A Fully Compliant Tristable Mechanism Employing Both Tensural and Compresural Segments

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Guimin Chen ◽  
Qi Han ◽  
Kaifang Jin
Keyword(s):  
Strain Energy ◽  
Stable Equilibrium ◽  
Compliant Mechanism ◽  
Overload Protection ◽  
Kinetostatic Model ◽  
Constraint Model

Abstract A multistable compliant mechanism is a device that can hold several distinct positions through the storage and release of the strain energy associated with deflections of the flexible members. This self-locking capability can benefit many applications such as threshold acceleration sensing, overload protection, and shape reconfiguration. This work presents a novel class of fully compliant tristable mechanisms called tensural–compresural tristable mechanisms (TCTMs), which forms three stable equilibrium positions through unique utilization of both tensural segments and compresural segments. To identify feasible designs, a kinetostatic model is developed using the chained beam-constraint-model (CBCM) for both tensural segments and compresural segments. Two TCTM designs accompanied with a prototype are presented to demonstrate the feasibility of this new tristable configuration and the effectiveness of the kinetostatic model.

Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Beam Theory ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Shear Effects ◽  
Kinetostatic Model ◽  
Constraint Model

Fully compliant bistable mechanisms (FCBMs) have numerous applications in both micro- and macroscale devices, but the nonlinearities associated with the deflections of the flexible members and the kinetostatic behaviors have made it difficult to design. Currently, the design of FCBMs relies heavily on nonlinear finite element modeling. In this paper, an analytical kinetostatic model is developed for FCBMs based on the beam constraint model (BCM) that captures the geometric nonlinearities of beam flexures that undergo relatively small deflections. An improved BCM (i.e., Timoshenko BCM (TBCM)) is derived based on the Timoshenko beam theory in order to include shear effects in the model. The results for three FCBM designs show that the kinetostatic model can successfully identify the bistable behaviors and make reasonable predictions for the locations of the unstable equilibrium points and the stable equilibrium positions. The inclusion of shear effects in the TBCM model significantly improves the prediction accuracy over the BCM model, as compared to the finite element analysis (FEA) results.

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.

Shape Optimization of a Compliant Mechanism for an Actively Conformable Rotor Airfoil

2004 ◽  
Author(s):  
Andrew Nissly ◽  
Phuriwat Anusonti-Inthra ◽  
Mary Frecker ◽  
Farhan Gandhi
Keyword(s):  
Shape Optimization ◽  
Cross Section ◽  
Strain Energy ◽  
Rotation Angle ◽  
Compliant Mechanism ◽  
Aerodynamic Loads ◽  
Optimal Geometry ◽  
Uniform Cross Section ◽  
Narrow Space ◽  
Actuation Strain

In the present study, the optimal shape of a limited amount of passive material in a compliant mechanism of predetermined topology was determined. The simple compliant mechanism with a small number of actuators can be packaged in the long, narrow space of the rotor airfoil cross-section. The compliant mechanism is designed for maximum rotation angle under actuation loads, and minimum deflection under aerodynamic loads. Rotation angle (RA) and Strain Energy (SE), are used as measures of the deflections created by the actuation and aerodynamic loads, respectively. The design objectives are achieved by maximizing a multi-criteria objective function that represents a ratio of the RA to SE. Shape optimization of the compliant mechanism is conducted and the results indicate that the optimal compliant mechanism consists of a passive substructure with uniform cross section. The optimal geometry of the compliant mechanism is also determined in a parametric study (optimal ratio of the length to height of 0.3), and this structure can produce rotation angle of 13 Deg/m. when the actuators provide 1% actuation strain. The deflection due to aerodynamic loads is extremely small. The performance of the mechanism is examined further with variations in material and actuator properties. Additional results include an analysis of a compliant mechanism structure based on a modified topology, which is introduced to reduce numbers of actuators.

Multistable Behavior of Compliant Kaleidocycles

2015 ◽  
Author(s):  
Thomas A. Evans ◽  
Brett G. Rowberry ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Strain Energy ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Neutral Stability ◽  
Energy Characteristics ◽  
Continuous Rotation

We present an analysis of the compliant kaleidocycle, a mechanism which, unlike other compliant mechanisms, may undergo continuous rotation. We analyze the strain energy characteristics of this mechanism during its motion and show that by varying the stiffness and orientation of the flexures, kaleidocycles may be designed to achieve customizable multistable behavior. These devices may be designed to include up to four distinct stable equilibrium positions and may also include regions of neutral stability.

A Framework for Energy-Based Kinetostatic Modeling of Compliant Mechanisms

2017 ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Ruiyu Bai ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Modeling Framework ◽  
Geometric Nonlinearities ◽  
Complementary Strain ◽  
Minimum Strain Energy ◽  
Constraint Model ◽  
Future Work

Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano’s first theorem and the Crotti-Engesser theorem, which don’t require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of using Castigliano’s first theorem and the Crotti-Engesser theorem with the explicit formulations in this framework. Future work will be focused on incorporating use of the principle of minimum strain energy and the principle of minimum complementary strain energy.

Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Guimin Chen ◽  
Yanjie Gou ◽  
Aimei Zhang
Keyword(s):  
Stable Equilibrium ◽  
Compliant Mechanism ◽  
Power Input ◽  
Successful Operation ◽  
Actuation Force ◽  
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 equations for determining the actuation force required to move a multistable mechanism are provided. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.

scholarly journals An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

2021 ◽  
pp. 1-18
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Ruiyu Bai ◽  
Weidong Zhu ◽  
Spencer P Magleby ◽  
...  
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Modeling Framework ◽  
Geometric Nonlinearities ◽  
Complementary Strain ◽  
Constraint Model

Abstract Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano's first theorem and the Crotti-Engesser theorem, which don't require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of the explicit formulations in this framework derived from Castigliano's first theorem and the Crotti-Engesser theorem.

scholarly journals Determining the range of allowable axial force for the third-order Beam Constraint Model

2018 ◽  
Vol 9 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen ◽  
Guangbo Hao
Keyword(s):  
Axial Force ◽  
Strain Energy ◽  
Beam Length ◽  
Positive Definite Quadratic Form ◽  
Third Order ◽  
Intermediate Range ◽  
Modeling Errors ◽  
Dimensional Boundary ◽  
Constraint Model ◽  
Nonlinear Behaviors

Abstract. The Beam Constraint Model (BCM) was developed for the purpose of accurately and analytically modeling nonlinear behaviors of a planar beam flexure over an intermediate range of transverse deflections (10 % of the beam length). The BCM is expressed in the form of Taylor's expansion associated with the axial force. It has been found that the BCM may yield large predicting errors (>  5 %) when the applied axial force goes beyond a certain boundary, even the deflection is still in the intermediate range. However, this boundary has not been clearly identified so far. In this work, we mathematically determine the non-dimensional boundary of the axial force by the condition that the strain energy expression of the BCM is a positive definite quadratic form, and by the buckling condition relate to compressing axial force. Several examples are analyzed to demonstrate the effects of the axial force on the modeling errors of the BCM. When using the BCM for modeling, it is always suggested to check if the axial force is within this boundary to avoid large modeling errors. If the axial force is beyond the boundary, the Chained Beam Constraint Model (CBCM) can be used instead.

Nonlinear Strain Energy Formulation to Capture the Constraint Characteristics of a Spatial Symmetric Beam

2011 ◽  
Author(s):  
Shiladitya Sen ◽  
Shorya Awtar
Keyword(s):  
Cross Sections ◽  
Strain Energy ◽  
Virtual Work ◽  
Nonlinear Strain ◽  
The Past ◽  
Transverse Bending ◽  
Spatial Beams ◽  
Cross Axis ◽  
Constraint Model ◽  
Energy Formulation

In the past, a beam constraint model (BCM) that captures pertinent geometric nonlinearities associated with large displacements has been proposed for slender spatial beams with uniform and symmetric cross-sections. By providing closed-form parametric relations between the end-loads and end-displacements of the beam, the BCM quantifies the constraint characteristics of the beam in terms of stiffness variations, parasitic error motions, and the cross-axis coupling. This paper presents a nonlinear strain and strain energy formulation for the spatial symmetric beam, based on assumptions that are consistent with the BCM. This strain energy derivation, employing the Principle of Virtual Work, provides a simpler mathematical approach for the analysis of flexure mechanisms with multiple spatial beams. Using this formulation, we obtain the stiffness relations in the transverse bending directions, the constraint relations in the axial and torsional directions, and the overall strain energy expression in terms of the beam end-loads and end-displacements. These expressions, collectively the BCM, are in form that is suitable for the analysis of multi-beam flexure mechanisms.

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.

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