Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model (PRBM) Concept

2012 ◽  
Author(s):  
Ashok Midha ◽  
Sushrut G. Bapat ◽  
Adarsh Mavanthoor ◽  
Vivekananda Chinta
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Rigid Body ◽  
Inflection Point ◽  
Equilibrium Equations ◽  
Displacement Boundary ◽  
Body Model ◽  
Rigid Body Model ◽  
Domain Concept ◽  
Selection Of

This paper provides an efficient method of analysis for a fixed-guided compliant beam with an inflection point, subjected to beam end load or displacement boundary conditions, or a combination thereof. To enable this, such a beam is modeled as a pair of well-established pseudo-rigid-body models (PRBMs) for fixed-free compliant beam segments. The analysis procedure relies on the properties of inflection in developing the necessary set of static equilibrium equations for solution. The paper further discusses the multiplicity of possible solutions, including displacement configurations, for any two specified beam end boundary conditions, depending on the locations of the effecting force and/or displacement boundary conditions. A unique solution may exist when a third beam end boundary condition is specified; however, this selection is not unconditional. A deflection domain concept is proposed to assist with the selection of the third boundary condition in a more realistic manner.

Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model Concept

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Ashok Midha ◽  
Sushrut G. Bapat ◽  
Adarsh Mavanthoor ◽  
Vivekananda Chinta
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Rigid Body ◽  
Inflection Point ◽  
Compliant Mechanism ◽  
Analysis Method ◽  
Model Concept ◽  
Displacement Boundary ◽  
Rigid Body Model ◽  
Selection Of

This paper provides an efficient method of analysis for a fixed-guided compliant beam with an inflection point, subjected to beam end load or displacement boundary conditions, or a combination thereof. To enable this, such a beam is modeled as a pair of well-established pseudo-rigid-body models (PRBMs) for fixed-free compliant beam segments. The analysis procedure relies on the properties of inflection in developing the necessary set of parametric, static equilibrium and compatibility equations for solution. The paper further discusses the multiplicity of possible solutions, including displacement configurations, for any two specified beam end displacement boundary conditions, depending on the locations and types of the effecting loads on the beam to meet these boundary conditions. A unique solution may exist when a third beam end displacement boundary condition is specified; however, this selection is not unconditional. A concept of characteristic deflection domain is proposed to assist with the selection of the third boundary condition to yield a realistic solution. The analysis method is also used to synthesize a simple, fully compliant mechanism utilizing the fixed-guided compliant segments.

Comparison of Molecular Simulation and Pseudo-Rigid-Body Model Predictions for a Carbon Nanotube–Based Compliant Parallel-Guiding Mechanism

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Christopher M. DiBiasio ◽  
Martin L. Culpepper ◽  
Robert Panas ◽  
Larry L. Howell ◽  
Spencer P. Magleby
Keyword(s):  
Rigid Body ◽  
Molecular Simulation ◽  
Moment Of Inertia ◽  
Bulk Deformation ◽  
Body Model ◽  
Kinematic Behavior ◽  
Model Predictions ◽  
Rigid Body Model ◽  
Simulation Results ◽  
Selection Of

We report on the accuracy of the pseudo-rigid-body model (PRBM) in predicting the behavior of a nanoscale parallel-guiding mechanism (nPGM) that uses two single-walled (5,5) carbon nanotubes (CNTs) as the flexural guiding elements. The nPGM has two regions of behavior: region 1 is governed by the bulk deformation of the nanotubes, and region 2 is characterized by hingelike flexing of four “kinks” that occur due to buckling of the nanotube walls. PRBM parameters for (5,5) CNTs are proposed. Molecular simulation results of region 1 behavior match PRBM predictions of (1) kinematic behavior with less than 7.3% error and (2) elastomechanic behavior with less than 5.7% error. Although region 1 is of more interest because of its well-defined and stable nature, region 2 motion is also investigated. We show that the PRBM parameters are dependent on the selection of the effective tube thickness and moment of inertia, the lesson being that designers must take care to consider the thickness and moment of inertia values when deriving PRBM constants.

Pseudo-Rigid-Body Model Chain Algorithm: Part 2 — Equivalent Representations for Combined Load Boundary Conditions

2006 ◽  
Author(s):  
Joby Pauly ◽  
Ashok Midha
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Compliant Mechanism ◽  
Loop Closure ◽  
Combined Load ◽  
Body Model ◽  
Rigid Body Model ◽  
Planar Vector ◽  
Flexible Segment ◽  
Model Chain

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 pseudo-rigid-body model chain algorithm provides reasonable approximations of the deformed shape of complex compliant members; however, it has one major limitation. The elastic deformation of each compliant segment under combined load boundary conditions is obtained by superposing the pseudo-rigid-body model displacements due to i) the force and ii) the moment loads, respectively. Hence, each segment needs to be characterized by two separate pseudo-rigid-body models in order to accurately determine its deformation kinematics. Such an idealization of compliant segments would present significant challenges when attempting to represent the pseudo-rigid-body model chain in vectorial form, as in planar vector loop-closure methods. Vectorial modeling would be possible if each flexible segment in the chain could be represented by an “equivalent pseudo-rigid-body model.” This paper proposes the concept of a rudimentary equivalent pseudo-rigid-body model to represent compliant segments with combined load boundary conditions in the pseudo-rigid-body model chain algorithm. Such a model may help overcome the difficulties confronted in the potential implementation of the pseudo-rigid-body model chain in planar vector loop-closure solution techniques.

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.

A Methodology for Determining Static Mode Shapes of a Compliant Mechanism Using the Pseudo-Rigid-Body Model (PRBM) Concept and the Degrees-of-Freedom Analysis

2019 ◽  
Author(s):  
Sushrut G. Bapat ◽  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mode Shapes ◽  
Model Concept ◽  
Static Mode ◽  
Displacement Boundary ◽  
Body Model ◽  
Rigid Body Model

Abstract Traditionally, the deflected configuration of compliant segments is determined through rigorous mathematical analysis using Newtonian mechanics. Application of these principles in evaluating the deformed configuration of compliant mechanisms, containing a variety of segment types, becomes cumbersome. This paper introduces a methodology to determine the expected deflected configuration(s) of a compliant mechanism, for a given set of load and/or displacement boundary conditions. The method utilizes the principle of minimum total potential energy, in conjunction with the degrees-of-freedom analysis and the pseudo-rigid-body model concept. The static mode shape(s) of compliant segments are integrated in identifying the possible functional configuration(s) of a given compliant mechanism’s structural configuration. The methodology, in turn, also facilitates the in situ determination of the deformed configuration of the constituent compliant segments. It thus assists in the identification of an appropriate pseudo-rigid-body model for design and analysis of a compliant mechanism.

A Methodology for Determining Static Mode Shapes of a Compliant Mechanism Using the Pseudo-Rigid-Body Model Concept and the Degrees-Of-Freedom Analysis

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Pratheek Bagivalu Prasanna ◽  
Sushrut G. Bapat ◽  
Ashok Midha ◽  
Vamsi Lodagala
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mode Shapes ◽  
Model Concept ◽  
Static Mode ◽  
Displacement Boundary ◽  
Body Model ◽  
Rigid Body Model

Abstract Traditionally, the deflected configuration of compliant segments is determined through rigorous mathematical analysis using Newtonian mechanics. Application of this approach in evaluating the deformed configuration of compliant mechanisms, containing a variety of segment types, becomes cumbersome. This paper introduces a methodology to determine the possible deflected configuration(s) of a compliant mechanism, for a given set of load and/or displacement boundary conditions. The methodology utilizes the principle of minimum potential energy, in conjunction with the degrees-of-freedom analysis and the pseudo-rigid-body model concept. The static mode shape(s) of compliant segments are integrated in identifying the possible deflected configuration(s) of a given compliant mechanism. The methodology facilitates the in situ determination of the possible deformed configuration(s) of the compliant mechanism and its constituent segments. This, in turn, assists in the important task of identifying an appropriate pseudo-rigid-body model for the design and analysis of a compliant mechanism. The proposed methodology is illustrated with examples, and supported with experimental validation.

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.

Mode Shapes in Compliant Mechanisms, and a Procedure to Identify Appropriate Pseudo-Rigid-Body Model Type

2015 ◽  
Author(s):  
Ashok Midha ◽  
Pratheek Bagivalu Prasanna
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Classical Mechanics ◽  
Deformation Mode ◽  
Mode Shapes ◽  
Displacement Boundary ◽  
Body Model ◽  
Basic Segment ◽  
Rigid Body Model

The mobility characteristics of compliant mechanisms are a function of the structural arrangement of the comprising segments and links, their types, as well as the load and/or displacement boundary conditions. It is hypothesized that an earlier defined concept of compliance number and stored strain energy in a compliant mechanism are strongly correlated. It therefore becomes necessary to define and better understand the characteristics of deformation mode shapes of compliant mechanisms. A compliant mechanism may exhibit a variety of mode shapes. In keeping with the classical mechanics notions, this paper systematically develops the mode shapes in compliant mechanisms, utilizing two distinct categories: i) segmental (elemental) mode shapes, and ii) mechanism (system) mode shapes. The possible mode shapes of the basic segment types are identified. Based on the energy storage capability of the segment types, segmental mode shapes are further classified into higher and lower order mode shapes. Similar identification is extended to compliant mechanisms as well, and the possible mechanism mode shapes are illustrated with the help of a few examples. Finally, the utility of this methodology in identifying an appropriate pseudo-rigid-body model (PRBM) corresponding to a given compliant mechanism is demonstrated. An experimental procedure aids in this process.

Pseudo-Rigid-Body Model for the Flexural Beam With an Inflection Point in Compliant Mechanisms

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Shun-Kun Zhu ◽  
Yue-Qing Yu
Keyword(s):  
Rigid Body ◽  
Inflection Point ◽  
Compliant Mechanisms ◽  
Angular Displacement ◽  
Flexible Beam ◽  
Body Model ◽  
Numerical Result ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Flexural Beam

The pseudo-rigid-body model (PRBM) used to simulate compliant beams without inflection point had been well developed. In this paper, two types of PRBMs are proposed to simulate the large deflection of flexible beam with an inflection point in different configurations. These models are composed of five rigid links connected by three joints added with torsional springs and one hinge without spring representing the inflection point in the flexural beam. The characteristic radius factors of the PRBMs are determined by solving the objective function established according to the relative angular displacement of the two rigid links jointed by the hinge via genetic algorithm. The spring stiffness coefficients are obtained using a linear regression technique. The effective ranges of these two models are determined by the load index. The numerical result shows that both the tip locus and inflection point of the flexural beam with single inflection can be precisely simulated using the model proposed in this paper.

Modeling Flexible Segments With Force and Moment End Loads via the Pseudo-Rigid-Body Model

2000 ◽  
Author(s):  
Scott M. Lyon ◽  
Larry L. Howell ◽  
Gregory M. Roach
Keyword(s):  
Rigid Body ◽  
Cantilever Beam ◽  
Inflection Point ◽  
Compliant Mechanisms ◽  
Body Model ◽  
Rigid Body Model

Abstract This paper presents the development of a new pseudo-rigid-body model to model the deflection path of flexible segments with force and moment loads. Three separate loading cases are presented including: a cantilever beam with applied end-force and moment in the same direction, a cantilever beam with the applied end-force and moment in opposite directions with no inflection point being produced in the beam, and a cantilever beam with the applied end-force and moment in opposite directions which produces an inflection point in the beam. These types of segments are common in compliant mechanisms so it is important to have a method for their design and analysis.

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