Problems of locus solved by mechanisms theory

Description

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