Constraint-Force-Based (CFB) Modeling of Compliant Mechanisms

2015 ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Static Equilibrium ◽  
Constraint Forces ◽  
Equilibrium Equations ◽  
Constraint Force ◽  
Element Analysis ◽  
External Forces ◽  
Force Equilibrium

Numerous works have been done on modeling compliant modules or joints, and the closed-form models of many widely-used compliant modules have been developed. However, the modeling of complex compliant mechanisms with considering external forces is still a challenging work. This paper introduces a constraint-force-based method to model compliant mechanisms. A compliant mechanism can be regarded as the combination of rigid stages and compliant modules. If a compliant mechanism is at static equilibrium under the influence of a series of external forces, all the rigid stages are also at static equilibrium. The rigid stages are restricted by the constraint forces of the compliant modules and the exerted external forces. This paper defines the constraint forces of the compliant modules to be variable constraint forces since the constraint forces vary with the deformation of the compliant modules, and defines the external forces as constant constraint forces due to the fact that the external forces are specific forces exerted which do not change with the deformation of the compliant mechanism. Therefore, the force equilibrium equations for all rigid stages in a compliant mechanism can be obtained based on the variable constraint forces and the constant constraint forces. Moreover, the model of the compliant mechanism can also be derived through solving all the force equilibrium equations. The constraint-force-based modeling method is finally detailed demonstrated via examples, and validated by the finite element analysis. Using this proposed modeling method, a complex compliant mechanism can be modelled with a particular emphasis on considering the position spaces of the associated compliant modules.

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.

A Method for Compliance Modeling of Five Degree-of-Freedom Overconstrained Parallel Robotic Mechanisms With 3T2R Output Motion

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Donghao Yang
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Fea Model ◽  
Stiffness Model ◽  
Compliance Modeling ◽  
The One

This paper presents an approach to compliance modeling of three-translation and two-rotation (3T2R) overconstrained parallel manipulators, especially for those with multilink and multijoint limbs. The expressions of applied wrenches (forces/torques) exerted on joints are solved with few static equilibrium equations based on screw theory. A systematic method is proposed for deriving the stiffness model of a limb with considering the couplings between the stiffness along the constrained wrench and the one along the actuated wrench based on strain energy analysis. The compliance model of a 3T2R overconstrained parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the compliance matrix obtained from the method is close to the one obtained from a finite-element analysis (FEA) model. The proposed method has the characteristics of involving low computational efforts and considering stiffness couplings of each limb.

Application of Rigid-Body-Linkage Static Balancing Techniques to Reduce Actuation Effort in Compliant Mechanisms

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
Amrith N. Hansoge ◽  
G. K. Ananthasuresh
Keyword(s):  
Rigid Body ◽  
General Framework ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Small Length ◽  
Element Analysis ◽  
Static Balancing ◽  
Free Length ◽  
First Order ◽  
Taylor’S Series

There are analytical methods in the literature where a zero-free-length spring-loaded linkage is perfectly statically balanced by addition of more zero-free-length springs. This paper provides a general framework to extend these methods to flexure-based compliant mechanisms through (i) the well know small-length flexure model and (ii) approximation between torsional springs and zero-free-length springs. We use first-order truncated Taylor's series for the approximation between the torsional springs and zero-free-length springs so that the entire framework remains analytical, albeit approximate. Three examples are presented and the effectiveness of the framework is studied by means of finite-element analysis and a prototype. As much as 70% reduction in actuation effort is demonstrated. We also present another application of static balancing of a rigid-body linkage by treating a compliant mechanism as the spring load to a rigid-body linkage.

Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Mesh Network ◽  
Adaptive Antenna ◽  
Optimal Size ◽  
Dimensional Synthesis ◽  
Element Analysis

This paper uses rigid-body mechanism topologies to synthesize fully distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. For a shape-change problem, a rigid-body mechanism solution is generated first to provide the base topology. This base topology defines a preselected design space for the structural optimization in one of two ways so as to obtain a compliant mechanism solution that is typically superior to the local minimum solutions obtained from searching more expansive design spaces. In the first strategy, the dimensional synthesis directly determines the optimal size and shape of the distributed compliant mechanism having exactly the base topology. In the second strategy, an initial mesh network established from the base topology is used to generate different topologies (in addition to the base), and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. The deformation of each generated compliant mechanism is evaluated using geometrically nonlinear finite element analysis (FEA). A two-objective genetic algorithm (GA) is employed to find a group of viable designs that trade off minimizing shape matching error with minimizing maximum stress. The procedure's utility is demonstrated with three practical examples—the first two approximating open-curve profiles of an adaptive antenna and the third approximating closed-curve profiles of a morphing wing.

Non-Dimensional Kinetoelastostatic Maps for Compliant Mechanisms

2013 ◽  
Author(s):  
Santosh D. B. Bhargav ◽  
Harish I. Varma ◽  
G. K. Ananthasuresh
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Slenderness Ratio ◽  
Element Analysis ◽  
Output Displacement ◽  
Static Responses ◽  
Slender Beams ◽  
Applied Forces ◽  
The Cross

How do we assess the capability of a compliant mechanism of given topology and shape? The kinetoelastostatic maps proposed in this paper help answer this question. These maps are drawn in 2D using two non-dimensional quantities, one capturing the nonlinear static response and the other the geometry, material, and applied forces. Geometrically nonlinear finite element analysis is used to create the maps for compliant mechanisms consisting of slender beams. In addition to the topology and shape, the overall proportions and the proportions of the cross-sections of the beam segments are kept fixed for a map. The finite region of the map is parameterized using a non-dimensional quantity defined as the slenderness ratio. The shape and size of the map and the parameterized curves inside it indicate the complete kinetoelastostatic capability of the corresponding compliant mechanism of given topology, shape, and fixed proportions. Static responses considered in this paper include input/output displacement, geometric amplification, mechanical advantage, maximum stress, etc. The maps can be used to compare mechanisms, to choose a suitable mechanism for an application, or re-design as may be needed. The usefulness of the non-dimensional maps is presented with multiple applications of different variety. Non-dimensional portrayal of snap-through mechanisms is one such example. The effect of the shape of the cross-section of the beam segments and the role of different segments in the mechanism as well as extension to 3D compliant mechanisms, the cases of multiple inputs and outputs, and moment loads are also explained. The effects of disproportionate changes on the maps are also analyzed.

Curve Decomposition Analysis for Fixed-Guided Beams With Application to Statically Balanced Compliant Mechanisms

2011 ◽  
Author(s):  
Charles Kim
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Parametric Design ◽  
Compliant Mechanism ◽  
Decomposition Analysis ◽  
Modeling Method ◽  
Proof Of Concept ◽  
Deflection Curve ◽  
Key Points ◽  
Deflection Analysis

Statically balanced compliant mechanisms require no holding force throughout their range of motion while maintaining the advantages of compliant mechanisms. In this paper, a post-buckled fixed-guided beam is proposed to provide the negative stiffness to balance the positive stiffness of a compliant mechanism. To that end, a unique curve decomposition modeling method is presented to simplify the large deflection analysis. The modeling method facilitates parametric design insight and elucidates key points on the force-deflection curve. Experimental results validate the analysis. Furthermore, static balancing with fixed-guided beams is demonstrated for a rectilinear proof-of-concept prototype.

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.

Design of a Continuum Mechanism that Matches the Movement of an Eight-bar Linkage

2020 ◽  
pp. 1-11
Author(s):  
Xueao Liu ◽  
J. Michael McCarthy
Keyword(s):  
Finite Element Analysis ◽  
Rigid Body ◽  
Design Methodology ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Initial Structure ◽  
Element Analysis ◽  
Kinematic Synthesis ◽  
Generic Structure ◽  
Straight Line

Abstract This paper presents a design methodology for mechanisms consisting of a single continuous structure, continuum mechanisms, that blends the kinematic synthesis of rigid-body mechanisms with topology optimization for compliant mechanisms. Rather than start with a generic structure that is shaped to achieve a required force deflection task for a compliant mechanism, our approach shapes the initial structure based on kinematic synthesis of a rigid body mechanism for the required movement, then the structure is shaped using Finite Element Analysis to achieve the required force deflection relationship. The result of this approach is a continuum mechanism with the same workpiece movement as the rigid link mechanism when actuated. An example illustrates the design process to obtain an eight-bar linkage that guides its workpiece in straight-line rectilinear movement. We show that the resulting continuum mechanism provides the desired rectilinear movement. A 210 mm physical model machined from Nylon-6 is shown to achieve 21.5mm rectilinear movement with no perceived deviation from a straight-line.

Efficient Development of Continuum/Compliant Planar Linkage Mechanisms

2019 ◽  
Author(s):  
Woo Rib Suh ◽  
J. Michael McCarthy ◽  
Edwin A. Peraza Hernandez
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Parameters ◽  
Element Analysis ◽  
Initial Node ◽  
Synthesis Of Mechanisms ◽  
Efficient Alternative ◽  
Computationally Intensive ◽  
The Given ◽  
The Continuum

Abstract This paper presents a method to develop continuum/compliant mechanisms based on planar bar-node linkage precursors. The method takes as inputs the initial node positions and connectivity data of a given bar-node linkage and converts it into a continuum/compliant mechanism having the same targeted motion. The line bars of the given bar-node linkage are thickened into trapezoidal planar members and the nodes are thickened by introducing fillets at each intersection of bars. The thicknesses of the bars and the shape parameters of the fillets in the continuum/compliant linkage are optimized to obtain the same targeted motion of the given bar-node linkage while keeping stresses below a maximum allowable value. Each design generated during the optimization process is evaluated using finite element analysis. The present method allows for the synthesis of mechanisms having the following advantages over conventional bar-node linkages: 1) They do not require complex ball or pin joints; 2) they can be readily 3-D printed and size-scaled, and 3) they can be optimized to decrease stresses below a maximum allowable value. Furthermore, the method uses a relatively small number of optimization variables (thicknesses of the members, shape-parameters of the fillets), making it an efficient alternative to more complex and computationally intensive methods for synthesizing compliant mechanisms such as those incorporating topology optimization.

scholarly journals On the analysis and design of a fully compliant large stroke slider-crank (rocker) mechanism

2020 ◽  
Vol 11 (1) ◽  
pp. 29-38 ◽  
Author(s):  
Çağıl Merve Tanık ◽  
Engin Tanık ◽  
Yiğit Yazıcıoğlu ◽  
Volkan Parlaktaş
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Element Analysis ◽  
Analysis And Design ◽  
Theoretical Approaches ◽  
Analysis Technique ◽  
Replacement Technique ◽  
Rigid Joints ◽  
Analytical Approaches ◽  
Crank Mechanism

Abstract. In the literature, authors have made contributions in the area of partially compliant slider-crank (rocker) mechanisms possessing rigid joints that may cause backlash inherently. On contrary, fully compliant mechanisms offer no backlash which is a valuable property for the cases where high precision is required. In this paper, we proposed a fully compliant slider-crank mechanism that performs large stroke. Kinematic performance of the mechanism is investigated analytically. Dimensions of the mechanism are optimized to obtain maximum translational output, while keeping deflections of flexible hinges equal to each other and as small as possible. A design table displaying stroke, axis drift of the output segment, and critical stresses of compliant segments are presented. As an example, a compliant mechanism is designed by using rigid body replacement technique. Then, via nonlinear finite element analysis technique, analytical results are verified. Finally, a prototype is built to compare output stroke and axis drift with analytical approaches. The results of experiments verified that the theoretical approaches are consistent.

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