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.

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%.

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.

scholarly journals A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

2009 ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Type Synthesis ◽  
Precision Engineering ◽  
Pattern Design ◽  
Design Constraint ◽  
Systematic Formulation

This paper presents a screw theory based approach for the type synthesis of compliant mechanisms with flexures. We provide a systematic formulation of the constraint-based approach which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint which can be described a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis and constraint pattern design are discussed with examples in details. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

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.

Preliminary Design Concepts for Compliant Mechanism Prosthetic Knee Joints

2004 ◽  
Author(s):  
Alexandre E. Gue´rinot ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
High Reliability ◽  
Preliminary Design ◽  
Prosthetic Knee ◽  
Design Concepts ◽  
Functional Specification ◽  
Prosthetic Joint ◽  
Compressive Loads ◽  
Cross Axis

Compliant mechanisms present several design advantages that may be exploited in prosthetic joint design — low friction and wear, low part count, light weight, high reliability, efficient manufacturing and assembly, etc. However, they also come with their share of challenges. For example, in the past compliant mechanisms have not been viable alternatives to rigid-body joints in high compression applications. Two principles, isolation and inversion, can be successfully applied to many compliant joints to increase their ability to withstand high compressive loads and make them viable design alternatives to some current prosthetic joint designs. This paper presents preliminary design concepts for a compliant prosthetic knee. The inverted cross-axis flexural pivot design is selected and a proof of concept prototype is constructed and tested. The prototype exceeds the functional specification of 550 lbs, and satisfies a maximum deflection of 140°, an infinite life for a deflection of 110°, and a weight under 2 lbs.

scholarly journals A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Flexible Joints ◽  
Precision Engineering ◽  
Design Constraint ◽  
Analysis And Synthesis ◽  
Prismatic Joints

This paper presents a screw theory based approach for the analysis and synthesis of flexible joints using wire and sheet flexures. The focus is on designing flexure systems that have a simple geometry, i.e., a parallel constraint pattern. We provide a systematic formulation of the constraint-based approach, which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint, which can be described by a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis, and constraint pattern design are discussed with examples in details. Lastly, a case study is provided to demonstrate the application of this approach to the design of compliant prismatic joints. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

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.

scholarly journals Review Article: Inventory of platforms towards the design of a statically balanced six degrees of freedom compliant precision stage

2011 ◽  
Vol 2 (2) ◽  
pp. 157-168 ◽  
Author(s):  
A. G. Dunning ◽  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Compensation Mechanism ◽  
Precision Engineering ◽  
Six Degrees Of Freedom ◽  
Actuation Force ◽  
Precision Stage ◽  
Compliant Parts ◽  
Great Scope

Abstract. For many applications in precision engineering, a six degrees of freedom (DoF) compliant stage (CS) with zero stiffness is desirable, to deal with problems like backlash, friction, lubrication, and at the same time, reduce the actuation force. To this end, the compliant stage (also known as compliant mechanism) can be statically balanced with a stiffness compensation mechanism, to compensate the energy stored in the compliant parts, resulting in a statically balanced compliant stage (SBCS). Statically balanced compliant stages can be a breakthrough in precision engineering. This paper presents an inventory of platforms suitable for the design of a 6 DoF compliant stage for precision engineering. A literature review on 3–6 DoF compliant stages, static balancing strategies and statically balanced compliant mechanisms (SBCMs) has been performed. A classification from the inventory has been made and followed up by discussion. An obviously superior architecture for a 6 DoF compliant stage was not found. All the 6 DoF stages are either non-statically balanced compliant structures or statically balanced non-compliant structures. The statically balanced non-compliant structures can be transformed into compliant structures using lumped compliance, while all SBCMs had distributed compliance. A 6 DoF SBCS is a great scope for improvements in precision engineering stages.

An Intrinsic Geometric Framework for the Building Block Synthesis of Single Point Compliant Mechanisms

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Single Point ◽  
Building Blocks ◽  
Geometric Framework ◽  
Compliance Matrix ◽  
Rotational Components ◽  
Compliance Requirements ◽  
Insight Into

In this paper, we implement a characterization based on eigentwists and eigenwrenches for the synthesis of a compliant mechanism at a given point. For 2D mechanisms, this involves characterizing the compliance matrix at a unique point called the center of elasticity, where translational and rotational compliances are decoupled. Furthermore, the translational compliance may be represented graphically as an ellipse and the coupling between the translational and rotational components as vectors. These representations facilitate geometric insight into the operations of serial and parallel concatenations. Parametric trends are ascertained for the compliant dyad building block and are utilized in example problems involving serial concatenation of building blocks. The synthesis technique is also extended to combination of series and parallel concatenation to achieve any compliance requirements.

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