Geometric Modeling and Optimization of Multi-Material Compliant Mechanisms Using Multi-Layer Wide Curves

2007 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Geometric Optimization ◽  
Optimization Approach ◽  
Variable Cross ◽  
Modeling And Optimization ◽  
Multiple Materials

Multi-material compliant mechanisms enhance the performance of regular single-material compliant mechanisms by adding a new design option, material type variation. This paper introduces a geometric modeling method for multimaterial compliant mechanisms by using multi-layer wide curves. Based on the introduced modeling method, a geometric optimization approach for multi-material compliant mechanisms is proposed. A multi-layer wide curve is a curve with variable cross-sections and multiple materials. In this paper, every connection in the multi-material compliant mechanism is represented by a multi-layer wide curve and the whole mechanism is modeled as a set of connected multi-layer wide curves. The geometric modeling and optimization of a multi-material compliant mechanism are considered as the generation and optimal selection of the control parameters of the corresponding multi-layer wide curves. The deformation and performance of multi-material compliant mechanisms is evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The effectiveness of the proposed geometric modeling and optimization procedures is verified by the demonstrated examples.

Geometric Modeling and Optimization of Multimaterial Compliant Mechanisms Using Multilayer Wide Curves

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Geometric Optimization ◽  
Optimization Approach ◽  
Variable Cross ◽  
Modeling And Optimization ◽  
Multiple Materials

Multimaterial compliant mechanisms enhance the performance of regular single-material compliant mechanisms by adding a new design option, material type variation. This paper introduces a geometric modeling method for multimaterial compliant mechanisms by using multilayer wide curves. Based on the introduced modeling method, a geometric optimization approach for multimaterial compliant mechanisms is proposed. A multilayer wide curve is a curve with variable cross sections and multiple materials. In this paper, every connection in the multimaterial compliant mechanism is represented by a multilayer wide curve, and the whole mechanism is modeled as a set of connected multilayer wide curves. The geometric modeling and the optimization of a multimaterial compliant mechanism are considered as the generation and the optimal selection of the control parameters of the corresponding multilayer wide curves. The deformation and performance of multimaterial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized, and the practical constraints are imposed during the optimization process. The effectiveness of the proposed geometric modeling and optimization procedures is verified by the demonstrated examples.

Geometric Modeling and Synthesis of Spatial Multimaterial Compliant Mechanisms and Structures Using Three-Dimensional Multilayer Wide Curves

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Three Dimensional ◽  
Modeling Method ◽  
Synthesis Process ◽  
Variable Cross ◽  
Finite Element Procedure ◽  
Multiple Materials

A 3D multilayer wide curve is a spatial curve with variable cross sections and multiple materials. The performance of multimaterial compliant mechanisms and structures is enhanced by integrating multiple materials into one-piece configurations. This paper introduces a geometric modeling method for spatial multimaterial compliant mechanisms and structures by using 3D multilayer wide curves. Based on the introduced modeling method, a geometric synthesis approach is proposed. In this paper, every connection in a spatial multimaterial compliant mechanism or structure is represented by a 3D multilayer wide curve and the whole compliant mechanism or structure is modeled as a set of connected wide curves. The geometric modeling and synthesis are considered as the generation and optimization of the control parameters of the corresponding 3D multilayer wide curves. The performance of spatial multimaterial compliant mechanisms and structures is evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the synthesis process. The effectiveness of the proposed geometric modeling and synthesis procedures is verified by the demonstrated examples.

Geometric Optimization of Spatial Multimaterial Compliant Mechanisms and Structures Using Three-Dimensional Multilayer Wide Curves

2009 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Geometric Optimization ◽  
Programming Algorithm ◽  
Variable Cross ◽  
Multiple Materials

Three-dimensional multilayer wide curves are spatial curves with variable cross sections and multiple materials. This paper introduces a geometric optimization method for spatial multimaterial compliant mechanisms and structures by using three-dimensional multilayer wide curves. In this paper, every multimaterial connection is represented by a three-dimensional multilayer wide curve and the whole spatial multimaterial compliant mechanism or structure is modeled as a set of connected three-dimensional multilayer wide curves. The geometric optimization of a spatial multimaterial compliant mechanism or structure is considered as the optimal selection of control parameters of the corresponding three-dimensional multilayer wide curves. The deformation and performance of spatial multimaterial compliant mechanisms and structures are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm. The effectiveness of the proposed geometric optimization procedure is verified by the demonstrated examples.

Geometric Optimization of Spatial Compliant Mechanisms Using Three-Dimensional Wide Curves

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Three Dimensional ◽  
Optimization Method ◽  
Geometric Optimization ◽  
Programming Algorithm ◽  
Variable Cross ◽  
Finite Element Procedure ◽  
And Performance

A three-dimensional wide curve is a spatial curve with variable cross sections. This paper introduces a geometric optimization method for spatial compliant mechanisms by using three-dimensional wide curves. In this paper, every material connection in a spatial compliant mechanism is represented by a three-dimensional wide curve and the whole spatial compliant mechanism is modeled as a set of connected three-dimensional wide curves. The geometric optimization of a spatial compliant mechanism is considered as the generation and optimal selection of the control parameters of the corresponding three-dimensional parametric wide curves. The deformation and performance of spatial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm.

Geometric Synthesis of Spatial Compliant Mechanisms Using Three-Dimensional Wide Curves

2008 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Three Dimensional ◽  
Programming Algorithm ◽  
Variable Cross ◽  
Finite Element Procedure ◽  
And Performance ◽  
Selection Of

A three-dimensional wide curve is a spatial curve with variable cross sections. This paper introduces a geometric synthesis method for spatial compliant mechanisms by using three-dimensional wide curves. In this paper, every connection in a spatial compliant mechanism is represented by a three-dimensional wide curve and the whole spatial compliant mechanism is modeled as a set of connected three-dimensional wide curves. The geometric synthesis of a spatial compliant mechanism is considered as the generation and optimal selection of control parameters of the corresponding three-dimensional parametric wide curves. The deformation and performance of spatial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm. The effectiveness of the proposed geometric procedures is verified by the demonstrated examples.

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.

Runner Optimization for In-Mold Assembly of Multi-Material Compliant Mechanisms

2011 ◽  
Author(s):  
Wojciech Bejgerowski ◽  
Satyandra K. Gupta
Keyword(s):  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Polymer Melt ◽  
Injection Molding Process ◽  
Optimization Approach ◽  
Assembly Process ◽  
Molding Process ◽  
Design Variables

The runner system in injection molding process is used to supply the polymer melt from injection nozzle to the gates of final part cavities. Realizing complex multi-material mechanisms by in-mold assembly process requires special runner layout design considerations due to the existence of the first stage components. This paper presents the development of an optimization approach for runner systems in the in-mold assembly of multi-material compliant mechanisms. First, the issues specific to the in-mold assembly process are identified and analyzed. Second, the general optimization problem is formulated by identification of all parameters, design variables, objective functions and constraints. Third, the implementation of the optimization problem in Matlab® environment is described based on a case study of a runner system for an in-mold assembly of a MAV drive mechanism. This multi-material compliant mechanism consists of seven rigid links interconnected by six compliant hinges. Finally, several optimization approaches are analyzed to study their performance in solving the formulated problem. The most appropriate optimization approach is selected. The case study showed the applicability of the developed optimization approach to runner systems for complex in-mold assembled multi-material mechanism designs.

scholarly journals Topology Optimization considering Nonsmooth Structural Boundaries in the Intersection Areas of the Components

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ruichao Lian ◽  
Shikai Jing ◽  
Zefang Shi ◽  
Zhijun He ◽  
Guohua Song
Keyword(s):  
Topology Optimization ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Optimization Approach ◽  
Structural Topology ◽  
Topology Description Function ◽  
Structural Responses ◽  
Structure Boundary ◽  
Compliance Problem ◽  
The Impact

In the structural topology optimization approaches, the Moving Morphable Component (MMC) is a new method to obtain the optimized structural topologies by optimizing shapes, sizes, and locations of components. However, the optimized structure boundary usually generates local nonsmooth areas due to incomplete connection between components. In the present paper, a topology optimization approach considering nonsmooth structural boundaries in the intersection areas of the components based on the MMC is proposed. The variability of components’ shape can be obtained by constructing the topology description function (TDF) with multiple thickness and length variables. The shape of components can be modified according to the structural responses during the optimization process, and the relatively smooth structural boundaries are generated in the intersection areas of the components. To reduce the impact of the initial layout on the rate of convergence, this method is implemented in a hierarchical variable calling strategy. Compared with the original MMC method, the advantage of the proposed approach is that the smoothness of the structural boundaries can be effectively improved and the geometric modeling ability can be enhanced in a concise way. The effectiveness of the proposed method is demonstrated for topology optimization of the minimum compliance problem and compliant mechanisms.

Design of Multimaterial Compliant Mechanisms Using Level-Set Methods

2005 ◽  
Vol 127 (5) ◽  
pp. 941-956 ◽  
Author(s):  
Michael Yu Wang ◽  
Shikui Chen ◽  
Xiaoming Wang ◽  
Yulin Mei
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Level Set Methods ◽  
Single Output ◽  
Geometric Boundary ◽  
Single Input ◽  
Applied Forces ◽  
Multiple Materials

A monolithic compliant mechanism transmits applied forces from specified input ports to output ports by elastic deformation of its comprising materials, fulfilling required functions analogous to a rigid-body mechanism. In this paper, we propose a level-set method for designing monolithic compliant mechanisms made of multiple materials as an optimization of continuum heterogeneous structures. Central to the method is a multiphase level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure. Combined with the classical shape derivatives, the level-set method yields an Eulerian computational system of geometric partial differential equations, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. The proposed method is demonstrated for single-input and single-output mechanisms and illustrated with several two-dimensional examples of synthesis of multimaterial mechanisms of force inverters and gripping and clamping devices. An analysis on the formation of de facto hinges is presented based on the shape gradient information. A scheme to ensure a well-connected topology of the mechanism during the process of optimization is also presented.

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