A Novel Synthesis Method for Three-Position Motion Generation With Planar Four-Bar Mechanisms

2012 ◽  
Author(s):  
Jianyou Han ◽  
Tong Yang
Keyword(s):  
Synthesis Method ◽  
Solution Space ◽  
The Other ◽  
Motion Generation ◽  
Numerical Examples ◽  
Novel Synthesis ◽  
Generation Problem

This paper deals with the three-position motion generation problem with two specific grounded link lengths. There are two infinities of solutions for selecting the two links on the derived contours of the link lengths. These points on the contours are circle points or center points. After one half of the basic four bar had been selected on the contour, two infinities of solutions remained. These solutions can be mapped in a plane to determine where the particular types of mechanisms occur. Furthermore after one half of the basic four bar had been selected on the contour, one infinity of solutions still remained on the other contour. This indicates two infinities of solutions are still remained for the two given link lengths. These contours can be displayed in the solution space in which the motion generation is defined. With these significant useful information the better mechanism can be obtained, which satisfies more design conditions. Expressions of the contours are derived. Two numerical examples are used for illustration, but the results can be applied to any three-position motion generation problem.

Finite Position Synthesis of 5-SS Platform Linkages Including Partially Specified Joint Locations

2017 ◽  
Author(s):  
Xin Ge ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Linear Structure ◽  
Motion Generation ◽  
Numerical Examples ◽  
Moving Points ◽  
Unified Algorithm ◽  
Moving Platform ◽  
Position Synthesis ◽  
Partial Specification ◽  
Generation Problem ◽  
Novel Algorithm

A 5-SS platform linkage generates a one-degree-of-freedom motion of a moving platform such that each of five moving points on the platform is constrained on a sphere, or in its degenerated case, on a plane. It has been well established a 5-SS platform linkage can be made to guide though seven positions exactly. This paper investigates the cases when the number of given positions are less than seven that allows for partial specification of locations of the moving points. A recently developed novel algorithm with linear structure in the design equations has been extended for the solution of the problem. The formulation of this expanded motion generation problem unifies the treatment of the input positions and constraints on the moving and fixed joints associated with the 5-SS platform linkage. Numerical examples are provided to show the effectiveness of the unified algorithm.

A Novel Synthesis Method for Nonperiodic Function Generation of an RCCC Mechanism

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Wenrui Liu ◽  
Jianwei Sun ◽  
Bangcheng Zhang ◽  
Jinkui Chu
Keyword(s):  
Synthesis Method ◽  
Normalization Method ◽  
Numerical Examples ◽  
Function Generation ◽  
Novel Synthesis ◽  
Feature Parameter ◽  
Design Requirements ◽  
Mechanism Function ◽  
Relationship Of ◽  
The Relationship

In this paper, the nonperiodic function synthesis of an RCCC mechanism is presented using a wavelet feature parameter (WFP) method. The output function and the sliding displacement of the RCCC mechanism are described by the wavelet approximate and wavelet details. Based on the relationship of wavelet details of the sliding displacement and its scaling, a normalization method for wavelet details of the sliding displacement is presented. The influence of proportional scaling of the linkage lengths is eliminated. An adaptive database is established. The problem of nonperiodic design requirements of RCCC mechanism function synthesis is solved. To demonstrate the feasibility of this method, two numerical examples are proposed. Based on the nonperiodic design requirements, the RCCC mechanisms are designed and simulated using matlab and catia software. The results show that the method proposed is effective for nonperiodic function generation of the RCCC mechanism with multiple positions.

Characteristic Surfaces for Three-Position Motion Generation With Planar Four-Bar Mechanisms

1987 ◽  
Vol 109 (2) ◽  
pp. 183-188
Author(s):  
C. R. Barker ◽  
J. Baumann
Keyword(s):  
Solution Space ◽  
Final Solution ◽  
Motion Generation ◽  
Numerical Example ◽  
All Solutions ◽  
Cartesian Plane ◽  
The Relationship ◽  
Generation Problem

This paper considers the relationship between the three-position motion generation problem and the solution space for planar four-bar mechanisms. After one half of the basic four bar had been selected, two infinities of solutions still remained. These solutions are mapped in a plane to determine where the particular types of mechanisms occur. A contour is then generated in the mapping plane which joins together all solutions which share a common characteristic in regard to their link lengths. This same contour can be displayed in the solution space and in the Cartesian plane in which the motion generation is defined. Significant useful information to assist in selecting the final solution is obtained. A numerical example is used for illustration, but the results can be applied to any three-position motion generation problem.

A Multi-Product Newsvendor Problem with Budget and Loss Constraints

2015 ◽  
Vol 14 (05) ◽  
pp. 1093-1110 ◽  
Author(s):  
Yanju Zhou ◽  
Xiaohong Chen ◽  
Xuanhua Xu ◽  
Changjun Yu
Keyword(s):  
Problem Solving ◽  
Marginal Utility ◽  
Solution Space ◽  
Budget Constraint ◽  
Newsvendor Problem ◽  
The Other ◽  
Threshold Values ◽  
Nonlinear Constraint ◽  
Numerical Examples ◽  
Approximate Approach

The solution space of a multi-product newsvendor problem (MPNP) with two constraints is analyzed and divided by four cases. One constraint is a loss constraint, which is nonlinear and has the integral symbol, while the other is a budget constraint. The threshold values of different solution regions are calculated and the corresponding solving methods for each case are provided, reducing the complexity of problem solving. The paper suggests the loss-based marginal utility deleting method solves non-negative constraint problems, and the linear approximate approach deals with nonlinear constraint optimal problems with an integral symbol in the model. Numerical examples are given, showing that the solving approach is more effective.

Natural Motion Generation of Biped Locomotion Robot using Hierarchical Evolutionary Algorithm in the Various Environments

1997 ◽  
Vol 9 (6) ◽  
pp. 496-502
Author(s):  
Takemasa Arakawa ◽  
◽  
Toshio Fukuda
Keyword(s):  
Evolutionary Algorithm ◽  
Energy Minimization ◽  
Dynamic Effect ◽  
The Other ◽  
Human Walking ◽  
Motion Trajectory ◽  
Biped Locomotion ◽  
Motion Generation ◽  
Natural Motion ◽  
Generation Problem

The purpose of this research is to generate natural motion in a biped locomotion robot, like a human walking in various environments. In this paper, we report on biped locomotion robots. We apply a hierarchical evolutionary algorithm in order to generate the trajectory of a biped locomotion robot through energy optimization, and attempt to generate a more natural motion by considering the dynamic effect. The hierarchical evolutionary algorithm consists of two layers: one is the GA layer which minimizes the total energy of all the actuators, and the other is the EP layer which optimizes the interpolated configuration of the biped locomotion robot. Then we formulate a trajectory generation problem as an energy minimization problem and we apply the hierarchical evolutionary algorithm. Furthermore, we build a trial biped locomotion robot which has 13 joints and is made of aluminum. Finally, we confirm that the calculated natural motion trajectory can be applied successfully to practical biped locomotion.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

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