scholarly journals Watt Six-Bar Compliant Mechanism Analysis based on Kinematic and Dynamic Responses

2021 ◽  
Vol 1 (1) ◽  
pp. 1-24
Author(s):  
Çağlar Uyulan ◽  
Batuhan İpek
Keyword(s):  
Compliant Mechanism ◽  
Design Method ◽  
Dynamic Responses ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
Euler Beam ◽  
Time Step ◽  
Constraint Matrix ◽  
Rigid Body Model ◽  
Kinematic Analyses

In this study, a complete guide to kinematic and kinetic analyses of a Watt type six-bar compliant mechanism is conducted incorporating the flexible buckling of the initially straight element. In the analysis procedure, the hybrid utilization of the pseudo-rigid-body model (PRBM) and the nonlinear Elastic theory of beam buckling is presented. This partially compliant mechanism comprises three rigid links and two flexible links. The kinematic analyses of the mechanisms are done by using the vector loop closure equations, the PRBM of a large deflection cantilever beam, and derivation of nonlinear algebraic equations considering the quasi-static equilibrium and load-deflection curve of the flexible parts. Each of the elastic parts makes up a buckling pinned-pinned flexible Euler beam. The vector loop equations are combined with Newton-Euler dynamic formulations to provide the simultaneous constraint matrix. After these operations, the full mechanism is simulated to get both accelerations and forces for each time step. Finally, the design method is validated through experimental results. The findings derived from the combination of buckling Elastica solution and PRBM approach enable the analysis of Watt's six-bar compliant mechanism.

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 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.

scholarly journals Identifying links between origami and compliant mechanisms

2011 ◽  
Vol 2 (2) ◽  
pp. 217-225 ◽  
Author(s):  
H. C. Greenberg ◽  
M. L. Gong ◽  
S. P. Magleby ◽  
L. L. Howell
Keyword(s):  
Graph Theory ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanism Analysis ◽  
Initial State ◽  
Graph Models ◽  
Analysis And Design ◽  
Body Model ◽  
Folding Paper ◽  
Rigid Body Model

Abstract. Origami is the art of folding paper. In the context of engineering, orimimetics is the application of folding to solve problems. Kinetic origami behavior can be modeled with the pseudo-rigid-body model since the origami are compliant mechanisms. These compliant mechanisms, when having a flat initial state and motion emerging out of the fabrication plane, are classified as lamina emergent mechanisms (LEMs). To demonstrate the feasibility of identifying links between origami and compliant mechanism analysis and design methods, four flat folding paper mechanisms are presented with their corresponding kinematic and graph models. Principles from graph theory are used to abstract the mechanisms to show them as coupled, or inter-connected, mechanisms. It is anticipated that this work lays a foundation for exploring methods for LEM synthesis based on the analogy between flat-folding origami models and linkage assembly.

A Compliant Bistable Mechanism Design Incorporating Elastica Buckling Beam Theory and Pseudo-Rigid-Body Model

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Ümit Sönmez ◽  
Cem C. Tutum
Keyword(s):  
Rigid Body ◽  
Mechanism Design ◽  
Kinematic Analysis ◽  
Compliant Mechanism ◽  
Beam Theory ◽  
Algebraic Equations ◽  
Body Model ◽  
Buckling Beam ◽  
Rigid Body Model ◽  
Bistable Mechanism

In this work, a new compliant bistable mechanism design is introduced. The combined use of pseudo-rigid-body model (PRBM) and the Elastica buckling theory is presented for the first time to analyze the new design. This mechanism consists of the large deflecting straight beams, buckling beams, and a slider. The kinematic analysis of this new mechanism is studied, using nonlinear Elastica buckling beam theory, the PRBM of a large deflecting cantilever beam, the vector loop closure equations, and numerically solving nonlinear algebraic equations. A design method of the bistable mechanism in microdimensions is investigated by changing the relative stiffness of the flexible beams. The actuation force versus displacement characteristics of several cases is explored and the full simulation results of one of the cases are presented. This paper demonstrates the united application of the PRBM and the buckling Elastica solution for an original compliant mechanism kinematic analysis. New compliant mechanism designs are presented to highlight where such combined kinematic analysis is required.

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.

Design of a Single-Acting Constant-Force Actuator Based on Dielectric Elastomers

2008 ◽  
Author(s):  
Giovanni Berselli ◽  
Rocco Vertechy ◽  
Gabriele Vassura ◽  
Vincenzo Parenti Castelli
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compliant Mechanism ◽  
Structural Parameters ◽  
Dielectric Elastomer ◽  
Constant Force ◽  
Element Analysis ◽  
Body Model ◽  
Rigid Body Model ◽  
Supporting Frame

The interest in actuators based on dielectric elastomer films as a promising technology in robotic and mechatronic applications is increasing. The overall actuator performances are influenced by the design of both the active film and the film supporting frame. This paper presents a single-acting actuator which is capable of supplying a constant force over a given range of motion. The actuator is obtained by coupling a rectangular film of silicone dielectric elastomer with a monolithic frame designed to suitably modify the force generated by the dielectric elastomer film. The frame is a fully compliant mechanism whose main structural parameters are calculated using a pseudo-rigid-body model and then verified by finite element analysis. Simulations show promising performance of the proposed actuator.

Dynamic Response of the Spectral Element Model by Using the FFT

2007 ◽  
Vol 345-346 ◽  
pp. 845-848
Author(s):  
Joo Yong Cho ◽  
Han Suk Go ◽  
Usik Lee
Keyword(s):  
Fourier Transforms ◽  
Initial Conditions ◽  
Element Model ◽  
Spectral Element ◽  
Dynamic Responses ◽  
Analysis Method ◽  
Euler Beam ◽  
Exact Analytical Solutions ◽  
Simply Supported ◽  
Spectral Analysis Method

In this paper, a fast Fourier transforms (FFT)-based spectral analysis method (SAM) is proposed for the dynamic analysis of spectral element models subjected to the non-zero initial conditions. To evaluate the proposed SAM, the spectral element model for the simply supported Bernoulli-Euler beam is considered as an example problem. The accuracy of the proposed SAM is evaluated by comparing the dynamic responses obtained by SAM with the exact analytical solutions.

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.

Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

1996 ◽  
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
First Order ◽  
Direct Differentiation ◽  
Multibody Dynamic ◽  
Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

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