KINEMATICS OF MACHINES

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GUJARAT TECHNOLOGICAL UNIVERSITY

MECHANICAL ENGINEERING

B.E. 3RD Semester

Subject Code: 2131906

KINEMATICS OF MACHINES

  1. Introduction of Mechanisms and Machines: – Concepts of Kinematics and Dynamics, Mechanisms and Machines, Planner and Spatial Mechanisms, Kinematics Pairs, Kinematic Chains, Kinematic Chains, Kinematic Diagrams, Kinematic Inversion. Four bar chain and Slider Crank Mechanisms and their inversion, Degree of freedom, Mobility and range of movement-Kutzbach and Grubler’s criterion, Number Synthesis, Grashof’s criterion.
  2. Synthesis and Analysis of Mechanisms:                                                                                                                                        Position analysis (Analytical Technique): Loop closure (Vector Loop) representation of linkages, Position analysis of Four bar, slider crank and inverted slider crank mechanisms, Coupler curve, Toggle and Limit Position, Transmission angle, Mechanical Advantage.                                                                                                                                                                        Dimensional Synthesis: Definitions of Type, Number and Dimensional Synthesis, Definition of Motion, Path and Function generation, precision position. Chebychev spacing, structural error, Freudenstein’s equation, two or three position synthesis (function generation only) of four bar and slider crank mechanisms by graphical and analytical methods.    Velocity and Acceleration Analysis: Velocity and Acceleration Diagrams, Instantaneous Centre of Velocity, Rubbing Velocity, Velocity and Acceleration Images, Corioli’s component of acceleration.                                                                          Special Mechanisms: Straight line mechanisms, Indicator diagram, Hooke’s Joint, Steering Mechanisms.
  3. Gear and Gear Trains:                                                                                                                                                                    Gears: Terminology, Law of Gearing, Characteristics of involute and cycloidal action, Interference and undercutting, Centre distance variation, minimum number of teeth, contact ratio, spur, helical, spiral, bevel and worm gear, problems. Gear Trains: Synthesis of Simple, compound & reverted gear trains, Analysis of epicyclic gear trains.
  4. Cams and Followers:                                                                                                                                                                                Introduction:  Classification of cams and followers, nomenclature, displacement diagram of follower motion, kinematic coefficients of follower motion.                                                                                                                                                                        Synthesis and Analysis: Determine of basic dimensions and synthesis of cam profiles using graphical methods. Came with specified contours.

Basic Kinematics

1
Introduction
2
Kinematic Link or Element
3
Machine
4
Structure
5
Constrained Motions
6
Kinematic Pairs
7
Kinematic Chain
8
Types of Joints in a Kinematic Chain
9
Closed and Open Kinematic Chain
10
Mechanism
11
Inversion of a Kinematic Chain
12
Grashoff’s Law
13
Degree of Freedom (DOF)
14
Mobility and Degree of Freedom (DOF)
15
Kutz Bach Criterion
16
Grubler’s Criterion

Synthesis and Analysis of Mechanism

1
Introduction
2
Classification of Synthesis Problems (Tasks of Kinematic Synthesis)
3
Dimensional Synthesis
4
Analytical Method for Dimensional Synthesis of Four Bar Chain Mechanism (Freudenstein’s Equation)
5
Synthesis of a Function Generation
6
Synthesis of Path Generation or Coupler Curve Synthesis
7
Three Position Motion Synthesis of Four Bar Chain Mechanism (Body Guidance)
8
Complex Algebra Method
9
Computer Applications in the Kinematic Analysis of Simple Mechanisms
10
Computer-Aided Analysis of Four-Bar Chain Mechanism

Velocity and Acceleration Analysis

1
Introduction
2
Linear and Angular Velocity
3
Representation of Velocity by Vectors
4
Velocity Analysis by Relative Velocity Method
5
Application of the Relative Velocity Method
6
Velocity Analysis by Instantaneous Centre Method
7
Three Centers in Line Theorem (Aronhold-Kennedy’s Theorem)
8
Steps to Locate Instantaneous Centers
9
Angular Velocity Ratio Theorem
10
Linear and Angular Acceleration
11
Motion of a Particle Moving in a Circular Path
12
Acceleration Diagram of a Link by Relative Acceleration Method
13
Outline Procedure of Drawing the Acceleration Diagram of a Mechanism
14
Coriolis Component of Acceleration
15
Klein’s Construction
16
Analytical Method

Special Mechanisms

1
Pantograph
2
Ratchet and Escapement Mechanism
3
Indexing Mechanism
4
Swinging or Rocking Mechanisms
5
Equivalent Linkage of Mechanism
6
Straight Line Generating Mechanisms
7
Automobile Steering Gear Mechanism
8
Hooke’s Joint or Universal Coupling

Gears

1
Introduction
2
History of Gears
3
Advantage and Disadvantage of Gear Drive
4
Classification of Gears
5
Comparison of Gears
6
Gear Tooth Terminology
7
Law of Gearing (Condition for Constant Velocity Ratio)
8
Velocity of Sliding of Teeth
9
Conjugate Profile
10
Forms of Gear Tooth Profile
11
Comparision of Cycloidal and Involute Tooth Gear
12
Standard Tooth Profiles or Systems
13
Length of Path of Contact
14
Length of Arc of Contact
15
Contact Ratio or Number of Pair of Teeth in Contact
16
Interference in Involute Gears
17
Undercutting
18
Critical or Minimum Number of Teeth to Avoid Interference
19
Methods to Avoid Interference
20
Effect of Cener Distance Variation on Velocity Ratio
21
Rack Shift
22
Fouling ( Interference in internal gears)
23
Friction between Gear Teeth
24
Static Force Analysis of Spur Gear
25
Introduction to Helical Gear”s
26
Terminology of Helical Gear
27
Virtual Number of Teeth or Number of Teeth on Equivalent Spur Gear
28
Force Analysis of Helical Gears
29
Velocity Ratio of Helical Gears
30
Centre Distance of Helical Gears
31
Introduction to Spiral Gears
32
Shaft Angle of Spiral Gears
33
Velocity of Sliding between Spiral Gears
34
Center Distance Between Two Spiral Gears
35
Efficiency of Spiral Gears
36
Introduction to Worm Gears
37
Terminology of Worm
38
Velocity Ratio and Center Distance Between Worm Gears
39
Efficiency of Worm Gearing
40
Introduction to Bevel Gears
41
Terminology of Bevel Gear
42
Pitch Cone Angles and Its Geometrical Relationship
43
Force Analysis of Bevel Gears

Gear Trains

1
Introduction
2
Simple Gear Train
3
Compound Gear Train
4
Reverted Gear Train
5
Design of Spur Gear Trains
6
Epicyclic Gear Train
7
Method of Finding Velocity Ratio of an Epicyclic Gear Train
8
Epicyclic Gear Train With Bevel Gears
9
Epicyclic Gear Train with Sun and Planet Wheel
10
Torque and Tooth Load in Epicyclic Gear Train
11
Types of Gear Box

Cams and Followers

1
Introduction
2
Classification of Followers
3
Classification of Cams
4
Terminology and Definitions
5
Types of Motion of the Follower
6
Motion of Follower with Uniform Velocity
7
Motion of Follower with Simple Harmonic Motion
8
Motion of Follower with Uniform Acceleration and Retardation
9
Motion of Follower With Cycloidal Motion
10
Determination of Cam Profile for a given Follower Motions
11
Analysis of CAM with Specified Countours
12
Jump Phenomenon
13
kinematically Equivalent System of Cam and Follower
14
Introduction to Advanced Cam Curves
15
Pressure Angle and Methods to Control Pressure Angle
16
Undercutting of Cam

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