A unified synthesis method for timing-path generation of planar four-bar linkages

2021 ◽  
pp. 1-18
Author(s):  
Rui Wu ◽  
Ruiqin Li ◽  
Hailong Liang ◽  
Fengping Ning
Keyword(s):  
Synthesis Method ◽  
Path Generation

Optimum Synthesis of Planar Mechanisms for Path Generation Based on a Combined Discrete Fourier Descriptor

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Wen-Yi Lin
Keyword(s):  
Synthesis Method ◽  
Optimization Method ◽  
Path Generation ◽  
Fourier Descriptor ◽  
Planar Mechanisms ◽  
Two Phase ◽  
Phase Synthesis ◽  
Optimum Synthesis ◽  
Centroid Distance ◽  
The One

A two-phase synthesis method is described, which is capable of solving quite challenging path generation problems. A combined discrete Fourier descriptor (FD) is proposed for shape optimization, and a geometric-based approach is used for the scale–rotation–translation synthesis. The combined discrete FD comprises three shape signatures, i.e., complex coordinates (CCs), centroid distance (CD), and triangular centroid area (TCA), which can capture greater similarity of shape. The genetic algorithm–differential evolution (GA–DE) optimization method is used to solve the optimization problem. The proposed two-phase synthesis method, based on the combined discrete FD, successfully solves the challenging path generation problems with a relatively small number of function evaluations. A more accurate path shape can be obtained using the combined FD than the one-phase synthesis method. The obtained coupler curves approximate the desired paths quite well.

scholarly journals Homotopy Directed Optimization to Design a Six-Bar Linkage for a Lower Limb With a Natural Ankle Trajectory

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Brandon Y. Tsuge ◽  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Lower Limb ◽  
Polynomial System ◽  
Optimization Technique ◽  
Synthesis Method ◽  
Optimization Techniques ◽  
Path Generation ◽  
Optimization Strategy ◽  
Direct Solution ◽  
New Formulation ◽  
Path Synthesis

This paper presents a synthesis method for the Stephenson III six-bar linkage that combines the direct solution of the synthesis equations with an optimization strategy to achieve increased performance for path generation. The path synthesis equations for a six-bar linkage can reach as many as 15 points on a curve; however, the degree of the polynomial system is 1046. In order to increase the number of accuracy points and decrease the complexity of the synthesis equations, a new formulation is used that combines 11 point synthesis with optimization techniques to obtain a six-bar linkage that minimizes the distance to 60 accuracy points. This homotopy directed optimization technique is demonstrated by obtaining a Stephenson III six-bar linkage that achieves a specified gait trajectory.

Synthesis of Rigid-Body Guidance Mechanism with Path and Pose Generation Independently

2014 ◽  
Vol 619 ◽  
pp. 115-120 ◽  
Author(s):  
Jing Shuai Liu ◽  
Song Lin
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Practical Method ◽  
Path Generation ◽  
Mechanism Synthesis ◽  
Link Mechanism ◽  
Combination Principle

This paper proposes a practical method for the synthesis of rigid-body guidance mechanism by dividing the guidance task into path and pose generation independently. As a first step, based on the mechanism combination principle, a basic four-bar mechanism for path generation is synthesized and a binary-link is combined to the mechanism for achieving the execute link’s poses, then the potential kinematic chain with ability to realize the desired coupler poses is selected from all of the combination possibilities. And then a strategy by fixing a Cam to the basic four-bar mechanism to control the linkage poses is also proposed. Finally, the Cam’s profile is synthesized and the combined cam-link mechanism is able to guide the coupler through all desired linkage positions. One example is presented to validate the proposed guidance mechanism synthesis method.

scholarly journals Mixed synthesis method of motion and path of planar four-bar linkages

2021 ◽  
Vol 12 (1) ◽  
pp. 443-449
Author(s):  
Rui Wu ◽  
Ruiqin Li ◽  
Hailong Liang ◽  
Fengping Ning
Keyword(s):  
Synthesis Method ◽  
Equation System ◽  
Optimal Combination ◽  
Synthesis Problem ◽  
Path Generation ◽  
Motion Synthesis ◽  
Filtering Algorithm ◽  
Four Bar Linkage

Abstract. The mixed synthesis of motion and path generation, which is also known as the Alt–Burmester problem, is an attractive problem for study. However, such a problem for the four-bar linkages which possess more than M poses (M>5) and mixed N path points has not been well-solved. In this work, a mixed synthesis method is developed for planar four-bar linkages to cope with the above problem. The developed method can quickly select an optimal combination that contains five poses and N points by using the conic filtering algorithm, which is based on the similar characteristics of the value and direction between the conic and coupler curves in a certain neighborhood. Next, the selected five poses are substituted into a simplified equation system of motion synthesis which includes four equations and four variables to solve the parameters of the planar four-bar linkage. Finally, a case is provided to validate the effectiveness of the developed method in the mixed synthesis problem.

Synthesis of a Spatial RRSS Mechanism for Path Generation Using the Numerical Atlas Method

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Wenrui Liu ◽  
Jianwei Sun ◽  
Jinkui Chu
Keyword(s):  
Rotation Angle ◽  
Synthesis Method ◽  
Path Generation ◽  
Feature Parameters ◽  
Atlas Method ◽  
Path Synthesis ◽  
The Mathematical Model ◽  
The Relationship ◽  
Generation Problem ◽  
Actual Size

Abstract An open path synthesis method for a spatial revolute-revolute-spherical-spherical (RRSS) mechanism is presented in this paper. The mathematical model for the trajectory curve is established. The characteristics of an RRSS mechanism in a standard installation position are revealed: the projection points of the coupler curve on the Oxy plane rotate by the corresponding input angles around the z-axis, and the generated points lie on an ellipse. Based on this finding, a 17-dimensional path generation problem can be translated into two lower-dimensional matching recognition problems and one actual size and installation position calculation problem. The path generation can be achieved by three steps. First, a database of four dimensional rotation angle parameters is established. By comparing the similarities between the mechanism feature curve of the prescribed open curve and its corresponding mechanism feature ellipse (MFE), the angles of installation, the initial angle of the input link, and the elliptic feature parameters of the desired RRSS mechanism can be approximately determined. Then, a 13-dimensional dynamic self-adapting numerical atlas database is established, which contains six basic dimensional types (BDTs) and seven wavelet feature parameters, and the BDTs of the desired RRSS mechanism are obtained. Finally, based on the relationship between the MFE of the prescribed curve and the BDTs of the desired RRSS mechanism, the calculation models for the actual link lengths and installation positions of the desired RRSS mechanism were established. Three examples are presented in this paper.

Optimal Synthesis of Mechanisms for Path Generation Using Refined Numerical Representation Based Model and AIS Based Searching Method

2004 ◽  
Vol 127 (4) ◽  
pp. 688-691 ◽  
Author(s):  
Yong Liu ◽  
Renbin Xiao
Keyword(s):  
Synthesis Method ◽  
Optimal Synthesis ◽  
Numerical Representation ◽  
Path Generation ◽  
Artificial Immune ◽  
Planar Mechanisms ◽  
Artificial Immune Network ◽  
Synthesis Of Mechanisms ◽  
Initial Sampling ◽  
Searching Method

This paper presents an optimal synthesis method for path generation of planar mechanisms, in which a new path-description method named refined numerical representation is proposed to define the object function of the optimization model for path generation, and then the artificial immune network searching method is introduced to search candidate solutions. As a result, desired mechanisms can be generated independent of the scale, rotation, and translation transformation as well as sampling uniformity of initial sampling points. Experiment results demonstrate the effectiveness of the approach.

On the Solution of Multi-Precision-Point Path Synthesis of Planar Four-Bar Mechanisms Based on Solution Region Methodology

2018 ◽  
Author(s):  
Jianyou Han ◽  
Wupeng Liu
Keyword(s):  
Infinite Number ◽  
Feasible Solution ◽  
Synthesis Method ◽  
Path Generation ◽  
Number Of Solutions ◽  
Region Method ◽  
Different Types ◽  
Design Requirements ◽  
Solution Region ◽  
Path Synthesis

In this paper, the solution region synthesis method for multi-precision-point path synthesis of planar four-bar mechanisms is presented. The solution region method is to represent an infinite number of mechanism solutions in a plane, in which the x-coordinate and the y-coordinate of the plane are both taken as the concerned parameters of the mechanisms. Then the feature curves of the mechanisms can be expressed in the plane. Firstly, the synthesis equations for the multi-precision-point path synthesis of planar four-bar mechanisms are established. Then according to the proposed defect judgment method, the defective solutions are eliminated, and an infinite number of solutions without defects are obtained. After considering and imposing design requirements, the linkages of different types and different curve types are represented in the solution region. Finally, Taking the path generation of eight points as the example, the methodology of establishing the solution region and the feasible solution region are presented, and the synthesis results are illustrated.

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