Mechanisms for Generating Mathematical Curves

Foreword
Preface
Contents
About the Authors
Part I Basic Theory of Mechanisms
1 Structural Analysis of Planar Mechanisms
	1.1 Kinematic Joints
	1.2 Kinematic Links and the Degree of Freedom
	1.3 Substitution of Fourth Class Joints
	1.4 Assur’s Principle and Kinematic Groups
	1.5 Kinematic and Structural Diagrams
	References
2 Kinematic Analysis of Planar Mechanisms
	2.1 Closed-Loop Method
		2.1.1 Kinematics of the Driving Links and Assur Groups
		2.1.2 Kinematics of the Slider-Crank Mechanism
	2.2 Kinematics of Third Order Triad
	References
Part II Synthesis and Analysis of Mechanisms for Generating Mathematical Curves
3 Mechanisms for Generating Straight Lines and Arcs
	3.1 An Approximate Rectilinear Guiding Mechanism
		3.1.1 The Synthesis of a New Mechanism
		3.1.2 The Structure and Kinematics of the New Mechanism
		3.1.3 Results Obtained
	3.2 Mechanism for Approximation of Arcs
		3.2.1 Trajectories
		3.2.2 Velocities and Accelerations
	References
4 Mechanisms for Generating Conical Curves
	4.1 Mechanism Ellipsograph
		4.1.1 Introduction
		4.1.2 The Mechanism Synthesis
		4.1.3 The Mechanism Analysis
		4.1.4 Results Obtained
	4.2 Mechanisms for Generating Parabolas
		4.2.1 Case of Parabola Based on Pedal Curve
		4.2.2 A New Mechanism for Generating Parabola
		4.2.3 Case for Generation of Parabola as Envelope of a Line
	4.3 Mechanisms for Generating Hyperbolas
		4.3.1 Case of Hyperbola Based on Pedal Curve
		4.3.2 A New Mechanism for Generating Hyperbola
	4.4 Conic-Generating Mechanism Based on a Locus Problem
		4.4.1 Geometrical Considerations
		4.4.2 The Mechanism Synthesis
		4.4.3 The Mechanism Analysis
		4.4.4 Results Obtained
	References
5 Mechanisms for Generating Some Plane Mathematical Curves
	5.1 Mechanisms for Generating Cissoids
		5.1.1 The Cissoid of a Circle
		5.1.2 The Straight Line Cissoid
	5.2 Mechanism for Generating Berard’s Curve
		5.2.1 The Mechanism Synthesis
		5.2.2 The Mechanism Analysis
		5.2.3 Results Obtained
	5.3 Mechanism for Generating the Egg-Shaped Curve
		5.3.1 Introduction
		5.3.2 The Mechanism Synthesis
		5.3.3 The Mechanism Analysis
		5.3.4 Results Obtained
		5.3.5 The Influence of Inputs on the Curve’s Shape
	5.4 Mechanism for Generating the Double Egg Curve
		5.4.1 The Mechanism Synthesis
		5.4.2 The Mechanism Analysis
		5.4.3 Results Obtained
		5.4.4 The Influence of Inputs on the Curve’s Shape
	5.5 Mechanism for Generating Bernoulli Quartic
		5.5.1 The Mechanism Synthesis
		5.5.2 The Mechanism Analysis
		5.5.3 Results Obtained
	5.6 Mechanism for Generating MacLaurin’s Trisectrix
		5.6.1 Introduction
		5.6.2 The Mechanism Synthesis
		5.6.3 The Mechanism Analysis
		5.6.4 Results Obtained
		5.6.5 The Influence of Inputs on the Curve’s Shape
	5.7 Mechanism for Generating the Ophiuride
		5.7.1 Introduction
		5.7.2 The Mechanism Synthesis
		5.7.3 The Mechanism Analysis
		5.7.4 Results Obtained
		5.7.5 Considerations Regarding the Mechanism Functionality
		5.7.6 The Influence of Input Data on the Curve’s Shape
	5.8 Mechanism for Generating Pascal’s Snail
		5.8.1 The Mechanism Synthesis
		5.8.2 The Mechanism Analysis
		5.8.3 Results Obtained
	References
6 Mechanism for Generating Spatial Curves
	6.1 Screw Mechanism
		6.1.1 Input Data
		6.1.2 Generation of Cylindrical Helix
		6.1.3 Generation of Conical Helix
		6.1.4 Generation of Complex Spatial Curves
	6.2 Six-Bar Linkage Mechanism
		6.2.1 Input Data
		6.2.2 Generation of Cylindrical Helix with Variable Pitch
		6.2.3 Generation of Conical Helix with Variable Pitch
		6.2.4 Generation of Complex Spatial Curves with Variable Pitch
	References