New Approach to the Dynamic Modeling of Compliant Mechanisms

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Wenjing Wang ◽  
Yueqing Yu
Keyword(s):  
Numerical Methods ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Compliant Mechanisms ◽  
Lagrange Equation ◽  
New Approach ◽  
Body Model ◽  
Rigid Body Model

A new dynamic model of compliant mechanisms is developed based on the pseudo-rigid-body model. The kinetic energy and potential energy of various kinds of compliant segments are derived using numerical methods at first. The dynamic equation of planar compliant mechanisms is then developed based on the Lagrange equation. The natural frequency is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the advantage of the proposed method for the dynamic analysis of compliant mechanisms.

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.

Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model

2005 ◽  
Vol 127 (4) ◽  
pp. 760-765 ◽  
Author(s):  
Yue-Qing Yu ◽  
Larry L. Howell ◽  
Craig Lusk ◽  
Ying Yue ◽  
Mao-Gen He
Keyword(s):  
Rigid Body ◽  
Natural Frequency ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Dynamic Equivalence ◽  
Body Model ◽  
Rigid Body Model ◽  
Flexible Mechanisms

Based on the principle of dynamic equivalence, a new dynamic model of compliant mechanisms is developed using the pseudo-rigid-body model. The dynamic equation of general planar compliant mechanisms is derived. The natural frequency of a compliant mechanism is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the effectiveness and advantage of the proposed method compared with the methods of FEA and flexible mechanisms.

A numerical method for static analysis of pseudo-rigid-body model of compliant mechanisms

2014 ◽  
Vol 228 (17) ◽  
pp. 3170-3177 ◽  
Author(s):  
Mohui Jin ◽  
Xianmin Zhang ◽  
Benliang Zhu
Keyword(s):  
Finite Elements ◽  
Potential Energy ◽  
Rigid Body ◽  
Numerical Method ◽  
Compliant Mechanisms ◽  
Potential Energy Function ◽  
Automated Analysis ◽  
Optimization Techniques ◽  
Body Model ◽  
Rigid Body Model

This paper presents a numerical method for analyzing the pseudo-rigid-body model of compliant mechanisms based on finite elements and the principle of minimum potential energy. The proposed method represents the links of pseudo-rigid-body model with truss elements. As a result, the pseudo-rigid-body model is modeled into a compliant system that consists of finite elements and springs. The static equilibrium position of the pseudo-rigid-body model can be obtained by minimizing the potential energy function of this compliant system. A comparison between the proposed method and the MinPE method is presented. Lastly, a case study is provided to demonstrate the application of this method in the automated analysis of pseudo-rigid-body models. This numerical method paves the way for introducing the topology optimization techniques into the synthesis of flexure-based compliant mechanisms.

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

2010 ◽  
Author(s):  
Quentin T. Aten ◽  
Shannon A. Zirbel ◽  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Potential Energy ◽  
Rigid Body ◽  
Equilibrium Position ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Virtual Work ◽  
Compliant Mechanism ◽  
Loop Equation ◽  
Body Model ◽  
Rigid Body Model

An under-actuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudo-rigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for under-actuated 1-DOF and 2-DOF pseudo-rigid-body models. Experimental force-deflection data is presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudo-rigid-body model, a 13-DOF pseudo-rigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with non-linear finite element analysis and experimental force-displacement data.

Dynamic Modeling of Compliant Mechanisms Based on 2R Pseudo-Rigid-Body Model

2012 ◽  
Vol 163 ◽  
pp. 277-280 ◽  
Author(s):  
Wen Jing Wang ◽  
Shu Sheng Bi ◽  
Li Ge Zhang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Large Deflections ◽  
Flexible Link ◽  
Flexible Links ◽  
Body Model ◽  
Rigid Body Model ◽  
New Type

Compliant mechanism is a kind of new type mechanism and its analysis is very complex because flexible links often under large deflections which introduce geometry nonlinearities. A new model (2R PRBM) can simulate accurately both the deflection path and angle of the flexible link. A new dynamic model of compliant mechanism is developed using the 2R PRBM. The dynamic equation of planar compliant mechanism is derived. The dynamic analysis on the natural frequency of compliant mechanism is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the advantage of the proposed method for the dynamic analysis of compliant mechanisms.

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.

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.

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