An Investigation Into Compliant Bistable Mechanisms

1998 ◽  
Author(s):  
Patrick G. Opdahl ◽  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Paper Briefly ◽  
Bistable Behavior ◽  
New Class ◽  
Force And Motion ◽  
Predicted Values ◽  
Motion Characteristics ◽  
Bistable Mechanism ◽  
Mechanism Theory

Abstract This paper proposes a new class of bistable mechanisms: compliant bistable mechanisms. These mechanisms gain their bistable behavior from the energy stored in the flexible segments which deflect to allow mechanism motion. This approach integrates desired mechanism motion and energy storage to create bistable mechanisms with dramatically reduced part count compared to traditional mechanisms incorporating rigid links, joints, and springs. This paper briefly reviews bistable mechanism theory, introduces some additional bistable mechanism characteristics, and integrates this theory with compliant mechanism theory. The resulting theory of bistable compliant mechanisms is validated by measuring the force and motion characteristics of several test mechanisms and comparing them to predicted values.

Bistable Compliant Four-Bar Mechanisms With a Single Torsional Spring

2006 ◽  
Author(s):  
Adarsh Mavanthoor ◽  
Ashok Midha
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Stored Energy ◽  
Element Analysis ◽  
Bistable Behavior ◽  
Torsional Spring ◽  
Bistable Mechanism

Significant reduction in cost and time of bistable mechanism design can be achieved by understanding their bistable behavior. This paper presents bistable compliant mechanisms whose pseudo-rigid-body models (PRBM) are four-bar mechanisms with a torsional spring. Stable and unstable equilibrium positions are calculated for such four-bar mechanisms, defining their bistable behavior for all possible permutations of torsional spring locations. Finite Element Analysis (FEA) and simulation is used to illustrate the bistable behavior of a compliant mechanism with a straight compliant member, using stored energy plots. These results, along with the four-bar and the compliant mechanism information, can then be used to design a bistable compliant mechanism to meet specified requirements.

Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior

2003 ◽  
Vol 125 (4) ◽  
pp. 701-708 ◽  
Author(s):  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Energy Storage ◽  
Rigid Body ◽  
Mechanism Design ◽  
Bistable Behavior ◽  
Strongly Coupled ◽  
Present Design ◽  
Stable Equilibria ◽  
Motion Characteristics ◽  
Bistable Mechanism ◽  
Design Challenges

Bistable mechanisms, which have two stable equilibria within their range of motion, are important parts of a wide variety of systems, such as closures, valves, switches, and clasps. Compliant bistable mechanisms present design challenges because the mechanism’s energy storage and motion characteristics are strongly coupled and must be considered simultaneously. This paper studies compliant bistable mechanisms which may be modeled as four-link mechanisms with a torsional spring at one joint. Theory is developed to predict compliant and rigid-body mechanism configurations which guarantee bistable behavior. With this knowledge, designers can largely uncouple the motion and energy storage requirements of a bistable mechanism design problem. Examples demonstrate the power of the theory in bistable mechanism design.

Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints

2004 ◽  
Vol 126 (4) ◽  
pp. 657-666 ◽  
Author(s):  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Energy Storage ◽  
Prior Knowledge ◽  
Compliant Mechanisms ◽  
Power Input ◽  
Local Minima ◽  
Stored Energy ◽  
Bistable Behavior ◽  
Micro Electro Mechanical Systems ◽  
Bistable Mechanism ◽  
Mechanical Devices

Bistable mechanical devices remain stable in two distinct positions without power input. They find application in valves, switches, closures, and clasps. Mechanically bistable behavior results from the storage and release of energy, typically in springs, with stable positions occurring at local minima of stored energy. Compliant mechanisms offer an elegant way to achieve this behavior by incorporating both motion and energy storage into the same flexible element. Interest in compliant bistable mechanisms has also recently increased because of the advantages of bistable behavior in many micro-electro-mechanical systems (MEMS). Design of compliant or rigid-body bistable mechanisms typically requires simultaneous consideration of both energy storage and motion requirements. This paper simplifies this process by developing theory that provides prior knowledge of mechanism configurations that guarantee bistable behavior. Configurations which include one or more translational, or slider, joints are studied in this work. Several different mechanism types are analyzed to determine compliant segment placement that will ensure bistable mechanism operation. Examples demonstrate the power of the theory in design.

Robust Design of Bistable Compliant Mechanisms Using the Bistability of a Clamped-Pinned Beam

2008 ◽  
Author(s):  
Young Seok Oh ◽  
Sridhar Kota
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Experimental Tests ◽  
Operating Conditions ◽  
Loading Conditions ◽  
Element Analysis ◽  
Bistable Behavior ◽  
Stable Position ◽  
Straight Beam ◽  
Free Beam

Our research investigates a new approach to design of bistable compliant mechanisms using the bistability of a clamped-free beam. Bistability plays an important role for a variety of applications since energy is applied only to move the mechanism from one stable position to another and no energy needs to be expended once a stable position is reached. Behavior of a bistable compliant mechanism, in general, is highly non-linear and relies on the buckling phenomenon. Normally, buckling is very sensitive to imperfections in manufacturing processes, operating conditions and boundary conditions. We present a method for designing bistable mechanisms that are robust against such imperfections by utilizing the behavior of a simple clamped-free beam. A solution for large deformation of a simple clamped-free beam is first obtained to study its bistable behavior under various loading conditions. If the load is greater than the critical buckling load, the beam can be deflected not only in the normal direction but also in a ‘reverse-lateral’ (RL) direction. First, an initially straight beam must be bent to a certain curvature under the action of the applied force. In the second loading condition, the partially bent beam is further loaded so that it buckles in the RL direction into a stable position. The magnitude and direction of the forces in both loading conditions that are conducive to bistability are thus determined. A compliant mechanism is then designed such that its output generates desired forces on the beam to deform it in the RL direction. We demonstrate that the RL deformation is less sensitive to the imperfections and ensures bistable behavior. Using clamped-pinned beams, two design examples (symmetric and asymmetric cases) of bistable compliant mechanisms are presented. Results show very good correlation between the finite element analysis and experimental tests on prototypes.

Fatigue and Failure Behavior of Homogeneous and Reinforced Compliant Mechanism Segments

2018 ◽  
Author(s):  
Joshua Crews ◽  
Lokeswarappa R. Dharani ◽  
Ashok Midha
Keyword(s):  
Compliant Mechanisms ◽  
Fatigue Testing ◽  
Compliant Mechanism ◽  
Qualitative Assessment ◽  
Failure Behavior ◽  
Test Results ◽  
New Class ◽  
Metallic Reinforcement ◽  
Baseline Test ◽  
Comprehensive Study

This paper presents a comprehensive study of the fatigue and failure behavior of both homogeneous and metallic-reinforced compliant segments. Baseline test results are presented for a homogeneous, fixed-free compliant segment constructed of thermoset urethane. The advantages of both polymeric and metallic materials for compliant mechanism construction are leveraged by designing and testing compliant test specimens containing a polymer casing and a metallic reinforcing element. Results obtained from fatigue testing of fixed-free compliant segments in a cyclic loading configuration show that the metallic-reinforced compliant specimens offer superior fatigue performance when compared to the homogeneous baseline specimens. Fractography, both macroscopic and microscopic, is used for a qualitative assessment of the failure behavior. 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.

scholarly journals Extensible-Link Kinematic Model for Determining Motion Characteristics of Compliant Mechanisms

2013 ◽  
Author(s):  
Justin Beroz ◽  
Shorya Awtar ◽  
A. John Hart
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Kinematic Model ◽  
Taylor Series Expansion ◽  
Motion Trajectory ◽  
Model Framework ◽  
Error Components ◽  
Straight Line Parallel ◽  
Line Parallel ◽  
Motion Characteristics

We present an extensible-link kinematic model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. This is accomplished by creating an analogous kinematic model consisting of links that change length over the course of actuation to represent elastic deformation of the compliant mechanism. Within the model, the motion trajectory is represented as an analytical function. By Taylor series expansion, the trajectory is expressed in a parametric formulation composed of load-independent and load-dependent terms. Here, the load-independent terms are entirely defined by the shape of the undeformed compliant mechanism topology, and all load-geometry interdependencies are captured by the load-dependent terms. This formulation adds insight to the process for designing compliant mechanisms for high accuracy motion applications because: (1) inspection of the load-independent terms enables determination of specific topology modifications for improving the accuracy of the motion trajectory; and (2) the load-dependent terms reveal the polynomial orders of principally uncorrectable error components of the motion trajectory. The error components in the trajectory simply represent the deviation of the actual motion trajectory provided by the compliant mechanism compared to the ideally desired one. We develop the generalized model framework, and then demonstrate its utility by designing a compliant micro-gripper with straight-line parallel jaw motion. We use the model to analytically determine all topology modifications for optimizing the jaw trajectory, and to predict the polynomial order of the uncorrectable trajectory components. The jaw trajectory is then optimized by iterative finite elements (FE) simulation until the polynomial order of the uncorrectable trajectory component becomes apparent.

Identification of Compliant Pseudo-Rigid-Body Mechanism Configurations Resulting in Bistable Behavior

2000 ◽  
Author(s):  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Energy Storage ◽  
Rigid Body ◽  
Mechanism Design ◽  
Bistable Behavior ◽  
Strongly Coupled ◽  
Present Design ◽  
Stable Equilibria ◽  
Motion Characteristics ◽  
Bistable Mechanism ◽  
Design Challenges

Abstract Bistable mechanisms, which have two stable equilibria within their range of motion, are important parts of a wide variety of systems, such as closures, valves, switches, and clasps. Compliant bistable mechanisms present design challenges because the mechanism’s energy storage and motion characteristics are strongly coupled and must be considered simultaneously. This paper studies compliant bistable mechanisms which may be modeled as four-link mechanisms with a torsional spring at one joint. Theory is developed to predict compliant and rigid-body mechanism configurations which guarantee bistable behavior. With this knowledge, designers can largely uncouple the motion and energy storage requirements of a bistable mechanism design problem. Examples demonstrate the power of the theory in bistable mechanism design.

A Lumped-Model Based Building-Block Concatenation for a Conceptual Compliant Mechanism Synthesis

2008 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Mechanical Efficiency ◽  
Size Optimization ◽  
Lumped Model ◽  
Storage Mechanism ◽  
Conceptual Designs ◽  
Motion Characteristics

Present building-block synthesis techniques for compliant mechanisms [4–7] account for the kinematic behavior of the mechanism alone, leaving the stiffness, manufacturability and mechanical efficiency to be determined by the shape-size optimization process. In this effort, we aim to generate practical and feasible conceptual designs by designing for kinematics and stiffness simultaneously. To enable this, we use a lumped spring-lever model, which intuitively characterizes the stiffness and the kinematics of a deformable-complaint building block with distinct input and output points. This model aids in the understanding of how the stiffness and the kinematics of building blocks combine when concatenated to form a mechanism. We use this understanding to synthesize compliant mechanisms by combining building blocks of known motion characteristics. A simple compliant-dyad building block is characterized for its lumped values of stiffness and kinematics. The concatenation of these dyad-building blocks is solved in detail, and guidelines for conceptual synthesis are proposed. Two practical examples are solved; a motion amplifier for a piezo-stack and a compliant energy storage mechanism for a staple-gun. The conceptual designs obtained from this approach are very close to the kinematic and the stiffness requirements of the application, thus minimizing the role of shape and size optimization to achieve the problem specification. The model, when extended to higher dimensions may be used to solve for precision positioning and other applications.

Designing Multi-Axis Force–Torque Sensors by Minimizing the Amplitudes of Their Nonlinear Displacements

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
R. Bekhti ◽  
P. Cardou ◽  
V. Duchaine
Keyword(s):  
Compliant Mechanisms ◽  
Jacobian Matrix ◽  
Compliant Mechanism ◽  
Nonlinear Behavior ◽  
Physical Interaction ◽  
Performance Indices ◽  
Force Mapping ◽  
External Forces ◽  
Robotic Applications ◽  
Mechanism Theory

Compliant multi-axis force–torque sensors play a crucial role in many emerging robotic applications, such as telemanipulation, haptic devices and human-robot physical interaction. In order to synthesize the compliant architectures at the core of these sensors, several researchers have devised performance indices from mechanism theory. This paper follows the same approach, but includes the innovation of using the changes in the compliant mechanism geometry as a new performance index. Once external forces are applied, the compliant mechanism deviates from its unloaded configuration, and thus, changes in geometry prevent the sensor from exhibiting a linear response. In order to minimize this nonlinear behavior, the potential sources of error are analyzed by applying linear algebra techniques to the expression of the Cartesian force mapping. Two performance indices are then presented and combined. The first index measures the variations of the Jacobian matrix about the unloaded configuration. The second index measures the amplification of the error arising from the joint displacements measurement. The resulting indices can be expressed symbolically, making them easier to evaluate and synthesize. Finally, we apply the performance indices we have developed to simple compliant mechanisms, and discuss the results.

Design of a Gimbaled Compliant Mechanism Stage for Precision Motion and Dynamic Control in Z, ΘX and ΘY Directions

2004 ◽  
Author(s):  
Spencer E. Szczesny ◽  
Amos G. Winter
Keyword(s):  
Compliant Mechanisms ◽  
Dynamic Testing ◽  
Compliant Mechanism ◽  
Dynamic Control ◽  
Precision Engineering ◽  
Compliance Requirements ◽  
Modes Of Vibration ◽  
Motion Characteristics ◽  
Cross Axis ◽  
Precision Motion

Obtaining precise motion control of a compliant mechanism is often hindered by competing kinematic, mechanic and dynamic requirements. Resonances limit the control bandwidth while compliance requirements limit the mechanism’s directional stiffness. This paper investigates the improvements possible for three-axis Z, θX and θY diaphragm flexure stages through the use of a design (T-Flex) with members complaint in bending and torsion. According to analytical modeling and FEA, the T-Flex is capable of removing problematic resonant modes of vibration without significantly increasing the axial or tilt stiffness. Bench-level experimentation was conducted on various configurations of compliant mechanisms to determine their effects on the motion characteristics for precision engineering applications. The results indicate that by pairing the T-Flex with a radially stiff compliant mechanism, gimbaled motion can be achieved, providing 7.0 nm/μm lateral cross-axis (parasitic) motions. The mechanism exhibits linear axial and tilt stiffness of 0.195 N/μm and 5.37×10−6 N-m/μrad, respectively. Dynamic testing agreed with the FEA prediction of the first natural frequency to within 10%. The T-Flex coupled with the stiff radial flexure has the potential to provide a precise three-axis configuration with a fundamental resonant frequency of 600 Hz.

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