complex nonlinearities caused by the compliance, and parameter uncertainties, good performance control method for the compliant collaborative robot is always a challenging task. Therefore, to overcome the challenge of the compliance, and uncertain dynamics, this paper develops an adaptive passive admittance control (APAC) approach for a novel compliant collaborative robot, whose compliant mechanism is constituted of the inerters, springs, and dampers. First, through force-current analogy between mechanical network and electrical network, the compliance of the proposed collaborative robot with the inerters, springs, and dampers, is represented by a novel and simplified admittance matrix to facilitate dynamics model of the proposed collaborative robot. Then, for the proposed compliant collaborative robot, an APAC strategy is presented to dispose of the uncertain parameters of the dynamics. The inertial matrix, Coriolis matrix, admittance matrix, and gravity vector of the compliant collaborative robot are expressed as linear representation of orthogonal basis functions by using function approximation technique (FAT). The boundedness of the robot dynamics is proved by detailed stability analysis which uses Lyapunov function. Finally, simulation results indicate that the proposed APAC of the compliant collaborative robot is effective.

Boosting Energy Return Using 3D Printed Midsoles Designed With Compliant Constant Force Mechanisms

Abstract The enhancement of midsole compressive energy return is associated with improved running economy. Traditional midsole materials such as ethylene vinyl acetate (EVA), thermoplastic polyurethane (TPU), and polyether block amide (PEBA) foams typically exhibit hardening force–displacement characteristics. On the other hand, a midsole with softening properties, which can be achieved through compliant constant force mechanisms (CFMs), can provide significant benefits in terms of energy storage and return. This study presents the development of such a midsole, incorporating 3D printed TPU CFM designs derived through structural optimization. The mechanical properties under cyclic loading were evaluated and compared with those of commercially available running shoes with state-of-the-art PEBA foam midsoles, specifically the Nike ZoomX Vaporfly Next% 2 (NVP). Our custom midsole demonstrated promising mechanical performance. At similar deformation levels, the new design increased energy storage by 58.1% and energy return by 47.0%, while reducing the peak compressive force by 24.3%. As per our understanding, this is the first study to prove that the inclusion of CFMs in the structural design of 3D printed midsoles can significantly enhance energy return.

Dynamic Behavior of Bistable Shallow Arches: From Intrawell to Chaotic Motion

Abstract Bistable shallow arches are ubiquitous in many engineering systems ranging from compliant mechanisms and biomedical stents to energy harvesters and passive fluidic controllers. In all these scenarios, the bistable states of the arch and the sudden transitions between them via snap-through instability are harnessed. However, bistable arches have been traditionally studied and characterized by triggering snap-through instability using quasi-static forces. Here, we analytically examine the effect of oscillatory loads on bistable arches and investigate the dynamic behaviors ranging from intrawell motion to periodic and chaotic interwell motion. The linear and nonlinear dynamic responses of both elastically and plastically deformed shallow arches are presented. Introducing an energy potential criterion, we classify the structure’s behavior within the parameter space. This energy-based approach allows us to explore the parameter space for high-dimensional models of the arch by varying the force amplitude and excitation frequency. Bifurcation diagrams, Lyapunov exponents, and maximum critical energy plots are presented to characterize the dynamic response of the system. Our results reveal that unstable solutions admitted through higher modes govern the critical energy required for interwell motion. This study investigates the rich nonlinear dynamic behavior of the arch element and it introduces an energy potential criterion that can scale easily to classify motion of arrays of bistable arches for future developments of multistable mechanical metamaterials.

Active compliant mechanisms for optimized actuation by LCE-based artificial muscles

Compliant mechanisms leverage deformation of materials for precise, lightweight solution to transfer force and motion. By incorporating smart materials, active compliant mechanisms are formed with self-embedded actuation source. Here, we propose lightweight active compliant mechanisms that mimic biological joints, which are capable of transmitting displacements and forces from the linear contraction of artificial muscles into desired magnitudes and directions using a compact structural design. The artificial muscles are braided from liquid crystal elastomer (LCE) fibers and heating threads, competent of generating large force and stroke. Meanwhile, the compliant mechanisms are designed by topology optimization to imitate the functions of biological joints. Combining the braided artificial muscles and optimized compliant mechanisms, these active compliant mechanisms effectively achieve transmission of centralized linear actuation into multiple and various output motions, which is verified by both numerical simulations and experiments. Furthermore, we demonstrate that the active compliant mechanisms can be used for potential surgical procedures such as in-body grasping, cavity dilation, drug delivery, and suturing. The demonstrated biomimetic motions of the active compliant mechanisms hold significant potential for applications in medical devices and soft robots.

Application of genetic algorithm for the synthesis of path-generating compliant mechanisms

This study demonstrates a significant achievement in using the Genetic Algorithms technique to design compliant mechanisms capable of tracking a predetermined non-linear output path. The main objective of this research is to develop a computational optimization framework for generating mechanisms that satisfy the specified input requirements with the highest precision. The authors present a tool that incorporates a Python interface and ANSYS MAPDL software for modeling, solving, and optimizing compliant mechanisms. The optimization objective and algorithm are outlined, followed by a report of the results and recommendations for future research directions.

A novel bridge-type compliant displacement amplification mechanism under compound loads based on the topology optimisation of flexure hinge and its application in micro-force sensing

The design and modelling of bridge-type compliant displacement amplification mechanisms (CDAMs) are key components in precision engineering. In this study, a bridge-type CDAM under compound loads with an optimum flexure hinge configuration is designed, analysed, and tested. For the case when the flexure hinge configuration is unknown, the internal force distribution for a bridge-type CDAM under compound loads is analysed, and the topology of the flexure hinge is optimised. By applying different volume constraints, the optimised flexure hinge configurations are all V-shaped. Subsequently, a static model of the V-shaped flexure hinge is established. For a bridge-type CDAM with V-shaped flexure hinges, the compliance matrix of the flexure hinge is combined with the relationship among the local compliance matrices in a serial mechanism; consequently, the analytical relationship between the output displacement, output force, and input force is derived. The CDAM is parametrically optimised to further improve the output performance. Simulations and experiments verify the topology optimisation result, static model, and parametric optimisation result. Finally, the CDAM and its static model are applied to the tensile manipulation and micro-force sensing in a microfiber tensile test.

Nonlinear Evaluation of a Large-Stroke Coiled L-Shape Compliant Guiding Mechanism With Constant Stiffness

Abstract Owing to the advantages of monolithic structure and little need for assembling, compliant guiding mechanisms appear to be an effective solution for decoupling multi-freedom precision motions but are still prone to geometric nonlinearities of parasitic error and stiffening effect for large strokes. This paper proposes a coiled L-shape compliant guiding mechanism featuring millimeter-scale strokes with a compact structure, constant stiffness, and minimized parasitic error. The coiled compliant guiding mechanism is formed by convolving L-shape flexure beams in a zigzag configuration with decoupled XY motions achieved. Its geometrically nonlinear parasitic error, variation in stiffness, and primary vibration are captured by using a dynamic beam constraint model (DBCM). It is theoretically, numerically, and experimentally found, by comparing with double parallel guiding mechanisms, that the kinetostatic and dynamic behaviors of the coiled L-shape compliant mechanism are nearly independent on the applied force within intermediate-deformation ranges. Such a weak geometric nonlinearity with the minimized influence of axially loaded stiffening and kinematics-arching effects is much different from the double parallel guiding mechanisms. The obtained results indicate that large strokes with constant stiffness and invariable resonance frequency can be realized, which also allows small parasitic errors.

Design of a Novel Large-Stroke Compliant Constant-Torque Mechanism Based on Chained Beam-Constraint Model

Abstract This study addressed the development of a novel compliant constant-torque mechanism (CCTM) that utilizes Bezier curved beams to provide a large stroke in the constant-torque operating range. Previous CCTMs are limited by their working stroke, which reduces their applicability. The proposed mechanism is based on an analytical model using the chained beam-constraint model (CBCM), which captures the kinetostatic behavior of flexible segments. A genetic algorithm based on the CBCM was used to obtain the optimal structure, which was then verified through finite element analysis and experimental results. The results show that the proposed CCTM provides good flatness with a deviation of 3.7% and a large stroke of 80 deg in the constant-torque working range, while maintaining compactness. This novel CCTM has the potential to provide a simple and effective solution for torque regulators in various applications.

Inerter-based Building Mass Damper: Optimization and experimental study

The Building Mass Damper is a design concept for vibration control of structures where the upper substructure effectively behaves as a Tuned Mass Damper (TMD) for the lower one. Unfortunately, its tuning usually requires softening or partial isolation of the upper substructure; limiting its applicability for retrofitting. The recently proposed Inerter-based Building Mass Damper (IBMD) is an in-parallel intervention on the upper substructure with an inerter and a damper. Thus, the inerter allows correct Tuning, the upper substructure provides the Mass, and the damper adds the Damping. Therefore, a very large mass-ratio TMD is obtained with marginal additional weight and minimal practical impact. In the present work, experimental tests supported by numerical simulations on a small two-story structure model quantitatively confirm the effectiveness of the IBMD. Besides, an innovative compliant mechanism design is introduced for the implementation of the translation-rotational converter that drives the inerter; which has minimal backlash and friction, still allowing large strokes. The experiments involved a frictional damper, which performed comparable to a linear viscous damper considered in the simulations.

Modeling Stiffness and Stress in Serpentine Flexures for Use in a Compliant Bone Plate

Abstract Serpentine flexures offer several advantages for use in linear motion mechanisms, including distributed compliance to reduce stress and increase range of motion. In this work, we develop an analytical model for predicting the moment, vertical deflection, and maximum stress experienced in serpentine flexures in response to an input vertical force. Two classes of serpentines are introduced and modeled with linear motion boundary conditions enforced. Finite element analysis demonstrates a mean model error of 0.86% for these metrics across many flexure topologies. Experimental testing is performed to validate the force–deflection response of three steel serpentine compliant mechanisms. The model is able to predict the experimental stiffness data with a mean error at yield of 5.3%, compared to 6.5% with finite element analysis. Large displacement simulations show the model could remain below 10% error for deflections 3–7 times beyond the mechanisms’ deflection at yield. Finally, the model’s utility is demonstrated in the design of a novel single-piece compliant fracture fixation plate that leverages serpentine flexures to deliver controlled axial motion for long bone secondary healing. Model-derived stress-equivalent flexures are compared in their transverse and torsional rigidity. The proposed model and specific findings can be leveraged to design linear motion mechanisms that incorporate serpentine flexures across a wide range of applications.

The Design and Testing of an Additive Manufacturing-Obtained Compliant Mechanism for the Complex Personalisation of Lenses in Clinical Optometry

The Design and Testing of an Additive Manufacturing-Obtained Compliant Mechanism for the Complex Personalisation of Lenses in Clinical Optometry

OpenVCAD: An open source volumetric multi-material geometry compiler

Modern additive manufacturing has made significant advancements in multi-material fabrication techniques that allow for position-specific control of material deposition. With these advancements, design tools have fallen behind machine capabilities in specifying volumetric information. Traditionally, design and fabrication workflows have expressed multi-material objects as several single-material bodies. By storing only the information about the surfaces of the geometries, information about the volumetric composition of the solids is unrepresented. The intense interest in compliant mechanisms and meta-materials demands a new design method that can support architecting material distribution throughout an object. To address these needs, we present OpenVCAD, an open-source volumetric design compiler with multi-material capabilities. OpenVCAD provides a scriptable suite of geometric and material design methods that enable efficient representation of objects with complex geometry and material distributions. OpenVCAD allows functional specification of multi-material volumes that are parameterized on spatial locations, yielding complex multi-material distributions that would be impossible to describe using alternative methods. This paper will present the OpenVCAD pipeline, compare it to related work, and demonstrate its use through the design and manufacturing of functionally graded multi-material components.

Numerical and Experimental Studies on 3D Printed Compliant Mechanisms in Gripper Applications

Numerical and Experimental Studies on 3D Printed Compliant Mechanisms in Gripper Applications

Enhancing the Design Space of Bistable Laminates by Tailoring the Attachment Boundary Conditions

Abstract Bistable and multistable laminates are structural elements with more than one stable equilibrium configuration. The bistability makes them very interesting for the design of compliant mechanisms. However, these laminates are extremely sensitive to boundary conditions and attachment methods. It has been shown prior in the literature that restrictive boundary conditions can lead to the loss of bistability or unwanted deformation modes. This article develops attachment concepts that leverage the structural behavior changes caused by boundary conditions to expand the design space of bistable elements for structural applications. A systematic means of using the boundary conditions to improve the stability margins and load introduction of bistable tape springs is demonstrated. The stability margins and the achievable angles have been quantified using an analytical model previously developed by Guest and Pellegrino. Subsequently, high-fidelity finite element (FE) simulations are done in abaqus™ to determine the limits of the proposed method in terms of localization effects. Based on the analytical model and simulation outcomes, layup, size, and attachment points are determined, and two prototypes are fabricated, illustrating the effectiveness of the proposed method in expanding the design space of traditional bistable tape springs.

A new cockroach-like compliant mechanism with SLA-3D printing for micromanipulation and micropolishing of biomaterials

The traditional compliant mechanisms often employ displacement amplification mechanisms to magnitude the workspace but their displacements are still smaller than 1 mm. Unlike previous studies, the present paper proposes a new conceptual design of compliant mechanism which is inspired from biomechanics of cockroach animal. The developed compliant mechanism for two specific functions, such as microgripper and micropositioner which can handle biomaterials. It can permit a large stroke over 1 mm. Modeling of the performances of the proposed mechanism are built by a couple of adaptive neuro fuzzy inference system (ANIFS) and particle swarm optimization (PSO) where PSO is to optimize the ANFIS. To enhance the performances of the mechanism, accelerated particle swarm optimization (APSO) is utilized to search the optimal design parameters. Lastly, the optimized mechanism is printed by Stereolithography (SLA) 3D technique, and the experimental verifications are performed. The results indicated that circumstance #1, the stroke is about 1.5279 mm, the frequency is 49.02103 Hz, the crosstalk error is 0.01108 mm, and the stress is 8.50514 MPa. In circumstance #2, the stroke is 1.44544 mm, the frequency is 54.51361 Hz, the crosstalk error is 0.0248 mm, and the stress is 8.35604 MPa. In last circumstance, the optimized results are achieved the stroke of 1.62369 mm, frequency of 51.62278 Hz, crosstalk of 0.028141 mm, and stress of 7.71713 MPa. The results indicated that the safety factor of three cases are over 2.5 to ensure a safe operation. The tested results are well satisfied with the simulated results.

Type Synthesis of a Novel 4‐Degrees‐of‐Freedom Parallel Bipedal Mechanism for Walking Robot

In this study, the conventional virtual chain method is refined and a 4‐degrees‐of‐freedom (DOF) parallel bipedal mechanism (PBM) for walking robots is presented. The proposed design has the advantages of low inertia, high load‐to‐weight ratio, and impact resistance. First, to solve the redundant motion‐transmission problem, a refined virtual chain method is proposed for the type synthesis of the 4‐DOF parallel thigh mechanism. Second, the relationship equation for each actuated wrench component in a reasonable actuated joint arrangement is derived, and the number and location of the actuated joints are determined. Third, by optimizing the design of the hip joint as a 2‐DOF counter‐centered five‐link spherical mechanism with different rotation centers, passive knee and ankle joints are designed based on the bionic principle. This design is performed to make the PBM isotropic and minimize inertia. The proposed PBM can withstand heavy loads and impacts owing to its humanoid crossed four‐link knee joint mechanism and compliant calf mechanism. Finally, the prototype is processed, and the rationality of the design and excellent performance of the PBM design are verified by dynamic and static simulations and gait experiments.

Bandgap tunability in pantographic metamaterials via flexure-based mechanisms

Inspired by flexure-based compliant mechanisms, we propose a novel pantographic system with broad, multiple bandgaps for wave and vibration control. This compliant mechanism embeds local inhomogeneities, such as flexure hinges, to achieve tunable bandgap properties. Using finite element analysis and Bloch’s theorem, we systematically study the bandgap properties of the pantographic lattice, including band structure diagrams, flexure hinge geometry effects, and vibration isolation in finite pantographic beam.

Design guidelines for the morphing of stiff lattice materials

Materials and structures with shape morphing capabilities are attractive in aerospace, maritime vehicles and robotics: such systems offer lighter weight, better distributed stresses, simpler kinematics, smaller numbers of actuators and higher reliability. Current morphing materials are either very compliant to achieve large shape changes (metamaterials, compliant mechanisms, hydrogels), or very stiff but with infinitesimal shape changes that require large actuation forces (metallic or composite sandwich panels with piezoelectric actuation). Morphing efficiency and structural stiffness are therefore mutually exclusive properties in current engineering morphing materials, which limit the range of their application. Here we propose a design for a stiff morphing beam made of “meta-elements” with unusual combinations of elastic properties, and which can be actuated from a simple push/pull at the base. To capture the performance of the beam we propose and use three metrics: The “morphing amplitude”, the “morphing compliance” and “structural stiffness”. We develop nonlinear finite elements to explore a wide range of designs, and to show some inevitable tradeoffs of stiffness and morphing. To aid the design of the structure we propose ternary diagrams to select optimum combinations of properties for the meta-elements. Finally, we fabricated and tested three prototypes of stiff morphing beams to validate the approach.

IGA-based topology optimization in the design of stress-constrained compliant mechanisms

Topology design of compliant mechanisms has gained wide popularity among the scientific community, and their use in the mechanical engineering field is being of upmost importance. In this paper, an isogeometric analysis (IGA) formulation is used to solve the topology optimization problem of compliant mechanisms. Stress constraints are introduced in the problem to guarantee the attainment of realistic solutions. For this purpose, an overweight constraint is considered for the design process, replacing the use of local stress constraints. The material distribution in the domain is modeled with quadratic B-splines and with a uniform relative density within each element of the mesh. These strategies to define the material layout are used to compare the IGA-based formulation with the finite element (FEM) formulation. The IGA formulation provides several advantages with respect to the classical FEM-based approaches that are shown and analyzed with an input-parameters sensitivity analysis. The sensitivity analysis and the assessment of the importance of introducing of stress constraints in the problem are developed by solving two benchmark problems. Regarding the sensitivity analysis of input parameters, the results show that the ratio between the material and the springs stiffnesses is the parameter with the largest influence on the solutions of the problem. Moreover, the advantages of the IGA formulations over FEM formulations are related with the computational time, the smoothness of the structural borders, and the non-appearance of the checkerboard patterns. With respect to the stress constraints, the results show that they have to be considered in order to avoid instability and structural integrity problems.