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.

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.

Classification of Compliant Mechanisms and Determination of the Degrees of Freedom Using the Concepts of Compliance Number and Pseudo-Rigid-Body Model

2019 ◽  
Author(s):  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha ◽  
Sushrut G. Bapat
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Body Model ◽  
Active Compliance ◽  
Kinematic Behavior ◽  
Rigid Body Model

Abstract Understanding the kinematic properties of a compliant mechanism has always proved to be a challenge. A concept of compliance number offered earlier emphasized the development of terminology that aided in its determination. A method to evaluate the elastic degrees of freedom associated with the flexible segments/links of a compliant mechanism using the pseudo-rigid-body model (PRBM) concept is provided. In this process, two distinct classes of compliant mechanisms are developed involving: (i) Active Compliance and (ii) Passive Compliance. Furthermore, these also aid in a better characterization of the kinematic behavior of a compliant mechanism. A more lucid interpretation of the significance of compliance number is provided. Applications of this method to both active and passive compliant mechanisms are exemplified. Finally, an experimental procedure that aids in visualizing the degrees of freedom as calculated is presented.

Accuracy and precision: A new viewon kinematic assessment of solid-state hinges and compliant mechanisms

2021 ◽  
pp. 1045389X2110643
Author(s):  
Lucio Flavio Campanile ◽  
Stephanie Kirmse ◽  
Alexander Hasse
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Measurement Theory ◽  
Reference Value ◽  
Strict Sense ◽  
Force System ◽  
Parasitic Motion ◽  
Accuracy And Precision ◽  
Compliant Systems

Compliant mechanisms are alternatives to conventional mechanisms which exploit elastic strain to produce desired deformations instead of using moveable parts. They are designed for a kinematic task (providing desired deformations) but do not possess a kinematics in the strict sense. This leads to difficulties while assessing the quality of a compliant mechanism’s design. The kinematics of a compliant mechanism can be seen as a fuzzy property. There is no unique kinematics, since every deformation need a particular force system to act; however, certain deformations are easier to obtain than others. A parallel can be made with measurement theory: the measured value of a quantity is not unique, but exists as statistic distribution of measures. A representative measure of this distribution can be chosen to evaluate how far the measures divert from a reference value. Based on this analogy, the concept of accuracy and precision of compliant systems are introduced and discussed in this paper. A quantitative determination of these qualities based on the eigenvalue analysis of the hinge’s stiffness is proposed. This new approach is capable of removing most of the ambiguities included in the state-of-the-art assessment criteria (usually based on the concepts of path deviation and parasitic motion).

An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms

2005 ◽  
Vol 128 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Charles J. Kim ◽  
Sridhar Kota ◽  
Yong-Mo Moon
Keyword(s):  
Conceptual Design ◽  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometry Optimization ◽  
Building Blocks ◽  
Cross Sectional ◽  
Rigid Body Model ◽  
Cross Sectional Size

As with conventional mechanisms, the conceptual design of compliant mechanisms is a blend of art and science. It is generally performed using one of two methods: topology optimization or the pseudo-rigid-body model. In this paper, we present a new conceptual design methodology which utilizes a building block approach for compliant mechanisms performing displacement amplification/attenuation. This approach provides an interactive, intuitive, and systematic methodology for generating initial compliant mechanism designs. The instant center is used as a tool to construct the building blocks. The compliant four-bar building block and the compliant dyad building block are presented as base mechanisms for the conceptual design. It is found that it is always possible to obtain a solution for the geometric advantage problem with an appropriate combination of these building blocks. In a building block synthesis, a problem is first evaluated to determine if any known building blocks can satisfy the design specifications. If there are none, the problem is decomposed to a number of sub-problems which may be solved with the building blocks. In this paper, the problem is decomposed by selecting a point in the design space where the output of the first building block coincides with the second building block. Two quantities are presented as tools to aid in the determination of the mechanism's geometry – (i) an index relating the geometric advantage of individual building blocks to the target geometric advantage and (ii) the error in the geometric advantage predicted by instant centers compared to the calculated value from FEA. These quantities guide the user in the selection of the location of nodes of the mechanism. Determination of specific cross-sectional size is reserved for subsequent optimization. An example problem is provided to demonstrate the methodology's capacity to obtain good initial designs in a straightforward manner. A size and geometry optimization is performed to demonstrate the viability of the design.

A Flexible-Link Model for Compliant Member Synthesis

2006 ◽  
Author(s):  
Ahmad Smaili ◽  
Mazen Hassanieh
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Elliptic Integral ◽  
New Approach ◽  
Proposed Model ◽  
Gradient Optimization ◽  
Rigid Body Model ◽  
Optimum Solution ◽  
Nonlinear Deformations

A new approach for the synthesis of a compliant link experiencing nonlinear deformations is herein introduced. The model is being proposed as an alternative to the pseudo-rigid-body model widely used in compliant mechanisms synthesis. The proposed approach is based on the exact elliptic integral equations that govern beam deformations. The model entails the determination of a few parameters in an optimum sense that would move the endpoint of the beam through several desired positions with minimal error. A tabu-gradient optimization algorithm is employed to search the design space for an optimum solution that minimizes the square of the error between the desired and the generated endpoint positions while satisfying a set of relevant constraints. Attributes of the model are highlighted by way of several examples. A brief outline on how the proposed model is used as the basis for compliant mechanism synthesis is presented and demonstrated by way of two examples.

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.

On the Mobility of Compliant Mechanisms

1994 ◽  
Author(s):  
Morgan D. Murphy ◽  
Ashok Midha ◽  
Larry L. Howell
Keyword(s):  
Mathematical Model ◽  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Final Design ◽  
Design Options ◽  
Potential Mobility ◽  
Topological Synthesis

Abstract The topological synthesis for a compliant mechanism leads to a very large number of design options from which to select a final design. Therefore, an evaluation of a mechanism’s ability to meet selected criteria provides a means of reducing a large number of possible designs to a smaller set of acceptable designs. One criterion deals with a mechanism’s potential mobility. For mechanisms containing flexible members, the response to inputs, in general, is comprised of both rigid-body and elastic deflections of their members. This paper deals primarily with the development of a technique for the determination of mobility characteristics of compliant mechanisms, employing a mathematical model previously developed for compliant mechanisms.

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