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.

Pseudo-Rigid-Body Model Chain Algorithm: Part 1 — Introduction and Concept Development

2006 ◽  
Author(s):  
Joby Pauly ◽  
Ashok Midha
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Loop Closure ◽  
Body Model ◽  
Rigid Body Model ◽  
Model Chain ◽  
Compliant Mechanism Design

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 chain algorithm is an alternate method for the design and analysis of compliant mechanisms. Though more versatile, insofar as the geometry and loading are concerned, it is not possible to implement this technique in analysis or synthesis problems involving loop-closure equations. This paper proposes the construction of a generalized “pseudo-rigid-body model chain;” it allows the use of pseudo-rigid-body models in conjunction with the chain algorithm to obtain the deformation kinematics of complex compliant members. Such a “pseudo-rigid-body model chain” would possess dual advantages of expediency of modeling through the use of pseudo-rigid-body representations of compliant segments, and the inherent flexibility of the chain algorithm to geometry and load boundary conditions. The proposed technique involves discretization of the planar continuum into initially straight, equal length compliant segments, whose deflections due to the applied load boundary conditions are then determined using appropriate pseudo-rigid-body models. Such a model could potentially be used in the solution of compliant mechanism design and analysis problems when coupled with the use of loop-closure equations.

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.

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

1996 ◽  
Vol 118 (1) ◽  
pp. 121-125 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanism Analysis ◽  
Model Concept ◽  
Loop Closure ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Kinematic Motion Analysis

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 loop-closure method for the analysis and synthesis of compliant mechanisms. 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.

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.

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.

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.

scholarly journals Design and Validation of a Single-SOI-Wafer 4-DOF Crawling Microgripper

Micromachines ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 376 ◽  
Author(s):  
Matteo Verotti ◽  
Alvise Bagolini ◽  
Pierluigi Bellutti ◽  
Nicola Pio Belfiore
Keyword(s):  
Finite Element Analysis ◽  
Rigid Body ◽  
Compliant Mechanism ◽  
Silicon On Insulator ◽  
Element Analysis ◽  
Deep Reactive Ion Etching ◽  
Theoretical Simulation ◽  
Body Model ◽  
Replacement Method ◽  
Rigid Body Model

This paper deals with the manipulation of micro-objects operated by a new concept multi-hinge multi-DoF (degree of freedom) microsystem. The system is composed of a planar 3-DoF microstage and of a set of one-DoF microgrippers, and it is arranged is such a way as to allow any microgripper to crawl over the stage. As a result, the optimal configuration to grasp the micro-object can be reached. Classical algorithms of kinematic analysis have been used to study the rigid-body model of the mobile platform. Then, the rigid-body replacement method has been implemented to design the corresponding compliant mechanism, whose geometry can be transferred onto the etch mask. Deep-reactive ion etching (DRIE) is suggested to fabricate the whole system. The main contributions of this investigation consist of (i) the achievement of a relative motion between the supporting platform and the microgrippers, and of (ii) the design of a process flow for the simultaneous fabrication of the stage and the microgrippers, starting from a single silicon-on-insulator (SOI) wafer. Functionality is validated via theoretical simulation and finite element analysis, whereas fabrication feasibility is granted by preliminary tests performed on some parts of the microsystem.

Preliminaries for a Spherical Compliant Mechanism: Pseudo-Rigid-Body Model Kinematics

2007 ◽  
Author(s):  
Saurabh Jagirdar ◽  
Craig P. Lusk
Keyword(s):  
Rigid Body ◽  
Compliant Mechanism ◽  
Beam Angle ◽  
Body Model ◽  
Spherical Mechanisms ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Limiting Case

The kinematic portion of a pseudo-rigid-body model (PRBM) is developed as a generalization from planar to spherical mechanisms. The topology of the spherical compliant segment and its rigid-body equivalent are derived from planar models by analogy. The nomenclature for the spherical PRBM is chosen to facilitate comparison with the planar PRBM. The motion of the compliant segment is calculated using FEA and PRBM parameters are determined. The characteristic radius and parametric angle coefficient are found to decrease as the angle subtended by the beam increases. The parameterization limit increases with increasing beam angle. The spherical PRBM is identical to the planar PRBM in the limiting case when beam angles become very small.

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