Curve Decomposition for Large Deflection Analysis of Fixed-Guided Beams With Application to Statically Balanced Compliant Mechanisms

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Charles Kim ◽  
Donna Ebenstein
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Parametric Design ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Negative Stiffness ◽  
Proof Of Concept ◽  
Deflection Curve ◽  
Key Points ◽  
Deflection Analysis

Statically balanced compliant mechanisms require no holding force throughout their range of motion while maintaining the advantages of compliant mechanisms. In this paper, a postbuckled fixed-guided beam is proposed to provide the negative stiffness to balance the positive stiffness of a compliant mechanism. To that end, a curve decomposition modeling method is presented to simplify the large deflection analysis. The modeling method facilitates parametric design insight and elucidates key points on the force–deflection curve. Experimental results validate the analysis. Furthermore, static balancing with fixed-guided beams is demonstrated for a rectilinear proof-of-concept prototype.

Curve Decomposition Analysis for Fixed-Guided Beams With Application to Statically Balanced Compliant Mechanisms

2011 ◽  
Author(s):  
Charles Kim
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Parametric Design ◽  
Compliant Mechanism ◽  
Decomposition Analysis ◽  
Modeling Method ◽  
Proof Of Concept ◽  
Deflection Curve ◽  
Key Points ◽  
Deflection Analysis

Statically balanced compliant mechanisms require no holding force throughout their range of motion while maintaining the advantages of compliant mechanisms. In this paper, a post-buckled fixed-guided beam is proposed to provide the negative stiffness to balance the positive stiffness of a compliant mechanism. To that end, a unique curve decomposition modeling method is presented to simplify the large deflection analysis. The modeling method facilitates parametric design insight and elucidates key points on the force-deflection curve. Experimental results validate the analysis. Furthermore, static balancing with fixed-guided beams is demonstrated for a rectilinear proof-of-concept prototype.

A Methodology for Compliant Mechanisms Design: Part I — Introduction and Large-Deflection Analysis

1992 ◽  
Author(s):  
A. Midha ◽  
I. Her ◽  
B. A. Salamon
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Companion Paper ◽  
Computational Techniques ◽  
Shooting Methods ◽  
Mechanism Synthesis ◽  
Calculation Algorithm ◽  
Deflection Analysis ◽  
Kinematic Properties

Abstract A broader research proposal seeks to systematically combine large-deflection mechanics of flexible elements with important kinematic considerations, in yielding compliant mechanisms which perform useful tasks. Specifically, the proposed design methodology will address the following needs: development of the necessary nomenclature, classification and definitions, and identification of the kinematic properties; categorization of mechanism synthesis types, both structurally as well as by function; development of efficient computational techniques for design; consideration of materials; and application and validation. Contained herein, in particular, is an introduction to the state-of-the-art in compliant mechanisms, and the development of an accurate chain calculation algorithm for use in the analysis of a large-deflection, cantilevered elastica. Shooting methods, which permit specification of additional boundary conditions on the elastica, as well as compliant mechanism examples are presented in a companion paper.

Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Karin Hoetmer ◽  
Geoffrey Woo ◽  
Charles Kim ◽  
Just Herder
Keyword(s):  
Force Feedback ◽  
High Efficiency ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Negative Stiffness ◽  
High Fidelity ◽  
Proof Of Concept ◽  
Design Considerations ◽  
Design And Testing

In some applications, nonconstant energy storage in the flexible segments of compliant mechanisms is undesired, particularly when high efficiency or high-fidelity force feedback is required. In these cases, the principle of static balancing can be applied, where a balancing segment with a negative stiffness is added to cancel the positive stiffness of the compliant mechanism. This paper presents a strategy for the design of statically balanced compliant mechanisms and validates it through the fabrication and testing of proof-of-concept prototypes. Three compliant mechanisms are statically balanced by the use of compressed plate springs. All three balanced mechanisms have approximately zero stiffness but suffer from a noticeable hysteresis loop and finite offset from zero force. Design considerations are given for the design and fabrication of statically balanced compliant mechanisms.

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 A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Nonlinearity ◽  
Adomian Decomposition Method ◽  
Analytical Form ◽  
Point Load ◽  
Large Deflections ◽  
Adomian Decomposition

The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

A CPRBM-based method for large-deflection analysis of contact-aided compliant mechanisms considering beam-to-beam contacts

2020 ◽  
Vol 145 ◽  
pp. 103700 ◽  
Author(s):  
Mohui Jin ◽  
Benliang Zhu ◽  
Jiasi Mo ◽  
Zhou Yang ◽  
Xianmin Zhang ◽  
...  
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Deflection Analysis

Geometric Modeling and Optimization of Multi-Material Compliant Mechanisms Using Multi-Layer Wide Curves

2007 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Geometric Optimization ◽  
Optimization Approach ◽  
Variable Cross ◽  
Modeling And Optimization ◽  
Multiple Materials

Multi-material compliant mechanisms enhance the performance of regular single-material compliant mechanisms by adding a new design option, material type variation. This paper introduces a geometric modeling method for multimaterial compliant mechanisms by using multi-layer wide curves. Based on the introduced modeling method, a geometric optimization approach for multi-material compliant mechanisms is proposed. A multi-layer wide curve is a curve with variable cross-sections and multiple materials. In this paper, every connection in the multi-material compliant mechanism is represented by a multi-layer wide curve and the whole mechanism is modeled as a set of connected multi-layer wide curves. The geometric modeling and optimization of a multi-material compliant mechanism are considered as the generation and optimal selection of the control parameters of the corresponding multi-layer wide curves. The deformation and performance of multi-material compliant mechanisms is evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The effectiveness of the proposed geometric modeling and optimization procedures is verified by the demonstrated examples.

Towards the Design of a Statically Balanced Compliant Laparoscopic Grasper Using Topology Optimization

2008 ◽  
Author(s):  
Ditske J. B. A. de Lange ◽  
Matthijs Langelaar ◽  
Just L. Herder
Keyword(s):  
Topology Optimization ◽  
Force Feedback ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Negative Stiffness ◽  
Compensation Mechanism ◽  
Laparoscopic Grasper ◽  
The Difference ◽  
Force Displacement ◽  
Compliant Mechanism Design

This paper presents the design of a grasping instrument for minimally invasive surgery. Due to its small dimensions a compliant mechanism seems promising. To obtain force feedback, the positive stiffness of the compliant grasper must be statically balanced by a negative-stiffness compensation mechanism. For the design of compliant mechanisms, topology optimization can be used. The goal of this paper is to investigate the applicability of topology optimization to the design of a compliant laparoscopic grasper and particularly a compliant negative-stiffness compensation mechanism. In this study, the problem is subdivided in the grasper part and the compensation part. In the grasper part the deflection at the tip of the grasper is optimized. This results in a design that has a virtually linear force-displacement characteristic that forms the input for the compensation part. In the compensation part the difference between the force-displacement characteristic of the grasper part and the characteristic of the compensation part is minimized. An optimization problem is formulated enabling a pre-stress to be incorporated, which is required to obtain the negative stiffness in the compensation part. We can conclude that topology optimization is a promising approach in the field of statically balanced compliant mechanism design, even though there is great scope improvement of the method.

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.

Constraint-Force-Based (CFB) Modeling of Compliant Mechanisms

2015 ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Static Equilibrium ◽  
Constraint Forces ◽  
Equilibrium Equations ◽  
Constraint Force ◽  
Element Analysis ◽  
External Forces ◽  
Force Equilibrium

Numerous works have been done on modeling compliant modules or joints, and the closed-form models of many widely-used compliant modules have been developed. However, the modeling of complex compliant mechanisms with considering external forces is still a challenging work. This paper introduces a constraint-force-based method to model compliant mechanisms. A compliant mechanism can be regarded as the combination of rigid stages and compliant modules. If a compliant mechanism is at static equilibrium under the influence of a series of external forces, all the rigid stages are also at static equilibrium. The rigid stages are restricted by the constraint forces of the compliant modules and the exerted external forces. This paper defines the constraint forces of the compliant modules to be variable constraint forces since the constraint forces vary with the deformation of the compliant modules, and defines the external forces as constant constraint forces due to the fact that the external forces are specific forces exerted which do not change with the deformation of the compliant mechanism. Therefore, the force equilibrium equations for all rigid stages in a compliant mechanism can be obtained based on the variable constraint forces and the constant constraint forces. Moreover, the model of the compliant mechanism can also be derived through solving all the force equilibrium equations. The constraint-force-based modeling method is finally detailed demonstrated via examples, and validated by the finite element analysis. Using this proposed modeling method, a complex compliant mechanism can be modelled with a particular emphasis on considering the position spaces of the associated compliant modules.

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