scholarly journals A Pseudo-Rigid-Body Model for Large Deflections of Fixed-Clamped Carbon Nanotubes

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Larry L. Howell ◽  
Christopher M. DiBiasio ◽  
Michael A. Cullinan ◽  
Robert M. Panas ◽  
Martin L. Culpepper
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Molecular Simulations ◽  
Design Parameters ◽  
Body Model ◽  
Initial Design ◽  
Rigid Body Model

Carbon nanotubes (CNTs) may be used to create nanoscale compliant mechanisms that possess large ranges of motion relative to their device size. Many macroscale compliant mechanisms contain compliant elements that are subjected to fixed-clamped boundary conditions, indicating that they may be of value in nanoscale design. The combination of boundary conditions and large strains yield deformations at the tube ends and strain stiffening along the length of the tube, which are not observed in macroscale analogs. The large-deflection behavior of a fixed-clamped CNT is not well-predicted by macroscale large-deflection beam bending models or truss models. Herein, we show that a pseudo-rigid-body model may be adapted to capture the strain stiffening behavior and, thereby, predict a CNT’s fixed-clamped behavior with less than 3% error from molecular simulations. The resulting pseudo-rigid-body model may be used to set initial design parameters for CNT-based compliant mechanisms. This removes the need for iterative, time-intensive molecular simulations during initial design phases.

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.

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.

Dynamic Characteristics of Planar Compliant Parallel-Guiding Mechanisms

2008 ◽  
Author(s):  
Wenjing Wang ◽  
Yueqing Yu
Keyword(s):  
Numerical Methods ◽  
Rigid Body ◽  
Natural Frequency ◽  
Dynamic Modeling ◽  
Dynamic Characteristics ◽  
Compliant Mechanisms ◽  
Design Parameters ◽  
Dynamic Effects ◽  
Body Model ◽  
Rigid Body Model

Dynamic effects are very important to improving the design of compliant mechanisms. An investigation on the dynamic characteristics of planar compliant parallel-guiding mechanism is presented. Based on the pseudo-rigid-body model, the dynamic model of planar compliant parallel-guiding mechanisms is developed using the numerical methods at first. The natural frequency is then calculated, and frequency characteristics of this mechanism are studied. The numerical results show the accuracy of the proposed method for dynamic modeling of compliant mechanisms, and the relationships between the natural frequency and design parameters are analyzed clearly.

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.

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

1996 ◽  
Vol 118 (1) ◽  
pp. 126-131 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha ◽  
T. W. Norton
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

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. 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.

A Compliant Straight-Line Shock Absorption Mechanism Using a Viscoelastic Pseudo-Rigid Body Model

2009 ◽  
Author(s):  
Carl A. Nelson
Keyword(s):  
Energy Dissipation ◽  
System Dynamics ◽  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Force Analysis ◽  
Absorption Mechanism ◽  
Body Model ◽  
Straight Line ◽  
Rigid Body Model

A compliant suspension linkage based on the Peaucellier mechanism is presented. The suspension uses large-deflection viscoelastic beams to achieve straight-line motion and to provide energy dissipation. Kinematics and force analysis of the linkage are presented. In preparing to simulate the system dynamics, it was noticed that no adaptation of the pseudo-rigid body model for viscoelastic beams had been previously presented. Therefore, a new general approach for modeling viscoelastic, large-deflection beams in compliant mechanisms is described within the context of the pseudo-rigid-body model. This method is applied in simulation of the Peaucellier-based compliant suspension under a variety of input conditions.

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.

Pseudo-Rigid-Body Model Chain Algorithm: Part 1 — Introduction and Concept Development

2006 ◽  
Author(s):  
Joby Pauly ◽  
Ashok Midha
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Loop Closure ◽  
Body Model ◽  
Rigid Body Model ◽  
Model Chain ◽  
Compliant Mechanism Design

Pseudo-rigid-body models help expedite the compliant mechanism design process by aiding the analysis and synthesis of candidate design solutions, using loop-closure techniques for rigid-body mechanisms. Presently, these models are available only for relatively simple compliant beam geometries and loading situations. The chain algorithm is an alternate method for the design and analysis of compliant mechanisms. Though more versatile, insofar as the geometry and loading are concerned, it is not possible to implement this technique in analysis or synthesis problems involving loop-closure equations. This paper proposes the construction of a generalized “pseudo-rigid-body model chain;” it allows the use of pseudo-rigid-body models in conjunction with the chain algorithm to obtain the deformation kinematics of complex compliant members. Such a “pseudo-rigid-body model chain” would possess dual advantages of expediency of modeling through the use of pseudo-rigid-body representations of compliant segments, and the inherent flexibility of the chain algorithm to geometry and load boundary conditions. The proposed technique involves discretization of the planar continuum into initially straight, equal length compliant segments, whose deflections due to the applied load boundary conditions are then determined using appropriate pseudo-rigid-body models. Such a model could potentially be used in the solution of compliant mechanism design and analysis problems when coupled with the use of loop-closure equations.

A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

1998 ◽  
Vol 120 (3) ◽  
pp. 392-400 ◽  
Author(s):  
A. Saxena ◽  
S. N. Kramer
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Elliptic Integral ◽  
Beam Equation ◽  
Large Deflections ◽  
Euler Beam ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

A Simple and Accurate Method for Determining Large Deflections in Complaint Mechanisms Subjected to End Forces and Moments

1998 ◽  
Author(s):  
A. Saxena ◽  
Steven N. Kramer
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Beam Equation ◽  
Integration Scheme ◽  
Large Deflections ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Abstract Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads for which, traditional methods of deflection analysis do not apply Nonlinearities introduced by these large deflections make the system comprising such members difficult to solve Parametric deflection approximations are then deemed helpful in the analysis and synthesis of compliant mechanisms This is accomplished by seeking the pseudo-rigid-body model representation of the compliant mechanism A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads with positive end moments A numerical integration technique using quadrature formulae has been employed to solve the nonlinear Bernoulli-Euler beam equation for the tip deflection Implementation of this scheme is relatively simpler than the elliptic integral formulation and provides nearly accurate results Results of the numerical integration scheme are compared with the beam finite element analysis An example for the synthesis of a compliant mechanism using the proposed model is also presented.

Sign in / Sign up

Export Citation Format

Share Document