123 静定トラス列挙アルゴリズムを利用した柔構造物の最適設計

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.

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.

This paper presents a mathematical approach to synthesizing a multi-stable behavior by combining multiple bi-stable equilibrium mechanisms in series. Behavior of a bi-stable compliant mechanism, in general, is highly non-linear. Combinations of such non-linearities to capture the behavior of multi-stable (more than two stable positions) mechanisms can be very challenging. We present a simplified mathematical scheme to capture the essential parameters of bi-stability such as force-thresholds that cause the jump to next stable position etc. to derive multi-stable behavior. This mathematical simplification enables us to characterize bi-stable mechanisms using piecewise lower-order polynomials and synthesize multi-stable mechanisms through combination of bi-stable behaviors in series. We present two case studies of combinations of two and three bi-stable behaviors to generate mechanisms with four and five stable positions respectively. A design example of a quadri-stable equilibrium rotational compliant mechanism consisting two bi-stable sub-mechanisms is presented to demonstrate the effectiveness of the approach.

Design of a variable-diameter wheel with a novel distributed compliant mechanism

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.

Compliant mechanisms are single-piece flexible structures that deliver the desired motion by undergoing elastic deformation as opposed to jointed rigid body motions of conventional mechanisms. Compliance in design leads to jointless, no-assembly (Fig. 1), monolithic mechanical devices and is particularly suited for applications with small range of motions. The compliant windshield wiper shown in Fig. 1 illustrates this paradigm of no-assembly. Conventional flexural mechanisms employ flexural joints that connect relatively rigid links as depicted in Fig. 2. Reduced fatigue life, high stress concentration and difficulty in fabrication are some of the drawbacks of flexural joints. Our focus is on designing compliant mechanisms with distributed compliance which employs flexural links (see Fig. 3) and have no joints (neither pin nor flexural joints) for improved reliability, performance, and ease of manufacture. Distributed compliant mechanisms derive their flexibility due to topology and shape of the material continuum rather than concentrated flexion at few regions. This paper focuses on the unique methodology employed to design jointless mechanisms with distributed compliance. The paper also illustrates a compliant stroke amplification mechanism that was recently designed, fabricated and tested for MEMS application.

Purpose Compliant mechanism has been receiving a great interest in precision engineering. However, analytical methods involving their behavior analysis is still a challenge because there are unclear kinematic behaviors. Especially, design optimization for compliant mechanisms becomes an important task when the problem is more and more complex. Therefore, the purpose of this study is to design a new hybrid computational method. The hybridized method is an integration of statistics, numerical method, computational intelligence and optimization. Design/methodology/approach A tensural bistable compliant mechanism is used to clarify the efficiency of the developed method. A pseudo model of the mechanism is designed and simulations are planned to retrieve the data sets. Main contributions of design variables are analyzed by analysis of variance to initialize several new populations. Next, objective functions are transformed into the desirability, which are inputs of the fuzzy inference system (FIS). The FIS modeling is aimed to initialize a single-combined objective function (SCOF). Subsequently, adaptive neuro-fuzzy inference system is developed to modeling a relation of the main geometrical parameters and the SCOF. Finally, the SCOF is maximized by lightning attachment procedure optimization algorithm to yield a global optimality. Findings The results prove that the present method is better than a combination of fuzzy logic and Taguchi. The present method is also superior to other algorithms by conducting non-parameter tests. The proposed computational method is a usefully systematic method that can be applied to compliant mechanisms with complex structures and multiple-constrained optimization problems. Originality/value The novelty of this work is to make a new approach by combining statistical techniques, numerical method, computational intelligence and metaheuristic algorithm. The feasibility of the method is capable of solving a multi-objective optimization problem for compliant mechanisms with nonlinear complexity.

The design of the canopy utilizes the conventional rigid body mechanisms which is vulnerable to the presence of backlash, friction of joints or wearing of mechanical parts which lead to short product life. Compliant mechanisms are employed to reduce these mechanical problems, owing to their zero-joint and monolithic structure. A reference design for the conventional canopy was chosen and modified through reviewing different patent designs. Six different configurations of the pseudo-rigid-body model (PRBM) were constructed, and the best configuration was selected. Kinematic synthesis with function generation was performed for the chosen PRBM using MATLAB. The obtained results from the kinematic synthesis were then used to calculate the dimensions and stresses of the flexural pivots for the compliant stretcher mechanism. Finite Element Analysis (FEA) simulation was then performed on each of the models and the obtained flexural pivot stresses were compared with that of the PRBM. This research successfully replaces all the rigid joints and links of the stretcher mechanism of the conventional canopy to form a monolithic structure of compliant stretcher mechanism.

Effects of joint clearance on the dynamics of a partly compliant mechanism: Numerical and experimental studies

A novel contact aided compliant mechanism called bend-and-sweep compliant mechanism is presented in this paper. This mechanism has nonlinear stiffness properties in two orthogonal directions. An angled compliant joint (ACJ) is the fundamental element of this mechanism. Geometric parameters of ACJs determine the stiffness of the compliant mechanism. This paper presents the design and optimization of bend-and-sweep compliant mechanism. A multi-objective optimization problem was formulated for design optimization of the bend-and-sweep compliant mechanism. The objectives of the optimization problem were to maximize or minimize the bending and sweep displacements, depending on the situation, while minimizing the von Mises stress and mass of each mechanism. This optimization problem was solved using NSGA-II (a genetic algorithm). The results of this optimization for a single ACJ during upstroke and downstroke are presented in this paper. Results of two different loading conditions used during optimization of a single ACJ for upstroke are presented. Finally, optimization results comparing the performance of compliant mechanisms with one and two ACJs are also presented. It can be inferred from these results that the number of ACJs and the design of each ACJ determines the stiffness of the bend-and-sweep compliant mechanism. These mechanisms can be used in various applications. The goal of this research is to improve the performance of ornithopters by passively morphing their wings. In order to achieve a bio-inspired wing gait called continuous vortex gait, the wings of the ornithopter need to bend, and sweep simultaneously. This can be achieved by inserting the bend-and-sweep compliant mechanism into the leading edge wing spar of the ornithopters.

Compliant mechanisms use the flexibility of the limbs for movement and are produced monolithic, without any conventional joint. These flexible mechanisms have wide applications in several fields such as sensors, grippers, parallel mechanisms, micro-electro-mechanical systems, high-precision devices, and biomedical and surgery robots. Topology optimization is regarded as one of the most frequently used approaches for designing compliant mechanisms. The present study aimed to develop the ground structure approach by meshing the design domain using curved beam elements. Moreover, it seeks to implement three different metaheuristic algorithms, including the genetic algorithm, the imperialist competition algorithm, and the equilibrium optimizer for the topology optimization problem. The structural analysis of the compliant mechanism is necessary for determining the values of the objective functions for the optimization process. In the present study, the finite element method was used to analyze the obtained compliant mechanism. Based on the results, an optimum compliant mechanism with both straight and curved beam elements had better performance compared with a compliant mechanism with only straight beams.

Bistable mechanisms provide two stable positions. Input power is not needed to maintain any of the two stable positions. To switch from one stable position to another, input power is required. Bistable mechanisms have many applications including valves, closures, switches and various other devices. Unlike conventional rigid-body bistable mechanisms that rely on relative motions of kinematic joints, bistable compliant mechanisms take advantage of elastic deformations of flexible members to achieve two stable positions. There are two symmetric buckled shapes in a precompressed beam that has one fixed end and one pinned end. The two buckled shapes match the two stable equilibrium positions of bistable compliant mechanisms. The precompressed beam can be rotationally actuated at the pinned end to snap from one buckled shape to another. Synthesizing precompressed beams as bistable mechanisms is challenging because of buckling instability and integrated force and deflection characteristics. In this paper, the buckled shape is derived for a precompressed beam with fixed and pinned ends. The input torque at the pinned end is analyzed for a precompressed beam to snap between its two symmetric buckled shapes. Precompressed beams are synthesized as bistable compliant mechanisms through axial compression and beam thickness in this paper.

Flexure-based compliant mechanisms are increasingly promising in precision engineering, robotics, and other applications, thanks to the excellent advantages of no friction, no backlash, no wear, and minimal assembly. However, their design and analysis are still challenging due to the coupling of kinematic-mechanical behaviors with large nonlinear deflections in comparison to their rigid-body counterparts. Optimal design is an important aspect in the field of compliant mechanisms and has attracted much attention during the last decades. Especially, when considering a multiobjective optimization design for compliant mechanisms, the problem is becoming more complicated. Thus, this article presents a new efficient hybrid computational method to resolve multiobjective optimization design of compliant mechanisms. A Scott Russell compliant mechanism is employed as the design example and to show the advantages of the proposed optimizing method. The proposed method is developed by hybridizing the desirability function approach, fuzzy logic system, adaptive neuro-fuzzy inference system (ANFIS), and lightning attachment procedure optimization (LAPO). First of all, a 3D finite element model is created and central composite design is employed to build a numerical matrix. First, design variables are refined by using analysis of variance and Taguchi approach in terms of considerably eliminating space of design variables. Subsequently, desirability values of two objective functions are determined and transferred into the fuzzy logic system. The output of the fuzzy logic system is considered as a single combined objective function. Next, modeling for fuzzy output is established via developing the ANFIS model. At last, the LAPO algorithm is adopted for solving the multiobjective optimization problem for the mechanism. Three numerical examples are investigated to validate the feasibility and the effectiveness of performance efficiency of the proposed methodology. The results find that the proposed methodology is more efficient than traditional Taguchi-based fuzzy logic. Besides, the performance efficiency of the proposed approach outperforms the Jaya algorithm and TLBO algorithm through the Wilcoxon signed rank test and Friedman test. The results of this article give a useful approach for complex optimization problems.

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

Significant reduction in cost and time of bistable mechanism design can be achieved by understanding their bistable behavior. This paper presents bistable compliant mechanisms whose pseudo-rigid-body models (PRBM) are four-bar mechanisms with a torsional spring. Stable and unstable equilibrium positions are calculated for such four-bar mechanisms, defining their bistable behavior for all possible permutations of torsional spring locations. Finite Element Analysis (FEA) and simulation is used to illustrate the bistable behavior of a compliant mechanism with a straight compliant member, using stored energy plots. These results, along with the four-bar and the compliant mechanism information, can then be used to design a bistable compliant mechanism to meet specified requirements.