Synthesis of Multi-Stable Equilibrium Compliant Mechanisms Using Combinations of Bi-Stable Mechanisms

2007 ◽  
Author(s):  
Young Seok Oh ◽  
Sridhar Kota
Keyword(s):  
Case Studies ◽  
Lower Order ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mathematical Approach ◽  
Linear Combinations ◽  
Stable Position ◽  
Non Linear ◽  
In Series

This paper presents a mathematical approach to synthesizing a multi-stable behavior by combining multiple bi-stable equilibrium mechanisms in series. Behavior of a bi-stable compliant mechanism, in general, is highly non-linear. Combinations of such non-linearities to capture the behavior of multi-stable (more than two stable positions) mechanisms can be very challenging. We present a simplified mathematical scheme to capture the essential parameters of bi-stability such as force-thresholds that cause the jump to next stable position etc. to derive multi-stable behavior. This mathematical simplification enables us to characterize bi-stable mechanisms using piecewise lower-order polynomials and synthesize multi-stable mechanisms through combination of bi-stable behaviors in series. We present two case studies of combinations of two and three bi-stable behaviors to generate mechanisms with four and five stable positions respectively. A design example of a quadri-stable equilibrium rotational compliant mechanism consisting two bi-stable sub-mechanisms is presented to demonstrate the effectiveness of the approach.

Synthesis of Multistable Equilibrium Compliant Mechanisms Using Combinations of Bistable Mechanisms

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Young Seok Oh ◽  
Sridhar Kota
Keyword(s):  
Case Studies ◽  
Lower Order ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Essential Elements ◽  
Deformation Pattern ◽  
Mathematical Approach ◽  
Stable Position ◽  
Highly Nonlinear

In this paper, we present a mathematical approach to synthesize multistable compliant mechanisms by combining multiple bistable equilibrium mechanisms. More specifically, we identify and categorize various types of bistabilities by characterizing the essential elements of their complicated deformation pattern. The behavior of a bistable compliant mechanism, in general, is highly nonlinear. Using combinations of such nonlinearities to capture the behavior of multistable (more than two stable positions) mechanisms can be quite challenging. To determine multistable behavior, our simplified mathematical scheme captures the essential parameters of bistability, such as the load-thresholds that cause the jump to the next stable position. This mathematical simplification enables us to characterize bistable mechanisms by using piecewise lower-order polynomials and, in turn, synthesize multistable mechanisms. Three case studies involving combinations of two, three, and four bistable behaviors are presented for the purpose of generating multistable mechanisms with up to 16 stable positions. The methodology enables us to design a compliant mechanism with a desired number of stable positions. A design example of a quadristable equilibrium rotational compliant mechanism consisting of two bistable submechanisms is presented to demonstrate the effectiveness of the approach.

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.

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.

Spatial Concept Synthesis of Compliant Mechanisms Utilizing Non-Linear Eigentwist Characterization

2018 ◽  
Author(s):  
Joep P. A. Nijssen ◽  
Giuseppe Radaelli ◽  
Just L. Herder ◽  
J. B. Ring ◽  
Charles J. Kim
Keyword(s):  
Large Deformation ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Planar Mechanisms ◽  
Spatial Concept ◽  
Spatial Design ◽  
Kinematic Behavior ◽  
Non Linear

Spatial compliant mechanism are challenging to design owing to their complex spatial kinetic and kinematic behavior. There are many synthesis methods to design compliant mechanisms, but they are often presented for planar mechanisms or have other limitations such as lack of designer input possibilities. In this paper a method based on the compliance ellipsoid is presented to create compliant mechanism topologies for spatial design cases. The result of this synthesis method is a qualitative concept which fundamentally creates the desired kinetic and kinematic profile. This concept can then be further refined using a large deformation eigentwist analysis, presented here. Lastly, these tools are used in a design example to show its potential.

Achieving Multistability Through Use of a Single Bistable Compliant Mechanism

2010 ◽  
Author(s):  
Guimin Chen ◽  
Yanjie Gou ◽  
Aimei Zhang
Keyword(s):  
Stable Equilibrium ◽  
Compliant Mechanism ◽  
Power Input ◽  
Successful Operation ◽  
New Approaches ◽  
Reconfigurable Robots ◽  
Bistable Mechanism

A compliant multistable mechanism is capable of steadily staying at multiple distinct positions without power input. Many applications including switches, valves, relays, positioners, and reconfigurable robots may benefit from multistability. In this paper, two new approaches for synthesizing compliant multistable mechanisms are proposed, which enable designers to achieve multistability through the use of a single bistable mechanism. The synthesis approaches are described and illustrated by several design examples. Compound use of both approaches is also discussed. The design potential of the synthesis approaches is demonstrated by the successful operation of several instantiations of designs that exhibit three, four, five, and nine stable equilibrium positions, respectively. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.

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.

Design of a Generic Zero Stiffness Compliant Joint

2010 ◽  
Author(s):  
Femke M. Morsch ◽  
Just L. Herder
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Great Promise ◽  
Optimized Design ◽  
Analytic Model ◽  
Total Potential ◽  
Fea Model ◽  
Compliant Joint ◽  
Joint Element ◽  
Cross Axis

The objective of this paper is to design a generic zero stiffness compliant joint. This compliant joint could be used as a generic construction element in a compliant mechanism. To avoid the spring-back behavior of conventional compliant joints, the principle of static balancing is applied, implying that for each position of the joint the total potential energy should be constant. To this end, a conventional balanced mechanism, consisting of two pivoted bodies which are balanced with two zero-free-length springs, is taken as an initial concept. The joint is replaced by a compliant cross-axis flexural pivot and each spring is replaced by a pair of compliant leaf springs. For both parts an analytic model was implemented and a configuration with the lowest energy fluctuation was found through optimization. A FEA model was used to verify the analytic model of the optimized design. A prototype was manufactured and tested. Both the FEA model and the experiment confirm the reduction of the needed moment to rotate the compliant joint. The experiment shows the balanced compliant joint is not completely balanced but the moment required to rotate the joint is reduced by 70%. Thus, a statically balanced compliant generic joint element was designed which bears great promise in designing statically balanced compliant mechanisms and making this accessible to any designer.

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.

Load-Transmitter Constraint Sets: Part I—An Effective Tool for Visualizing Load Flow in Compliant Mechanisms and Structures

2010 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Deformation Behavior ◽  
Design Methodology ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Load Flow ◽  
Mathematical Framework ◽  
Design Synthesis ◽  
Fundamental Building Block ◽  
Block Based

Visualizing load flow aids in conceptual design synthesis of machine components. In this paper, we present a mathematical framework to visualize load flow in compliant mechanisms and structures. This framework uses the concept of transferred forces to quantify load flow from input to the output of a compliant mechanism. The key contribution of this paper is the identification a fundamental building block known as the Load-Transmitter Constraint (LTC) set, which enables load flow in a particular direction. The transferred force in each LTC set is shown to be independent of successive LTC sets that are attached to it. This enables a continuous visualization of load flow from the input to the output. Furthermore, we mathematically relate the load flow with the deformation behavior of the mechanism. We can thus explain the deformation behavior of a number of compliant mechanisms from literature by identifying its LTC sets to visualize load flow. This method can also be used to visualize load flow in optimal stiff structure topologies. The insight obtained from this visualization tool facilitates a systematic building block based design methodology for compliant mechanisms and structural topologies.

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