Building Block Based Topology Synthesis Algorithm to Optimize the Natural Frequency in Large Stroke Flexure Mechanisms

2020 ◽  
Author(s):  
Mathijs E. Fix ◽  
Dannis M. Brouwer ◽  
Ronald G. K. M. Aarts
Keyword(s):  
Natural Frequency ◽  
Building Block ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Compliant Mechanisms ◽  
Large Range ◽  
Building Blocks ◽  
Synthesis Algorithm ◽  
Block Based ◽  
High Support

Abstract Flexure based compliant mechanisms suited for a large range of motion can be designed by handling the challenges arising from combining low compliance in the desired directions, high support stiffness, low stresses and high unwanted natural frequencies. Current topology optimization tools typically can’t model large deflections of flexures, are too conceptual or are case specific. In this research, a new spatial topological synthesis algorithm based on building blocks is proposed to optimize the performance of an initial design. The algorithm consists of successive shape optimizations and layout syntheses. In each shape optimization the dimensions for some layout are optimized. The layout synthesis strategically replaces the most “critical” building block with a better option. To maximize the first unwanted natural frequency the replacement strategy depends the strain energy distribution of the accompanying mode shape. The algorithm is tested for the design of a 1-DOF flexure hinge. The obtained final layout agrees with results known from literature.

Conceptual designs of multi-degree of freedom compliant parallel manipulators composed of wire-beam based compliant mechanisms

2014 ◽  
Vol 229 (3) ◽  
pp. 538-555 ◽  
Author(s):  
Guangbo Hao ◽  
Haiyang Li
Keyword(s):  
Rigid Body ◽  
Building Block ◽  
Compliant Mechanisms ◽  
Building Blocks ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Conceptual Designs ◽  
Rigid Body Model ◽  
Block Based

This paper proposes conceptual designs of multi-degree(s) of freedom (DOF) compliant parallel manipulators (CPMs) including 3-DOF translational CPMs and 6-DOF CPMs using a building block based pseudo-rigid-body-model (PRBM) approach. The proposed multi-DOF CPMs are composed of wire-beam based compliant mechanisms (WBBCMs) as distributed-compliance compliant building blocks (CBBs). Firstly, a comprehensive literature review for the design approaches of compliant mechanisms is conducted, and a building block based PRBM is then presented, which replaces the traditional kinematic sub-chain with an appropriate multi-DOF CBB. In order to obtain the decoupled 3-DOF translational CPMs (XYZ CPMs), two classes of kinematically decoupled 3-PPPR (P: prismatic joint, R: revolute joint) translational parallel mechanisms (TPMs) and 3-PPPRR TPMs are identified based on the type synthesis of rigid-body parallel mechanisms, and WBBCMs as the associated CBBs are further designed. Via replacing the traditional actuated P joint and the traditional passive PPR/PPRR sub-chain in each leg of the 3-DOF TPM with the counterpart CBBs (i.e. WBBCMs), a number of decoupled XYZ CPMs are obtained by appropriate arrangements. In order to obtain the decoupled 6-DOF CPMs, an orthogonally-arranged decoupled 6-PSS (S: spherical joint) parallel mechanism is first identified, and then two example 6-DOF CPMs are proposed by the building block based PRBM method. It is shown that, among these designs, two types of monolithic XYZ CPM designs with extended life have been presented.

scholarly journals Building block method: a bottom-up modular synthesis methodology for distributed compliant mechanisms

2012 ◽  
Vol 3 (1) ◽  
pp. 15-23 ◽  
Author(s):  
G. Krishnan ◽  
C. Kim ◽  
S. Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Building Blocks ◽  
Load Flow ◽  
Optimization Techniques ◽  
Geometric Representation ◽  
Recent Developments ◽  
Block Based ◽  
Synthesis Methodology ◽  
Automated Optimization

Abstract. Synthesizing topologies of compliant mechanisms are based on rigid-link kinematic designs or completely automated optimization techniques. These designs yield mechanisms that match the kinematic specifications as a whole, but seldom yield user insight on how each constituent member contributes towards the overall mechanism performance. This paper reviews recent developments in building block based design of compliant mechanisms. A key aspect of such a methodology is formulating a representation of compliance at a (i) single unique point of interest in terms of geometric quantities such as ellipses and vectors, and (ii) relative compliance between distinct input(s) and output(s) in terms of load flow. This geometric representation provides a direct mapping between the mechanism geometry and their behavior, and is used to characterize simple deformable members that form a library of building blocks. The design space spanned by the building block library guides the decomposition of a given problem specification into tractable sub-problems that can be each solved from an entry in the library. The effectiveness of this geometric representation aids user insight in design, and enables discovery of trends and guidelines to obtain practical conceptual designs.

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.

Design Synthesis of 2-D Compliant Mechanisms Utilizing Serial Concatenation of Building Blocks

2009 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Unique Point ◽  
Compliance Matrix ◽  
Design Synthesis ◽  
Parametric Variation ◽  
Point Of Interest

In this section we implement a characterization based on eigen-twists and eigen-wrenches for the deformation of a compliant mechanism at a given point of interest. For 2-D mechanisms, this involves characterizing the compliance matrix at a unique point called the center of elasticity. At the center of elasticity, the translation and rotational compliances are decoupled. We give an intuitive graphical understanding of compliance at this point by representing the translational compliance as an ellipse and the coupling between the translational and rotational parameters as vectors (Coupling vectors). This representation gives us an intuitive understanding of series and parallel combination of building blocks. We obtain a parametric variation of these quantities for a compliant dyad building block, and show with examples how a mechanism can be synthesized by a combination of building blocks to obtain desired deformation requirements. We also propose a combination of series and parallel concatenation to achieve more than one specification simultaneously. Such a characterization can be extended to synthesize involving multiple ports.

Functional Characterization of Compliant Building Blocks Utilizing Eigentwists and Eigenwrenches

2008 ◽  
Author(s):  
Charles J. Kim
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Deformable Body ◽  
Functional Characterization ◽  
Building Blocks ◽  
Future Research ◽  
Special Cases ◽  
Block Approach

Compliant mechanisms are devices which utilize the flexibility of their constituent members to transmit motion and forces. Unlike their rigid body counterparts, compliant mechanisms typically contain no traditional joints. The focus of this research is the development of a building block approach for the synthesis of compliant mechanisms. Building block methods better facilitate the augmentation of designer intuition while offering a systematic approach to open-ended problems. In this paper, we investigate the use of the eigentwists and eigenwrenches of a deformable body to characterize basic kinematic function. The eigentwists and eigenwrenches are shown to demonstrate parametric behavior when applied to the compliant dyad building block, and in special cases may be compared to compliance ellipsoids. The paper concludes by articulating future research in a building block approach to compliant mechanism synthesis.

Grouping of Planetary Gear Modes With Significant Tooth Mesh Deflection

2012 ◽  
Author(s):  
Tristan M. Ericson ◽  
Robert G. Parker
Keyword(s):  
Natural Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Planetary Gears ◽  
System Parameters ◽  
Planet Gear ◽  
Parameter Values ◽  
Grouping Behavior

High natural frequencies of planetary gears tend collect into groups. The modes at these natural frequencies are characterized by motion of the planet gears with strain energy in the tooth meshes and planet bearings. Each group has one rotational, one translational, and one planet mode. The groups change in natural frequency together when system parameters are varied. The grouping behavior is disrupted with significant differences in planet-to-planet gear parameter values.

A Building Block Approach to the Conceptual Synthesis of Compliant Mechanisms Utilizing Compliance and Stiffness Ellipsoids

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Charles J. Kim ◽  
Yong-Mo Moon ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Single Point ◽  
Rapid Prototype ◽  
Building Blocks ◽  
Single Input Single Output ◽  
Kinematic Behavior ◽  
Insight Into ◽  
Block Approach

In this paper, we investigate a methodology for the conceptual synthesis of compliant mechanisms based on a building block approach. The building block approach is intuitive and provides key insight into how individual building blocks contribute to the overall function. We investigate the basic kinematic behavior of individual building blocks and relate this to the behavior of a design composed of building blocks. This serves to not only generate viable solutions but also to augment the understanding of the designer. Once a feasible concept is thus generated, known methods for size and geometry optimization may be employed to fine-tune performance. The key enabler of the building block synthesis is the method of capturing kinematic behavior using compliance ellipsoids. The mathematical model of the compliance ellipsoids facilitates the characterization of the building blocks, transformation of problem specifications, decomposition into subproblems, and the ability to search for alternate solutions. The compliance ellipsoids also give insight into how individual building blocks contribute to the overall kinematic function. The effectiveness and generality of the methodology are demonstrated through two synthesis examples. Using only a limited set of building blocks, the methodology is capable of addressing generic kinematic problem specifications for compliance at a single point and for a single-input, single-output compliant mechanism. A rapid prototype of the latter demonstrates the validity of the conceptual solution.

Membrane and Bending Strain in Cylindrical Shell Vibrations

2009 ◽  
Author(s):  
Basem Alzahabi ◽  
Henry Kowalski
Keyword(s):  
Natural Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Operating Conditions ◽  
Total Strain ◽  
Design Stage ◽  
Total Strain Energy ◽  
Scaled Model ◽  
Membrane Strain

Cylindrical Shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. Therefore, investigating the dynamic characteristics of cylindrical shells is very critical in developing a strategy for modal vibration control for specific operating conditions. Reduction of vibration amplitudes and in sound radiation is most efficiently achieved at the design stage, and the acoustic signatures may be determined by considering operational scenarios, and modal characteristics. In cylindrical shells, mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes, and unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. The ratio of membrane strain energy to total strain energy is high for modes with simple modal patterns and decrease toward zero as the number of nodal (n) lines increase, while the ratio of bending energy to total strain energy is small for simple nodal patterns and increase with increase in complexity of it. Modes associated with membrane deformation require a lot of strain energy while modes associated with bending deformation require less strain energy. The lowest natural frequency occurs where the sum of the two energies are at minimum. Moreover, the natural frequencies that are controlled by membrane strain energy are approximately independent of the shell thickness change. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then the experimental modal analysis of the scaled model utilizing strain gauges was performed to decouple the strain components. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.

On the Geometry of Stiffness and Compliance Under Concatenation

2019 ◽  
Author(s):  
Charles J. Kim
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Building Blocks ◽  
Design Rules ◽  
Multiple Mechanism ◽  
Kinematic Behavior ◽  
Geometric Nature

Abstract Eigentwists and eigenwrenches capture the stationary stiffness behavior of compliant mechanisms and can be related to a mechanism’s primary kinematic behavior. The nature of concatenation of multiple mechanism building blocks is not well-understood. In this paper, we consider the mechanics of concatenation and develop design rules that capture the geometric nature of concatenation in terms of eigenwrenches and eigentwists. The rules are illustrated through mechanisms from the literature. The design rules have potential to provide intelligent guidance for systematic building block synthesis of compliant mechanisms.

Sign in / Sign up

Export Citation Format

Share Document