Finding All Solutions to Unconstrained Nonlinear Optimization for Approximate Synthesis of Planar Linkages Using Continuation Method

1999 ◽  
Vol 121 (3) ◽  
pp. 368-374 ◽  
Author(s):  
A.-X. Liu ◽  
T.-L. Yang
Keyword(s):  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Kinematic Synthesis ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Unconstrained Nonlinear Optimization ◽  
Optimum Solution ◽  
Planar Linkages ◽  
Four Bar Linkage

Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the suitable initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and three examples are given to illustrate the advantages of the proposed method.

Finding All Solutions to Approximate Synthesis of Planar Linkages for Function Generation, Rigid-Body Guidance and Path Generation

1996 ◽  
Author(s):  
An-Xin Liu ◽  
Ting-Li Yang
Keyword(s):  
Rigid Body ◽  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Optimum Solution

Abstract Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and 3 examples are given to illustrate the advantages of the proposed method.

THE KINEMATIC SYNTHESIS OF STEERING MECHANISMS

2000 ◽  
Vol 24 (3-4) ◽  
pp. 453-476 ◽  
Author(s):  
Jin Yao ◽  
Jorge Angeles
Keyword(s):  
Polynomial Equation ◽  
Global Optimum ◽  
Polynomial Equations ◽  
Kinematic Synthesis ◽  
Local Optima ◽  
Speed Reduction ◽  
Design Variables ◽  
Transmission Quality ◽  
Four Bar Linkage ◽  
Maximum Transmission

We propose a computational-kinematics approach based on elimination procedures to synthesize a steering four-bar linkage. In this regard, we aim at minimizing the root-mean square error of the synthesized linkage in meeting the steering condition over a number of linkage configurations within the linkage range of motion. A minimization problem is thus formulated, whose normality conditions lead to two polynomial equations in two unknown design variables. Upon eliminating one of these two variables, a monovariate polynomial equation is obtained, whose roots yield all locally-optimum linkages. From these roots, the global optimum, as well as unfeasible local optima, are readily identified. The global optimum, however, turns out to be impractical because of the large differences in its link lengths, which we refer to as dimensional unbalance. To cope with this drawback, we use a kinematically-equivalent focal mechanism, i.e., a six-bar linkage with an input-output function identical to that of the four-bar linkage. Given that the synthesized linkage requires a rotational input, as opposed to most existing steering linkages, which require a translational input, we propose a spherical four-bar linkage to drive the steering linkage. The spherical linkage is synthesized so as to yield a speed reduction as close as possible to 2:1 and to have a maximum transmission quality.

Real Continuation Method and its Application in Kinematic Synthesis

2000 ◽  
Author(s):  
Liu Anxin ◽  
Yang Tingli
Keyword(s):  
High Efficiency ◽  
Continuation Method ◽  
Linear Equations ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Real Solutions ◽  
Non Linear ◽  
Four Bar Linkage ◽  
Non Linear Equations

Abstract Real continuation method for finding real solutions to non-linear equations is proposed. Synthesis of planar four-bar linkage for path generation with nine precision points is studied using this method. The proposed method has high efficiency and can best be used for solving synthesis problems.

Development of Global Optimization Method for Design of Turbine Stages

2005 ◽  
Author(s):  
Hiroyuki Kawagishi ◽  
Kazuhiko Kudo
Keyword(s):  
Genetic Algorithm ◽  
Global Optimization ◽  
Simulated Annealing ◽  
Optimum Design ◽  
Optimization Method ◽  
Global Optimum ◽  
Global Optimization Method ◽  
Optimum Solution ◽  
Global Optimum Solution ◽  
Number Of Iterations

A new optimization method which can search for the global optimum solution and decrease the number of iterations was developed. The performance of the new method was found to be effective in finding the optimum solution for single- and multi-peaked functions for which the global optimum solution was known in advance. According to the application of the method to the optimum design of turbine stages, it was shown that the method can search the global optimum solution at approximately one seventh of the iterations of GA (Genetic Algorithm) or SA (Simulated Annealing).

scholarly journals An Optimization Method for the Configuration of Inter Array Cables for Floating Offshore Wind Farm

2017 ◽  
Author(s):  
Yann Poirette ◽  
Martin Guiton ◽  
Guillaume Huwart ◽  
Delphine Sinoquet ◽  
Jean Marc Leroy
Keyword(s):  
Wind Farm ◽  
Optimization Problem ◽  
Initial Point ◽  
Trust Region ◽  
Optimization Method ◽  
Global Optimum ◽  
Offshore Wind ◽  
Finite Element Software ◽  
Constrained Problems ◽  
Floating Offshore Wind Turbines

IFP Energies nouvelles (IFPEN) is involved for many years in various projects for the development of floating offshore wind turbines. The commercial deployment of such technologies is planned for 2020. The present paper proposes a methodology for the numerical optimization of the inter array cable configuration. To illustrate the potential of such an optimization, results are presented for a case study with a specific floating foundation concept [1]. The optimization study performed aims to define the least expensive configuration satisfying mechanical constraints under extreme environmental conditions. The parameters to be optimized are the total length, the armoring, the stiffener geometry and the buoyancy modules. The insulated electrical conductors and overall sheath are not concerned by this optimization. The simulations are carried out using DeepLines™, a Finite Element software dedicated to simulate offshore floating structures in their marine environment. The optimization problem is solved using an IFPEN in-house tool, which integrates a state of the art derivative-free trust region optimization method extended to nonlinear constrained problems. The latter functionality is essential for this type of optimization problem where nonlinear constraints are introduced such as maximum tension, no compression, maximum curvature and elongation, and the aero-hydrodynamic simulation solver does not provide any gradient information. The optimization tool is able to find various local feasible extrema thanks to a multi-start approach, which leads to several solutions of the cable configuration. The sensitivity to the choice of the initial point is demonstrated, illustrating the complexity of the feasible domain and the resulting difficulty in finding the global optimum configuration.

scholarly journals Optimization Design of the Over-All Dimensions of Centrifugal Compressor Stage

1988 ◽  
Author(s):  
Wang Qinghuan ◽  
Sun Zhiqin
Keyword(s):  
Centrifugal Compressor ◽  
Computer Aided Design ◽  
Optimization Design ◽  
Optimization Method ◽  
Complex Method ◽  
Compressor Stage ◽  
Local Optima ◽  
Centrifugal Compressor Stage ◽  
Optimum Solution ◽  
Nonlinear Objective Function

A new procedure employed in computer-aided design of centrifugal compressor stage to determine its over-all dimensions is described in this paper. By the use of the COMPLEX METHOD, the arbitrary number of variables to be optimized can be specified to remove the hidden danger of the local optima which stems from adopting a few, for example two or three, variables to be optimized. This procedure is available for any complicated implicit nonlinear objective function and ensures establishment of a true optimum solution. Numerical calculations have been carried out by using the computer program described here to check the ability of the optimization method. The results obtained by the calculations agree fairly well with that obtained by experiments.

A Design Methodology for System Parameters Synthesis of Elastic Planar Linkages: Theory

1992 ◽  
Vol 114 (4) ◽  
pp. 536-541 ◽  
Author(s):  
Zine-Eddine Boutaghou ◽  
A. G. Erdman
Keyword(s):  
Design Methodology ◽  
Design Sensitivity ◽  
Element Analysis ◽  
System Parameters ◽  
Sensitivity Equations ◽  
The Finite Element Analysis ◽  
Planar Linkages ◽  
Multi Body ◽  
Four Bar Linkage ◽  
Theoretical Considerations

Existing formulations predict the displacement and stresses in multi-body systems that result from known system parameters. In contrast, the proposed design methodology enables structured selection of system parameters necessary to produce desired elastic displacements, stresses, and frequencies. This design process involves the development of inverse design equations, the finite element analysis, and the design sensitivity equations to obtain converged solutions satisfying desired design constraints. Part 1 (Theory) considers the theoretical considerations involved. Part 2 (Applications) applies the methodology to design a four-bar linkage and a six-bar linkage.

scholarly journals Rethinking of Construction Robot in the Whole Project Life Cycle

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Yvkai Zhang
Keyword(s):  
Evaluation System ◽  
Large Scale ◽  
Global Optimum ◽  
Building Performance ◽  
Future Directions ◽  
Modular Systems ◽  
Project Life Cycle ◽  
Complete Set ◽  
Optimum Solution ◽  
Project Life

Assistive technology and evaluation system are expected to effectively solve the challenges of using robots in construction activities and improve the efficiency and building performance. Still, challenges are still need to be addressed before using robots for construction on a large scale. This Studies were corresponded to the identified areas for further critical review, and the development of research and application in each area was systematically analyzed to identify future directions for both the academia and the industry. More speci?cally, this review focus on determining the requirement of technology and application profile for robots, and based on the above analysis, a complete set of construction framework for robot was proposed, which integrates robots and activities with the various modular systems and digital technology to get global optimum solution.

scholarly journals A two-stage evolutionary optimization approach for an irrigation system design

2016 ◽  
Vol 19 (1) ◽  
pp. 115-122 ◽  
Author(s):  
Milan Cisty ◽  
Zbynek Bajtek ◽  
Lubomir Celar
Keyword(s):  
Water Distribution ◽  
Irrigation System ◽  
Optimal Solution ◽  
Water Distribution Network ◽  
Search Space ◽  
Optimization Method ◽  
Global Optimum ◽  
Optimization Approach ◽  
Nsga Ii ◽  
Irrigation Network

In this work, an optimal design of a water distribution network is proposed for large irrigation networks. The proposed approach is built upon an existing optimization method (NSGA-II), but the authors are proposing its effective application in a new two-step optimization process. The aim of the paper is to demonstrate that not only is the choice of method important for obtaining good optimization results, but also how that method is applied. The proposed methodology utilizes as its most important feature the ensemble approach, in which more optimization runs cooperate and are used together. The authors assume that the main problem in finding the optimal solution for a water distribution optimization problem is the very large size of the search space in which the optimal solution should be found. In the proposed method, a reduction of the search space is suggested, so the final solution is thus easier to find and offers greater guarantees of accuracy (closeness to the global optimum). The method has been successfully tested on a large benchmark irrigation network.

Two Precision Position Synthesis of Planar Linkages With Positional Rectification

1996 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Numerical Algorithms ◽  
All Solutions ◽  
Pass Through ◽  
Planar Linkages ◽  
Position Synthesis ◽  
Exact Positions

Abstract Precision position synthesis is used to generate planar linkages that pass through two exact positions and an additional number of approximate positions. The approximate positions provide a means of rectifying the solution linkages such that all solutions presented are more likely to describe a motion that remains within acceptable positional bounds. The rectification method involves the development of three different numerical algorithms that may be applied to a particular step in the dyad/triad method of precision position synthesis. The three algorithms presented can be applied in a variety of combinations to allow for the synthesis of both simple (four-bar) and complex (multiloop) planar linkages.

Sign in / Sign up

Export Citation Format

Share Document