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.

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.

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.

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.

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.

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®.

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.

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.

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.

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