Compliant Bistable Mechanisms Research Articles

Task-driven geometric synthesis method of a bistable compliant mechanism for the rigid guidance problem

Abstract. Compliant bistable mechanisms are specialized mechanisms that have specific self-locking characteristics in two positions. They are widely used in aerospace, micro-electromechanical systems, and high-precision manufacturing. The coupling of kinematic with elastomechanical behaviors of compliant mechanisms, known as kinetostatics, increases the difficulty of synthesizing compliant mechanisms. Currently, most research relies on optimization approaches to find compliant mechanisms that meet motion requirements. To address this challenge, this paper proposes a geometric synthesis method for compliant bistable mechanisms to solve the rigid guidance problem. The pole similarity transformation characteristics of planar beams and the static equilibrium characteristic of bistable mechanisms at stable positions are utilized to decouple the kinematic synthesis and static analysis. The proposed method introduces a task-driven synthesis process, where the critical structural parameters in compliant mechanisms are determined based on the desired guidance positions of motion tasks. This approach eliminates the need for a tedious and time-consuming iterative optimization process. The resulting bistable mechanisms have two stable positions that correspond to the desired guidance positions of the motion task. To illustrate the effectiveness of the geometric synthesis method, a two-position problem of a compliant bistable mechanism is provided as an example.

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.

The synthesis method of series-based bistable compliant mechanisms for rigid-body guidance problem based on geometrical similarity transformation of pole maps

Abstract Designing guidance mechanisms using bistable mechanisms with two stable positions is a common low-power solution for maintaining the guidance position without continuous external energy input. However, the coupling between kinematics and statics in compliant bistable mechanisms poses a challenge for their application in mechanism synthesis. To address this issue, this paper introduces the pole similarity transformation theory into the synthesis of compliant mechanisms and proposes a general synthesis method for planar serial-based compliant bistable mechanisms. This method models the compliant mechanism using the strain energy method and analyzes the bistable characteristics of the mechanism within its motion plane using the saddle point searching method. By doing so, the proposed method can identify stable positions without predetermined motion trajectories, making it more suitable for designing compliant bistable mechanisms with general planar motion. Additionally, this method utilizes the pole map to describe the stable positions of the rigid components in the compliant mechanism and establishes an information database for compliant bistable mechanisms. Through leveraging the pole similarity transformation, the pole maps of the mechanisms in the information database are matched with the pole map of the motion task, thus achieving the synthesis of planar serial-based compliant bistable mechanisms for the rigid-body guidance problem. The paper provides a detailed explanation of the mechanism synthesis process and demonstrates its application through a case study.

Design and analysis of a microgripper for trans-scale clamping based on a compliant multistable mechanism.

Piezoelectric actuators commonly used in microgrippers have a small stroke, and their accuracy is reduced by the transmission amplification unit, which leads to a contradiction between the clamping range and the clamping accuracy in existing piezoelectric-actuated microgrippers. This paper proposes a design scheme to divide the total clamping range of the microgripper into segments based on the compliant multistable mechanism (CMM). First, by using the stable equilibrium positions of the CMM, the total clamping range of the microgripper is divided into multiple smaller clamping sub-intervals to accommodate objects of different scales. Then, the theoretical models of the displacement amplification ratio of the microgripper amplification mechanism and the stiffness of the microgripper in different clamping sub-intervals are established, and the force-displacement characteristics of the CMM are analyzed. Next, through finite element simulation, the correctness of the theoretical analyses is verified, and it is shown that objects between 0 µm and 1.650mm can be clamped using four clamping sub-intervals under a five times displacement amplification ratio. Finally, a microgripper of the CMM consisting of two three-segment fully compliant bistable mechanisms connected in series is designed and machined, and microgripper segmented clamping experiments are conducted. The experimental results demonstrate the feasibility of the design scheme proposed in this paper.

Development of a Fully Compliant Bistable Mechanism Based on Circular Beams with Enhanced Pitch Stiffness

Compliant bistable mechanisms with planar configurations demonstrate two in-plane stable states through the nonlinear deformations of in-plane flexible segments, which are widely used in the field of shock sensors and threshold sensors. In these mechanisms, consistent dynamic and static bistable behaviors are difficult to maintain under the influence of an out-of-plane load. This is limited in some applications where precise displacement is required. To this end, we developed a bistable mechanism with circular beams instead of conventional straight beams, such that enhanced robustness against external loads in the out-of-plane region is obtained. An analytical kinetostatic model is established to predict the bistable behavior of the proposed mechanism, which is further verified using finite element simulations and experimental results. Compared with the prototype of the straight-beam-based bistable mechanism, the developed circular-beam bistable mechanism demonstrates improved pitch stiffness along the out-of-plane rotation and robustness against off-axis load conditions. The proposed bistable mechanism design can be extended to applications of sensors subjected to out-of-plane loads.

Design of Deployable Structures by Using Bistable Compliant Mechanisms.

A deployable structure can significantly change its geometric shape by switching lattice configurations. Using compliant mechanisms as the lattice units can prevent wear and friction among multi-part mechanisms. This work presents two distinctive deployable structures based on a programmable compliant bistable lattice. Several novel parameters are introduced into the bistable mechanism to better control the behaviour of bistable mechanisms. By adjusting the defined geometry parameters, the programmable bistable lattices can be optimized for specific targets such as a larger deformation range or higher stability. The first structure is designed to perform 1D deployable movement. This structure consists of multi-series-connected bistable lattices. In order to explore the 3D bistable characteristic, a cylindrical deployable mechanism is designed based on the curved double tensural bistable lattice. The investigation of bistable lattices mainly involves four types of bistable mechanisms. These bistable mechanisms are obtained by dividing the long segment of traditional compliant bistable mechanisms into two equal parts and setting a series of angle data to them, respectively. The experiment and FEA simulation results confirm the feasibility of the compliant deployable structures.

Buckling Control of Piezolaminated Beams for Compliant Bistable Mechanisms

Buckling Control of Piezolaminated Beams for Compliant Bistable Mechanisms

Fully compliant bistable mechanisms with enhanced pitch stiffness

For compliant bistable mechanisms with planar configurations and exhibiting two in-plane stable states, their flexible beams are supposed to undergo in-plane bending deflections, but the out-of-plane deflections can significantly influence the kinetostatics of the mechanism, resulting in inconsistent bistable behaviors when off-axis or eccentric loads present. In this paper, we propose a novel bistable mechanism utilizing torsion-stiffness enhanced flexible beams to restrain the shuttle from out-of-plane rotation. An analytical kinetostatic model is developed for the proposed bistable mechanism. Five bistable examples are presented to demonstrate the effectiveness of the proposed bistable mechanism in suppressing unwanted motions and the correctness of the proposed kinetostatic model. The results show that the novel bistable designs are much stiffer along the out-of-plane rotation thus are more robust against off-axis or eccentric loading condition, especially when the shuttle is displaced to a position around the second equilibrium stable position (where the flexible beams are in the post-buckling states).

Influence of non-ideal fixed-end constraints on kinetostatic behaviors of compliant bistable mechanisms

Bistable mechanisms can maintain two distinct positions without energy consumption, which made them widely used in many special situations. The performance of bistable mechanisms may suffer from its non-ideal fixed-end constraints (the deformation of its ostensibly rigid frame), which may even incapacitate the bistability of the mechanisms. To capture the influence of non-ideal constraints on the behaviors of the mechanisms, a kinetostatic model for bistable mechanisms is presented in this paper. In the model, behaviors of both the frame and flexible beams are considered and characterized using the Chained Beam Constraint Model (CBCM). Three examples are modeled and analyzed to show the effectiveness of the model for evaluating the influence of non-ideal constraints on the behaviors of the mechanisms. The results are validated by the results of finite element analysis as well as experiments.

A novel fully compliant tensural-compresural bistable mechanism

Bistable mechanisms, which can maintain two distinct positions without power input, have been widely used for harvesting vibration energy, constructing metamaterials, sensing threshold acceleration, and achieving adaptable damping. In this work, we propose a novel configuration of fully compliant bistable mechanisms called tensural-compresural bistable mechanisms (TCBMs), in which both tensural segments (compliant segments that are subject to combined tensile and bending loads) and compresural segments (compliant segments that are subject to combined compressive and bending loads) are employed. The combination use of tensural and compresural segments makes TCBMs much easier to be tailored for different design requirements. Although compresural segments are incorporated, potential problems associated with buckling can always be avoided by using compresural segments with smaller slenderness as compared to the tensural segments. To facilitate the design of TCBMs, two kinetostatic models are developed by using the beam constraint model and the chained beam constraint model, respectively. Several TCBM designs accompanied with a prototype test are presented to demonstrate the feasibility of the new bistable configuration and the use of the two kinetostatic models.

Nonlinear kinetostatic modeling of double-tensural fully-compliant bistable mechanisms

In double-tensural fully compliant bistable mechanisms (DTBMs), all of the compliant segments are loaded in tension when deflected, thus the problems associated with buckling are avoided. Because the stiffening of the compliant segments due to tensile loads plays an important role in achieving the bistable behaviors, it is critical to capture the relevant geometric nonlinearities when modeling DTBMs. Based on the beam constraint model (BCM) and the chained beam constraint model (CBCM), two kinetostatic models are developed for DTBMs in this work: Model I models both of the tensural segments using BCM, while Model II models the shorter tensural segment using BCM and the longer tensural segment using CBCM with two BCM elements. The two models well predict the bistability and the kinetostatic behaviors of a DTBM as compared to the finite element results. Although Model II is a little more complicated than Model I, it improves the modeling accuracy, especially at the negative stiffness region of the kinetostatic curve.

Bistable Mechanisms for Space Applications.

Compliant bistable mechanisms are monolithic devices with two stable equilibrium positions separated by an unstable equilibrium position. They show promise in space applications as nonexplosive release mechanisms in deployment systems, thereby eliminating friction and improving the reliability and precision of those mechanical devices. This paper presents both analytical and numerical models that are used to predict bistable behavior and can be used to create bistable mechanisms in materials not previously feasible for compliant mechanisms. Materials compatible with space applications are evaluated for use as bistable mechanisms and prototypes are fabricated in three different materials. Pin-puller and cutter release mechanisms are proposed as potential space applications.

Design optimization of segment-reinforced bistable mechanisms exhibiting adjustable snapping behavior

Controlling the nonlinear bistable mechanics is crucial for the development of advanced bistable devices ranging from quantitative mass sensing to smart material/structures. However, for a large amount of pre-shaped bistable mechanisms, one or two specific bistable characteristics such as two switching forces, stroke and bistable index parameter cannot fulfill the special application requirements. Due to the complex coupling effects among different bistable mechanical properties, it is really difficult to modify one specific bistable character without affecting others by just modifying the structure parameters once the bistable configuration and boundary constraints are fixed. With the accurate mechanical analysis of MEMS bistable mechanisms, a novel optimization based method for designing specific bistable characteristic is proposed by modifying the beam local segment’s geometry for optimizing the bistable index parameter and two switching forces respectively. Accordingly, five bistable compliant mechanisms are reconstructed symmetrically or asymmetrically for achieving different bistable mechanics. Also, the sharp change on the nonlinear force- displacement curve induced by the mode switching is analyzed. For experimental study, a quasi-cosine-shaped beam with reinforced local segments is manufactured by hot forming beryllium bronze sheet. The good agreement between the numerical simulation and experimental results validates the effectiveness of the optimization-based bistability design method, thus expanding the potential application range of compliant bistable mechanisms.

Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model

Fully compliant bistable mechanisms (FCBMs) have numerous applications in both micro- and macroscale devices, but the nonlinearities associated with the deflections of the flexible members and the kinetostatic behaviors have made it difficult to design. Currently, the design of FCBMs relies heavily on nonlinear finite element modeling. In this paper, an analytical kinetostatic model is developed for FCBMs based on the beam constraint model (BCM) that captures the geometric nonlinearities of beam flexures that undergo relatively small deflections. An improved BCM (i.e., Timoshenko BCM (TBCM)) is derived based on the Timoshenko beam theory in order to include shear effects in the model. The results for three FCBM designs show that the kinetostatic model can successfully identify the bistable behaviors and make reasonable predictions for the locations of the unstable equilibrium points and the stable equilibrium positions. The inclusion of shear effects in the TBCM model significantly improves the prediction accuracy over the BCM model, as compared to the finite element analysis (FEA) results.

A function for characterizing complete kinetostatic behaviors of compliant bistable mechanisms

Abstract. In this paper, a straightforward and accurate numerical modeling (a rational function called "tri-root bistable function") are proposed to represent the complete nonlinear bistable force-displacement characteristics. The rational function has a cubic polynomial numerator and quadratic polynomial denominator. With three different kinds of compliant bistable mechanisms, the tri-root bistable function is proved effective and accurate, and that it is capable of capturing the key features of a bistable kinetostatic curve accurately with fewer parameters. Then, for the classic fully-compliant bistable mechanism, six closed-form equations are presented and used to describe the relationships between the tri-root bistable function parameters and the mechanism's design parameters, which are achieved using a multi-variable nonlinear regression. The regression analysis is validated by nonlinear finite element analysis. Finally, a fully-compliant statically balanced mechanism consisting of three different classic fully-compliant bistable mechanisms is illustrated to show the capability of the proposed method in designing compliant multi-stable mechanisms.

A 3-DOF Pseudo-Rigid-Body Model for Tension-Based Compliant Bistable Mechanisms

Compliant bistable mechanisms,devices with two distinct stable equilibrium positions,are used in a variety of applications,such as switches,clasps,and valves.Many kinds of compliant bistable mechanisms were proposed and studied during the past decade.Among them,tension-based compliant bistable mechanisms,that incorporate tension pivots as their flexible members,feature in short travel distance and low power consuming.So far,the design of this kind of bistable mechanisms is done using finite element method through trial and error,thus is time-consuming.By treating the tension pivots as fixed-guided segments and their elongation as a spring,we developed a novel three degree-of-freedom (3-DOF) pseudo-rigid-body model (PRBM) for this kind of bistable mechanisms.The principle of virtual work is used to derive the force-deflection relationship of the PRBM model.The comparison between the PRBM results and the experimental results of the force-deflection characteristics shows that the PRBM can predict not only the bistable behavior of the tension-based bistable mechanisms,but also their soft spring-like post-bistable behavior and the spring-like force-deflection characteristics when pulling in the reverse direction from the as-fabricated position,which is called reverse behavior.The 3-DOF PRBM can be used to design and identify tension-based bistable mechanisms.Using the PRBM instead of the trial-and-error method can greatly reduce the development time of this kind of bistable mechanisms.

Bistable Buckled Beam: Modeling of Actuating Force and Experimental Validations

Compliant bistable mechanisms are a class of mechanical systems that benefit from both compliance, allowing easy manufacturing on a small scale, and bistability, which provides two passive and stable positions. These properties make them first-class candidates not only for microswitches but also several other robotic appliances. This paper investigates the actuation of a simple bistable mechanism, the bistable buckled beam. It is pointed out that the position of the actuation has a significant impact on the behavior of the system. A new model is proposed and discussed, with experimental validations to compare central and offset loading, highlighting the strengths of each.

Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints

Bistable mechanical devices remain stable in two distinct positions without power input. They find application in valves, switches, closures, and clasps. Mechanically bistable behavior results from the storage and release of energy, typically in springs, with stable positions occurring at local minima of stored energy. Compliant mechanisms offer an elegant way to achieve this behavior by incorporating both motion and energy storage into the same flexible element. Interest in compliant bistable mechanisms has also recently increased because of the advantages of bistable behavior in many micro-electro-mechanical systems (MEMS). Design of compliant or rigid-body bistable mechanisms typically requires simultaneous consideration of both energy storage and motion requirements. This paper simplifies this process by developing theory that provides prior knowledge of mechanism configurations that guarantee bistable behavior. Configurations which include one or more translational, or slider, joints are studied in this work. Several different mechanism types are analyzed to determine compliant segment placement that will ensure bistable mechanism operation. Examples demonstrate the power of the theory in design.

Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior

Bistable mechanisms, which have two stable equilibria within their range of motion, are important parts of a wide variety of systems, such as closures, valves, switches, and clasps. Compliant bistable mechanisms present design challenges because the mechanism’s energy storage and motion characteristics are strongly coupled and must be considered simultaneously. This paper studies compliant bistable mechanisms which may be modeled as four-link mechanisms with a torsional spring at one joint. Theory is developed to predict compliant and rigid-body mechanism configurations which guarantee bistable behavior. With this knowledge, designers can largely uncouple the motion and energy storage requirements of a bistable mechanism design problem. Examples demonstrate the power of the theory in bistable mechanism design.

SMA actuated compliant bistable mechanisms

This article introduces the concept, analysis, as well as the design of shape memory alloy (SMA) actuated compliant bistable mechanisms. Compliant bistable mechanisms and SMA linear actuators have noteworthy advantages. When they are combined, not only their advantageous characteristics are preserved, but also some disadvantages can be eliminated. Thus, comparing to a stand-alone SMA actuator, SMA actuated compliant mechanisms have the advantages of requiring no input to stay at the stable positions, high repeatability in positioning, lightweight and simple control. Complexity in analysis, design, and control of SMA actuators and other shortcomings of SMA actuators, such as short output stroke and small output force, are either eliminated or improved.