Four-Bar Path Generation Synthesis by a Continuation Method

1989 ◽  
Author(s):  
T. Subbian ◽  
D. R. Flugrad
Keyword(s):  
Nonlinear Equations ◽  
Continuation Method ◽  
System Of Nonlinear Equations ◽  
Path Generation ◽  
Four Bar Linkage

Abstract A different approach for the synthesis of four bar planar path generating mechanisms is presented. A continuation method is used to solve the system of nonlinear equations derived for the path generating problem. A brief description of the method is provided followed by the development of equations representing the four bar linkage. The implementation of the method for five position path generation is discussed in detail and the solutions for two examples are presented.

Four-Bar Path Generation Synthesis by a Continuation Method

1991 ◽  
Vol 113 (1) ◽  
pp. 63-69 ◽  
Author(s):  
T. Subbian ◽  
D. R. Flugrad
Keyword(s):  
Nonlinear Equations ◽  
Continuation Method ◽  
System Of Nonlinear Equations ◽  
Path Generation ◽  
Four Bar Linkage

A different approach for the synthesis of four-bar planar path generating mechanisms is presented. A continuation method is used to solve the system of nonlinear equations derived for the path generating problem. A brief description of the method is provided followed by the development of equations representing the four-bar linkage. The implementation of the method for five position path generation is discussed in detail and the solutions for two examples are presented.

Synthesis of the four-bar linkage as path generation by choosing the shape of the connecting rod

2020 ◽  
Vol 234 (13) ◽  
pp. 2643-2652 ◽  
Author(s):  
SM Varedi-Koulaei ◽  
H Rezagholizadeh
Keyword(s):  
Analytical Solution ◽  
Nonlinear Equations ◽  
Linear Equations ◽  
Solution Process ◽  
Current Method ◽  
Path Generation ◽  
Connecting Rod ◽  
Complicated Process ◽  
Four Bar Linkage ◽  
Analytical Synthesis

This paper presents a method for path generation synthesis of a four-bar linkage that includes both graphical and analytical synthesis and both cases of with and without prescribed timing. The advantage of the proposed method over available techniques is that it is easier and does not need the complicated process (especially in graphical case). In an analytical solution, this method needs the solution of the linear equations, unlike the previous methods, in that they have required the solution of the nonlinear equations. Moreover, in the current method, one can choose the shape of the coupler, while, in other methods, the shape of the coupler is the result of the solution process. The proposed algorithm can be used for path generation synthesizing of a four-bar linkage for three precision points.

Real Continuation Method and its Application in Kinematic Synthesis

2000 ◽  
Author(s):  
Liu Anxin ◽  
Yang Tingli
Keyword(s):  
High Efficiency ◽  
Continuation Method ◽  
Linear Equations ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Real Solutions ◽  
Non Linear ◽  
Four Bar Linkage ◽  
Non Linear Equations

Abstract Real continuation method for finding real solutions to non-linear equations is proposed. Synthesis of planar four-bar linkage for path generation with nine precision points is studied using this method. The proposed method has high efficiency and can best be used for solving synthesis problems.

scholarly journals Modifications of the continuation method for the solution of systems of nonlinear equations

1979 ◽  
Vol 2 (2) ◽  
pp. 299-308
Author(s):  
G. R. Lindfield ◽  
D. C. Simpson
Keyword(s):  
Nonlinear Equations ◽  
Continuation Method ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Modified Method ◽  
Wide Range

Modifications are proposed to the Davidenko-Broyden algorithm for the solution of a system of nonlinear equations. The aim of the modifications is to reduce the overall number of function evaluations by limiting the number of function evaluations for any one subproblem. To do this alterations are made to the strategy used in determining the subproblems to be solved. The modifications are compared with other methods for a wide range of test problems, and are shown to significantly reduce the number of function evaluations for the difficult problems. For the easier problems the modified method is equivalent to the Davidenko-Broyden algorithm.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

Synthesis and Balancing of Cam-Modulated Linkages

1987 ◽  
Author(s):  
P. Pracht ◽  
P. Minotti ◽  
M. Dahan
Keyword(s):  
Systematic Approach ◽  
Kinematic Chain ◽  
Path Generation ◽  
Industrial Manipulator ◽  
High Speeds ◽  
Structural Error ◽  
Mass Balancing ◽  
Four Bar Linkage ◽  
Robotic Applications ◽  
Class Of Functions

Abstract Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

Eliminating Structural Error in Real-Time Adjustable Four-Bar Path Generators Using Iterative Learning Control

2004 ◽  
Author(s):  
Hong-Jen Chen ◽  
Richard W. Longman ◽  
Meng-Sang Chew
Keyword(s):  
Control Systems ◽  
Real Time ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Path Generation ◽  
Structural Error ◽  
Four Bar Linkage

Fundamental concepts of Iterative Learning Control (ILC) are applied to path generating problems in mechanisms. As an illustration to such class of problems, an adjustable four-bar linkage is used. The coupler point of a four-bar traces a coupler curve that will in general deviate from the desired coupler path. Except at the precision points, the coupler curve will exhibit some structural error, which is the deviation from the specified curve. The structural error will repeat itself every cycle at exactly the same points over the range of interest. Since ILC is a methodology that was developed to handle similar repetitive errors in control systems, it is believed that it will be well served to apply it to this class of problems. Results show that ILC can be simple to implement, and it is found to be very well suited for such path generation problems.

scholarly journals Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012046
Author(s):  
Nikolay M. Evstigneev
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Continuation Method ◽  
Fourier Method ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
System Of Nonlinear Equations ◽  
Arc Length ◽  
Navier Stokes Equations ◽  
Numerical Bifurcation

Abstract The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

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