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.
Author(s): Iulian Popescu, Xenia Calbureanu, Alina Duta
Series: Springer Tracts in Mechanical Engineering
Publisher: Springer
Year: 2020
Language: English
Pages: 287
City: Cham
Preface
Contents
1 Introduction
1.1 The Locus Problem in Geometry
1.2 Some Basics from the Mechanisms Theory
References
2 Loci Generated by the Point of a Line Which Moves One End on a Circle and the Other on a Line
References
3 Loci Generated by the Point of Intersection of Two Lines
References
4 Loci Generated by the Points on a Line Which Move on Two Concurrent Lines
4.1 Case 1
4.2 Case 2
References
5 Loci Generated by the Points on a Bar Which Slides with the Heads on Two Fixed Lines
5.1 The Straight Lines are Considered to be the Axes of the Fixed Xoy System
5.2 The Straight Lines Are Arbitrary
References
6 Loci Generated by Two Segment Lines Bound Between Them
6.1 Case 1
6.2 Case 2
6.3 Case 3
References
7 Problem of a Locus with Four Intercut Lines
7.1 The Trajectory of C Point
7.2 The Trajectory of H Point
References
8 “Kappa” and “Kieroid” Curves Resulted as Loci
8.1 The “Kappa’ Curve
8.2 The “Kieroid” Curve
References
9 The ‘Butterfly’ Locus Type
References
10 Nephroida and Rhodonea as Loci
10.1 Nephroida as Locus
10.2 The Rhodonea as an Aesthetic Locus
References
11 Successions of Aesthetic Rhodonea
References
12 Loci in the Triangle
References
13 Loci of Points Belonging to a Quadrilateral
13.1 The Case of the Heights Built from A and D Points on the Connecting Rod
13.2 The Case of Heights Drawn from B Point on the CD Side and from C Point on AB Side
13.3 The Case of Heights Built from B and D Points on the AC Diagonal
13.4 The Case of Heights Built from A and C Points on the BD Diagonal
13.5 The Loci for the Cross-Points of the Heights Built in the Four-Bar Mechanism
13.6 The Loci for the Cross-Points of the Mid-Perpendiculars
13.7 The Loci of the Medians Cross-Points
13.8 The Loci of the Bisecting Lines Cross-Points
13.9 The Locus of the Quadrilateral’s Diagonals’ Cross Point
References
14 The Locus for the Cross-Point of the Diagonals in a Pentagon
14.1 The Loci of the K Point
14.2 The Loci of the G Point
14.3 The Loci of the L Point
14.4 The Loci of the F Point
14.5 The Loci of H Point
References
15 Correlation Between Track Generation and Synthesis of Mechanisms
References
