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.

Extensible-Link Kinematic Model for Characterizing and Optimizing Compliant Mechanism Motion

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Justin Beroz ◽  
Shorya Awtar ◽  
A. John Hart
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Kinematic Model ◽  
Model Development ◽  
Taylor Series Expansion ◽  
Analytical Determination ◽  
Motion Trajectory ◽  
Model Framework ◽  
Error Components

We present an analytical model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. Model development consists of identifying particular material points and their connecting vectorial lengths in a manner that represents the mechanism topology; whereby these lengths may extend over the course of actuation to account for the elastic deformation of the compliant mechanism. The motion trajectory is represented within the model as an analytical function in terms of these vectorial lengths, whereby its Taylor series expansion constitutes a parametric formulation composed of load-independent and load-dependent terms. This 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 that reduce or eliminate certain error components of the motion trajectory; and (2) the load-dependent terms reveal the polynomial orders of principally uncorrectable error components in the 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. A generalized model framework is developed, and its utility demonstrated via the design of a compliant microgripper with straight-line parallel jaw motion. The model enables analytical determination of all geometric modifications for minimizing the error trajectory of the jaw, and prediction of the polynomial order of the uncorrectable trajectory components. The jaw trajectory is then optimized using iterative finite elements simulations until the polynomial order of the uncorrectable trajectory component becomes apparent; this reduces the error in the jaw trajectory by 2 orders of magnitude over the prescribed jaw stroke. This model serves to streamline the design process by identifying the load-dependent sources of trajectory error in a compliant mechanism, and thereby the limits with which this error may be redressed by topology modification.

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.

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.

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.

Modeling Compliant Parallel Robots

2006 ◽  
Author(s):  
Annika Raatz ◽  
Frank Trauden ◽  
Ju¨rgen Hesselbach
Keyword(s):  
Dynamic Model ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Flexure Hinges ◽  
Parallel Structures ◽  
Rigid Body Model ◽  
Long Time

Since long time flexure hinges have been used in high precision devices instead of conventional bearings, e.g. ball or sliding bearings. Due to the natural lack of backlash, friction and slip-stick effects in flexure hinges, the accuracy of positioning or measurement devices can be highly increased. Recent applications for flexure hinges are seen in parallel robots. The integration of flexure hinges in parallel structures is quite simple because all joints, except for the drives, are passive. Since flexure hinges gain their mobility from an elastic and plastic deformation of matter, their kinematic behavior differs from the kinematics of ideal rotational joints. This leads to deviations of the compliant mechanism and its rigid body model. In this paper a kinematic model is proposed which allows for a compensation of the introduced hinge errors. Furthermore the dynamic model of a compliant parallel robot is derived and verified by means of simulation studies. This dynamic model can be used e.g. for model-based robot control algorithms or for the dimensioning of drives for compliant mechanisms.

Position-Space-Based Compliant Mechanism Reconfiguration Approach and Its Application in the Reduction of Parasitic Motion

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao ◽  
Richard C. Kavanagh
Keyword(s):  
Parallel Mechanism ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Shape ◽  
Position Space ◽  
Element Analysis ◽  
Parasitic Motion ◽  
Compliant Parallel Mechanism ◽  
Motion Characteristics ◽  
Cross Axis

This paper introduces a position-space-based reconfiguration (PSR) approach to the reconfiguration of compliant mechanisms. The PSR approach can be employed to reconstruct a compliant mechanism into many new compliant mechanisms, without affecting the mobility of the compliant mechanism. Such a compliant mechanism can be decomposed into rigid stages and compliant modules. Each of the compliant modules can be placed at any one permitted position within its position space, which does not change the constraint imposed by the compliant module on the compliant mechanism. Therefore, a compliant mechanism can be reconfigured through selecting different permitted positions of the associated compliant modules from their position spaces. The proposed PSR approach can be used to change the geometrical shape of a compliant mechanism for easy fabrication, or to improve its motion characteristics such as cross-axis coupling, lost motion, and motion range. While this paper focuses on reducing the parasitic motions of a compliant mechanism using this PSR approach, the associated procedure is summarized and demonstrated using a decoupled XYZ compliant parallel mechanism as an example. The parasitic motion of the XYZ compliant parallel mechanism is modeled analytically, with three variables which represent any permitted positions of the associated compliant modules in their position spaces. The optimal positions of the compliant modules in the XYZ compliant parallel mechanism are finally obtained based on the analytical results, where the parasitic motion is reduced by approximately 50%. The reduction of the parasitic motion is verified by finite-element analysis (FEA) results, which differ from the analytically obtained values by less than 7%.

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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