Hernandez Rodriguez 2023a - Revision history

Rimni at 12:29, 31 May 2023

2023-05-31T12:29:31Z

Rimni at 11:08, 31 May 2023

2023-05-31T11:08:24Z

Rimni at 10:43, 31 May 2023

2023-05-31T10:43:42Z

Rimni: /* 3.2. Benchmark 2 */

2023-05-31T10:43:10Z

‎3.2. Benchmark 2

Rimni at 10:40, 31 May 2023

2023-05-31T10:40:33Z

Rimni: /* 3.2. Benchmark 2 */

2023-05-31T10:35:38Z

‎3.2. Benchmark 2

Rimni at 10:29, 31 May 2023

2023-05-31T10:29:48Z

Rimni at 10:24, 31 May 2023

2023-05-31T10:24:18Z

Rimni at 10:22, 31 May 2023

2023-05-31T10:22:50Z

Rimni: /* 3. Validation */

2023-05-31T10:16:19Z

‎3. Validation

← Older revision		Revision as of 12:29, 31 May 2023
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−	SIDIGETRA was used to find a crank-rocker mechanism. The design parameters used were: >Itermax<math display="inline">=2000</math>, acceptable FO<math display="inline">=0.95</math>, Population<math display="inline">=1000</math>, Pc<math display="inline">=0.5</math>, Pm<math display="inline">=0.05</math>, Maximum coordinate<math display="inline">=10</math>, Minimum coordinate<math display="inline">= -10</math>. Results obtained: Iterations performed<math>=2000</math>, FO<math>=0.82757</math>. It is observed that the prescribed points and the obtained points are visibly close to each other [[#img-6\|Figure 6]]). The mechanism found by SIDIGETRA generates the desired trajectory with a 4.11% average percentage relative error in the X-coordinates and a 0.70% average percentage relative error in the Y-coordinates.	+	SIDIGETRA was used to find a crank-rocker mechanism. The design parameters used were: >Itermax<math display="inline">=2000</math>, acceptable FO<math display="inline">=0.95</math>, Population<math display="inline">=1000</math>, Pc<math display="inline">=0.5</math>, Pm<math display="inline">=0.05</math>, Maximum coordinate<math display="inline">=10</math>, Minimum coordinate<math display="inline">= -10</math>. Results obtained: Iterations performed<math>=2000</math>, FO<math>=0.82757</math>. It is observed that the prescribed points and the obtained points are visibly close to each other ([[#img-6\|Figure 6]]). The mechanism found by SIDIGETRA generates the desired trajectory with a 4.11% average percentage relative error in the X-coordinates and a 0.70% average percentage relative error in the Y-coordinates.

	<div id='img-6'></div>		<div id='img-6'></div>

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 ==References ==
-[1]. Erdman, A. G. and Sandor, G.N. ''Diseño de Mecanismos. Análisis y síntesis''. Third edition. Prentice Hall Hispanoamericana S.A. Naucalpán, Juarez, México. 1998.
+<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-[2]. Mabie, H. H y Reinholtz, Ch. F. Mechanisms and Dynamics of Machinery. Second edition. Limusa, S.A. D.F., México. 2007.
+[1] Erdman A.G.,  Sandor G.N. Diseño de mecanismos. Análisis y síntesis. Prentice Hall Hispanoamericana S.A. Naucalpán, Juarez, México, 3rd edition, 1998.
-[3]. Norton, R. Design of Machinery. Synthesis and Analysis of Machines and Mechanisms. Third Edition. McGraw – Hill. D.F., México. 2005.
+[2] Mabie H.H., Reinholtz Ch.F. Mechanisms and dynamics of machinery. Limusa, S.A. D.F., México, 2nd edition, 2007.
-[4]. Rodríguez, J. ''Nociones Fundamentales para la Síntesis Estructural de Mecanismos Planos''. Facultad de Ingeniería. Universidad del Zulia. Maracaibo, Venezuela. 2011.
+[3] Norton R. Design of machinery. Synthesis and analysis of machines and mechanisms. McGraw – Hill. D.F., México, 3rd edition, 2005.
-[5]. Shigley, J. E. and Uicker, J. J. Theory of Machines and Mechanisms. McGraw – Hill. Naucalpán de Juarez, México. 1988.
+[4] Rodríguez J. Nociones fundamentales para la síntesis estructural de mecanismos planos. Facultad de Ingeniería, Universidad del Zulia, Maracaibo, Venezuela, 2011.
-[6]. Nieto N., J. ''Síntesis de Mecanismos''. Editorial AC. Madrid, España. 1978.
+[5] Shigley J.E.,  Uicker J.J. Theory of machines and mechanisms. McGraw – Hill, Naucalpán de Juarez, México, 1988.
-[7]. Rao, S. ''Engineering Optimization. Theory and Practice''. Fourth edition. Wiley. United states. 2009.
+[6] Nieto N.J. Síntesis de mecanismos. Editorial AC. Madrid, España, pp. 203, 1978.
-[8]. Gen, M. y Chen, R. ''Genetic Algorithms & Engineering Optimization''.  Wiley. 2000.
+[7] Rao S. Engineering optimization. Theory and practice.  Wiley, United states, 4th edition, 2009.
-[9]. Peón Escalante, R., Méndez Gamboa, J., Villanueva López, C., Pech Oy, D.  Síntesis Dimensional Óptima de un Mecanismo Planar RRRR usando Algoritmos Genéticos. ''Ingeniería, Revista Académica de la FI-UADY'', 13-3, pp. 5-16, ISSN: 1665-529X. 2009.
+[8] Gen M., Chen R. Genetic algorithms and engineering optimization.  Wiley, pp. 512, 2000.

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 <div id='img-7'></div>
-{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:50%;"
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:60%;"
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-|style="text-align: center;padding-right:10px;"| [[Image:Draft_Hernandez_561122732-image9.png|300px]]
+|style="text-align: center;padding-right:10px;"| [[Image:Draft_Hernandez_561122732-image9.png|350px]]
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 <div id='img-7'></div>
-{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:70%;"
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-|style="text-align: center;"| [[File:Hernandez_Rodriguez_2023a_2857_192px-Draft_Hernandez_561122732-image10-c.png|698px]]
+|style="text-align: center;"| [[File:Hernandez_Rodriguez_2023a_2857_192px-Draft_Hernandez_561122732-image10-c.png|198px]]
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-The SIDIGETRA program was used to dimension a crank-rocker mechanism with <math display="inline">Itermax=5000</math>, acceptable <math display="inline">FO=0.98</math>, <math display="inline">Population=1000</math>, <math display="inline">Pc=0.5</math>, <math display="inline">Pm=0.05</math>, and maximum and minimum coordinate values set to 4 and -4, respectively. The program performed 5000 iterations and found an <math display="inline">FO</math> value of <math>0.96306</math>. [[#img-4|Figure 4]](a) shows the results obtained by SIDIGETRA, and [[#img-4|Figure 4]](b) shows the visualization of the synthesized mechanism with a simulation performed using a commercial computer tool that allows for graphical comparison of trajectories.
+The SIDIGETRA program was used to dimension a crank-rocker mechanism with Itermax<math display="inline">=5000</math>, acceptable FO<math display="inline">=0.98</math>, Population<math display="inline">=1000</math>, Pc<math display="inline">=0.5</math>, Pm=<math display="inline">0.05</math>, and maximum and minimum coordinate values set to 4 and -4, respectively. The program performed 5000 iterations and found an <math display="inline">FO</math> value of <math>0.96306</math>. [[#img-4|Figure 4]](a) shows the results obtained by SIDIGETRA, and [[#img-4|Figure 4]](b) shows the visualization of the synthesized mechanism with a simulation performed using a commercial computer tool that allows for graphical comparison of trajectories.
 <div id='img-4'></div>
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-SIDIGETRA was used to find a crank-rocker mechanism. The design parameters used were: <math display="inline">Itermax=2000</math>, acceptable <math display="inline">FO=0.95</math>, <math display="inline">Population=1000</math>, <math display="inline">Pc=0.5</math>, <math display="inline">Pm=0.05</math>, <math display="inline">Maximum coordinate=10</math>, <math display="inline">Minimum coordinate= -10</math>. Results obtained: <math>Iterations performed=2000</math>, <math>FO=0.82757</math>. It is observed that the prescribed points and the obtained points are visibly close to each other [[#img-6|Figure 6]]). The mechanism found by SIDIGETRA generates the desired trajectory with a 4.11% average percentage relative error in the X-coordinates and a 0.70% average percentage relative error in the Y-coordinates.
+SIDIGETRA was used to find a crank-rocker mechanism. The design parameters used were: >Itermax<math display="inline">=2000</math>, acceptable FO<math display="inline">=0.95</math>, Population<math display="inline">=1000</math>, Pc<math display="inline">=0.5</math>, Pm<math display="inline">=0.05</math>, Maximum coordinate<math display="inline">=10</math>, Minimum coordinate<math display="inline">= -10</math>. Results obtained: Iterations performed<math>=2000</math>, FO<math>=0.82757</math>. It is observed that the prescribed points and the obtained points are visibly close to each other [[#img-6|Figure 6]]). The mechanism found by SIDIGETRA generates the desired trajectory with a 4.11% average percentage relative error in the X-coordinates and a 0.70% average percentage relative error in the Y-coordinates.
 <div id='img-6'></div>
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-Now, we want to know if it is possible to generate the same trajectory using a double crank mechanism using the same design parameters. [[#img-7|Figure 7]] shows the results obtained by SIDIGETRA and a commercial mechanism analysis program, and it can be observed that the generated trajectory is satisfactorily close to the desired trajectory. <math>Iterations performed=2000</math>, <math>FO=0.48722</math>.
+Now, we want to know if it is possible to generate the same trajectory using a double crank mechanism using the same design parameters. [[#img-7|Figure 7]] shows the results obtained by SIDIGETRA and a commercial mechanism analysis program, and it can be observed that the generated trajectory is satisfactorily close to the desired trajectory. Iterations performed<math>=2000</math>, FO<math>=0.48722</math>.
 <div id='img-7'></div>
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-|style="text-align: center;"| [[File:Hernandez_Rodriguez_2023a_2857_192px-Draft_Hernandez_561122732-image10-c.png|398px]]
+|style="text-align: center;"| [[File:Hernandez_Rodriguez_2023a_2857_192px-Draft_Hernandez_561122732-image10-c.png|698px]]
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-|style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a)
+|style="text-align: center;font-size: 75%;padding:10px;"|(a)
-|style="text-align: center;font-size: 75%;padding-bottom:10px;"|(b)
+|style="text-align: center;font-size: 75%;padding:10px;"|(b)
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-The average percentage relative error for the <math>X</math> coordinates is 8.8% and for the <math>Y</math> coordinates is 1.8%, which shows that SIDIGETRA found the desired trajectory. However, by comparing the <math>FO</math> values, the user can have a selection criterion between the inversions according to the precision requirements to solve a need.
+The average percentage relative error for the <math>X</math> coordinates is 8.8% and for the <math>Y</math> coordinates is 1.8%, which shows that SIDIGETRA found the desired trajectory. However, by comparing the FO values, the user can have a selection criterion between the inversions according to the precision requirements to solve a need.
 ==4. Conclusions==

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