Using nodal coordinates as variables for the dimensional synthesis of mechanisms

Significance 

For a long time, the technique of the lower deformation energy has been successfully employed for the synthesis of mechanisms. This technique has been seen to be versatile, yet powerful a method for assisting in the design of mechanisms. So far, most of the implementations of this method have utilized the dimensions of the mechanism as the synthesis variables, as it brings along some advantages as well as some drawbacks. For instance, the assembly configuration is not usually considered in the optimization process, a flaw that ensures that the same initial configuration is used when computing the deformed positions in each synthesis point. Consequently, it translates into a reduction of the total search space. A possible solution to this problem is the use of a set of initial coordinates as variables for the synthesis, which has been successfully applied to other methods. This also has some additional advantages, such as: the fact that any generated mechanism can be assembled. Unfortunately, the change from dimensions to initial coordinates coerces a reformulation of the optimization problem when using derivatives if one wants them to be analytically derived.

Recently, Dr. Vanessa García-Marina at University of the Basque Country in collaboration with Dr. Igor Fernández de Bustos, Mr. Gorka Urkullu and Dr. Mikel Abasolo at University of the Basque Country explored the use of initial coordinates for the synthesis of mechanisms using SQP and the deformation energy error function. They presented relevant mathematical developments and validate them using examples. Their work is currently published in the research journal, Meccanica.

In brief, the research method employed commenced with a thorough review of the deformed energy method. Next, the researchers reasoned out the choice of using initial coordinates as synthesis variables along with the deformed energy method. They then developed the energetic error function using initial coordinates and later presented the analytic expressions. Lastly, some remarks on the optimization method were made.

The authors observed that the inclusion of the initial coordinates as optimization variables enabled the assembly configuration to be encompassed in the optimization process, which was seen to be of utmost significance in the definition of the mechanism. They also noted that the coordinates of the fixed points were also variables of the optimization and thus, one did not need to include workarounds to optimize them. They also realized that all of the possible solution vectors defined a mechanism which always could be assembled, which not always remained acceptable when using dimensions.

In summary, the study by Vanessa García-Marina and her colleagues presented a novel approach to the dimensional synthesis of mechanism which, although based in the same concepts as previous developments, introduced fundamental changes in its conception. From the observations presented, it can be concluded that the new algorithm inherits not only the advantages of the former approach, but also some of its drawbacks, specially the problem of the low stiffness mechanisms. All in all, reformulation along with a proper comparison of the use of both alternatives using sequential quadratic programming methods have been seen as worthwhile solutions.

Using nodal coordinates as variables for  dimensional synthesis of mechanisms-Advances-in-Engineering
Credit: Figure 14 (Meccanica (2018) volume 53, page 1981–1996.)

About the author

Dr. Vanessa García-Marina gives lectures in the Department of Mechanical Engineering, University of the Basque Country, Spain, since 2003. She received her BSc degree in Industrial Engineering and PhD degree in Mechanical Engineering from University of the Basque Country, Spain, in 2001 and 2015 respectively. During 2002 she worked for the firma Rinder who specialized in light systems for motorcycles mainly, then in 2003 she worked for the Bizkaia’s provincial council, and after that, she began her work giving lectures in the university.

She has collaborated in 5 research projects, contributed to 20 national and international conferences, and organized 4 conferences and seminars in the School of Engineering of Vitoria, where she develops her teaching activities. She is member of the Spanish Association of Mechanical Engineering, and member of the Spanish Association of Automotive Professionals.

Her research interests include kinematic analysis and optimum synthesis of mechanisms, multibody dynamics, and computational mechanics applied to structural analysis by finite elements.

About the author

Dr. Igor Fernández de Bustos gives lectures in the Department of Mechanical Engineering, University of the Basque Country, Spain, since 1999. He received his BSc degree in Industrial Engineering and PhD degree in Mechanical Engineering from University of the Basque Country, Spain, in 1999 and 2004 respectively. His lectures are focused in structural dynamics, aerospace engineering and computational methods in engineering. He has participated in more than 100 publications, including conferences, journal papers and more. He is member of the Spanish Association of Mechanical Engineering.

His research interests include kinematic analysis and optimum synthesis of mechanisms, multibody dynamics, computational mechanics applied to structural analysis by finite elements and motorcycle dynamics.

About the author

Mr. Gorka Urkullu is a member of the Mechanical Analysis and Design research group in the Faculty of Engineering of Bilbao, which is part of University of the Basque Country. He received his BSc degree in Industrial Engineering from the University of the Basque Country in 2011. After that, he worked for Tecnalia Research and Innovation and during this stage, he focused on the simulation of the cold forming processes with large deformations using finite elements method. In 2014, he obtained his MSc degree in Space Science and Technology from the University of the Basque Country. Following the Final Master´s Dissertation, he began to participate with the Mechanical Analysis and Design research group. Finally, he enrolled as PhD student in 2015. He has authored/co-authored of 3 three articles in prestigious journals, such as Mechanism and Machine Theory, Journal of Computational and Applied Mathematics or Meccanica and has collaborated in 5 national and international Congresses.

His research interests include dynamic analysis of multibody systems, optimum synthesis of mechanisms and computational mechanics applied to structural analysis by finite elements.

About the author

Dr. Mikel Abasolo gives lectures in the Department of Mechanical Engineering, University of the Basque Country, Spain, since 2007. He develops his teaching activities in the School of Engineering of Bilbao, in the field of machine design and analysis, finite element method and static and fatigue analysis. He obtained the BSc degree in Industrial Engineering and PhD degree in Mechanical Engineering from University of the Basque Country in 2005 and 2012 respectively.

He has authored/coauthored 24 papers in JCR journals, as well as more than 25 conference papers. He has directed 3 PhD theses, and has collaborated in more than 25 research projects and works for companies.

His research lines cover the analytical and numerical simulation and characterization of the structural response and resistance of several mechanical elements such as bolted joints, conventional and wire slewing bearings, spherical plain bearings and dental implants, among others.

Reference

V. Garcia-Marina, I. Fernandez de Bustos, G. Urkullu, M. Abasolo. Using nodal coordinates as variables for the dimensional synthesis of mechanisms. Meccanica (2018) volume 53, page 1981–1996.

Go To Meccanica (2018)

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