Problems of Locus Solved by Mechanisms Theory

This book reports on an original approach to problems of loci. It shows how the theory of mechanisms can be used to address the locus problem. It describes the study of different loci, with an emphasis on those of triangle and quadrilateral, but not limited to them. Thanks to a number of original drawings, the book helps to visualize different type of loci, which can be treated as curves, and shows how to create new ones, including some aesthetic ones, by changing some parameters of the equivalent mechanisms. Further, the book includes a theoretical discussion on the synthesis of mechanisms, giving some important insights into the correlation between the generation of trajectories by mechanisms and the synthesis of those mechanisms when the trajectory is given, and presenting approximate solutions to this problem. Based on the authors' many years of research and on their extensive knowledge concerning the theory of mechanisms, and bridging between geometry and mechanics, this book offers a unique guide to mechanical engineers and engineering designers, mathematicians, as well as industrial and graphic designers, and students in the above-mentioned fields alike.

Explains how to apply the theory of mechanisms for solving the locus problem Shows how to develop the equivalent mechanism, starting from the geometric problem Describes a set of new mechanisms to generate original curves and trajectories

Autorentext

Iulian Popescu, Emeritus Professor, Ph.D. in Engineering, is a full member of the Academy of Technical Sciences of Romania. He was teaching the course on Mechanisms and Machines Theory at the Faculty of Mechanics of the University of Craiova, Romania, for about 35 years. He supervised 25 Ph.D. students and published 31 books on Mechanisms in Romanian language. He has co-authored the book Mechanisms for Generating Mathematical Curves, published by Springer in 2020.

Madalina Xenia Calbureanu Popescu is Professor Habil. Eng. at the Faculty of Mechanics of the University of Craiova. Her research area covers the vast and multi-disciplinary field of dynamics, with applications in mechanical and civil engineering. She has been investigating cinematic elements and vibrations, as well as dynamic responses of structures subjected to seismic action. A further area of interest is concerned with heat and mass transfer, including applications in the field of energy efficiency. With more than 100 publications in both journal and conference papers, and book chapters, she is also a senior member of International Engineering and Technology Institute.

Alina Duta, Ph.D., has been serving as Associate Professor at the Faculty of Mechanics of the University of Craiova. She received a Doctor in Technical Sciences from "Politehnica" University of Bucharest in 1998. She has authored 3 books about descriptive geometry and graphics in Romanian language and more than 100 articles published in journals and proceedings of national and international symposiums. Her research work is mainly concerned with topics in geometry, such as the geometry of curves, and modelling and simulation of technological processes. She is a member of "International Society for Geometry and Graphics" (ISGG).

Inhalt
Introduction.- Loci Generated By The Point Of A Line Which Moves One End On A Circle And The Other On A Line.- Loci Generated By The Point Of Intersection Of Two Lines.- Loci Generated By The Points On A Line Which Move On Two Concurrent Lines.- Loci Generated By The Points On A Bar Which Slides With The Heads On On Two Fixed Lines.- Loci Generated By Two Segment Lines Bound Between Them.- Problem Of A Locus With Four Intercut Lines.- KAPPA and "KIEROID" Curves Resulted as Loci.- The Butterfly Locus Type.- Nephroida and Rhodonea as Loci.- Successions Of Aesthetic Rhodonea.- Loci In The Triangle.- Loci Of Points Belonging To A Quadrilateral.- The Locus For The Cross-Point Of The Diagonals In A Pentagon.- Correlation Between Track Generation And Synthesis Of Mechanisms.