Kinematics and Dynamics of Machinery

2.

Position and Displacement Analysis

2.1.

Fundamental Concepts

2.1.1.

Position Variables

2.1.2.

Displacement Definitions

2.1.3.

Coordinate Systems

2.1.4.

Reference Frames

2.2.

Graphical Methods

2.2.1.

Drawing Mechanisms to Scale

2.2.1.1.

Scale Selection Principles

2.2.1.2.

Layout Techniques

2.2.1.3.

Accuracy Considerations

2.2.2.

Determining Limiting Positions

2.2.2.1.

Dead Center Positions

2.2.2.2.

Extreme Positions of Links

2.2.2.3.

Toggle Positions

2.2.3.

Graphical Position Analysis of Four-Bar Linkage

2.2.3.1.

Construction Procedure

2.2.3.2.

Multiple Assembly Configurations

2.2.4.

Graphical Position Analysis of Slider-Crank Mechanism

2.2.4.1.

Construction Procedure

2.2.4.2.

Limiting Positions

2.2.5.

Graphical Analysis of Complex Mechanisms

2.3.

Analytical Methods

2.3.1.

Coordinate Systems and Vectors

2.3.1.1.

Cartesian Coordinate System

2.3.1.2.

Polar Coordinate System

2.3.1.3.

Vector Representation of Links

2.3.1.4.

Position Vector Equations

2.3.2.

Loop Closure Equations

2.3.2.1.

Vector Loop Method

2.3.2.2.

Formulation for Four-Bar Linkage

2.3.2.3.

Formulation for Slider-Crank Mechanism

2.3.2.4.

Complex Mechanisms

2.3.3.

Position Analysis of Four-Bar Linkage

2.3.3.1.

Analytical Solution Methods

2.3.3.2.

Input-Output Relationships

2.3.3.3.

Coupler Point Position

2.3.3.4.

Branch and Circuit Defects

2.3.4.

Position Analysis of Slider-Crank Mechanism

2.3.4.1.

Analytical Solution for Slider Position

2.3.4.2.

Crank and Connecting Rod Angles

2.3.4.3.

Offset Slider-Crank Analysis

2.3.5.

Computer-Aided Position Analysis

2.3.5.1.

Numerical Methods

2.3.5.2.

Iterative Solutions

2.3.5.3.

Software Applications

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