Evolutionary Design of Planar Kinematic Chains

1998 ◽  
Author(s):  
David R. Nielsen ◽  
Kazem Kazerounian
Keyword(s):  
Genetic Algorithm ◽  
Kinematic Chain ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Design Flexibility ◽  
Novel Approach ◽  
Chain Link ◽  
Synthesis Of Mechanisms ◽  
New Ideas ◽  
Crossover And Mutation

Abstract A procedure is developed to optimize planar mechanism type. A Genetic Algorithm is used to cycle populations of kinematic chain link adjacency matrices, through selection, crossover, and mutation. During this optimization, fit kinematic chains survive while unfit kinematic chains do not. Upon convergence, synthesized kinematic chains of high fitness remain. This technique was lead to be called the Genetic Algorithm for Type Synthesis (GATS). GATS introduces four new ideas for the type synthesis of mechanisms. First, it does not permute all possible kinematic chains. It searches for the best kinematic chains depending on a designer’s specifications. Second, larger size mechanisms can be generated because of the genetic algorithm’s evolutionary naturalness. Third, a novel approach was applied to genetic algorithms to allow the encodings to mutate in size. This allowed for addition or elimination of links in kinematic chains during evolution. Forth, a new property was deduced from mechanism topography that describes the mechanism design flexibility.

An Algorithm for Automatic Sketching of Planar Kinematic Chains

1985 ◽  
Vol 107 (1) ◽  
pp. 106-111 ◽  
Author(s):  
D. G. Olson ◽  
T. R. Thompson ◽  
D. R. Riley ◽  
A. G. Erdman
Keyword(s):  
Graph Theory ◽  
Line Graph ◽  
Kinematic Chain ◽  
Graph Representation ◽  
Synthesis Process ◽  
Line Graphs ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Computer Aided

One of the problems encountered in attempting to computerize type synthesis of mechanisms is that of automatically generating a computer graphics display of candidate kinematic chains or mechanisms. This paper presents the development of a computer algorithm for automatic sketching of kinematic chains as part of the computer-aided type synthesis process. Utilizing concepts from graph theory, it can be shown that a sketch of a kinematic chain can be obtained from its graph representation by simply transforming the graph into its line graph, and then sketching the line graph. The fundamentals of graph theory as they relate to the study of mechanisms are reviewed. Some new observations are made relating to graphs and their corresponding line graphs, and a novel procedure for transforming the graph into its line graph is presented. This is the basis of a sketching algorithm which is illustrated by computer-generated examples.

Structure Types Synthesis of Multiloop Spatial Kinematic Chains With General Variable Constraints

1998 ◽  
Author(s):  
Yufeng Luo ◽  
Tingli Yang ◽  
Ali Seireg
Keyword(s):  
Kinematic Chain ◽  
Structure Type ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Systematic Procedure ◽  
Independent Loops

Abstract A systematic procedure is presented for the structure type synthesis of multiloop spatial kinematic chains with general variable constraints in this paper. The parameters and the structure types of the contracted graphs and the branch chains used to synthesize such kinematic chains are given for kinematic chains with up to four independent loops. The assignments for the constraints values of all the loops in a kinematic chain are discussed. Using these as the basis, the structure types of the multiloop spatial kinematic chains with hybrid constraints could be synthesized.

A Genetic Algorithm Based Procedure for Extracting Optimal Solutions From a Morphological Chart

2007 ◽  
Author(s):  
Santosh Tiwari ◽  
Joshua Summers ◽  
Georges Fadel
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problem ◽  
Mathematical Representation ◽  
Optimal Solutions ◽  
Proof Of Concept ◽  
Optimization Framework ◽  
Mutation Operators ◽  
Novel Approach ◽  
Morphological Chart ◽  
Crossover And Mutation

A novel approach using a genetic algorithm is presented for extracting globally satisfycing (Pareto optimal) solutions from a morphological chart where the evaluation and combination of “means to sub-functions” is modeled as a combinatorial multi-objective optimization problem. A fast and robust genetic algorithm is developed to solve the resulting optimization problem. Customized crossover and mutation operators specifically tailored to solve the combinatorial optimization problem are discussed. A proof-of-concept simulation on a practical design problem is presented. The described genetic algorithm incorporates features to prevent redundant evaluation of identical solutions and a method for handling of the compatibility matrix (feasible/infeasible combinations) and addressing desirable/undesirable combinations. The proposed approach is limited by its reliance on the quantifiable metrics for evaluating the objectives and the existence of a mathematical representation of the combined solutions. The optimization framework is designed to be a scalable and flexible procedure which can be easily modified to accommodate a wide variety of design methods that are based on the morphological chart.

A Survey of One Class of 7-Jointed Serially Connected Robots: Type-Synthesis to Obtain Controllably Dexterous Workspace

1989 ◽  
Vol 111 (2) ◽  
pp. 163-175 ◽  
Author(s):  
J. K. Davidson
Keyword(s):  
Screw Theory ◽  
Kinematic Chain ◽  
Synthesis Process ◽  
Geometric Description ◽  
Type Synthesis ◽  
End Effector ◽  
Identification Process ◽  
Kinematic Chains ◽  
Five Axes

A type-synthesis process, which is based on screw theory and geometry, is developed to identify certain robots, each of which can provide controllably dexterous workspace of a tool-point. The identification process is confined to only those robots which control the motion of the end-effector with seven series-connected joints, the axes for the outermost three of which are concurrent. Forty six types of robots are so identified, and, for each, the results are (i) a suitable kinematic chain for the arm and (ii) suitable angle-dimensions for the links of the arm, where the angle-choices are limited to the values 0, ± π/2, and π. A geometric description of the dominant function for control is included. The same kinematic chains are surveyed for all possible parallel and right-angle arrangements of adjacent axes in the four links of the arm. Again utilizing screw theory, 160 robots are identified which do not posses full-cycle axis-dependence among some or all of the first five axes.

Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory

2004 ◽  
Vol 126 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Screw Theory ◽  
General Procedure ◽  
Linear Equations ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Small Joint ◽  
Actuated Joints

A method is proposed for the type synthesis of 3-DOF (degree-of-freedom) translational parallel manipulators (TPMs) based on screw theory. The wrench systems of a translational parallel kinematic chain (TPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of TPMs. The type synthesis of legs for TPKCs, the type synthesis of TPKCs as well as the selection of actuated joints of TPMs are dealt with in sequence. An approach to derive the full-cycle mobility conditions for legs for TPKCs is proposed based on screw theory and the displacement analysis of serial kinematic chains undergoing small joint motions. In addition to the TPKCs proposed in the literature, TPKCs with inactive joints are synthesized. The phenomenon of dependent joint groups in a TPKC is revealed systematically. The validity condition of actuated joints of TPMs is also proposed. Finally, linear TPMs, which are TPMs whose forward displacement analysis can be performed by solving a set of linear equations, are also revealed.

Control of Closed Kinematic Chains Using A Singularly Perturbed Dynamics Model

2005 ◽  
Vol 128 (1) ◽  
pp. 142-151 ◽  
Author(s):  
Zhiyong Wang ◽  
Fathi H. Ghorbel
Keyword(s):  
Kinematic Chain ◽  
Perturbation Parameter ◽  
Parallel Robot ◽  
Differential Algebraic Equations ◽  
Singularly Perturbed ◽  
Algebraic Equations ◽  
Kinematic Chains ◽  
Novel Approach ◽  
Lyapunov Function Method ◽  
Perturbed Model

In this paper, we propose a novel approach to the control of closed kinematic chains (CKCs). This method is based on a recently developed singularly perturbed model for CKCs. Conventionally, the dynamics of CKCs are described by differential-algebraic equations (DAEs). Our approach transfers the control of the original DAE system to the control of an artificially created singularly perturbed system in which the slow dynamics corresponds to the original DAE when the perturbation parameter tends to zero. Compared to control schemes that rely on solving nonlinear algebraic constraint equations, the proposed method uses an ordinary differential equation (ODE) solver to obtain the dependent coordinates, hence, eliminates the need for Newton-type iterations and is amenable to real-time implementation. The composite Lyapunov function method is used to show that the closed-loop system, when controlled by typical open kinematic chain schemes, achieves asymptotic trajectory tracking. Simulations and experimental results on a parallel robot, the Rice planar Delta robot, are also presented to illustrate the efficacy of our method.

The Compound Union Theory and Method of Type Synthesis of Geared Linkage Kinematic Chains

2000 ◽  
Author(s):  
Chuan-He Liu ◽  
Ting-Li Yang
Keyword(s):  
Kinematic Chain ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
New Concepts ◽  
Type Code

Abstract The compound union theory and method of type synthesis of geared linkage kinematic chains is developed in this paper. The theory includes the new concepts, such as the basic geared kinematic chain, the compound union and the type code etc., the new constitution principle of geared linkage kinematic chains and four new theorems that are essential for type synthesis of geared linkage kinematic chains. One typical example and its results of the type synthesis are also given. It is proved that the compound union theory and method is systematic, strict, simple, practical and efficient.

Optimization of Different Fitness Functions Using Reproduction, Crossover and Mutation of Genetic Algorithm With Binary Number Scheduling

2021 ◽  
Author(s):  
J PRINCE JEROME CHRISTOPHER ◽  
K LINGADURAI ◽  
G SHANKAR
Keyword(s):  
Genetic Algorithm ◽  
Fitness Function ◽  
Number System ◽  
Binary Number ◽  
Genetic Operators ◽  
Fitness Functions ◽  
Decimal Number ◽  
Novel Approach ◽  
Operator Mutation ◽  
Crossover And Mutation

Abstract Genetic algorithms are search algorithms based on the mechanics of natural selection and natural genetics. In this paper, we investigate a novel approach to the binary coded testing process based on a genetic algorithm. This paper consists of two parts. Thefirst part addresses the problem in the traditional way of using the decimal number system to define the fitness function to study the variations of counts and the variations of probability against the fitness functions. Second, the initialpopulationsare defined using binary coded digits (genes). For the evaluation of the high fitness function values,three genetic operators, namely, reproduction, crossover and mutation, are randomly used. The results show the importance of the genetic operator, mutation, which yields the peak values for the fitness function based on binary coded numbers performed in a new way.

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