Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods

1997 ◽  
Vol 119 (4) ◽  
pp. 504-510 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Design Space ◽  
Initial Guess ◽  
Global Search ◽  
Search Method ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Local Optima ◽  
Structural Error ◽  
Synthesis Of Mechanisms

Generally, success in synthesis of mechanisms for path generation is limited to finding a reasonable local optima at best in spite of a very good initial guess. The most widely used Structural Error objective function is not effective in leading to practical solutions as it misrepresents the nature of the design problem by requiring the shape, size, orientation and position of the coupler curve to be optimized all at once. In this paper, we present an effective objective function based on Fourier descriptors that evaluates only the shape differences between two curves. This function is first minimized using a stochastic global search method derived from simulated annealing followed by Powell’s method. The size, orientation and position of the desired curve are addressed in a later stage by determining analogous points on the desired and candidate curves. In spite of highly non-linear mechanisms design space, our method discovers near-global and practical solutions consistently without requiring any initial guess.

Globally-Optimal Synthesis of Mechanisms for Path Generation Using Simulated Annealing and Powell’s Method

1996 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Simulated Annealing ◽  
Global Search ◽  
Synthesis Process ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Starting Point ◽  
Synthesis Of Mechanisms ◽  
Good Starting Point ◽  
Solution Mechanism ◽  
Set Of Points

Abstract Success in synthesis of mechanisms for path generation usually depends on providing a good starting point to the optimizer. This paper presents a completely automatic method that performs a global search from a random starting point. A two-step synthesis process involves searching for a coupler curve of optimal shape followed by optimization of size, orientation, and position of the solution mechanism. For the first step, an objective function evaluating shape difference between two curves, irrespective of the differences in their sizes, orientation, and position, is defined based on Fourier descriptors of the curves. This function is minimized using a stochastic global search method derived from simulated annealing, followed by Powell’s method for fast convergence. In the second stage, using properties of Fourier descriptors, a set of points is located on the solution curve that is analogous to points specified on the desired curve. The size, orientation, and position of the solution mechanism is then determined by minimizing the distance between analogous points.

An Elitist Ants-Search Based Method for Optimum Synthesis of Rigid-Linkage Mechanisms

2015 ◽  
Author(s):  
Nadim Diab ◽  
Ahmad Smaili
Keyword(s):  
Objective Function ◽  
Linear Constraints ◽  
Optimization Techniques ◽  
Path Generation ◽  
Generation Task ◽  
Optimum Synthesis ◽  
Structural Error ◽  
Constant Quantity ◽  
Future Work ◽  
Exploration Exploitation

Mechanical linkages are widely used in the industry and the synthesis of such mechanisms may require optimization depending on the number of precision positions required. Many intelligent optimization techniques (Genetic, Tabu, Simulated Annealing, etc) have been proposed in the literature, one of them being the Ant-Search which was first proposed by the authors in 2007. In this paper, a Modified Ant-Search (MAS) technique is proposed to optimize the synthesis of a four-bar mechanism with a path generation task. Two major improvements are applied over the previous algorithm: ants pheromone update and exploration/exploitation techniques are both modified. Unlike the previous work where a constant quantity of pheromones was added during each iteration, in this paper, the pheromone deposit rate is proportional to the error of the objective function. Such a modification in the pheromone update rule is expected to differentiate between the behaviors of different ants and better govern their motion in the subsequent iterations. Moreover, the second major improvement targets the exploration/exploitation techniques followed by the ants. Unlike the previous work where exploration dominates during the early iteration stages and exploitation during the late ones, this work implements a more dynamic strategy where ants enter and leave the exploration/exploitation processes as governed by parameters related to the objective function error and pheromone deposit levels. Such modifications applied to the Ant-Search (AS) technique are expected to ensure a better chance of converging to a global minimum. The MAS technique is applied for a few path generation tasks with prescribed timing along with a set of linear constraints. Results are compared with previous work in the literature where the newly proposed technique showed appreciable improvement as evaluated by the structural error objective function. Future work possibilities are also introduced.

scholarly journals A Parametrization-Invariant Fourier Approach to Planar Linkage Synthesis for Path Generation

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Xiangyun Li ◽  
Peng Chen
Keyword(s):  
Design Space ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Arc Length ◽  
Efficient Synthesis ◽  
Practical Applications ◽  
Classic Problem ◽  
Fourier Theory ◽  
Planar Linkages ◽  
Synthesis Approach

This paper deals with the classic problem of the synthesis of planar linkages for path generation. Based on the Fourier theory, the task curve and the synthesized four-bar coupler curve are regarded as the same curve if their Fourier descriptors match. Using Fourier analysis, a curve must be given as a function of time, termed a parametrization. In practical applications, different parametrizations can be associated with the same task and coupler curve, respectively; however, these parametrizations are Fourier analyzed to different Fourier descriptors, thus resulting in the mismatch of the task and coupler curve. In this paper, we present a parametrization-invariant method to eliminate the influence of parametrization on the values of Fourier descriptors by unifying given parametrizations to the arc length parametrization; meanwhile, a new design space decoupling scheme is introduced to separate the shape, size, orientation, and location matching of the task and four-bar curve, which leads naturally to an efficient synthesis approach.

Synthesis and Balancing of Cam-Modulated Linkages

1987 ◽  
Author(s):  
P. Pracht ◽  
P. Minotti ◽  
M. Dahan
Keyword(s):  
Systematic Approach ◽  
Kinematic Chain ◽  
Path Generation ◽  
Industrial Manipulator ◽  
High Speeds ◽  
Structural Error ◽  
Mass Balancing ◽  
Four Bar Linkage ◽  
Robotic Applications ◽  
Class Of Functions

Abstract Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

A More Effective Formulation of the Path Generation Mechanism Synthesis Problem

1994 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Error Function ◽  
Mathematical Optimization ◽  
Optimization Methods ◽  
Complex Nature ◽  
Mechanism Synthesis ◽  
Structural Error ◽  
Crank Angle ◽  
The Common ◽  
Selection Of

Abstract Use of mathematical optimization methods for synthesis of path-generating mechanisms has had only limited success due to the very complex nature of the commonly used Structural Error objective function. The complexity arises, in part, because the objective function represents not only the error in the shape of the coupler curve, but also the error in location, orientation and size of the curve. Furthermore, the common introduction of timing (or crank angle), done generally to facilitate selection of corresponding points on the curve for calculating structural error, has little practical value and unnecessarily limits possible solutions. This paper proposes a new objective function, based on Fourier Descriptors, which allows search for coupler curve of the desired shape without reference to location, orientation, or size. The proposed objective function compares overall shape properties of curves rather than making point-by-point comparison and therefore does not requires prescription of timing. Experimental evidence is provided to show that it is much easier to search the space of the proposed objective function compared to the structural error function.

Eliminating Structural Error in Real-Time Adjustable Four-Bar Path Generators Using Iterative Learning Control

2004 ◽  
Author(s):  
Hong-Jen Chen ◽  
Richard W. Longman ◽  
Meng-Sang Chew
Keyword(s):  
Control Systems ◽  
Real Time ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Path Generation ◽  
Structural Error ◽  
Four Bar Linkage

Fundamental concepts of Iterative Learning Control (ILC) are applied to path generating problems in mechanisms. As an illustration to such class of problems, an adjustable four-bar linkage is used. The coupler point of a four-bar traces a coupler curve that will in general deviate from the desired coupler path. Except at the precision points, the coupler curve will exhibit some structural error, which is the deviation from the specified curve. The structural error will repeat itself every cycle at exactly the same points over the range of interest. Since ILC is a methodology that was developed to handle similar repetitive errors in control systems, it is believed that it will be well served to apply it to this class of problems. Results show that ILC can be simple to implement, and it is found to be very well suited for such path generation problems.

scholarly journals Multi Objective Simulated Annealing Approach for Facility Layout Design

2018 ◽  
Vol 3 (4) ◽  
pp. 365-380 ◽  
Author(s):  
Safiye Turgay
Keyword(s):  
Simulated Annealing ◽  
Objective Function ◽  
Material Handling ◽  
Simulated Annealing Algorithm ◽  
Facility Layout ◽  
Layout Design ◽  
Local Optima ◽  
Facility Layout Design ◽  
Multi Objective ◽  
Annealing Algorithm

Facility layout design problem considers the departments’ physcial layout design with area requirements in some restrictions such as material handling costs, remoteness and distance requests. Briefly, facility layout problem related to optimization of the layout costs and working conditions. This paper proposes a new multi objective simulated annealing algorithm for solving of the unequal area in layout design. Using of the different objective weights are generated with entropy approach and used in the alternative layout design. Multi objective function takes into the objective function and constraints. The suggested heuristic algorithm used the multi-objective parameters for initialization. Then prefered the entropy approach determines the weight of the objective functions. After the suggested improved simulated annealing approach applied to whole developed model. A multi-objective simulated annealing algorithm is implemented to increase the diversity and reduce the chance of getting layout conditions in local optima.

Generalized Field-Development Optimization With Derivative-Free Procedures

SPE Journal ◽  
2014 ◽  
Vol 19 (05) ◽  
pp. 891-908 ◽  
Author(s):  
Obiajulu J. Isebor ◽  
David Echeverría Ciaurri ◽  
Louis J. Durlofsky
Keyword(s):  
Computational Cost ◽  
Optimization Method ◽  
Optimal Number ◽  
Global Search ◽  
Search Method ◽  
Pattern Search ◽  
Mixed Integer ◽  
Categorical Variables ◽  
Field Development ◽  
Derivative Free

Summary The optimization of general oilfield development problems is considered. Techniques are presented to simultaneously determine the optimal number and type of new wells, the sequence in which they should be drilled, and their corresponding locations and (time-varying) controls. The optimization is posed as a mixed-integer nonlinear programming (MINLP) problem and involves categorical, integer-valued, and real-valued variables. The formulation handles bound, linear, and nonlinear constraints, with the latter treated with filter-based techniques. Noninvasive derivative-free approaches are applied for the optimizations. Methods considered include branch and bound (B&B), a rigorous global-search procedure that requires the relaxation of the categorical variables; mesh adaptive direct search (MADS), a local pattern-search method; particle swarm optimization (PSO), a heuristic global-search method; and a PSO-MADS hybrid. Four example cases involving channelized-reservoir models are presented. The recently developed PSO-MADS hybrid is shown to consistently outperform the standalone MADS and PSO procedures. In the two cases in which B&B is applied, the heuristic PSO-MADS approach is shown to give comparable solutions but at a much lower computational cost. This is significant because B&B provides a systematic search in the categorical variables. We conclude that, although it is demanding in terms of computation, the methodology presented here, with PSO-MADS as the core optimization method, appears to be applicable for realistic reservoir development and management.

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