Multistable Behavior of Compliant Kaleidocycles

2015 ◽  
Author(s):  
Thomas A. Evans ◽  
Brett G. Rowberry ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Strain Energy ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Neutral Stability ◽  
Energy Characteristics ◽  
Continuous Rotation

We present an analysis of the compliant kaleidocycle, a mechanism which, unlike other compliant mechanisms, may undergo continuous rotation. We analyze the strain energy characteristics of this mechanism during its motion and show that by varying the stiffness and orientation of the flexures, kaleidocycles may be designed to achieve customizable multistable behavior. These devices may be designed to include up to four distinct stable equilibrium positions and may also include regions of neutral stability.

Synthesizing Precompressed Beams As Bistable Compliant Mechanisms

2017 ◽  
Author(s):  
Mohammed Abdullah Maaz Siddiqui ◽  
Hong Zhou
Keyword(s):  
Rigid Body ◽  
Axial Compression ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Input Power ◽  
Elastic Deformations ◽  
Buckling Instability ◽  
Beam Thickness ◽  
Fixed End ◽  
Input Torque

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.

Modeling and Experimental Validation of Actuating a Bistable Buckled Beam Via Moment Input

2015 ◽  
Vol 82 (5) ◽  
Author(s):  
Jonathon Cleary ◽  
Hai-Jun Su
Keyword(s):  
Theoretical Model ◽  
Experimental Test ◽  
Experimental Validation ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Computational Tool ◽  
Specific Mechanism ◽  
Test Setup ◽  
Buckled Beams ◽  
Buckled Beam

Bistable mechanisms have two stable equilibrium positions separated by a higher energy unstable equilibrium position. They are well suited for microswitches, microrelays, and many other macro- and micro-applications. This paper discusses a bistable buckled beam actuated by a moment input. A theoretical model is developed for predicting the necessary input moment. A novel experimental test setup was created for experimental verification of the model. The results show that the theoretical model is able to predict the maximum necessary input moment within 2.53%. This theoretical model provides a guideline to design bistable compliant mechanisms and actuators. It is also a computational tool to size the dimensions of buckled beams for actuating a specific mechanism.

A Study of Conditions That Affect the Distribution of Compliance in Compliant Mechanisms

2008 ◽  
Author(s):  
Stephen L. Canfield ◽  
Daniel L. Chlarson ◽  
Alexander Shibakov ◽  
Joseph D. Richardson ◽  
Anupam Saxena
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Optimization Process ◽  
Objective Functions ◽  
Compatibility Analysis ◽  
Pareto Sets ◽  
Show Evidence ◽  
Final Design ◽  
Additional Constraints ◽  
Insight Into

Researchers in the field of optimal synthesis of compliant mechanisms have been working to develop design tools that yield distributed compliant devices from a continuum design domain. However, it has been demonstrated in the literature that much of this work has resulted in mechanisms that localize compliance rather than distribute it as desired. Inaccurate representation of the stiffness or strain energy due to the existence of point flexures in the mechanism was identified as the cause of this behavior by early researchers. To eliminate this cause, several approaches have been tried to improve the design of distributed mechanisms, for example additional constraints on the optimization process, alternate parameterization techniques that avoid point flexures and additional objective functions evaluated as Pareto sets. In this paper, the authors further investigate the fundamental reasons for the prevalence of lumped designs. Representative simple compliant mechanisms are investigated analytically and numerically and the influence of various additional objectives on the final design is evaluated. To extrapolate these results to more complex mechanisms, examples are constructed that show evidence that a preference remains for lumped compliance, despite the countermeasures that have been applied. Pareto compatibility analysis developed by the authors is used to analyze the influence of various objectives on the distributive nature of the final design. These conditions that influence the distribution of compliance fall into two basic categories: those specific to the numerical methods applied and those of purely mechanical (i.e. fundamental) nature. This work will examine conditions of the latter type and will demonstrate that such a preference for lumped compliance exists. This preference is shown to be contained in the classic objectives; flexibility and stiffness. Based on these results, greater insight into the optimization process is gained and applied to improve the search for distributed compliant mechanisms.

Study on Characteristics of Energy for Hard Roof Fracture in Island Workface

2013 ◽  
Vol 734-737 ◽  
pp. 694-697
Author(s):  
Xu Feng Pang ◽  
Ke Xue Zhang
Keyword(s):  
Strain Energy ◽  
Typical Case ◽  
Energy Characteristics ◽  
Hard Roof ◽  
Coal Bump ◽  
Bending Strain ◽  
Before And After ◽  
Mechanical Models

According to the characteristics of the island workface with hard roof, various mechanical models of hard roof in island workface are established, to analyze energy characteristics of hard roof before and after the first fracture in island workface with all round gobs, derived their simplified formulas of bending strain energy for hard roof before and after the first fracture, and using these formulas to estimate the bending strain energy for the typical case of coal bump, reveals the energy cause of coal bump and verify the validity of these formulas.

A Framework for Energy-Based Kinetostatic Modeling of Compliant Mechanisms

2017 ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Ruiyu Bai ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Modeling Framework ◽  
Geometric Nonlinearities ◽  
Complementary Strain ◽  
Minimum Strain Energy ◽  
Constraint Model ◽  
Future Work

Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano’s first theorem and the Crotti-Engesser theorem, which don’t require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of using Castigliano’s first theorem and the Crotti-Engesser theorem with the explicit formulations in this framework. Future work will be focused on incorporating use of the principle of minimum strain energy and the principle of minimum complementary strain energy.

scholarly journals An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

2021 ◽  
pp. 1-18
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Ruiyu Bai ◽  
Weidong Zhu ◽  
Spencer P Magleby ◽  
...  
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Modeling Framework ◽  
Geometric Nonlinearities ◽  
Complementary Strain ◽  
Constraint Model

Abstract Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano's first theorem and the Crotti-Engesser theorem, which don't require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of the explicit formulations in this framework derived from Castigliano's first theorem and the Crotti-Engesser theorem.

Topology Optimization of Compliant Mechanisms Explicitly Considering Desired Kinematics and Stiffness Constraints

2016 ◽  
Author(s):  
Alexander Hasse
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Single Input Single Output ◽  
Output Displacement ◽  
Single Output ◽  
Input And Output ◽  
Optimization Formulation ◽  
Topology And Shape Optimization ◽  
Optimization Parameters ◽  
Single Input

A mechanism is designed to transform forces and/or displacements from an input to one or multiple outputs. This transformation is essentially ruled by the kinematics, i.e. the defined ratio between input and output displacements. Although the kinematics forms the basis for the design of conventional mechanisms, approaches for the topology and shape optimization of compliant mechanisms do not normally explicitly include the kinematics in their optimization formulation. The kinematics is more or less an outcome of the optimization process. A defined kinematics can only be realized by iteratively adjusting process-specific optimization parameters within the optimization formulation. Moreover, existing approaches normally minimize the strain energy that is stored in the compliant mechanisms according to a defined input and output displacement — although in some applications a certain amount of strain energy is required. This paper presents a new optimization formulation that solves the aforementioned problems. It is based on the principles of designing compliant mechanisms with selective compliance formerly presented by the author. The formulation is derived by means of an intensive workup of the design problem of compliant mechanisms. The method is validated for different design examples ranging from standard single-input/single-output mechanisms (force inverters) to multi-output mechanisms (shape-adaptive structures).

Reliability-Based Optimal Design of a Bistable Compliant Mechanism

1993 ◽  
Author(s):  
L. L. Howell ◽  
S. S. Rao ◽  
A. Midha
Keyword(s):  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Probabilistic Constraints ◽  
Probabilistic Design ◽  
Design Studies ◽  
Stable Equilibrium Position ◽  
Crank Mechanism ◽  
Insight Into ◽  
Input Torque

Abstract Compliant mechanisms obtain at least some of their motion from the deflection of their flexible members. Advantages of such mechanisms include the reduction of manufacturing and assembly cost and time. Bistable mechanisms are particularly useful in applications where two stable equilibrium positions are required, such as switches, gates, and closures. Fatigue is a major concern in many compliant mechanisms due to the cyclic stresses induced on the flexible members. In this paper, a method for the probabilistic design of a bistable compliant slider-crank mechanism is proposed. Link lengths, material properties, and cross-section dimensions are taken as random variables. Probabilistic constraints on the maximum and minimum required input torque, location of stable equilibrium position, and overall size are included. The objective function is the maximization of the mechanism reliability in fatigue. Several design studies are performed to gain further insight into the nature of the problem.

Use of Penalty Function in Topological Synthesis and Optimization of Strain Energy Density of Compliant Mechanisms

1997 ◽  
Author(s):  
Mary I. Frecker ◽  
Sridhar Kota ◽  
Noboru Kikuchi
Keyword(s):  
Energy Density ◽  
Penalty Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Compliant Mechanisms ◽  
High Stress ◽  
Optimal Solution ◽  
Optimality Criteria ◽  
Second Stage ◽  
Starting Point

Abstract A penalty function approach is used in conjunction with a multi-criteria optimization method for topology synthesis of compliant mechanisms. This method can help facilitate convergence to physically meaningful solutions for problems with a large number of design variables. The second part of the paper is an investigation of the element strain energy density of the optimal solution, where a second stage size optimization routine is developed. The solution from the topology optimization is used as a starting point for the resizing algorithm, which uses an optimality criteria method based on the overall average strain energy density. This second stage optimization more uniformly distributes the element strain energy densities in order to avoid localized areas of high stress or strain.

Pseudo-Rigid-Body Models of Compliant DNA Origami Mechanisms

2015 ◽  
Author(s):  
Lifeng Zhou ◽  
Alexander E. Marras ◽  
Carlos E. Castro ◽  
Hai-jun Su
Keyword(s):  
Rigid Body ◽  
Strain Energy ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanical Energy ◽  
Energy Landscape ◽  
Thermal Fluctuations ◽  
Dna Origami ◽  
Double Stranded Dna ◽  
Flexible Parts

In this paper, we introduce the strategy of designing and analyzing compliant nanomechanisms fabricated with DNA origami which we call compliant DNA origami mechanism (CDOM). The rigid, compliant and flexible parts are constructed by a bunch of double-stranded DNA (dsDNA) helices, fewer dsDNA helices and single-stranded DNA (ssDNA) strands respectively. Just like in macroscopic compliant mechanisms, a CDOM generates its motion via deformation of at least one structural member. During the motion, strain energy is stored and released in the mechanism. These CDOM can suppress thermal fluctuations due to the internal mechanical energy barrier for motion. An example of compliant hinge joint and a bistable four-bar CDOM fabricated with DNA origami are discussed at the end of this paper. The classic pseudo-rigid-body (PRB) model for compliant mechanism is successfully employed to the analysis of these DNA origami nanomechanisms. This PRB model has been used to guide the design of a bistable CDOM for a desired energy landscape.

Sign in / Sign up

Export Citation Format

Share Document