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.

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

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Jianyou Han ◽  
Wupeng Liu
Keyword(s):  
Computer Program ◽  
Infinite Number ◽  
Feasible Solution ◽  
Path Generation ◽  
Characteristic Curves ◽  
Different Types ◽  
Design Requirements ◽  
Solution Region ◽  
Synthesis Methodology ◽  
Path Synthesis

Abstract In this paper, the solution region synthesis methodology (abbreviated as SRSM below) for the eight-precision-point path synthesis of planar four-bar mechanisms is presented. The so-called solution region synthesis methodology represents an infinite number of mechanism solutions in a plane, and the solution region is the area where the mechanism solutions are distributed in the plane. The x-coordinate and the y-coordinate of the plane are both taken as the concerned parameters of mechanisms. Furthermore, characteristic curves of mechanisms can be expressed in the plane. In addition, a defect judgment method is proposed, which can be realized in the computer program. The defective solutions can be eliminated efficiently, and the solutions without defects are obtained using the proposed method. After considering and imposing additional design requirements, the linkages of different types and different curve shapes are classified in the solution region. Finally, taking the path generation for 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.

Solution Region Synthesis Method for Six Positions Synthesis of 5-SS Spatial Linkage

2016 ◽  
Author(s):  
Jianyou Han ◽  
Guangzhen Cui ◽  
Junjie Hu
Keyword(s):  
Systematic Approach ◽  
Synthesis Method ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Region Method ◽  
Solution Region ◽  
The One

This paper presents a systematic approach to perform the dimensional synthesis of spatial 5-SS (spherical-spherical) link-ages for six specified positions of the end-effector. The dimensional synthesis equations for a SS link are formulated and solved. We synthesize five SS links to connect the base and end-effector, and then obtain the one-degree-of-freedom spatial 5-SS linkage, which can move through six specified positions. We use the solution region method to build the planar solution region expressing the linkages, due to there are infinite linkages for six positions synthesis. It is convenient to select the linkages from the solution region for designers. The applicability of the proposed approach is illustrated by the example.

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.

A Synthesis and Optimal Method for Straight Line Mechanism with Burmester Points

2011 ◽  
Vol 199-200 ◽  
pp. 1240-1243 ◽  
Author(s):  
Lai Rong Yin ◽  
Jian You Han ◽  
Tong Yang
Keyword(s):  
Infinite Number ◽  
Line Length ◽  
Point Contacts ◽  
Optimal Method ◽  
Region Method ◽  
Straight Line ◽  
Solution Region ◽  
Straight Line Mechanism ◽  
Ball Point

When a Burmester point coincides with the Ball point at the inflection circle pole, given a fixed joint and the point, which is on the expecting straight-line and direction can synthesize an infinite number of mechanisms with coupler curve having a five-point contacts with its tangent, namely, Burmester point. Any displacement is corresponding to three four-bar straight-line linkages with the synthesis formulations given. The property charts, which include the bar ratio, the sum of bars, the relative straight-line length, mechanism types, and so on, are drawn by developing a mechanism software based on vc++6.0 with the solution region method. So the users can find out the involved linkages information intuitively, and also the aimlessness in choosing optimal mechanisms is avoided effectively.

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.

Solution region synthesis methodology of planar eight-bar linkage for four specified positions of a 4R chain

2020 ◽  
Vol 234 (24) ◽  
pp. 4813-4826
Author(s):  
Guangzhen Cui ◽  
Jianyou Han ◽  
Yanqiu Xiao ◽  
Caidong Wang
Keyword(s):  
Feasible Solution ◽  
Solution Curve ◽  
Defect Identification ◽  
Different Types ◽  
Practical Engineering ◽  
Solution Region ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

The solution region methodology for solving the problem of four-bar linkage synthesis with four specified positions was extended to solve the problem of eight-bar linkage synthesis. The processes to build solution regions for synthesizing different types of eight-bar linkages are described, and the methods of building solution regions are divided into five types. First, the synthesis equation is derived, and the curve expressed by the synthesis equation is called the solution curve. Second, the process to build the spatial solution regions from the solution curves is detailed, and a new defect identification method is developed for building the spatial feasible solution region, which is a set of linkage solutions meeting four positions and excluding defects. Finally, linkage solutions that do not meet practical engineering requirements are eliminated from the spatial feasible solution region to obtain the useful spatial solution region. The examples demonstrate the feasibility of the proposed method. The proposed synthesis methodology is simple and easy to program, and provides reference for four specified position synthesis of other multi-bar linkages.

Free-surface flows with two stagnation points

1996 ◽  
Vol 324 ◽  
pp. 393-406 ◽  
Author(s):  
J.-M. Vanden-Broeck ◽  
F. Dias
Keyword(s):  
Free Surface ◽  
Infinite Number ◽  
Wave Breaking ◽  
Free Surface Flows ◽  
Number Of Solutions ◽  
Surface Flows ◽  
Stagnation Points ◽  
Surface Profiles ◽  
Countably Infinite

Symmetric suction flows are computed. The flows are free-surface flows with two stagnation points. The configuration is related to the modelling of wave breaking at the bow of a ship. It is shown that there is a countably infinite number of solutions and that the free-surface profiles are characterized by waves.

A Proposed Method to Group the Solutions From Dimensional Synthesis: Planar Triads for Six Precision Position

1992 ◽  
Author(s):  
Xiancheng Lu ◽  
Chuen-Sen Lin
Keyword(s):  
Infinite Number ◽  
Numerical Solutions ◽  
Angular Displacement ◽  
Dimensional Synthesis ◽  
Number Of Solutions ◽  
Jacobian Matrices ◽  
Design Task ◽  
Numerical Examples ◽  
Computer Automation ◽  
Constraint Sets

Abstract In this paper, a method has been proposed to group into six sets the infinite number of solutions from dimensional synthesis of planar triads for six precision positions. The proposed method reveals the relationships between the different configurations of the compatibility linkage and the sets of numerical solutions from dimensional synthesis. By checking the determinant signs and the contunities of values of the sub-Jacobian matrices and their derivatives with respect to the independent angular displacement for all constraint sets in the compatibility linkage, it enables the computer to identify and group the synthesized solutions. Numerical examples have been given to verify the applicability of this method. Six sets of the partial triad Burmester curves have been plotted based on grouped solutions. Suitable solutions can be easily found from the partial triad Burmester curves and utilized for the prescribed design task. This method provides a useful tool to group the dimensional synthesis solutions and enhances the computer automation in the design of linkage mechanisms.

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