Complete Solutions to Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy With M-Homogenization

1992 ◽  
Author(s):  
Anoop K. Dhingra ◽  
Jyun-Cheng Cheng ◽  
Dilip Kohli
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Numerical Results ◽  
Path Generation ◽  
Link Function ◽  
Homotopy Methods ◽  
Motion Generation ◽  
The Matrix ◽  
Function Generators ◽  
Complete Solutions

Abstract This paper presents complete solutions to the function, motion and path generation problems of Watt’s and Stephenson six-link, slider-crank and four-link mechanisms using homotopy methods with m-homogenization. It is shown that using the matrix method for synthesis, applying m-homogeneous group theory, and by defining compatibility equations in addition to the synthesis equations, the number of homotopy paths to be tracked can be drastically reduced. For Watt’s six-link function generators with 6 thru 11 precision positions, the number of homotopy paths to be tracked in obtaining all possible solutions range from 640 to 55,050,240. For Stephenson-II and -III mechanisms these numbers vary from 640 to 412,876,800. For 6, 7 and 8 point slider-crank path generation problems, the number of paths to be tracked are 320, 3840 and 17,920, respectively, whereas for four-link path generators with 6 thru 8 positions these numbers range from 640 to 71,680. It is also shown that for body guidance problems of slider-crank and four-link mechanisms, the number of homotopy paths to be tracked is exactly same as the maximum number of possible solutions given by the Burmester-Ball theories. Numerical results of synthesis of slider-crank path generators for 8 precision positions and six-link Watt and Stephenson-III function generators for 9 prescribed positions are also presented.

Synthesis of Six-link, Slider-crank and Four-link Mechanisms for Function, Path and Motion Generation Using Homotopy with m-homogenization

1994 ◽  
Vol 116 (4) ◽  
pp. 1122-1131 ◽  
Author(s):  
A. K. Dhingra ◽  
J. C. Cheng ◽  
D. Kohli
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Path Generation ◽  
Link Function ◽  
Homotopy Methods ◽  
Motion Generation ◽  
Function Generator ◽  
Numerical Examples ◽  
The Matrix ◽  
Function Generators

This paper presents solutions to the function, motion and path generation problems of Watt’s and Stephenson six-link, slider-crank and four-link mechanisms using homotopy methods with m-homogenization. It is shown that using the matrix method for synthesis, applying m-homogeneous group theory, and by defining auxiliary equations in addition to the synthesis equations, the number of homotopy paths to be tracked is drastically reduced. To synthesize a Watt’s six-link function generator for 6 through 11 precision positions, the number of homotopy paths to be tracked to obtain all possible solutions range from 640 to 55,050,240. For Stephenson-II and -III mechanisms these numbers vary from 640 to 412,876,800. It is shown that slider-crank path generation problems with 6, 7 and 8 prescribed positions require 320, 3840 and 17,920 paths to be tracked, respectively, whereas for four-link path generators with 6 through 8 specified positions, these numbers range from 640 to 71, 680. The number of homotopy paths to be tracked to body guidance problems of slider-crank and four-link mechanisms is exactly the same as the maximum number of possible solutions given by Burmester-Ball theories. Numerical examples dealing with the synthesis of slider-crank path generators for 8 precision positions, and six-link Watt and Stephenson-III function generators for 9 prescribed positions are also presented.

Multiply Separated Synthesis of Six-Link Mechanisms Using Parallel Homotopy With M-Homogenization

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
M. Zhang
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Parallel Implementation ◽  
Homotopy Methods ◽  
Numerical Work ◽  
Function Generation ◽  
Connection Machine ◽  
The Matrix ◽  
Generation Problem ◽  
Complete Solutions

Abstract This paper presents complete solutions to the function generation problem of six-link Watt and Stephenson mechanisms, with multiply separated precision positions (PP), using homotopy methods with m-homogenization. It is seen that using the matrix method for synthesis, applying m-homogeneous group theory and by defining auxiliary equations in addition to the synthesis equations, the number of homotopy paths to be tracked in obtaining all possible solutions to the synthesis problem can be drastically reduced. Numerical work dealing with the synthesis of Watt and Stephenson mechanisms for 6 and 9 multiply separated precision points is presented. For both mechanisms, it is seen that complete solutions for 6 and 9 precision points can be obtained by tracking 640 and 286,720 paths, respectively. A parallel implementation of homotopy methods on the Connection Machine on which several thousand homotopy paths can be tracked concurrently is also discussed.

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

scholarly journals Multivariate analytical methods for simultaneous estimation of Atenolol and Hydrochlorothiazide in bulk and tablet dosage form

2021 ◽  
Vol 6 (4) ◽  
pp. 205-208
Author(s):  
Sreenivasa Charan Archakam ◽  
Keerthisikha Palur ◽  
Praveen Kumar Arava
Keyword(s):  
Linear Regression ◽  
Matrix Method ◽  
Linear Regression Analysis ◽  
Molar Absorptivity ◽  
Simultaneous Estimation ◽  
Linear Regression Method ◽  
Spectrophotometric Methods ◽  
The Matrix ◽  
Ft Ir ◽  
Tablet Dosage

The present study aimed to develop simple, accurate and precise FTIR and UV spectrophotometric methods for the quantification of Atenolol and Hydrochlorothiazide in bulk and tablet dosage forms. FT-IR method like classical least squares (CLS) was developed within the range of 2366.69-3433.44; 1564.40-1673.30 cm- UV methods like Cramer’s matrix method (method-I) and linear regression analysis (Method II) were developed and they are based upon constructing the matrix set by using molar absorptivity values at 275.60 nm and 270.40 nm. The assay values for FTIR- CLS method were 102% and 108 % for Atenololand Hydrochlorothiazide respectively. Cramer’s matrix method results were found to be 95.15% and 104% for Atenolol and Hydrochlorothiazide respectively and for linear regression method they were found to be 98.50% and 106% (w/w).

scholarly journals Protecting River Environment through Proper Management of Material Mining by Matrix Method (Case Study of A'la River in Iran)

2018 ◽  
Vol 3 (12) ◽  
pp. 1301
Author(s):  
Farhang Azarang ◽  
Ghazal Jafari ◽  
Maryam Karami Karami ◽  
Mahmood Shafaie Bejestan
Keyword(s):  
Matrix Method ◽  
Sediment Load ◽  
Direct Impact ◽  
Mining Method ◽  
River Engineering ◽  
Critical Importance ◽  
Mine Area ◽  
The Matrix ◽  
Available Volume

Regarding the importance of rivers, appropriate management of aggregate mining is of great significance. Mining of river materials has a direct impact on environmental conditions of the river. Today, aggregate mining management represents a crucial topic in river engineering. Often selected based on the pattern of the considered river, matrix method provides a suitable approach to improve the river aggregate mining management. The present research aims at presenting the application of the matrix method in river material mining location evaluation. Given the capabilities of the matrix method for determining potential of mine area and aggregate mining method, this method can be seen as a suitable solution for reducing negative environmental impacts of river material mining. A'la River is one of the most important rivers streaming in Khouzestan Province (Iran), with its sediment load and mining potential being of critical importance. In this research, the reach of A'la River at the intersection of Rood-Zard River and Rahmhormoz diversion dam was studied for aggregate mining and application of matrix method. The main purpose of this work is to study the application of matrix method to A'la River. The results indicate braided pattern of the river and appropriateness of the matrix method. Available volume of aggregate for mining within the mentioned reach of A'la River was estimated as 50,000 m3, and scraping method at a maximum depth of 1 m was proposed for mining of the aggregates.

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