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.

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.

The Development of Force-Deflection Relationships for Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Virtual Work ◽  
Compliant Mechanism ◽  
Flexible Link ◽  
Model Concept ◽  
Body Model ◽  
Design Flexibility ◽  
Rigid Body Model ◽  
Manufacturing Time

Abstract The advantages of compliant or flexible link mechanisms include increased design flexibility and reduction in manufacturing time and cost. The analysis of such mechanisms may be difficult and time consuming due to the nonlinearities introduced by large deflections. Also, unlike rigid-body mechanisms, the type and form of motion of a compliant mechanism is dependent on the location and magnitude of applied loads. The pseudo-rigid-body model concept has been developed to simplify the analysis of compliant mechanisms by allowing them to be modeled as rigid-link mechanisms with springs. This work uses the principle of virtual work and the pseudo-rigid-body model concept to develop force-deflection relationships for compliant mechanisms. Several examples are presented, and general design equations are derived for pseudo-rigid-body four-bar and slider-crank 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.

Compliant Pantographs via the Pseudo-Rigid-Body Model

1998 ◽  
Author(s):  
Andrew J. Nielson ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Test Results ◽  
Rigid Link ◽  
Body Model ◽  
Design Flexibility ◽  
Model Predictions ◽  
Rigid Body Model ◽  
Classical Mechanism

Abstract This paper uses a familiar classical mechanism, the pantograph, to demonstrate the utility of the pseudo-rigid-body model in the design of compliant mechanisms to replace rigid-link mechanisms, and to illustrate the advantages and limitations of the resulting compliant mechanisms. To demonstrate the increase in design flexibility, three different compliant mechanism configurations were developed for a single corresponding rigid-link mechanism. The rigid-link pantograph consisted of six links and seven joints, while the corresponding compliant mechanisms had no more than two links and three joints (a reduction of at least four links and four joints). A fourth compliant pantograph, corresponding to a rhomboid pantograph, was also designed and tested. The test results showed that the pseudo-rigid-body model predictions were accurate over a large range, and the mechanisms had displacement characteristics of rigid-link mechanisms in that range. The limitations of the compliant mechanisms included reduced range compared to their rigid-link counterparts. Also, the force-deflection characteristics were predicted by the pseudo-rigid-body model, but they did not resemble those for a rigid-link pantograph because of the energy storage in the flexible segments.

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.

Classification of Compliant Mechanisms and Determination of the Degrees of Freedom Using the Concepts of Compliance Number and Pseudo-Rigid-Body Model

2019 ◽  
Author(s):  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha ◽  
Sushrut G. Bapat
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Body Model ◽  
Active Compliance ◽  
Kinematic Behavior ◽  
Rigid Body Model

Abstract Understanding the kinematic properties of a compliant mechanism has always proved to be a challenge. A concept of compliance number offered earlier emphasized the development of terminology that aided in its determination. A method to evaluate the elastic degrees of freedom associated with the flexible segments/links of a compliant mechanism using the pseudo-rigid-body model (PRBM) concept is provided. In this process, two distinct classes of compliant mechanisms are developed involving: (i) Active Compliance and (ii) Passive Compliance. Furthermore, these also aid in a better characterization of the kinematic behavior of a compliant mechanism. A more lucid interpretation of the significance of compliance number is provided. Applications of this method to both active and passive compliant mechanisms are exemplified. Finally, an experimental procedure that aids in visualizing the degrees of freedom as calculated is presented.

On a Generalized Approach for Design of Compliant Mechanisms Using the Pseudo-Rigid-Body Model Concept

2014 ◽  
Author(s):  
Sushrut G. Bapat ◽  
Ashok Midha ◽  
Ashish B. Koli
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Motion Generation ◽  
Model Concept ◽  
Finite Element Software ◽  
Body Model ◽  
Wide Range ◽  
Rigid Body Model ◽  
Torque Values

This paper provides a generalized approach for the design of compliant mechanisms. The paper discusses the implicit uncoupling, between the kinematic and energy/torque equations, enabled by the pseudo-rigid-body model concept, and utilizes it for designing a variety of compliant mechanism types for a wide-range of user specifications. Pseudo-rigid-body four-bar mechanisms, with one to four torsional springs located at the revolute joints, are considered to demonstrate the design methodology. Mechanisms are designed for conventional tasks, such as function, path and motion generation, and path generation with prescribed timing, with energy/torque specified at the precision-positions. State-of-the-art rigid-body synthesis techniques are applied to the pseudo-rigid-body model to satisfy the kinematic requirements. Energy/torque equations are then used to account for the necessary compliance according to the user specifications. The approach utilizes a conventional, simple yet efficient optimization formulation to solve energy/torque equations that allow a designer to i) achieve realistic solutions, ii) specify appropriate energy/torque values, and iii) reduce the sensitivities associated with the ‘synthesis with compliance’ approach. A variety of examples are presented to demonstrate the applicability and effectiveness of the approach. All of the examples are verified with the finite element software ANSYS®.

Multiple-Segment-Pseudo-Rigid-Body Model Concept in Compliant Mechanism Design and Analysis

2000 ◽  
Author(s):  
Gregory A. Mettlach ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Methods ◽  
Model Concept ◽  
Displacement Boundary ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Beam Type

Abstract The concept of a pseudo-rigid-body model for a flexible member proven very instrumental in the design and analysis of compliant mechanisms. It provides a means by which a compliant mechanism may be modeled as an equivalent pseudo-rigid-body mechanism. This makes it possible for compliant mechanisms to be analyzed and designed using a wealth of existing methods for rigid-body mechanisms. Oftentimes, however, it is not possible to model a compliant member with a typical pseudo-rigid-body model. This may be due to a force or displacement boundary condition applied to a compliant member at a point other than the beam end. For situations such as these, a planar, multiple-segment pseudo-rigid-body model concept is introduced which allows arbitrary beam type compliant members, regardless of geometry, loading, or boundary conditions, to be modeled as an assemblage of rigid members with torsional springs at characteristic pivots. This methodology enables existing analysis and synthesis methods to be applied in the design of complex compliant mechanisms.

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