A Large-Deflection Annulus-Shape Flexure Hinge Based on Curved Beams

2008 ◽  
Author(s):  
Shanshan Zhao ◽  
Shusheng Bi ◽  
Jingjun Yu ◽  
Minglei Sun ◽  
Guanghua Zhong
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Accurate Method ◽  
Flexure Hinge ◽  
Curved Beam ◽  
Curved Beams ◽  
Element Analysis ◽  
Rigid Body Model ◽  
Compliant Joint ◽  
Design Tradeoffs

A curved flexure element such as an initially-curved beam can deflect largely and facilely. Using curved flexure elements in compliant mechanisms allows the mechanism to move a longer distance or undergo a larger rotation angle stroke than using conventional notch flexures. This paper presents a novel large-deflection annulus-shaped flexure hinge covering multiple curved-beam flexure elements. It has been shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in some improved performances of the flexure hinge. Additional fixed RCM characteristic of isosceles-trapezoidal flexure modules existed in this compliant joint further improve its accuracy. A master-motion pseudo-rigid-body model provides a simple and accurate method to analyze the force-deflection behavior of this new rotary flexure hinge. The accuracy of the model is verified by comparing outcomes to non-linear finite element analysis. The result shows the proposed rotary flexure hinge has a large stroke angle, a low axial and radial stiffness.

Parametric Deflection Approximations for Initially Curved, Large-Deflection Beams in Compliant Mechanisms

1996 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Curved Beam ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Fundamental Type ◽  
Applied Forces ◽  
Flexible Member

Abstract The analysis of systems containing highly flexible members is made difficult by the nonlineararities caused by large deflections of the flexible members. The analysis and design of many such systems may be simplified by using pseudo-rigid-body approximations in modeling the flexible members. The pseudo-rigid-body model represents flexible members as rigid links, joined at pin joints with torsional springs. Appropriate values for link lengths and torsional spring stiffnesses are determined such that the deflection path and force-deflection relationships are modeled accurately. Pseudo-rigid-body approximations have been developed for initially straight beams with externally applied forces at the beam end. This work develops approximations for another fundamental type of flexible member, the initially curved beam with applied force at the beam end. This type of flexible member is commonly used in compliant mechanisms. An example of the use of the resulting pseudo-rigid-body approximations in compliant mechanisms is included.

The Modeling of Leaf-Type Isosceles-Trapezoidal Flexural Pivots

2007 ◽  
Author(s):  
Xu Pei ◽  
Jingjun Yu ◽  
Guanghua Zong ◽  
Shusheng Bi
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compliant Mechanisms ◽  
Accurate Method ◽  
Leaf Segment ◽  
Element Analysis ◽  
Leaf Type ◽  
Linear Finite Element ◽  
Body Model ◽  
Rigid Body Model

A Leaf-type Isosceles-trapezoidal Flexural (LITF) pivot can be of great practical use for designing compliant mechanisms. The analysis of load-deflection behavior for such a pivot is essential to the study on the mechanisms which are composed of the pivots. A pseudo-rigid-body model provides a simple and accurate method. Based on the analysis of a single special loaded leaf segment, a four-bar model is presented. The four-bar model is further simplified to a pin-joint model for the simpler applications. The accuracy of both models is demonstrated by comparing results to those of non-linear finite element analysis. At last, the two models are applied to analyze the cartwheel hinge as an example.

Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model

2018 ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Guangbo Hao ◽  
Weidong Zhu
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Accurate Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Nonlinear Load ◽  
Circular Arc ◽  
Analysis And Design ◽  
Discretization Schemes ◽  
Constraint Model

Understanding and analyzing large and nonlinear deflections is one of the major challenges of designing compliant mechanisms. Initially curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross-sections, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

Large-Deflection Analysis of General Beams in Contact-Aided Compliant Mechanisms Using Chained Pseudo-Rigid-Body Model

2020 ◽  
Vol 12 (3) ◽  
Author(s):  
Mohui Jin ◽  
Zhou Yang ◽  
Collin Ynchausti ◽  
Benliang Zhu ◽  
Xianmin Zhang ◽  
...  
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Reaction Force ◽  
Curved Beams ◽  
Nonlinear Method ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Force Moment

Abstract The nonlinear analysis and design of contact-aided compliant mechanisms (CCMs) are challenging. This paper presents a nonlinear method for analyzing the deformation of general beams that contact rigid surfaces in CCMs. The large deflection of the general beam is modeled by using the chained pseudo-rigid-body model. A geometry constraint from the contact surface is developed to constrain the beam’s deformed configuration. The contact analysis problem is formulated based on the principle of minimum potential energy and solved using an optimization algorithm. Besides, a novel technique based on the principle of work and energy is proposed to calculate the reaction force/moment of displacement-loaded cases. Several analysis examples of the compliant mechanisms with straight or curved beams are used to verify the proposed method. The results show that the proposed method and technique can evaluate the deformation of beam-based CCMs and the reaction force/moment with acceptable accuracy, respectively.

Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

Abstract Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. Flexible segments which maintain a constant end angle are discussed, and an example mechanism is analyzed. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.

scholarly journals Multi-objective optimization of a type of ellipse-parabola shaped superelastic flexure hinge

2016 ◽  
Vol 7 (1) ◽  
pp. 127-134 ◽  
Author(s):  
Zhijiang Du ◽  
Miao Yang ◽  
Wei Dong
Keyword(s):  
Compliant Mechanisms ◽  
Pareto Frontier ◽  
Flexure Hinge ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Element Analysis ◽  
Multi Objective ◽  
Flexure Hinges ◽  
Static Responses ◽  
Motion Range

Abstract. Flexure hinges made of superelastic materials is a promising candidate to enhance the movability of compliant mechanisms. In this paper, we focus on the multi-objective optimization of a type of ellipse-parabola shaped superelastic flexure hinge. The objective is to determine a set of optimal geometric parameters that maximizes the motion range and the relative compliance of the flexure hinge and minimizes the relative rotation error during the deformation as well. Firstly, the paper presents a new type of ellipse-parabola shaped flexure hinge which is constructed by an ellipse arc and a parabola curve. Then, the static responses of superelastic flexure hinges are solved via non-prismatic beam elements derived by the co-rotational approach. Finite element analysis (FEA) and experiment tests are performed to verify the modeling method. Finally, a multi-objective optimization is performed and the Pareto frontier is found via the NSGA-II algorithm.

The Compliant A-Arm Suspension

Aerospace ◽  
2003 ◽  
Author(s):  
Timothy Allred ◽  
Larry L. Howell ◽  
Spencer P. Magleby ◽  
Robert H. Todd
Keyword(s):  
Compliant Mechanisms ◽  
Commercial Application ◽  
Leaf Spring ◽  
Large Deflections ◽  
Element Analysis ◽  
Performance Variables ◽  
Body Model ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Depth Study

The use compliant mechanisms in a suspension system has been demonstrated with leaf spring mechanisms. In this research a novel compliant configuration called the Compliant A-Arm (C-A-Arm) suspension is selected for in-depth study. Closed-from equations are derived for linear small-deflection stiffness equations. Large deflections are analyzed using finite element analysis. A pseudo-rigid-body model is developed to approximate mechanism deflections and stiffness for large deflections. The results suggest that the C-A-Arm configuration may be a viable suspension alternative for future commercial application. In addition, this configuration offers a number of performance variables that could be the basis for an active control system. This paper represents a necessary first step in modeling this new configuration.

Design and Analysis of a Contact-Aided Variable Stiffness Flexure Hinge (CVSFH)

2021 ◽  
Author(s):  
Shenyuan Dai ◽  
Lifang Qiu ◽  
Qichao Chen ◽  
Yanlin Li
Keyword(s):  
Contact Interaction ◽  
Compliant Mechanisms ◽  
Rectangular Cross Section ◽  
Variable Stiffness ◽  
Theoretical Equation ◽  
Flexure Hinge ◽  
Element Analysis ◽  
Equivalent Mechanical Model ◽  
Different Dimensions ◽  
Motion Characteristics

Abstract Flexure hinges are the basis of compliant mechanisms. The stiffness is one of the important indexes to evaluate the performance of a flexure hinge, and the rotation angle when the stiffness changes affects its motion characteristics. Thus, based on the constant rectangular cross-section flexure hinge and contact interaction, this paper proposed a contact-aided variable stiffness flexure hinge (CVSFH). With the deformation under an external load, the contact interaction with different parts of the CVSFH itself can achieve the purpose of variable stiffness. The equivalent mechanical model is built and the theoretical equation of the stiffness is given. CVSFHs with different dimensions are designed, and a finite element analysis (FEA) is done. The FEA results of the design examples are coincide with the theoretical results, which verifies the feasibility of the design and the correctness of the theoretical equation.

scholarly journals Modeling and Parameter Study of Bistable Spherical Compliant Mechanisms

2011 ◽  
Author(s):  
Chester L. Smith ◽  
Craig P. Lusk
Keyword(s):  
Compliant Mechanisms ◽  
Current Model ◽  
Plane Motion ◽  
Parameter Study ◽  
Beam Model ◽  
New Model ◽  
Novel Device ◽  
Rigid Body Model ◽  
Compliant Joint ◽  
Motion Characteristics

The Bistable Spherical Compliant Mechanisms (BSCM) is a novel device capable of large, repeatable, out-of-plane motion, characteristics that are somewhat difficult to achieve with surface micro-machined MEMS. An improved pseudo-rigid-body model to predict the behavior of the BSCM is presented. The new model was used to analyze seven different versions of the device, each with a different compliant joint length. The new model, which adds torsion, is compared with a Finite-Element beam model. The new model more closely approximates the results yielded by FEA than previous models used to analyze the BSCM. Future work is needed to quantify stress-stiffening interactions between bending and torsion. Both FEA and the current model show that increasing the length of the compliant segment decreases the amount of force required to actuate the device.

A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots

1994 ◽  
Vol 116 (1) ◽  
pp. 280-290 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Trial And Error ◽  
Flexible Link ◽  
Body Model ◽  
Input And Output ◽  
Rigid Body Model ◽  
Element Type ◽  
Body Joints

Compliant or flexible-link mechanisms gain some or all of their motion from the relative flexibility of their joints rather than from rigid-body joints only. Unlike rigid-body mechanisms, energy is not conserved between the input and output ports of compliant mechanisms because of energy storage in the flexible members. This effect and the nonlinearities introduced by large deflections complicate the analysis of such mechanisms. The design of compliant mechanisms in industry is currently accomplished by expensive trial and error methods. This paper introduces a method to aid in the design of a class of compliant mechanisms wherein the flexible sections (flexural pivots) are small in length compared to the relatively rigid sections. The method includes a definition and use of a pseudo-rigid-body model, and the use of a large-deflection finite element type algorithm. An example is used to illustrate the design technique described.

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