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.

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.

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.

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.

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®.

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.

Stress Analysis of a Fixed-Free Compliant Segment Using the Pseudo-Rigid-Body Model (PRBM) Concept

2017 ◽  
Author(s):  
Joshua Crews ◽  
Ashok Midha ◽  
Lokeswarappa R. Dharani
Keyword(s):  
Rigid Body ◽  
Stress Analysis ◽  
Compliant Mechanisms ◽  
Flexural Rigidity ◽  
Spring Steel ◽  
Analysis Method ◽  
Cross Sectional ◽  
Displacement Boundary ◽  
Rigid Body Model ◽  
Metallic Reinforcement

A method is presented to analyze stress in ambient-temperature, fixed-free compliant segments subjected to end load or displacement boundary conditions. The analysis method outlined herein relies on key outputs from the pseudo-rigid-body models (PRBMs). Simplified equations for stress are presented for both homogeneous and metallic-reinforced segments. Stresses in both the polymer compliant segment and the metallic reinforcing element are addressed to enable a comprehensive stress analysis method. The stress analysis method is exemplified by using two design cases: one, a homogeneous compliant segment, and two, a compliant segment reinforced with a spring steel element. The results showed that introducing a metallic reinforcement increases the flexural rigidity, but does not reduce the bending stress in the casing unless the cross-sectional thickness is reduced. This vein of research is undertaken using metallic reinforcement (inserts) toward the development of a new class of compliant mechanisms with significantly greater performance, particularly insofar as the problems of fatigue and creep are concerned.

A Generalized Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Energy Storage ◽  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanism Analysis ◽  
Model Concept ◽  
Loop Closure ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Abstract Compliant mechanisms gain at least some of their motion from flexible members. The combination of large-deflection beam analysis, kinematic motion analysis, and energy storage makes the analysis of compliant mechanisms difficult. The design of mechanisms often requires iteration between synthesis and analysis procedures. In general, the difficulty in analysis has limited the use of compliant mechanisms to applications where only simple functions and motions are required. The pseudo-rigid-body model concept promises to be the key to unifying the compliant and rigid-body mechanism theories. It simplifies compliant mechanism analysis by determining an equivalent rigid-body mechanism that accurately models the kinematic characteristics of a compliant mechanism. Once this model is obtained, many well known concepts from rigid-body mechanism theory become amenable for use to analyze and design compliant mechanisms. The pseudo-rigid-body-model concept is used to develop a generalized loop-closure method for the analysis and synthesis of compliant mechanisms. Synthesis is divided into two major categories: (i) rigid-body replacement synthesis, wherein only kinematic constraints are considered, and (ii) synthesis for compliance, wherein considerations of the energy storage and input/output force/torque characteristics of compliant mechanisms are utilized. The method allows compliant mechanisms to be designed for tasks that would have earlier been assumed to be unlikely, if not impossible, applications of compliant mechanisms. Examples of function, motion, and path generation of compliant mechanisms are presented for the first time.

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.

Sign in / Sign up

Export Citation Format

Share Document