Synthesizing Precompressed Beams As Bistable Compliant Mechanisms

2017 ◽  
Author(s):  
Mohammed Abdullah Maaz Siddiqui ◽  
Hong Zhou
Keyword(s):  
Rigid Body ◽  
Axial Compression ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Input Power ◽  
Elastic Deformations ◽  
Buckling Instability ◽  
Beam Thickness ◽  
Fixed End ◽  
Input Torque

Bistable mechanisms provide two stable positions. Input power is not needed to maintain any of the two stable positions. To switch from one stable position to another, input power is required. Bistable mechanisms have many applications including valves, closures, switches and various other devices. Unlike conventional rigid-body bistable mechanisms that rely on relative motions of kinematic joints, bistable compliant mechanisms take advantage of elastic deformations of flexible members to achieve two stable positions. There are two symmetric buckled shapes in a precompressed beam that has one fixed end and one pinned end. The two buckled shapes match the two stable equilibrium positions of bistable compliant mechanisms. The precompressed beam can be rotationally actuated at the pinned end to snap from one buckled shape to another. Synthesizing precompressed beams as bistable mechanisms is challenging because of buckling instability and integrated force and deflection characteristics. In this paper, the buckled shape is derived for a precompressed beam with fixed and pinned ends. The input torque at the pinned end is analyzed for a precompressed beam to snap between its two symmetric buckled shapes. Precompressed beams are synthesized as bistable compliant mechanisms through axial compression and beam thickness in this paper.

Reliability-Based Optimal Design of a Bistable Compliant Mechanism

1993 ◽  
Author(s):  
L. L. Howell ◽  
S. S. Rao ◽  
A. Midha
Keyword(s):  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Probabilistic Constraints ◽  
Probabilistic Design ◽  
Design Studies ◽  
Stable Equilibrium Position ◽  
Crank Mechanism ◽  
Insight Into ◽  
Input Torque

Abstract Compliant mechanisms obtain at least some of their motion from the deflection of their flexible members. Advantages of such mechanisms include the reduction of manufacturing and assembly cost and time. Bistable mechanisms are particularly useful in applications where two stable equilibrium positions are required, such as switches, gates, and closures. Fatigue is a major concern in many compliant mechanisms due to the cyclic stresses induced on the flexible members. In this paper, a method for the probabilistic design of a bistable compliant slider-crank mechanism is proposed. Link lengths, material properties, and cross-section dimensions are taken as random variables. Probabilistic constraints on the maximum and minimum required input torque, location of stable equilibrium position, and overall size are included. The objective function is the maximization of the mechanism reliability in fatigue. Several design studies are performed to gain further insight into the nature of the problem.

Reliability-Based Optimal Design of a Bistable Compliant Mechanism

1994 ◽  
Vol 116 (4) ◽  
pp. 1115-1121 ◽  
Author(s):  
L. L. Howell ◽  
S. S. Rao ◽  
A. Midha
Keyword(s):  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Probabilistic Constraints ◽  
Probabilistic Design ◽  
Design Studies ◽  
Stable Equilibrium Position ◽  
Crank Mechanism ◽  
Insight Into ◽  
Input Torque

Compliant mechanisms obtain at least some of their motion from the deflection of their flexible members. Advantages of such mechanisms include the reduction of manufacturing and assembly cost and time. Bistable mechanisms are particularly useful in applications where two stable equilibrium positions are required, such as switches, gates, and closures. Fatigue is a major concern in many compliant mechanisms due to the cyclic stresses induced on the flexible members. In this paper, a method for the probabilistic design of a bistable compliant slider-crank mechanism is proposed. Link lengths, material properties, and cross-section dimensions are taken as random variables. Probabilistic constraints on the maximum and minimum required input torque, location of stable equilibrium position, and overall size are included. The objective function is the maximization of the mechanism reliability in fatigue. Several design studies are performed to gain further insight into the nature of the problem.

Design of Compliant Mechanisms for Minimizing Input Power in Dynamic Applications

2006 ◽  
Vol 129 (10) ◽  
pp. 1064-1075 ◽  
Author(s):  
Tanakorn Tantanawat ◽  
Sridhar Kota
Keyword(s):  
Energy Storage ◽  
Rigid Body ◽  
Power Flow ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Input Power ◽  
Power Requirement ◽  
Effective Manner ◽  
Flapping Mechanism

In this paper, we investigate power flow in compliant mechanisms that are employed in dynamic applications. More specifically, we identify various elements of the energy storage and transfer between the input, external load, and strain energy stored within the compliant transmission. The goal is to design compliant mechanisms for dynamic applications by exploiting the inherent energy storage capability of compliant mechanisms in the most effective manner. We present a detailed case study on a flapping mechanism, in which we compare the peak input power requirement in a rigid-body mechanism with attached springs versus a distributed compliant mechanism. Through this case study, we present two approaches: (1) generative-load exploitation and (2) reactance cancellation, to describe the role of stored elastic energy in reducing the peak input power requirement. We propose a compliant flapping mechanism and its evaluation using nonlinear transient analysis. The input power needed to drive the proposed compliant flapping mechanism is found to be 50% less than a rigid-link four-bar flapping mechanism without a spring, and 15% less than the one with a spring. This reduction of peak input power is primarily due to the exploitation of elasticity in compliant members. The results show that a compliant mechanism can be a better alternative to a rigid-body mechanism with attached springs.

Design of Compliant Mechanisms for Minimizing Input Power in Dynamic Applications

2006 ◽  
Author(s):  
Tanakorn Tantanawat ◽  
Sridhar Kota
Keyword(s):  
Energy Storage ◽  
Rigid Body ◽  
Power Flow ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Input Power ◽  
Power Requirement ◽  
Effective Manner ◽  
Flapping Mechanism

In this paper, we investigate power flow in compliant mechanisms that are employed in dynamic applications. More specifically, we identify various elements of the energy storage and transfer between the input, external load, and the strain energy stored within the compliant transmission. The goal is to design complaint mechanisms for dynamic applications by exploiting the inherent energy storage capability of compliant mechanisms in the most effective manner. We present a detailed case study on a flapping mechanism in which we compare the peak input power requirement in a rigid-body mechanism with attached springs versus a distributed compliant mechanism. Through this case study, we present two different approaches, (1) generative-load exploitation and (2) reactance cancellation, to describe the role of stored elastic energy in reducing the required input power. In contrast to a conventional mechanism with a spring, stress and strain in a compliant mechanism are more uniformly distributed. The entire mechanism stores energy rather than just a spring, providing more energy storage per unit mass. We propose a compliant flapping mechanism and its evaluation using nonlinear transient analysis. The input power requirement of the proposed compliant flapping mechanism is found to be 48% and 10% less than those of the four-bar flapping mechanism without and with a spring, respectively. The results show that a compliant mechanism can be a better alternative to a rigid-body mechanism with attached springs.

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.

Parametric Deflection Approximations for Initially Curved, Large-Deflection Beams in Compliant Mechanisms

1996 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Curved Beam ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Fundamental Type ◽  
Applied Forces ◽  
Flexible Member

Abstract The analysis of systems containing highly flexible members is made difficult by the nonlineararities caused by large deflections of the flexible members. The analysis and design of many such systems may be simplified by using pseudo-rigid-body approximations in modeling the flexible members. The pseudo-rigid-body model represents flexible members as rigid links, joined at pin joints with torsional springs. Appropriate values for link lengths and torsional spring stiffnesses are determined such that the deflection path and force-deflection relationships are modeled accurately. Pseudo-rigid-body approximations have been developed for initially straight beams with externally applied forces at the beam end. This work develops approximations for another fundamental type of flexible member, the initially curved beam with applied force at the beam end. This type of flexible member is commonly used in compliant mechanisms. An example of the use of the resulting pseudo-rigid-body approximations in compliant mechanisms is included.

Type Synthesis of Compliant Mechanisms Employing a Simplified Approach to Segment Type

1994 ◽  
Author(s):  
Morgan D. Murphy ◽  
Ashok Midha ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Type Synthesis ◽  
Simplified Approach ◽  
Design Procedures ◽  
Synthesis Techniques ◽  
Design Solutions ◽  
Synthesis Methodology

Abstract The formulation of design procedures for rigid-body mechanisms has benefited from the application of type-synthesis techniques. Therefore, with modifications to allow for inclusions of compliance, type synthesis is seen as a useful tool in the design of compliant mechanisms. Previous efforts have developed methods that result in a large number of possible design solutions to a given problem. This paper deals primarily with the development of a simplified compliant-mechanism type-synthesis methodology that limits the number of design solutions considered. The techniques are derived by modifying existing compliant mechanism type-synthesis techniques to yield a simpler model with greater pragmatic value.

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