Application of the Exact Gradient Approach in Optimal Synthesis of Mechanisms

1993 ◽  
Author(s):  
Jawaharlal Mariappan ◽  
Sundar Krishnamurty
Keyword(s):  
Generalized Solution ◽  
Optimization Method ◽  
Solution Procedure ◽  
Optimal Synthesis ◽  
Synthesis Process ◽  
Mechanism Synthesis ◽  
Approximate Methods ◽  
Synthesis Of Mechanisms ◽  
Gradient Based ◽  
Gradient Approach

Abstract This paper presents the application of the unified exact gradient approach to optimal synthesis of mechanisms. The exact gradient approach is a systematic and efficient solution procedure that is applicable for any type of mechanism synthesis problem. In this approach, the exact gradients necessary for optimization are developed using a generalized solution procedure based on matrix methods. Availability of exact gradients in this approach enables the utilization of any gradient-based optimization method in mechanism synthesis process. As a result, this approach will be computationally most efficient, since it will not require direct search methods, or, finite difference approximate methods to find optimal solutions. These salient features of this approach are demonstrated with the aid of several mechanism problems and the results discussed.

Development of a Unified Exact Gradient Approach to Optimal Synthesis of Mechanisms

1993 ◽  
Author(s):  
Jawaharlal Mariappan ◽  
Sundar Krishnamurty
Keyword(s):  
Optimization Methods ◽  
Solution Procedure ◽  
Optimal Synthesis ◽  
Synthesis Process ◽  
Optimal Solutions ◽  
Mechanism Synthesis ◽  
Approximate Methods ◽  
Efficient Manner ◽  
Synthesis Of Mechanisms ◽  
Gradient Based

Abstract This paper presents the development of a unified approach to optimal synthesis of mechanisms using exact gradients. The uniqueness of this approach lies in its ability to find optimal solutions to different type of mechanism problems in a systematic and efficient manner. In this approach, the exact gradients necessary for optimization are developed using a generalized methodical solution procedure based on matrix methods. This enables direct utilization of efficient gradient-based optimization methods in the mechanism synthesis process, thus eliminating the need for time-consuming direct search methods, or, the use of finite difference approximate methods to estimate gradients during optimization. The development of exact gradients and its integration with mechanism synthesis process, thus, offers the most effective approach for finding optimal solutions in generic mechanisms.

A Density Gradient Approach to Topology Optimization Under Design-Dependent Boundary Loading

2018 ◽  
Author(s):  
Cunfu Wang ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Density Gradient ◽  
Optimization Method ◽  
Spatial Gradient ◽  
Computationally Efficient ◽  
Physical Density ◽  
Gradient Based ◽  
Design Dependent Loads ◽  
Previous Iteration ◽  
Gradient Approach

The paper proposes a density gradient based approach to topology optimization under design-dependent boundary loading. In the density-based topology optimization method, we impose the design dependent loads through spatial gradient of the density. We transform design-dependent boundary loads into a volume form through volume integral of density gradient. In many applications where loadings only need to be exerted on partial boundary, we introduce an auxiliary loading density to keep track of the loading boundary. During the optimization, the loading density is updated by tracking the changes of the physical density in the vicinity of the loading boundary at previous iteration. The proposed approach is easy to implement and computationally efficient. In addition, by adding more auxiliary density fields, the proposed approach is applicable to multiple design-dependent loads. To prevent the intersection of different loading boundaries, a Heaviside projection based integral constraint is developed. Both heat conduction problems under convection loading and elastic problems under hydrostatic pressure loading are presented to illustrate the effectiveness and efficiency of the method.

Using Exact Gradients in Mechanism Design

1992 ◽  
Author(s):  
J. Mariappan ◽  
S. Krishnamurty
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Optimization Method ◽  
Mechanism Synthesis ◽  
Nonlinear Functional ◽  
Good Convergence ◽  
Reduced Gradient Method ◽  
Highly Nonlinear ◽  
Gradient Based ◽  
Difference Methods

Abstract This paper presents a new approach for mechanism synthesis using exact gradients in optimization. Currently, finite difference methods or similar approximate techniques are used to evaluate the derivatives that are necessary for performing mechanism optimization using gradient-based methods. Typical mechanism synthesis problems involve highly nonlinear functional relationship, and the use of finite difference methods in such problems often leads to an excessive number of function evaluations, algorithm failures, and inaccurate results. Instead, an alternative approach using exact gradients will completely eliminate all of the above problems, and will result in a faster and efficient convergence. This paper also discusses the identification of an appropriate optimization method, namely, the generalized reduced gradient method for mechanisms synthesis based on its good convergence properties, reliability, intermediate feasibility, and efficiency. Numerical examples are included to illustrate the advantages of using exact gradients and the results are discussed.

Topology Optimization of Planar Gear-Linkage Mechanisms

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Neung Hwan Yim ◽  
Seok Won Kang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Mechanism Synthesis ◽  
Gear Design ◽  
Linkage Design ◽  
Gradient Based ◽  
Mechanical Elements ◽  
Topology Optimization Method

Topology optimization for mechanism synthesis has been developed for the simultaneous determination of the number and dimension of mechanisms. However, these methods can be used to synthesize linkage mechanisms that consist only of links and joints because other types of mechanical elements such as gears cannot be simultaneously synthesized. In this study, we aim to develop a gradient-based topology optimization method which can be used to synthesize mechanisms consisting of both linkages and gears. For the synthesis, we propose a new ground model defined by two superposed design spaces: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks, each of which is assumed to rotate as an output gear, while the linkage design space is discretized by zero-length-spring-connected rigid blocks. Another set of zero-length springs is introduced to connect gear blocks to rigid blocks, and their stiffness values are varied to determine the existence of gears when they are necessary to produce the desired path. After the proposed topology-optimization-based synthesis formulation and its numerical implementation are presented, its effectiveness and validity are checked with various synthesis examples involving gear-linkage and linkage-only mechanisms.

Turning Functions in Optimal Synthesis of Mechanisms

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Fernando Nadal ◽  
Juan A. Cabrera ◽  
Alex Bataller ◽  
Juan J. Castillo ◽  
Antonio Ortiz
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Algorithm ◽  
Optimal Synthesis ◽  
Mechanism Synthesis ◽  
Synthesis Of Mechanisms

In this paper, we describe the use of turning functions to compare errors between the coupler and the target paths. The main reason to use turning functions is that the measured error does not depend on the mechanism scale or the position and rotation of the fixed link. Therefore, the searching space for the optimization algorithm is reduced. To carry out mechanism synthesis, we use an evolutionary algorithm. The effectiveness of the proposed method has been demonstrated in five synthesis examples.

An Improved Shape Annealing Method for Truss Topology Generation

1994 ◽  
Author(s):  
Giridhar Reddy ◽  
Jonathan Cagan
Keyword(s):  
Simulated Annealing ◽  
Optimization Method ◽  
Geometric Constraints ◽  
Truss Structures ◽  
Model Design ◽  
Topology Generation ◽  
Truss Topology ◽  
Gradient Based ◽  
Annealing Algorithm ◽  
Annealing Method

Abstract A method for the design of truss structures which encourages lateral exploration, pushes away from violated spaces, models design intentions, and produces solutions with a wide variety of characteristics is introduced. An improved shape annealing algorithm for truss topology generation and optimization, based on the techniques of shape grammars and simulated annealing, implements the method. The algorithm features a shape grammar to model design intentions, an ability to incorporate geometric constraints to avoid obstacles, and a shape optimization method using only simulated annealing with more consistent convergence characteristics; no traditional gradient-based techniques are employed. The improved algorithm is illustrated on various structural examples generating a variety of solutions based on a simple grammar.

Application of Gradient Based IR Thermography to the GRP Structures Inspection

2011 ◽  
Vol 488-489 ◽  
pp. 682-685 ◽  
Author(s):  
Lovre Krstulović-Opara ◽  
Endri Garafulić ◽  
Branko Klarin ◽  
Željko Domazet
Keyword(s):  
Pulse Heating ◽  
Non Destructive Testing ◽  
Ir Thermography ◽  
Destructive Testing ◽  
Heat Flows ◽  
Testing Method ◽  
Reinforced Polymer ◽  
Gradient Based ◽  
Non Destructive ◽  
Gradient Approach

The article presents application of non destructive testing method based on the pulse heating infrared thermography used to detect material anomalies for the case of glass reinforced polymer structures. The goal of presented research, based on the thermal gradient approach, is to establish the procedure capable of filtering out anomalies from other thermal influences caused by thermal reflections of surrounding objects, geometry influences and heat flows for observed object.

Synthesis of a High-Precision Missile Homing System with an Permissible Stability Margin of the Normal Acceleration Stabilization System

2021 ◽  
Vol 22 (7) ◽  
pp. 365-373
Author(s):  
Quang Thong Do
Keyword(s):  
High Precision ◽  
Parametric Optimization ◽  
Stability Margin ◽  
Optimization Method ◽  
Synthesis Process ◽  
Stabilization System ◽  
Gain Margin ◽  
The Stability ◽  
Automatic Systems ◽  
Normal Acceleration

The proportional guidance method-based missile homing systems (MHS) have been widely used the real-world environments. In these systems, in order to destroy the targets at different altitudes, a normal acceleration stabilization system (NASS) is often utilized. Therefore, the MHS are complex and the synthesis of these systems are a complex task. However, it is necessary to synthesize NASS during the synthesis of the MHS. To simplify the synthesis process, a linear model of the NASS is used. In addition, we make use of the available commands in Control System Toolbox in MATLAB. Because the Toolbox has the commands to describe the transfer function, determine the stability gain margin, and the values of the transient respond of the linear automatic systems. Thus, this article presents two methods for synthesizing the missile homing systems, including (i) a method for synthesizing the MHS while ensuring the permissible stability gain margin of the NASS, and (ii) a method for synthesizing the MHS while ensuring the permissible stability margin of the NASS by overshoot. These techniques are very easy to implement using MATLAB commands. The synthesis of the proposed MHS is carried out by the parametric optimization method. To validate the performance of the proposed techniques, we compare them withthe MHS synthesized by ensuring the stability margin of the NASS bythe oscillation index. The results show that, two our proposed methods and the existing method provide the same results in terms of high-precision. Nevertheless, the proposed methods are simple and faster than the conventional method. The article also investigates the effect of gravity, longitudinal acceleration of the rocket, andblinding of the homing head on the accuracy of the synthesized MHS. The results illustrate that they have a little effect on its accuracy.

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