On Adjustable Planar Four-Bar Motion Generation With Order, Branch and Circuit Defect Rectification

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Qiong Shen ◽  
Wen-Tzong Lee ◽  
Kevin Russell
Keyword(s):  
Nonlinear Equation ◽  
Objective Function ◽  
Inequality Constraints ◽  
Equation System ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Order Branch ◽  
Circuit Defects ◽  
Displacement Model ◽  
Defect Elimination

This work is an incremental extension of adjustable planar four-bar kinematic synthesis theory to consider not only synthesis, but also the elimination of the defects inherent in synthesis. A nonlinear equation system for moving pivot-adjustable planar four-bar motion generation that includes constraints for order defect, branch defect and circuit defect elimination is presented in this work. In the objective function of the equation system, the error between the prescribed and achieved precision positions is minimized. The equation system includes inequality constraints to eliminate order defects and branch defects. The equation system also includes a complete planar four-bar displacement model to eliminate circuit defects.

On RCCC Linkage Motion Generation With Defect Elimination for an Indefinite Number of Precision Positions

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Wen-Tzong Lee ◽  
Jose Cosme ◽  
Kevin Russell
Keyword(s):  
Optimization Model ◽  
Software Package ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Analysis Software ◽  
Order Branch ◽  
Indefinite Number ◽  
Cylindrical Joint ◽  
Circuit Defects ◽  
Defect Elimination

A general optimization model for the dimensional synthesis of defect-free revolute-cylindrical-cylindrical-cylindrical joint (or RCCC) motion generators is formulated and demonstrated in this work. With this optimization model, the RCCC dimensions required to approximate an indefinite number of precision positions are calculated. The model includes constraints to eliminate order branch and circuit defects—defects that are common in dyad-based dimensional synthesis. Therefore, the novelty of this work is the development of a general optimization model for RCCC motion generation for an indefinite number of precision positions that simultaneously considers order, branch, and circuit defect elimination. This work conveys both the benefits and drawbacks realized when implementing the optimization model on a personal computer using the commercial mathematical analysis software package matlab.

scholarly journals Optimal Path Analysis for Solving Nonlinear Equations with Finite Local Error

2022 ◽  
Vol 16 ◽  
pp. 94-104
Author(s):  
Xiaoxiao Ma ◽  
Xiaojuan Chen
Keyword(s):  
Nonlinear Equation ◽  
Path Analysis ◽  
Objective Function ◽  
Nonlinear Equations ◽  
Optimal Path ◽  
Optimal Solution ◽  
Equation System ◽  
Local Error ◽  
Analysis Method ◽  
Long Time

Because the traditional method of solving nonlinear equations takes a long time, an optimal path analysis method for solving nonlinear equations with limited local error is designed. Firstly, according to the finite condition of local error, the optimization objective function of nonlinear equations is established. Secondly, set the constraints of the objective function, solve the optimal solution of the nonlinear equation under the condition of limited local error, and obtain the optimal path of the nonlinear equation system. Finally, experiments show that the optimal path analysis method for solving nonlinear equations with limited local error takes less time than other methods, and can be effectively applied to practice

On the evaluation of a general model for optimum revolute cylindrical cylindrical cylindrical path generation

2018 ◽  
Vol 42 (2) ◽  
pp. 156-163
Author(s):  
Wen-Tzong Lee ◽  
Jose Cosme ◽  
Kevin Russell
Keyword(s):  
Personal Computer ◽  
Mathematical Analysis ◽  
Optimization Model ◽  
Software Package ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Analysis Software ◽  
Order Branch ◽  
Circuit Defects ◽  
Defect Elimination

A general optimization model for the dimensional synthesis of defect free revolute cylindrical cylindrical cylindrical (RCCC) joint path generators is formulated, implemented and evaluated in this work. With this optimization model, RCCC dimensions required to approximate precision points are calculated. The model includes constraints to eliminate order, branch and circuit defects, which are common in dyad-based dimensional synthesis. Therefore, the originality of this work is the development of a general optimization model for RCCC path generation that simultaneously considers order, branch, and circuit defect elimination. This work demonstrates both the benefits and drawbacks realized when implementing the optimization model on a personal computer using the commercial mathematical analysis software package Matlab.

Effect of cracks and pitting defects on gear meshing

2012 ◽  
Vol 226 (11) ◽  
pp. 2805-2815 ◽  
Author(s):  
Alfonso Fernandez del Rincon ◽  
Fernando Viadero ◽  
Miguel Iglesias ◽  
Ana de-Juan ◽  
Pablo Garcia ◽  
...  
Keyword(s):  
Finite Element ◽  
Computational Models ◽  
Inequality Constraints ◽  
Variable Stiffness ◽  
Element Model ◽  
Equation System ◽  
Transmission Error ◽  
Computational Effort ◽  
Gear Mesh ◽  
Non Linear

The development of vibration-based condition monitoring techniques, especially those focused on prognosis, requires the development of better computational models that enable the simulation of the vibratory behaviour of mechanical systems. Gear transmission vibrations are governed by the so-called gear mesh frequency and its harmonics, due to the variable stiffness of the meshing process. The fundamental frequency will be modulated by the appearance of defects which modify the meshing features. This study introduces an advanced model to assess the consequences of defects such as cracks and pitting on the meshing stiffness and other related parameters such as load transmission error or load sharing ratio. Meshing forces are computed by imposing the compatibility and complementarity conditions, leading to a non-linear equation system with inequality constraints. The calculation of deformations is subdivided into a global and a local type. The former is approached by a finite element model and the latter via a non-linear Herztian-based formulation. This procedure enables a reduced computational effort, in contrast to conventional finite element models with contact elements. The formulation used to include these defects is described in detail and their consequences are assessed by a quasi-static analysis of a transmission example.

An Improved Harmony Search Algorithm for a Planar Parallel Robot Synthesis

2018 ◽  
Vol 35 ◽  
pp. 185-197
Author(s):  
Badreddine Aboulissane ◽  
Dikra El Haiek ◽  
Larbi El Bakkali
Keyword(s):  
Search Algorithm ◽  
Harmony Search ◽  
Parallel Robot ◽  
Harmony Search Algorithm ◽  
Path Generation ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Design Variables ◽  
Joint Coordinates ◽  
Improved Harmony Search

The objective of kinematic synthesis is to determine the mechanism dimensions such as link lengths, positions or joint coordinates, in order to approximate its output parameters such as link positions, trajectory points, and displacement angles. Kinematic synthesis is classified into three categories: function generation, path generation, and motion generation. This paper is dedicated only to path generation. As the number of trajectory points increases, analytical methods are limited to obtain precisely mechanism solutions. In that case, numerical methods are more efficient to solve such problems. Our study proposes an improved heuristic algorithm applied to four-bar mechanism path-generation. The objective of this work is to find optimum dimensions of the mechanism and minimize the error between the generated trajectory and the desired one, taking into consideration constraints such as: Grashof condition, transmission angle, and design variables constraints. Finally, our results are compared with those found by other evolutionary algorithms in the literature.

scholarly journals Mathematical model for determining rational machining conditions for flat grinding with the wheel periphery on machines with a rectangular table

2018 ◽  
Vol 224 ◽  
pp. 01112
Author(s):  
Dmitriy L. Skuratov ◽  
Dmitriy G. Fedorov ◽  
Dmitriy V. Evdokimov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Linear Inequality ◽  
Inequality Constraints ◽  
Machining Time ◽  
Functional Parameters ◽  
Linear Inequality Constraints ◽  
Machining Quality ◽  
Machining Conditions ◽  
Grinding Operations

A mathematical model is presented for determining the rational machining conditions for flat grinding operations by the rim of a wheel on machines with a rectangular table consisting of a linear objective function and linear inequality constraints. As the objective function, the equation, determining the main machining time, was used. And constraints which are related to the functional parameters and parameters determining the machining quality and the kinematic capabilities of the machine were used as inequality constraints.

A Weighted Flexible Tolerance Algorithm for Constrained Minimization

1975 ◽  
Vol 97 (4) ◽  
pp. 1291-1294 ◽  
Author(s):  
M. A. Townsend ◽  
F. Y. Lam
Keyword(s):  
Objective Function ◽  
Search Algorithm ◽  
Inequality Constraints ◽  
Constrained Minimization ◽  
Rapid Convergence ◽  
Flexible Polyhedron ◽  
Equality And Inequality Constraints ◽  
Direct Search Algorithm ◽  
Tolerance Method ◽  
Nonlinear Equality

A direct search algorithm based upon the flexible tolerance method developed by Paviani and Himmelblau [1] for minimization of a functional subject to nonlinear equality and inequality constraints is proposed and evaluated. The modification incorporates a weighting on the direction of search in which the flexible polyhedron formed orients itself toward the gradient of the objective function (and clings to all active constraints). This is accomplished by weighting the centroid, in the sense of minimization, of the polyhedron with respect to the objective function. A number of problems have been solved satisfactorily by this algorithm, generally with more rapid convergence.

scholarly journals On finding a point in the relative interior of a polyhedral set and degeneracy in geometric programming

1978 ◽  
Vol 20 (4) ◽  
pp. 487-494 ◽  
Author(s):  
T. R. Jefferson ◽  
C. H. Scott
Keyword(s):  
Objective Function ◽  
Geometric Programming ◽  
Dual Problem ◽  
Optimization Theory ◽  
Inequality Constraints ◽  
Linear Constraints ◽  
Relative Interior ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Nonlinear Objective Function

AbstractGeometric programming is now a well-established branch of optimization theory which has its origin in the analysis of posynomial programs. Geometric programming transforms a mathematical program with nonlinear objective function and nonlinear inequality constraints into a dual problem with nonlinear objective function and linear constraints. Although the dual problem is potentially simpler to solve, there are certain computational difficulties to be overcome. The gradient of the dual objective function is not defined for components whose values are zero. Moreover, certain dual variables may be constrained to be zero (geometric programming degeneracy).To resolve these problems, a means to find a solution in the relative interior of a set of linear equalities and inequalities is developed. It is then applied to the analysis of dual geometric programs.

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