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Compliant Mechanisms (CMs) have presented their inherently advantageous properties since the nature of CMs is to utilize elastic deformation of the built-in elementary flexible members to transfer motion, force and energy. To predict the performances of CMs and optimize their designs, modeling CMs turns out to be a major concern in this field, particularly, such as high-precision flexure-based CMs. Reported in the literature, the well-known Beam Constraint Model (BCM) expressed in Cartesian coordinate system serves as an effective tool to model the deflection of flexures. Inspired by BCM, in this paper, we take one step further to propose a Body-frame Beam Constraint Model (BBCM) to handle buckling and intermediate-range deflections under typical beam-end loading conditions. Numerical and analytical analysis also proves that BBCM can also provide reliable accuracy in complex loading conditions and complex beam geometries within small-to-intermediate-range deflections and may accurately characterize large deflections under some specific loading conditions as well. • We propose a body-frame beam constraint model for intermediate-range deflections. • The proposed model is analytical, closed-form and concise. • The proposed model considers buckling initiation and intermediate-range buckling. • The proposed model considers different types of loading besides beam-end loading. • The proposed model considers continuous deflected beam shapes and the energy stored. [ABSTRACT FROM AUTHOR]

Compliant Mechanisms (CMs) serve as a promising alternative for transferring motion, force and energy compared to rigid mechanisms. The mentioned desired function is achieved by making the most of the elastic deflection of all built-in flexible members in CMs, such as slender straight beams and slender initially curved beams (ICBs). Therefore, accurately characterizing the deformation of these slender beams plays a considerable role in modeling CMs. As is well-known in the field of CMs, static planar large deflection of slender beams can be modeled via Euler Bernoulli beam theory, and it is essentially a boundary value problem (BVP). In this paper, we propose to use Taylor series method and Padé approximant to solve this BVP in a more efficient manner compared to the previous work. Its accuracy and efficiency have been compared with weighted residual method and also verified by solid-mechanics-based Finite Element Method (FEM) respectively. The feasibility of the proposed method has also been proved in terms of synthesizing CMs where three representative cases are studied. • We solved large beam-deflection problems by Taylor series method. • We solved large beam-deflection problems by Padé approximant. • We provided convergence analysis on the 2 methods. • We proved the feasibility of modeling CMs using the 2 methods. [ABSTRACT FROM AUTHOR]

Compliant Mechanisms (CMs) have been a hot research spot in recent years due to their distinguished mechanism concept from conventional rigid-body mechanisms: CMs can transfer motion, force, and energy only through the deflection of flexible components. Therefore, the accurate and efficient kinetostatic modeling for these elementary flexible components plays a rather important role regarding conducting synthesis of a studied compliant mechanism. In this paper, we have reviewed the commonly-used beam modeling methods in CMs, most of which are essentially dedicated to handling geometrically nonlinear Euler–Bernoulli beam theory. Mathematically speaking, this beam model is essentially a boundary value problem (BVP) of an ordinary differential equation (ODE). We then introduced certain commonly used numerical methods for BVPs to solve the problem where straight beams and circular initially curved beams (ICBs) are studied as two example cases. We have also demonstrated the detailed derivation of these methods and the numerical results along with the corresponding insights on them as well. Besides, we have modeled 2 representative revolute mechanisms (straight-beam-based cross-axis compliant revolute joint and circular-beam-based compliant revolute joint) to prove the feasibility of synthesizing CMs using these numerical methods. Error analysis is presented thereafter, which also confirms the effectiveness of these numerical methods. • We formulated the large beam-deflection problem as a general nonlinear BVP. • We reviewed the commonly used methods for modeling beam deflection in CMs. • We introduced efficient numerical methods to solve beam deflection problems. • We provided comments and analysis about all the mentioned methods. [ABSTRACT FROM AUTHOR]

Compliant Mechanisms (CMs) present several desired properties for mechanical applications only depending on elastic deformation of the involved compliant beams/flexures. As reported in the current literature, most CM designs utilize straight beams and initially curved beams (ICBs) as the fundamental flexible members. In CM research community, many great contributions regarding modeling these elementary flexible members have been achieved. In this paper, a comprehensive modeling methodology, based on beam theory, has been established to characterize the static planar deflection of slender beam. Then such a methodology has been applied to solve 8 loading scenarios of large beam-deflection problems that exist in the design of CMs. Essentially speaking, all these beam-deflection problems are treated as a type of boundary value problems (BVPs) of an ordinary differential equation (ODE) and solved by a modified collocation method. After that, this methodology has been used to model some representative CMs with large-deflection strokes, such as compliant parallelograms. • We presented a comprehensive modeling strategy for beams and CMs. • We proposed a modified collocation method. • We applied the proposed method to solve 8 beam-deflection problems. • We modeled four representative large-deflection CMs via the proposed method. [ABSTRACT FROM AUTHOR]

• We proposed an efficient compliance analysis method of initially curved beams. • We validated the method using Finite Element Analysis. • We conducted compliance analysis and optimization of ICB-based mechanisms. • We used weighted-sum method and genetic algorithm for the optimization process. Compliant Mechanisms (CMs) present several desired properties for mechanical designs. Conventional rigid-body mechanisms composed of rigid links connected at kinematic joints, serve as devices to transfer motion, force and energy by the movements of rigid links whereas CMs are able to present the same function only through deflection of flexible members. Most designs of CMs in the current literature employ straight beams as the elementary flexible members whereas initially curved beams (ICBs) also provide potential advantages for CMs such as large range of motion and small strain range. This paper presents an efficient spatial compliance analysis method of general ICBs. The spatial compliance analysis of different types of ICBs (such as varying-curvature beams and varying-cross-section beams) was conducted, followed by Finite Element Analysis (FEA) verification. Next, the modeling and optimization of two types of CMs including ICB-based parallelogram mechanisms and ICB-based Ortho-planar springs were carried out by applying screw theory under the framework of position space concept and parameter normalization strategy where a class of anti-buckling translational parallelograms with high load-bearing capacity and a type of compact 2R1T (2 rotational DOF and 1 translational DOF) compliant kinematic joints were obtained. The corresponding FEA was conducted to verify the optimal results. [ABSTRACT FROM AUTHOR]

• We present a novel compliant parallelogram mechanism. • We use general tensural-compresural beams. • We develop and validate the nonlinear kinetostatic model. • We conduct a comprehensive analysis of parameters for four single design objectives. The paper proposes a novel type of Compliant Mechanism (CM) called Planar Compliant Parallelogram Mechanism (PCPM) for translational movement by synthesizing 8 compliant beams. Half of the beams are arranged in an inverted way while the other half of them are non-inverted, and both the inverted beams and non-inverted beams are arranged symmetrically. The arrangement empowers the mechanism to have a tensural-compresural characteristic with the robustness against beam buckling regardless of the high-payload direction. Moreover, the new mechanism introduces more design parameters than the traditional parallelogram mechanism, providing a broader design space for performance optimization. A nonlinear and analytical model of the mechanism was derived first depending on the Timoshenko Beam Constraint Model (TBCM) for quick design, followed by nonlinear FEA validation. Constraints and other conditions were determined beforehand to prepare for the comprehensive parameter analysis. Comprehensive analysis of geometric parameters was carried out for four single design objectives based on the aforementioned analytical model. It is shown that two types of optimized design were obtained from the parameter analysis where one design involves distributed compliance. Experimental testing was conducted to validate the primary motion stiffness of the distributed-compliance involved design. [ABSTRACT FROM AUTHOR]

Compliant deployable mechanisms (CDMs), as a novel and promising type of mechanisms, have been gradually used in medical industry, aerospace and other engineering fields that require high space utilization and compactness. Therefore, it is necessary to develop a general and efficient methodology to design and analyze CDMs. This paper proposes a general framework for designing and analyzing CDMs. The proposed framework has been verified by finite element method (FEM) first. Then, for practical validation, we design two types of compliant deployable mechanisms for different application scenarios within this framework, and experimental testing has been conducted to prove the feasibility of the proposed framework. Compared to the existing methods for designing CDMs, this framework demonstrates a more general scheme where different engineering scenarios can be taken into account to meet the design requirements, presenting several desired advantages over the existing methods, such as higher accuracy and less computational expense. • We propose a general framework for designing compliant deployable mechanisms (CDMs). • The framework also has the advantages of high accuracy and low calculation costs. • We present two types of CDMs to provide feasible schemes for future applications. [ABSTRACT FROM AUTHOR]

High-precision displacement platforms are of great significance in micro/nanoscale manipulation, ultraprecision manufacturing, biological manipulation, and scanning probe microscopes. This paper presents a novel compliant planar parallelogram mechanism (CPPM) for high-precision translational motion utilizing 8 flexible initially curved beams (ICBs). Compared with the existing high-precision displacement platforms for traditional motion, CPPM combines the characteristics of large motion ranges, bidirectional anti-buckling and high load-bearing. Moreover, this new mechanism introduces more design parameters compared to traditional parallelogram mechanisms, thus generating other desired characteristics by optimizing these parameters. In this paper, a general mathematical model is first derived for quick design and model-based optimization, followed by nonlinear finite element method (FEM) validation. Three desired performance characteristics in compliant translational mechanisms are proposed thereafter to obtain three optimized designs through global optimization of the preset geometric parameters. Experimental results verify the accuracy of the mathematical model and demonstrate centimeter-level high-precision positioning within a large motion range. Finally, a comparative discussion of the anti-buckling mechanisms for translation is presented. • We present a compliant planar parallelogram mechanism with desired performances. • We use general tensural–compresural initially curved beams. • We develop and validate the mathematical model. • We optimize geometric parameters globally for three desired performance characteristics. [ABSTRACT FROM AUTHOR]

Precision operations, such as micro-injection and micro-assembly tasks, require accurate and constant torque output. Compliant constant torque mechanisms (CCTMs) can be considered as a potential alternative due to the characteristic of accurate and constant torque output without the need for complex control algorithms and structures. Therefore, it is essential to propose a general, designer-friendly, and efficient design methodology for the design of CCTMs. In this paper, we propose a methodology for designing compliant constant torque mechanisms based on a co-design process between Cartesian coordinate system and Frenet frame. We use geometrically exact beam theory to model the static deflection of the built-in flexible beams so as to analyze the overall mechanism. We transform the design of this mechanism into a typical constrained optimization problem, and solve it via highly efficient numerical methods to achieve the desired design objectives given the user-defined constraints and satisfy some specific engineering requirements. Our optimized design is thoroughly evaluated and validated through finite element method and experimental testing, demonstrating a significantly improved performance compared to existing designs. • A general methodology is proposed for designing constant torque mechanisms. • A novel model for complex-shape beams is proposed and verified by FEM. • Two desired designs are achieved via model-based optimization. • The optimized designs present better performance compared to the existing designs. • A prototype is fabricated and experimental results demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]