The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

2021 ◽  
pp. 1-18
Author(s):  
Brandon Sargent ◽  
Collin Ynchausti ◽  
Todd G Nelson ◽  
Larry L Howell
Keyword(s):  
Large Deflections ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Body Model ◽  
Minimal Error ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Expected Values ◽  
Deflection Theory ◽  
Sample Set

Abstract This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of <0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

2021 ◽  
Author(s):  
Brandon S. Sargent ◽  
Collin R. Ynchausti ◽  
Todd G. Nelson ◽  
Larry L. Howell
Keyword(s):  
Large Deflections ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Body Model ◽  
Minimal Error ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Expected Values ◽  
Deflection Theory ◽  
Sample Set

Abstract This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of < 0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

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 of a Single-Acting Constant-Force Actuator Based on Dielectric Elastomers

2008 ◽  
Author(s):  
Giovanni Berselli ◽  
Rocco Vertechy ◽  
Gabriele Vassura ◽  
Vincenzo Parenti Castelli
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compliant Mechanism ◽  
Structural Parameters ◽  
Dielectric Elastomer ◽  
Constant Force ◽  
Element Analysis ◽  
Body Model ◽  
Rigid Body Model ◽  
Supporting Frame

The interest in actuators based on dielectric elastomer films as a promising technology in robotic and mechatronic applications is increasing. The overall actuator performances are influenced by the design of both the active film and the film supporting frame. This paper presents a single-acting actuator which is capable of supplying a constant force over a given range of motion. The actuator is obtained by coupling a rectangular film of silicone dielectric elastomer with a monolithic frame designed to suitably modify the force generated by the dielectric elastomer film. The frame is a fully compliant mechanism whose main structural parameters are calculated using a pseudo-rigid-body model and then verified by finite element analysis. Simulations show promising performance of the proposed actuator.

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.

Large Stroke Series Compliant Mechanism

2012 ◽  
Vol 490-495 ◽  
pp. 1104-1108 ◽  
Author(s):  
Ming Cai Shan ◽  
Wei Ming Wang ◽  
Shu Yuan Ma ◽  
Shuang Liu
Keyword(s):  
Theoretical Model ◽  
Maximum Stress ◽  
Compliant Mechanism ◽  
Critical Parameters ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Body Model ◽  
System A ◽  
Rigid Body Model ◽  
The Difference

To increase the stroke of precision positioning system, a novel series compliant mechanism is presented which is based on elliptical flexure hinges. Pseudo-rigid-body model and energy method are applied to establish the theoretical model of stiffness and maximum stress, which are critical parameters for the large stroke compliant mechanism. The relationships are analyzed between geometric parameters of the series complaint mechanism, stiffness and maximum stress. According that, the series compliant mechanism is designed with the stroke more than 5mm and stiffness less than 3.2N/mm. The difference is less than 5% between the results of finite element analysis and theoretical model computation, which proves the correctness of the application design.

scholarly journals Design and Validation of a Single-SOI-Wafer 4-DOF Crawling Microgripper

Micromachines ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 376 ◽  
Author(s):  
Matteo Verotti ◽  
Alvise Bagolini ◽  
Pierluigi Bellutti ◽  
Nicola Pio Belfiore
Keyword(s):  
Finite Element Analysis ◽  
Rigid Body ◽  
Compliant Mechanism ◽  
Silicon On Insulator ◽  
Element Analysis ◽  
Deep Reactive Ion Etching ◽  
Theoretical Simulation ◽  
Body Model ◽  
Replacement Method ◽  
Rigid Body Model

This paper deals with the manipulation of micro-objects operated by a new concept multi-hinge multi-DoF (degree of freedom) microsystem. The system is composed of a planar 3-DoF microstage and of a set of one-DoF microgrippers, and it is arranged is such a way as to allow any microgripper to crawl over the stage. As a result, the optimal configuration to grasp the micro-object can be reached. Classical algorithms of kinematic analysis have been used to study the rigid-body model of the mobile platform. Then, the rigid-body replacement method has been implemented to design the corresponding compliant mechanism, whose geometry can be transferred onto the etch mask. Deep-reactive ion etching (DRIE) is suggested to fabricate the whole system. The main contributions of this investigation consist of (i) the achievement of a relative motion between the supporting platform and the microgrippers, and of (ii) the design of a process flow for the simultaneous fabrication of the stage and the microgrippers, starting from a single silicon-on-insulator (SOI) wafer. Functionality is validated via theoretical simulation and finite element analysis, whereas fabrication feasibility is granted by preliminary tests performed on some parts of the microsystem.

A Pseudo-Rigid-Body Model for Rolling-Contact Compliant Beams

2007 ◽  
Author(s):  
Allen B. Mackay ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Rolling Contact ◽  
Model Parameters ◽  
Displacement Curve ◽  
Cantilever Beams ◽  
Body Model ◽  
Rigid Body Model ◽  
Contact Surfaces ◽  
Definition Of ◽  
Force Displacement

This paper presents a pseudo-rigid-body model (PRBM) for rolling-contact compliant beams (RCCBs). The loading conditions and boundary conditions for the RCCB can be simplified to an equivalent cantilever beam that has the same force-deflection characteristics as the RCCB. Building on the PRBM for cantilever beams, this paper defines a model for the force-deflection relationship for RCCBs. The definition of the RCCB PRBM includes the pseudo-rigid-body model parameters that determine the shape of the beam, the length of the corresponding pseudo-rigid-body links and the stiffness of the equivalent torsional spring. The behavior of the RCCB is parameterized in terms of a single parameter defined as clearance, or the distance between the contact surfaces. RCCBs exhibit a unique force-displacement curve where the force is inversely proportional to the clearance squared.

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.

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