This document provides definitions and terminology related to mechanisms in machines. It discusses key concepts such as:
1) Kinematic links or elements, which are parts of a machine that move relative to other parts.
2) Kinematic pairs, which are connections between two links that constrain their relative motion. Common types include sliding, turning, rolling, and screw pairs.
3) Kinematic chains and mechanisms, which are combinations of kinematic pairs that transmit motion. A mechanism has one fixed link.
4) Degrees of freedom, which refer to the number of independent parameters needed to define a linkage's position. Most practical mechanisms have one degree of freedom.
This document provides an introduction to mechanisms and kinematics. It defines mechanisms as assemblies of rigid bodies connected by joints that allow specified motions. Kinematics is the study of relative motion between parts without considering forces. There are different types of kinematic joints (binary, ternary) and pairs (sliding, turning, rolling) that connect links and constrain their motion. The degrees of freedom of a mechanism can be calculated using Kutzbach's criterion which considers the number of links, joints and higher pairs. Simple and compound machines are formed from combinations of mechanisms.
Kinematics of machines can involve either analyzing an existing mechanism's motion or synthesizing a new mechanism to achieve a desired motion. Kinematic synthesis involves selecting the type of mechanism, determining the number of links needed, and defining the link dimensions. Dimensional synthesis aims to develop link dimensions such that the mechanism's output motion matches the desired motion at select precision points, often spaced using Chebyshev's method to minimize error between points. Slider-crank mechanisms can be synthesized by relating the slider displacement to crank angle at precision points defined using Chebyshev spacing.
The document discusses different types of mechanisms and their inversions. It describes three main types of kinematic chains: four bar chains, single slider crank chains, and double slider crank chains. It provides examples of inversions for each type. For four bar chains, inversions include double cranks and crank-rocker mechanisms. Inversions of single slider crank chains include pendulum pumps, oscillating cylinder engines, and rotary internal combustion engines. Inversions of double slider crank chains include elliptical couplings and scotch yoke mechanisms.
This document outlines the course objectives and first chapter of a textbook on Mechanism of Machinery. The course aims to teach students about linkage mechanisms, kinematic and kinetic analysis of machines, and design of components like cams and gears.
The first chapter introduces basic definitions of links, joints, types of motion, and coordinate systems. It defines the degree of freedom of a mechanism as the minimum number of variables needed to define its configuration. The chapter objectives are for students to understand fundamental mechanism terms, different motions, and how to determine a mechanism's degrees of freedom.
1) The document discusses the basics of mechanisms and kinematics including definitions of kinematics, machines, links, kinematic pairs, and degrees of freedom.
2) It describes different types of kinematic pairs and constraints as well as examples like four bar linkages.
3) Common inversions of mechanisms are analyzed, including the slider crank chain used in engines and Grashoff's law for four bar linkages.
This document defines and classifies the components of mechanisms. It discusses links, kinematic pairs, kinematic chains, mechanisms, and machines. Links can be unary, binary, ternary or quaternary based on the number of nodes. Kinematic pairs combine two links and allow specific relative motions. Pairs are classified by contact type, constraint, and possible motions such as revolute, prismatic, or spherical. A kinematic chain transmits defined motion by coupling pairs. A mechanism is a kinematic chain with one fixed link. Mobility is determined using Gruebler's criterion involving links, pairs, and degrees of freedom. Kinematic inversion obtains different mechanisms from the same chain by fixing different links.
This document provides an introduction to mechanisms and kinematics. It defines mechanisms as assemblies of rigid bodies connected by joints that allow specified motions. Kinematics is the study of relative motion between parts without considering forces. There are different types of kinematic joints (binary, ternary) and pairs (sliding, turning, rolling) that connect links and constrain their motion. The degrees of freedom of a mechanism can be calculated using Kutzbach's criterion which considers the number of links, joints and higher pairs. Simple and compound machines are formed from combinations of mechanisms.
Kinematics of machines can involve either analyzing an existing mechanism's motion or synthesizing a new mechanism to achieve a desired motion. Kinematic synthesis involves selecting the type of mechanism, determining the number of links needed, and defining the link dimensions. Dimensional synthesis aims to develop link dimensions such that the mechanism's output motion matches the desired motion at select precision points, often spaced using Chebyshev's method to minimize error between points. Slider-crank mechanisms can be synthesized by relating the slider displacement to crank angle at precision points defined using Chebyshev spacing.
The document discusses different types of mechanisms and their inversions. It describes three main types of kinematic chains: four bar chains, single slider crank chains, and double slider crank chains. It provides examples of inversions for each type. For four bar chains, inversions include double cranks and crank-rocker mechanisms. Inversions of single slider crank chains include pendulum pumps, oscillating cylinder engines, and rotary internal combustion engines. Inversions of double slider crank chains include elliptical couplings and scotch yoke mechanisms.
This document outlines the course objectives and first chapter of a textbook on Mechanism of Machinery. The course aims to teach students about linkage mechanisms, kinematic and kinetic analysis of machines, and design of components like cams and gears.
The first chapter introduces basic definitions of links, joints, types of motion, and coordinate systems. It defines the degree of freedom of a mechanism as the minimum number of variables needed to define its configuration. The chapter objectives are for students to understand fundamental mechanism terms, different motions, and how to determine a mechanism's degrees of freedom.
1) The document discusses the basics of mechanisms and kinematics including definitions of kinematics, machines, links, kinematic pairs, and degrees of freedom.
2) It describes different types of kinematic pairs and constraints as well as examples like four bar linkages.
3) Common inversions of mechanisms are analyzed, including the slider crank chain used in engines and Grashoff's law for four bar linkages.
This document defines and classifies the components of mechanisms. It discusses links, kinematic pairs, kinematic chains, mechanisms, and machines. Links can be unary, binary, ternary or quaternary based on the number of nodes. Kinematic pairs combine two links and allow specific relative motions. Pairs are classified by contact type, constraint, and possible motions such as revolute, prismatic, or spherical. A kinematic chain transmits defined motion by coupling pairs. A mechanism is a kinematic chain with one fixed link. Mobility is determined using Gruebler's criterion involving links, pairs, and degrees of freedom. Kinematic inversion obtains different mechanisms from the same chain by fixing different links.
This document provides an overview of dynamics of machines including:
1. It defines force, applied force, constraint forces, and types of constrained motions like completely, incompletely, and successfully constrained motions.
2. It discusses static force analysis, dynamic force analysis, and conditions for static and dynamic equilibrium.
3. It covers concepts like inertia, inertia force, inertia torque, D'Alembert's principle, and principle of superposition.
4. It derives expressions for forces acting on the reciprocating parts of an engine while neglecting the weight of the connecting rod.
Cams are used to convert rotary motion to oscillatory motion or vice versa. They are commonly used in internal combustion engines to operate valves. This chapter discusses the fundamentals of cam and follower design including the different types of cams, followers, motions, and cam profiles. The objectives are to understand basic concepts and terminology and learn how to design a cam and follower set to achieve a desired output motion.
This document discusses the law of gearing in three main points:
1) The common normal at the point of contact between gear teeth must always pass through the pitch point. This is the fundamental condition for designing gear teeth profiles.
2) The angular velocity ratio between two gears must remain constant throughout meshing.
3) The angular velocity ratio is inversely proportional to the ratio of the distances of the pitch point P from the gear centers O1 and O2. The common normal intersecting the line of centers at P divides the center distance inversely proportional to the angular velocity ratio.
Kinematic link, Types of links, Kinematic pair, Types of constrained motions, Types of Kinematic pairs, Kinematic chain, Types of joints, Mechanism, Machine, Degree of freedom, Mobility of Mechanism, Inversion, Grashoff’s law, Four-Bar Chain and its Inversions, Slider crank Chain and its Inversions, Double slider crank Chain and its Conversions, Mechanisms with Higher pairs, Equivalent Linkages and its Cases - Sliding Pairs in Place of Turning Pairs, Spring in Place of Turning Pairs, Cam Pair in Place of Turning Pairs
The document discusses the four bar linkage mechanism. It consists of four rigid links connected by four pin joints, forming a quadilateral. The length of one link cannot exceed the sum of the other three links. A variety of mechanisms can be formed from slight variations to the four bar linkage, including changing link proportions or combining multiple linkages. The four bar linkage is the simplest closed loop mechanism and has one degree of freedom. Inversions of the four bar linkage include the beam engine, locomotive coupling rod, and Watt's indicator mechanism. The single slider crank chain converts rotary to reciprocating motion and vice versa using one sliding and three turning pairs. Inversions include pendulum pumps, oscillating cylinder engines, and internal
This document discusses different types of gear trains including simple, compound, reverted, and epicyclic gear trains. It provides details on the components, configurations, terminology, and methods for calculating speed and velocity ratios for each type of gear train. Key points covered include how simple gear trains involve one gear on each shaft, compound gear trains have multiple gears on a shaft, reverted gear trains have coaxial input and output shafts, and epicyclic gear trains allow shaft axes to move relative to a fixed axis. Formulas and a tabular method are presented for analyzing epicyclic gear trains.
Three types of gear trains are described:
1. Simple gear trains involve one gear on each shaft to transmit power.
2. Compound gear trains have more than one gear on a shaft, allowing for larger speed reductions.
3. Epicyclic gear trains have gears mounted on shafts that can move relative to a fixed axis, enabling high velocity ratios with moderate sized gears. Epicyclic trains are used in automotive differentials and machinery.
This document discusses different types of gear trains:
1. Simple gear train which uses one gear on each shaft to transmit motion.
2. Compound gear train which uses more than one gear on a shaft.
3. Reverted gear train where the first and last gears are co-axial and rotate in the same direction.
4. Epicyclic gear train where the gear axes can move relative to a fixed axis, allowing one gear to drive another in circular motion.
Formulas for speed ratio and train value are provided for each gear train type. Examples of applications like differentials are also mentioned.
Unit 7-gear trains, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
The document discusses kinematics of machines and mechanisms. It covers topics such as kinematics, types of links, kinematic pairs, classification of kinematic pairs based on contact and motion, degrees of freedom, kinematic chains, joints, inversion of mechanisms, and straight line generators. Examples of mechanisms are provided to illustrate concepts like the 4-bar linkage, Scott-Russell straight line mechanism, Peaucellier straight line mechanism, and mechanical advantage.
KInematic of Machine(Mechanical Engineering)Surendr Bhil
This document discusses kinematics and mechanisms. It defines kinematics as the branch of mechanics that describes the motion of bodies without considering the causes of motion. Kinematics examines displacement, velocity, and acceleration over time through graphical representations. Common mechanisms discussed include four-bar linkages, single slider-crank chains, and double slider-crank chains. Kinematic pairs constrain the motion between links and can be lower pairs with surface contact or higher pairs with point/line contact. Kinematic inversions occur when different links in a chain are fixed, resulting in different mechanisms.
The document contains 38 questions related to machine design. The questions cover topics such as standardization of sizes, tolerances, fits, design of joints, shafts, levers, frames and other machine elements. Design calculations are required to determine dimensions that satisfy given loading and stress criteria. Materials, their properties and appropriate factors of safety are provided. References for solutions and examples are given from standard machine design textbooks.
12. Design of Machine Elements -Belt drive.pptxPraveen Kumar
This document discusses the design of belt drives. It begins with an introduction to belt drives, their advantages and disadvantages. It then discusses belt drive selection criteria and types of belts and materials. The document covers various types of flat belt drives including open, crossed, and compound drives. It derives relationships for velocity ratio and belt tensions. It also addresses slip and creep in belts and how they affect power transmission efficiency. The summary covers the key aspects and applications of belt drive design.
- The document discusses degrees of freedom (DOF) and Gruebler's criterion for calculating DOF. It then explains Grashof's four-bar mechanism and the conditions for it to have full rotation.
- Kinematic inversions are introduced as the process of obtaining different mechanisms from the same kinematic chain by fixing different links. The four possible inversions of a four-bar chain are described.
- Examples of inversions include the beam engine (crank and lever), the coupling rod of a locomotive (double crank), and Watt's indicator mechanism (double lever).
The document discusses three types of rear axle casings: 1) Split type which has two halves bolted together and requires removing the entire rear axle for repairs; 2) Banjo or separate carrier type which has a one-piece casing that carries the differential unit and allows removing half shafts for repairs; and 3) Salisbury or integral carrier type which is like the banjo type but has permanent housing tubes welded to the differential housing, making it the most widely used type today.
Fundamentals of kinematics and mechanismsajitkarpe1986
This document discusses kinematic mechanisms. It begins with defining key terms like links, pairs, and degrees of freedom. It then covers different types of links and pairs, including sliding, turning, rolling, and screw pairs. Methods for analyzing mechanisms like Kutzbach's criterion and Grubler's criterion are presented. Several examples of basic kinematic chains and their inversions including four bar chains and slider crank mechanisms are discussed in detail.
the presentation consists of various important terms that are generally linked with the analysis of a common four bar mechanism which are as follows - coupler curves, toggle positions, transmission angles, mechanical advantage, acc analysis and coriolis component.
This document contains a theory question bank related to mechanisms and kinematics. It includes 51 questions covering various topics such as definitions of terms like kinematic chain, degrees of freedom, types of constraints; inversions of mechanisms; calculation of degrees of freedom; explanations of mechanisms like steering gears, Whitworth quick return, Geneva, Oldham's coupling, and elliptical trammel; Grashoff's law; and more. It also contains 20 multiple choice questions testing knowledge of kinematic pairs, links, steering gears, inversions, and other topics.
The document discusses the analysis and synthesis of mechanisms and machines. It provides definitions and explanations of key concepts related to kinematics and dynamics of machines including links, kinematic pairs, degrees of freedom, mechanisms, and machines. The summary discusses the analysis of existing mechanisms to study their motions and forces, while synthesis involves designing the parts of a mechanism. Key types of links, kinematic pairs, and methods for determining degrees of freedom of mechanisms are also summarized.
This document provides an overview of dynamics of machines including:
1. It defines force, applied force, constraint forces, and types of constrained motions like completely, incompletely, and successfully constrained motions.
2. It discusses static force analysis, dynamic force analysis, and conditions for static and dynamic equilibrium.
3. It covers concepts like inertia, inertia force, inertia torque, D'Alembert's principle, and principle of superposition.
4. It derives expressions for forces acting on the reciprocating parts of an engine while neglecting the weight of the connecting rod.
Cams are used to convert rotary motion to oscillatory motion or vice versa. They are commonly used in internal combustion engines to operate valves. This chapter discusses the fundamentals of cam and follower design including the different types of cams, followers, motions, and cam profiles. The objectives are to understand basic concepts and terminology and learn how to design a cam and follower set to achieve a desired output motion.
This document discusses the law of gearing in three main points:
1) The common normal at the point of contact between gear teeth must always pass through the pitch point. This is the fundamental condition for designing gear teeth profiles.
2) The angular velocity ratio between two gears must remain constant throughout meshing.
3) The angular velocity ratio is inversely proportional to the ratio of the distances of the pitch point P from the gear centers O1 and O2. The common normal intersecting the line of centers at P divides the center distance inversely proportional to the angular velocity ratio.
Kinematic link, Types of links, Kinematic pair, Types of constrained motions, Types of Kinematic pairs, Kinematic chain, Types of joints, Mechanism, Machine, Degree of freedom, Mobility of Mechanism, Inversion, Grashoff’s law, Four-Bar Chain and its Inversions, Slider crank Chain and its Inversions, Double slider crank Chain and its Conversions, Mechanisms with Higher pairs, Equivalent Linkages and its Cases - Sliding Pairs in Place of Turning Pairs, Spring in Place of Turning Pairs, Cam Pair in Place of Turning Pairs
The document discusses the four bar linkage mechanism. It consists of four rigid links connected by four pin joints, forming a quadilateral. The length of one link cannot exceed the sum of the other three links. A variety of mechanisms can be formed from slight variations to the four bar linkage, including changing link proportions or combining multiple linkages. The four bar linkage is the simplest closed loop mechanism and has one degree of freedom. Inversions of the four bar linkage include the beam engine, locomotive coupling rod, and Watt's indicator mechanism. The single slider crank chain converts rotary to reciprocating motion and vice versa using one sliding and three turning pairs. Inversions include pendulum pumps, oscillating cylinder engines, and internal
This document discusses different types of gear trains including simple, compound, reverted, and epicyclic gear trains. It provides details on the components, configurations, terminology, and methods for calculating speed and velocity ratios for each type of gear train. Key points covered include how simple gear trains involve one gear on each shaft, compound gear trains have multiple gears on a shaft, reverted gear trains have coaxial input and output shafts, and epicyclic gear trains allow shaft axes to move relative to a fixed axis. Formulas and a tabular method are presented for analyzing epicyclic gear trains.
Three types of gear trains are described:
1. Simple gear trains involve one gear on each shaft to transmit power.
2. Compound gear trains have more than one gear on a shaft, allowing for larger speed reductions.
3. Epicyclic gear trains have gears mounted on shafts that can move relative to a fixed axis, enabling high velocity ratios with moderate sized gears. Epicyclic trains are used in automotive differentials and machinery.
This document discusses different types of gear trains:
1. Simple gear train which uses one gear on each shaft to transmit motion.
2. Compound gear train which uses more than one gear on a shaft.
3. Reverted gear train where the first and last gears are co-axial and rotate in the same direction.
4. Epicyclic gear train where the gear axes can move relative to a fixed axis, allowing one gear to drive another in circular motion.
Formulas for speed ratio and train value are provided for each gear train type. Examples of applications like differentials are also mentioned.
Unit 7-gear trains, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
The document discusses kinematics of machines and mechanisms. It covers topics such as kinematics, types of links, kinematic pairs, classification of kinematic pairs based on contact and motion, degrees of freedom, kinematic chains, joints, inversion of mechanisms, and straight line generators. Examples of mechanisms are provided to illustrate concepts like the 4-bar linkage, Scott-Russell straight line mechanism, Peaucellier straight line mechanism, and mechanical advantage.
KInematic of Machine(Mechanical Engineering)Surendr Bhil
This document discusses kinematics and mechanisms. It defines kinematics as the branch of mechanics that describes the motion of bodies without considering the causes of motion. Kinematics examines displacement, velocity, and acceleration over time through graphical representations. Common mechanisms discussed include four-bar linkages, single slider-crank chains, and double slider-crank chains. Kinematic pairs constrain the motion between links and can be lower pairs with surface contact or higher pairs with point/line contact. Kinematic inversions occur when different links in a chain are fixed, resulting in different mechanisms.
The document contains 38 questions related to machine design. The questions cover topics such as standardization of sizes, tolerances, fits, design of joints, shafts, levers, frames and other machine elements. Design calculations are required to determine dimensions that satisfy given loading and stress criteria. Materials, their properties and appropriate factors of safety are provided. References for solutions and examples are given from standard machine design textbooks.
12. Design of Machine Elements -Belt drive.pptxPraveen Kumar
This document discusses the design of belt drives. It begins with an introduction to belt drives, their advantages and disadvantages. It then discusses belt drive selection criteria and types of belts and materials. The document covers various types of flat belt drives including open, crossed, and compound drives. It derives relationships for velocity ratio and belt tensions. It also addresses slip and creep in belts and how they affect power transmission efficiency. The summary covers the key aspects and applications of belt drive design.
- The document discusses degrees of freedom (DOF) and Gruebler's criterion for calculating DOF. It then explains Grashof's four-bar mechanism and the conditions for it to have full rotation.
- Kinematic inversions are introduced as the process of obtaining different mechanisms from the same kinematic chain by fixing different links. The four possible inversions of a four-bar chain are described.
- Examples of inversions include the beam engine (crank and lever), the coupling rod of a locomotive (double crank), and Watt's indicator mechanism (double lever).
The document discusses three types of rear axle casings: 1) Split type which has two halves bolted together and requires removing the entire rear axle for repairs; 2) Banjo or separate carrier type which has a one-piece casing that carries the differential unit and allows removing half shafts for repairs; and 3) Salisbury or integral carrier type which is like the banjo type but has permanent housing tubes welded to the differential housing, making it the most widely used type today.
Fundamentals of kinematics and mechanismsajitkarpe1986
This document discusses kinematic mechanisms. It begins with defining key terms like links, pairs, and degrees of freedom. It then covers different types of links and pairs, including sliding, turning, rolling, and screw pairs. Methods for analyzing mechanisms like Kutzbach's criterion and Grubler's criterion are presented. Several examples of basic kinematic chains and their inversions including four bar chains and slider crank mechanisms are discussed in detail.
the presentation consists of various important terms that are generally linked with the analysis of a common four bar mechanism which are as follows - coupler curves, toggle positions, transmission angles, mechanical advantage, acc analysis and coriolis component.
This document contains a theory question bank related to mechanisms and kinematics. It includes 51 questions covering various topics such as definitions of terms like kinematic chain, degrees of freedom, types of constraints; inversions of mechanisms; calculation of degrees of freedom; explanations of mechanisms like steering gears, Whitworth quick return, Geneva, Oldham's coupling, and elliptical trammel; Grashoff's law; and more. It also contains 20 multiple choice questions testing knowledge of kinematic pairs, links, steering gears, inversions, and other topics.
The document discusses the analysis and synthesis of mechanisms and machines. It provides definitions and explanations of key concepts related to kinematics and dynamics of machines including links, kinematic pairs, degrees of freedom, mechanisms, and machines. The summary discusses the analysis of existing mechanisms to study their motions and forces, while synthesis involves designing the parts of a mechanism. Key types of links, kinematic pairs, and methods for determining degrees of freedom of mechanisms are also summarized.
This document provides instruction on determining velocities and angular velocities in mechanisms using the relative velocity method. It contains 5 problems:
1) Finding the angular velocity of a link in a 4-bar chain mechanism.
2) Determining velocities in a steam engine mechanism including the piston, connecting rod, and points on the connecting rod.
3) Finding the linear velocity of a slider and angular velocity of a link in a mechanism when the crank is at a specified angle.
4) Drawing a velocity diagram for an engine mechanism and determining the slider and link accelerations.
5) Determining velocities and angular velocities, and then accelerations, in a toggle mechanism where the crank speed is increasing.
The document contains definitions and concepts related to kinematics and machine elements. It defines terms like kinematic link, structure, higher pair, kinematic chain, kinematic pair, mechanism, inversion, and types of kinematic chains. It also discusses concepts related to velocity and acceleration analysis, gears, belts, clutches, brakes, bearings, cams, vibration, and balancing of rotating masses.
This document provides information about gear trains and epicyclic gear trains. It includes examples of how to calculate speed ratios and determine speeds of various gears in different configurations of epicyclic gear trains using the tabular method. Several problems are also provided at the end for determining speeds and directions of rotation of gears in various epicyclic gear train arrangements given certain input conditions.
This document describes the design of a six-legged walking mechanism. It discusses designing each leg with six linkages that can convert rotational motion to walking motions. It also discusses using a tripod gait where three legs on each side move together in alternating triangular support patterns. The transmission system is designed with a single motor that drives three shafts connected by sprockets and chains to synchronize the six legs through their respective four-bar linkage designs.
this is my presentation of theory of machine subject. the topic of this presentation is static force analysis. In gujarat technological university mechanical engineering third year syllabus topic. there are many types of forces described in this ppt. and examples and domestic use.
This document provides an introduction to mechanisms and kinematics. It defines kinematics as the study of motion without considering forces, specifically looking at position, displacement, rotation, speed, velocity and acceleration. Kinematic analysis determines these values and provides geometry dimensions and the operation range of a mechanism. Dynamic analysis considers power capacity, stability and member loads. A machine is a device using mechanical power with interrelated parts, while a mechanism is the portion transferring motion and forces from a power source to output. Common mechanism components and joints are defined.
The document provides details about the syllabus of a course on Kinematics of Machinery. It is divided into 5 units. Unit I discusses mechanisms, kinematic pairs, degrees of freedom and inversions. Unit II covers velocity and acceleration analysis using graphical and relative velocity methods. Unit III focuses on straight line motion mechanisms. Unit IV discusses cams and cam mechanisms. Unit V is about higher pairs like gears, gear trains, epicyclic gears and their analysis. The document also provides the session planner and question bank for the course.
This document discusses kinematics of machinery and mechanisms. It defines a machine as a collection of mechanisms that transmit force from a power source to overcome resistance. Mechanisms are made up of links connected by kinematic pairs, which allow relative motion between elements. There are lower and higher pairs based on the nature of contact between elements. The document also discusses degrees of freedom, Grubler's criterion for calculating degrees of freedom, and examples of kinematic chains including constrained, unlocked, and unconstrained chains.
Theory of machines by rs. khurmi_ solution manual _ chapter 11Darawan Wahid
This document provides solutions to problems involving belt drives, including calculations of speed ratios, tensions, power transmission, and efficiency. It solves for:
1) The speeds of driven pulleys using no-slip and slip equations, with sample speeds of 239.4 r.p.m and 232.22 r.p.m.
2) Transmitted power of 3.983 kW for a pulley drive system with given parameters.
3) A belt width of 67.4 mm needed to transmit 7.5 kW between pulleys without exceeding tension limits.
This document provides an introduction to kinematics and the analysis of mechanisms using velocity and acceleration diagrams. It discusses:
1. Key concepts in mechanisms including different types of motion transformations and common mechanism components like four-bar linkages.
2. How to determine the displacement, velocity, and acceleration of points within a mechanism using either mathematical equations or graphical methods using velocity and acceleration diagrams.
3. How to construct velocity diagrams by determining the absolute and relative velocities of points and drawing them as vectors. This allows solving for unknown velocities.
4. How to extend the method to acceleration diagrams to determine centripetal and other accelerations which are important for calculating inertia forces.
The document provides examples
This document discusses different types of gears used in mechanical systems to transmit rotational motion between parallel or intersecting shafts. It describes spur gears, helical gears, bevel gears, and worm gears. Key terminology for gears like pitch circle, diametral pitch, module, addendum, dedendum, and contact ratio are defined. The fundamental law of gearing relating the rotational speeds of meshing gears is explained. Involute tooth profiles and pressure angles are also covered.
Unit 1-introduction to Mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
The document discusses static force analysis and equilibrium of mechanisms. It covers topics like static equilibrium, equilibrium of two and three force members, members with two forces and torque, free body diagrams, and the principle of virtual work. Examples of static force analysis of four bar and slider-crank mechanisms are presented. Methods to determine the forces and torques required for static equilibrium are demonstrated through graphical techniques like force triangles and the principle of virtual work.
The document discusses the history and development of chocolate over centuries. It details how cocoa beans were first used by Mesoamerican cultures before being introduced to Europe, where it became popular in drinks and confections. The document also notes that modern chocolate production methods were established in the 19th century to allow chocolate to be consumed on a larger scale.
This document provides equations and calculations for determining the mean cycles to failure (x-bar) and standard deviation of cycles to failure (s_x) for a sample of fatigue test data. The sample data consists of the number of cycles to failure (x) and applied force (f) for 10 tests. The mean x-bar is calculated as the sum of the product of f and x divided by the sum of f, which equals 122.9 kcycles. The standard deviation s_x is calculated using the variance formula, which equals 30.3 kcycles.
This document discusses the theory of machinery and kinematic analysis. It defines theory of machinery as the branch of engineering science dealing with relative motion between machine parts and forces acting on them. The theory is subdivided into kinematics, dynamics, kinetics, and statics. Kinematic links, pairs, and chains are also defined and classified. Common kinematic pairs like sliding, turning, rolling, and screw pairs are described along with examples. Finally, single and double slider crank chains, a crank and slotted lever quick return mechanism, and friction are briefly covered.
3131906 - INTRODUCTION OF MECHANISMS AND MACHINES Takshil Gajjar
The document discusses various concepts related to kinematics and mechanisms including:
- Kinematic links that make up mechanisms and their types including rigid, flexible, and fluid links.
- Kinematic pairs and their classification based on relative motion and contact between elements. Common pairs include sliding, turning, rolling, screw, and spherical pairs.
- Kinematic chains formed by coupling kinematic pairs to transmit motion from one link to another. The simplest kinematic chain is the four-bar chain.
- Degrees of freedom and mobility of mechanisms, which is the number of independent coordinates needed to define the configuration. Formulas like Kutzbach's criterion are used to calculate this.
1. The document discusses kinematic pairs which are the contacts between links in a mechanism that constrain their relative motion. It describes the types of kinematic pairs such as lower pairs which have surface contact, and higher pairs which have point or line contact.
2. Key types of kinematic pairs are described based on their relative motion, including revolute pairs which allow rotation, prismatic pairs which allow linear translation, cylindrical pairs which allow both rotation and translation, and spherical pairs which allow three degrees of freedom.
3. The document also compares the differences between mechanisms, machines, and structures. Mechanisms modify and transmit motion between moving parts, machines transform energy and do work, and structures transmit forces without internal motion between
1. The document discusses the fundamentals and types of mechanisms in machine theory. It covers kinematics, dynamics, types of links, kinematic pairs, and classifications of kinematic pairs.
2. A kinematic chain is formed when kinematic pairs are coupled together to transmit motion. The relationships between the number of links, pairs, and joints in a kinematic chain are explained.
3. Common kinematic chains including four-bar chains, single slider-crank chains, and double slider-crank chains are described. Inversions of mechanisms by fixing different links are used to obtain different mechanisms.
Material and mechanical 5082_Lecture_1.pdfDrBarkatUllaha
Theory of Machines and Mechanism may be defined as the branch of engineering that deals with the study of relative motion between machine parts and the forces acting on them. It is essential for engineers to understand when designing machines. There are four main branches: kinematics studies motion without forces, dynamics studies forces during motion, kinetics deals with inertia forces from mass and motion, and statics studies forces when parts are at rest. Joints connect links to transmit motion and force, and can be classified by motion type, contact type, connection type, and number of links joined. The number of degrees of freedom determines the inputs needed to predict output motion.
The basic of KOM is include “Mechanisms” and “Machines”. The word Mechanism has many meanings. In kinematics, a mechanism is a means of transmitting, controlling, or constraining relative movement .
This document discusses basics of kinematic mechanisms including definitions of key terms like kinematic links, pairs, chains, and degrees of freedom. It describes different types of kinematic pairs such as sliding, turning, and rolling pairs. It also discusses kinematic chains and how they are formed by coupling kinematic pairs so that motion is transmitted through the links in a constrained way. Examples of different types of links, pairs, and chains are provided.
This document provides information about the Kinematics of Machines course offered by the Department of Mechanical Engineering at JSS Academy of Technical Education in Bangalore, India. It lists the textbook and reference books for the course, as well as the course outcomes which include being able to describe machine concepts and mechanisms, identify mechanism motions, analyze planar mechanisms analytically and graphically, analyze motion transmission elements like gears and cams, and utilize kinematic aspects for machine design. The document also provides an overview of the topics to be covered in the course, including basic definitions, kinematic chains, inversions, and types of kinematic pairs and linkages.
This document provides information about the Kinematics of Machines course offered by the Department of Mechanical Engineering at JSS Academy of Technical Education in Bangalore, India. It lists the course code, textbooks, reference books, course outcomes, and chapter topics that will be covered. The topics include basic definitions related to kinematic elements, pairs, chains, and mechanisms. It also describes common kinematic chains like four-bar linkages, single slider-crank mechanisms, and double slider-crank mechanisms. Specific examples and applications of each type are provided.
Module 1 introduction to kinematics of machinerytaruian
This document provides information about the Kinematics of Machines course offered by the Department of Mechanical Engineering at JSS Academy of Technical Education in Bangalore, India. It lists the course code, textbooks, reference books, course outcomes, and chapter topics that will be covered. The topics include basic definitions related to kinematic elements, pairs, chains, and mechanisms. It describes types of kinematic pairs and chains, including four-bar chains, single slider-crank chains, and double slider-crank chains. It also covers degrees of freedom, Grubler's criterion, and inversions of mechanisms.
This document discusses links and kinematic pairs in mechanical mechanisms. It defines a link as a single resistant body or combination of bodies with inflexible connections that moves relative to other parts. Links are classified by the number of ends they connect to other links. Kinematic pairs connect links and allow relative motion between them. Pairs are classified by their type of contact, relative motion, and constraint between links. Common pairs include turning, sliding, rolling, and screw pairs. The document provides examples of links and pairs in slider-crank mechanisms.
This document provides study materials for the course ME3491 Theory of Machines including an overview of the topics covered in Unit I on kinematics of mechanisms. It defines key terms like mechanisms, kinematic links, kinematic pairs, and kinematic chains. It also discusses various types of kinematic pairs and chains as well as analytical methods and computer approaches for kinematic analysis. The document concludes with sample two-mark questions and answers on topics related to kinematic analysis of mechanisms.
1. A mechanism is the mechanical portion of a machine that transfers motion and forces from a power source to an output. It consists of rigid linkages and joints that transmit motion and/or force in a predetermined fashion.
2. Key components of a mechanism include links, joints, and kinematic pairs. Links are rigid bodies that connect via various kinematic pairs like lower pairs (area contact) and higher pairs (line/point contact).
3. The motion of links is characterized by the kinematic pairs that connect them, including sliding, rolling, turning, and screw pairs that define the relative motions between links like rotation, translation, and their combination.
This document provides an introduction to kinematics of machines. It defines key terms like kinematics, mechanisms, machines, degrees of freedom, and types of links and motion. It also describes different types of kinematic pairs that constrain relative motion between links, including lower pairs like sliding and revolute pairs, and higher pairs. The main topics covered are the basic concepts, definitions, and analytical tools used in the kinematic analysis of machines.
This document provides an overview of kinematics of machinery and mechanisms. It discusses:
1) The basics of mechanisms, including their function to transfer motion and forces. Kinematics deals with relative motion between machine parts, while dynamics deals with forces acting on moving parts.
2) Common kinematic pairs like sliding, turning, rolling, and spherical pairs that constrain relative motion between links. Lower pairs have surface contact while higher pairs have line or point contact.
3) Methods for analyzing the motion of mechanisms like velocity and acceleration diagrams, instantaneous centers of velocity, and criteria for determining degrees of freedom.
4) Applications of kinematic analysis to specific mechanisms like slider-crank, four-bar link
This document provides an overview of kinematics theory and concepts related to mechanisms and machines. It defines key terms like mechanisms, kinematic pairs, degrees of freedom, and mobility. It also describes common mechanisms like the slider-crank and four-bar mechanisms. Examples of constrained motions and different types of links, joints, and chains are explained.
This document provides an introduction to machine fundamentals and mechanical engineering concepts. It defines a machine as a device that transmits and modifies energy to perform a specific task through interconnected components. Machines are designed to achieve a specific motion or force transformation and have defined inputs and outputs. The document then discusses different types of machines and provides examples. It defines links and kinematic pairs that connect machine components and allows relative motion. Different types of links, pairs, and kinematic chains are described. The document concludes with discussing different types of motions involved in mechanisms.
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MET 304 Welded joints example-3-solutionhotman1991
The maximum stress in the reinforced weld of a bracket plate is calculated to be 10,408.5 psi. The plate is subjected to a load of 2,200 lbs applied 6.5 inches from the weld. The geometry and load are used to calculate the polar moment of area, torque, and radial distance to determine the torsional stress. This stress is resolved into vertical and horizontal components, and combined with the direct vertical stress from the load to find the total vertical and resultant stresses. The resultant stress is then multiplied by a concentration factor to determine the maximum stress in the weld.
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The document discusses various types of mechanical joints including welded joints. It describes common welding processes like oxy-fuel gas welding, shield metal arc welding, and gas tungsten arc welding. The document also covers welding joints, terminology, design considerations, stress analysis of welded joints under different loading conditions, and includes examples of calculating stresses in welded joints.
MET 304 Mechanical joints riveted_jointshotman1991
Riveting was commonly used to join metal parts before welding but is now less common. Rivets are cylindrical shafts inserted through holes in materials to be joined and formed into heads on both ends. Riveted joints can fail due to bending, shearing of rivets, crushing of rivets or plates, or tearing of materials. The document provides equations to calculate load capacities of riveted joints based on factors like rivet material properties, number of rivets, and whether rivets are in single or double shear. Design of riveted joints involves selecting rivet size, number and layout to optimize strength and load distribution.
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This document discusses different types of cams and cam mechanisms. It describes various types of followers based on their contacting surface, motion, and path of motion. It also defines important cam terminology used to describe cam profiles such as base circle, trace point, pressure angle, pitch point, pitch circle, and lift. The document provides examples of cam profiles that produce uniform velocity, simple harmonic, uniform acceleration/retardation, and cycloidal motions in the follower. It includes example problems of constructing cam profiles for different follower motions and specifications.
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This document discusses riveted joints, including their applications, materials used, types of joints, and failure modes. Riveted joints are used in pressure vessels, boilers, tanks, bridges, ships, airplanes, cranes, buildings, and machinery. The document describes rivets and their components. It explains the types of riveted joints, including lap and butt joints. It then covers the potential failure modes of riveted joints, such as bending of rivets or plates, shearing of rivets, crushing of rivets or plates, rupture of plates by tension, and tearing or shearing of margins. The document provides examples of calculations for determining the load capacity of a ri
The document discusses different types of shaft keys, how they transmit torque, and their design. It describes various key shapes, sizes, and tapers for different duty levels. Formulas are provided for calculating the crushing strength and shear strength of keys based on the torque transmitted, key dimensions, and material properties. An example problem demonstrates selecting a suitable square key size for a given shaft and torque requirement by analyzing both crushing strength and shear strength.
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1. MET 305 MECHANICS OF MACHINES THEORY-1
MECHANISMS
Definitions and Terminology
1. Introduction
The subject Theory of Machines may be defined as that branch of Engineering-science, which deals
with the study of relative motion between the various parts of a machine, and forces which act on
them. The knowledge of this subject is very essential for an engineer in designing the various parts of
a machine.
1.1 Sub-divisions of Theory of Machines
The Theory of Machines may be sub-divided into the following four branches :
1. Kinematics. It is that branch of Theory of Machines which deals with the relative
motion between the various parts of the machines.
2. Dynamics. It is that branch of Theory of Machines which deals with the forces and their
effects, while acting upon the machine parts in motion.
3. Kinetics. It is that branch of Theory of Machines which deals with the inertia forces which
arise from the combined effect of the mass and motion of the machine parts
4. Statics. It is that branch of Theory of Machines which deals with the forces and their
effects while the machine parts are at rest. The mass of the parts is assumed to be
negligible.
1.2 A machine is a device which receives energy and transforms it into some useful work. A
machine consists of a number of parts or bodies. In this chapter, we shall study the
mechanisms of the various parts or bodies from which the machine is assembled. This is
done by making one of the parts as fixed, and the relative motion of other parts is
determined with respect to the fixed part.
2. Kinematic link or Element
Any part of a machine, which moves relative to some other part, is known as a kinematic
link (or simply link) or an element. A link may consist of several parts, which are rig idly
fastened together, so that they do not move relative to one another. For example, in a
reciprocating steam engine, as shown above, crank, connecting rod, piston, engine frame
and main bearings are the four links.
A link or an element need not to be a rigid body, but it must be a resistant body. A body is
said to be a resistant body if it is capable of transmitting the required forces with negligible
deformation. Thus a link should have the following two characteristics:
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2. MET 305 MECHANICS OF MACHINES THEORY-1
1. It should have relative motion, and
2. It must be a resistant body.
2.1 Types of Links
In order to transmit motion, the driver and the follower may be connected by the following
three types of links:
2.1.1. Rigid link A rigid link is one, which does not undergo any deformation while
transmitting motion. Strictly speaking, rigid links do not exist. However, as the deformation
of a connecting rod, crank etc. of a reciprocating steam engine is not appreciable, they can
be considered as rigid links.
2.1.2. Flexible link A flexible link is one which is partly deformed in a manner not to affect
the transmission of motion. For example, belts, ropes, chains and wires are flexible links and
transmit tensile forces only.
2.1.3. Fluid link. A fluid link is one which is formed by having a fluid in a receptacle and the
motion is transmitted through the fluid by pressure or compression only, as in the case of
hydraulic presses, jacks and brakes.
2.2 Structure
It is an assemblage of a number of resistant bodies (known as members) having no relative
motion between them and meant for carrying loads having straining action. A railway
bridge, a roof truss, machine frames etc., are the examples of a structure.
2.3 Difference between a Machine and a Structure (frame)
The following are the main differences between a machine and a structure.
1. The parts of a machine move relative to one another, whereas the members of a
structure do not move relative to one another.
2. A machine transforms the available energy into some useful work, whereas in a
structure no energy is transformed into useful work.
3. The links of a machine may transmit both power and motion, while the members of
a structure transmit forces only.
3. Kinematic pair
When two links or elements are connected in such a way that the relative motion between
them is completely or successfully constrained, they form a kinematic pair.
3.1 Types of Constrained Motions
Following are the three types of constrained motions:-
3.1.1 Completely constrained motion
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When the motion between a pair is limited to a definite direction irrespective of the
direction of force applied, then the motion is said to be a completely constrained motion.
Shaft with collars in a circular hole Square bar in a square hole
The motion of a square bar in a square hole and the motion of a shaft with collars at each
end in a circular hole, are also examples of completely constrained motion.
3. 1.2. Incompletely constrained motion
When the motion between a pair can take place in more than one direction, then the
motion is called an incompletely constrained motion. The change in the direction of
impressed force may alter the direction of relative motion between the pair. A circular bar
or shaft in a circular hole is an example of an incompletely constrained motion as it may
either rotate or slide in a hole. These both motions have no relationship with the other.
Shaft in a circular hole Shaft in a foot step bearing
3.1.3. Successfully constrained motion
When the motion between the elements, forming a pair, is such that the constrained
motion is not completed by itself, but by some other means, then the motion is said to be
successfully constrained motion. Consider a shaft in a foot-step bearing as shown above.
The shaft may rotate in a bearing or it may move upwards. This is a case of incompletely
constrained motion. But if the load is placed on the shaft to prevent axial upward
movement of the shaft, then the motion of the pair is said to be successfully constrained
motion. The motion of an I.C. engine valve (these are kept on their seat by a spring) and the
piston reciprocating inside an engine cylinder are also the examples of successfully
constrained motion.
3.2 Classification of Kinematic Pairs
The kinematic pairs may be classified according to the following considerations:
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3.2.1. According to the type of relative motion between the elements The kinematic pairs
according to type of relative motion between the elements may be classified as discussed
below:
(a) Sliding pair. When the two elements of a pair are connected in such a way that
one can only slide relative to the other, the pair is known as a sliding pair. The piston and
cylinder, cross-head and guides of a reciprocating steam engine, ram and its guides in
shaper, tail stock on the lathe bed etc. are the examples of a sliding pair. A little
consideration will show that a sliding pair has a completely constrained motion.
(b) Turning pair. When the two elements of a pair are connected in such a way that
one can only turn or revolve about a fixed axis of another link, the pair is known as turning
pair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal
bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their
axles etc. are the examples of a turning pair. A turning pair also has a completely
constrained motion.
(c) Rolling pair. When the two elements of a pair are connected in such a way that
one rolls over another fixed link, the pair is known as rolling pair. Ball and roller bearings are
examples of rolling pair.
(d) Screw pair. When the two elements of a pair are connected in such a way that
one element can turn about the other by screw threads, the pair is known as screw pair.
The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.
(e) Spherical pair. When the two elements of a pair are connected in such a way
that one element (with spherical shape) turns or swivels about the other fixed element, the
pair formed is called a spherical pair. The ball and socket joint, attachment of a car mirror,
pen stand etc., are the examples of a spherical pair.
3.2.2. According to the type of contact between the elements The kinematic pairs
according to the type of contact between the elements may be classified as discussed
below:
(a) Lower pair. When the two elements of a pair have a surface contact when
relative motion takes place and the surface of one-element slides over the surface of the
other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs
and screw pairs form lower pairs. High Friction
(b) Higher pair. When the two elements of a pair have a line or point contact when
relative motion takes place and the motion between the two elements is partly turning and
partly sliding, then the pair is known as higher pair. A pair of friction discs, toothed gearing,
belt and rope drives, ball and roller bearings and cam and follower are the examples of
higher pairs. Low Friction
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5. MET 305 MECHANICS OF MACHINES THEORY-1
4. Kinematic Chain
A kinematic chain may be defined as a combination of kinematic pairs, joined in such a way
that each link forms a part of two pairs and the relative motion between the links or
elements is completely or successfully constrained. For example, the crankshaft of an
engine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rod
with the crank forms a second kinematic pair, the piston with the connecting rod forms a
third pair and the piston with the cylinder forms a fount pair. The total combination of
these links is a kinematic chain.
5. Mechanism
When one of the links of a kinematic chain is fixed, for transmitting or transforming motion
the chain is known as mechanism. e.g. Engine indicators, typewriter etc. A mechanism with
four links is known as simple mechanism, and the mechanism with more than four links is
known as compound mechanism. When a mechanism is required to transmit power or to do
some particular type of work, it then becomes a machine. In such cases, the various links or
elements have to be designed to withstand the forces (both static and kinetic) safely.
A little consideration will show that a mechanism may be regarded as a machine in which
each part is reduced to the simplest form to transmit the required motion.
6. Degrees of freedom (Mobility)
The number of degrees of freedom of a linkage is the number of independent parameters
we must specify to determine the position of every link relative to the frame or fixed link.
The number of degrees of freedom of a linkage may also be called the mobility of the
linkage. If the instantaneous configuration of a system may be completely defined by
specifying one independent variable, that system has one degree of freedom. Most
practical mechanisms have one degree of freedom.
An unconstrained rigid body has six degrees of freedom: translation in three coordinate
directions and rotation about three coordinate axes. A body that is restricted to motion in a
plane has three degrees of freedom: translation in two coordinate directions and rotation
within the plane.
7. Inversion of Mechanism
We have already discussed that when one of links is fixed in a kinematic chain, it is called a
mechanism. So we can obtain as many mechanisms as the number of links in a kinematic
chain by fixing, in turn, different links in a kinematic chain. This method of obtaining
different mechanisms by fixing different links in a kinematic chain is known as inversion of
the mechanism.
It may be noted that the relative motions between the various links is not changed in any
manner through the process of inversion, but their absolute motions (those measured with
respect to the fixed link) may be changed drastically.
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6. MET 305 MECHANICS OF MACHINES THEORY-1
Note: The part of a mechanism, which initially moves with respect to the frame or fixed link
is called driver and that part of the mechanism to which motion is transmitted is called
follower. Most of the mechanisms are reversible, so that same link can play the role of a
driver and follower at different times. For example, in a reciprocating steam engine, the
piston is the driver and flywheel is a follower while in a reciprocating air compressor, the
flywheel is a driver.
8. Grashof’s Law. A very important consideration while designing a mechanism to be driven
by a motor, obviously, is to ensure that the input link can make complete revolution.
Mechanisms in which no link makes complete revolution would not be useful in such
applications. For four bar chain there is a simple test of whether this is the case.
Grashof’s Law states that, for a planer four-bar linkage, the sum of the shortest and the
longest link length cannot be greater than the sum of the remaining two link lengths, if
there is a continuous relative motion between two members.
9. Types of Kinematic Chains
The most important kinematic chains are those which consist of four lower pairs, each pair being a
sliding pair or a turning pair. The following three types of kinematic chains with four lower pairs are
important from the subject point of view The following three types of kinematic chains with
four lower pairs are important from the subject point of view:
1. Four bar chain or quadric cyclic chain
2. Single slider crank chain, and
3. Double slider crank chain.
These kinematic chains are discussed, in detail, in the following articles.
9.1 Four Bar Chain or Quadric Cycle Chain
Four bar chain
We have already discussed that the kinematic chain is a combination of four or more
kinematic pairs, such that the relative motion between the links or elements is completely
constrained. The simplest and the basic kinematic chain is a four bar chain or quadric cycle
chain, it consists of four links, each of them forms a turning pair at A, B, C and D.
9.2 Inversions of Four Bar Chain
Though there are many inversions of the four bar chain, yet the following are important
from the subject point of view:
9.2.1. Beam engine (crank and lever mechanism)
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Beam engine.
Parts of the mechanism of a beam engine (also known as crank and lever mechanism) which
consists of four links, is shown above. In this mechanism, when the crank rotates about the
fixed centre A, the lever oscillates about a fixed centre D. The end E of the lever CDE is
connected to a piston rod which reciprocates due to the rotation of the crank. In other
words, the purpose of this mechanism is to convert rotary motion into reciprocating
motion.
9.2.2. Coupling rod of a locomotive (Double crank mechanism)
Coupling rod of a locomotive
The mechanism of a coupling rod of a locomotive (also known as double crank mechanism)
which consists of four links is shown above. In this mechanism, the links AD arid BC (having
equal length) act as cranks and are connected to the respective wheels. The link CD acts as a
coupling rod and the link AB is fixed in order to maintain a constant centre to centre
distance between them. This mechanism is meant for transmitting rotary motion from one
wheel to the other wheel.
9.2.3. Pantograph (Double Lever Mechanism)
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When it is desired to duplicate some motion exactly but to a reduced or enlarged scale,
some short of copying device in the form of Pantograph is used. It is basically a quadric
cycle chain in the form of a parallelogram.
9.2.3. a Indicator mechanism (Double lever mechanism)
Watt's indicator mechanism
A Watt's indicator mechanism (also known as Watt's straight line mechanism or double
lever mechanism) which consists of four links is shown above. The four links are BC
extended to A, CD extended to E, BF and DF. Displacement of the joint F is directly
proportional to the pressure of gas or steam which acts on the indicator plunger. On any
small displacement of the mechanism, the tracing point E at the end of the link CE traces
out approximately a straight line.
The initial position of the mechanism is shown by full lines, whereas the dotted lines show
the position of the mechanism when the gas or steam pressure acts on the indicator
plunger.
9.3 Single Slider Crank Chain
A single slider crank chain is a modification of the basic four bar chain. It consists of one
sliding pair and three turning pairs. It is usually, found in reciprocating steam engine
mechanism, this type of mechanism converts rotary motion into reciprocating motion and
vice versa.
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Single slider crank chain
The link 1 corresponds to the frame of the engine, which is fixed. The link 2 corresponds to
the crank link 3 corresponds to the connecting rod and link 4 corresponds to cross-head. As
the crank rotates, the cross-head reciprocates in the guides and thus the piston reciprocates
in the cylinder.
9.4 Inversions of Single Slider Crank Chain
We have seen in the previous article that a single slider crank chain is a four-link mechanism.
We know that by fixing, in turn, different links in a kinematic chain, an inversion is obtained
and we can obtain as many mechanisms as the links in a kinematic chain. It is thus obvious,
that four inversions of a single slider crank chain are possible. These inversions are found in
the following mechanisms.
9.4.1. Pendulum pump or Bull engine
Pendulum pump
In this mechanism, the inversion is obtained by fixing the cylinder or link 4 (i.e. sliding pair), as
shown. In this case, when the crank (link 2) rotates, the connecting rod (link 3) oscillates
about a pin pivoted to the fixed link 4 at A and the piston attached to the piston rod (link 1)
reciprocates. The duplex pump which is used to supply feed water to boilers have two pistons
attached to link 1.
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9.4.2. Oscillating cylinder engine
The arrangement of oscillating cylinder engine mechanism, as shown in Fig. 5.24, is used to
convert reciprocating motion into rotary motion. In this mechanism, the link 3 forming the
turning pair is fixed. The link 3 corresponds to the connecting rod of a reciprocating steam
engine mechanism. When the crank (link 2) rotates, the piston attached to piston rod (link
1) reciprocates and the cylinder (link 4) oscillates about a pin pivoted to the fixed link at A.
9.4.3. Rotary internal combustion engine or Gnome engine
Sometimes back, rotary internal combustion engines were used in aviation. But now-a-days
gas turbines are used in its place. It consists of seven cylinders in one plane and all revolves
about fixed centre D, as shown in Fig. 5.25, while the crank (link 2) is fixed. In this
mechanism, when the connecting rod (link 4) rotates, the piston (link 3) reciprocates inside
the cylinders forming link 1
Rotary internal combustion engine
.
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9.4.4. Crank and slotted lever quick return motion mechanism.
Crank and slotted lever quick return motion mechanism
This mechanism is mostly used in shaping machines, slotting machines and in rotary internal
combustion engines. In this mechanism, the link AC (i.e. link 3) forming the turning pair is
fixed. The link 3 corresponds to the connecting rod of a reciprocating steam engine. The
driving crank CB revolves with uniform angular speed about the fixed centre C. A sliding
block attached to the crank pin at B slides along the slotted bar AP and thus causes AP to
oscillate about the pivoted point A. A short link PR transmits the motion from AP to the
ram, which carries the tool and reciprocates along the line of stroke. The line of stroke of
the ram is perpendicular to AC produced.
In the extreme positions, AP1 and AP2 are tangential to the circle and the cutting tool is at the
end of the stroke. The forward or cutting stroke occurs when the crank rotates from the
position CB1, to CB2 (or through an angle β) in the clockwise direction. The return stroke occurs
when the crank rotates from the position CB2 to CB1, (or through angle α) in the clockwise
direction.
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.
Whitworth quick return motion mechanism
9.4.5 Whitworth quick return motion mechanism
This mechanism is mostly used in shaping and slotting machines. In this mechanism, the link CD
(link 2) forming the turning pair is fixed. The link 2 corresponds to a crank in a reciprocating
steam engine. The driving crank CA (link 3) rotates at a uniform angular speed. The slider (link
4) attached to the crank pin at A, slides along the slotted bar PA (link 1) which oscillates at a
pivoted point D. The connecting rod PR carries the ram at R to which a cutting tool is fixed. The
motion of the tool is constrained along the line RD produced, i.e. along a line passing through D
and perpendicular to CD.
When the driving crank CA moves from the position CA1 to CA2 (or the link DP from position
DP1 to DP2) through an angle a in the clockwise direction, the tool moves from the left hand
end of its stroke to the right hand end through a distance 2 PD.
Now when the driving crank moves from the position CA2 to CA1 (or the link DP from DP2to
DP1) through an angle β in the clockwise direction, the tool moves back from right hand end of
its stroke to the left hand end.
A little consideration will show that the time taken during the left to right movement of the
ram (i.e. during forward or cutting stroke) will be equal to the time taken by the driving crank
to move from CA1 to CA2. Similarly, the time taken during the right to left movement of the
ram (or during the idle or return stroke) will be equal to the time taken by the driving crank to
move from CA2 to CA1
Since the crank link CA rotates at uniform angular velocity therefore time taken during the
cutting stroke (or forward stroke) is more than the time taken during the return stroke. In other
words, the mean speed of the ram during cutting stroke is less than the mean speed during the
return stroke.
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9.5. Double Slider Crank Chain
A kinematic chain which consists of two turning pairs and two sliding pairs is known as double
slider crank chain.. We see that the link 2 and link 1 form one turning pair and link 2 and link 3
form the second turning pair. The link 3 and link 4 form one sliding pair and link 1 and link 4
form the second sliding pair.
9.6. Inversions of Double Slider Crank Chain
The following three inversions of a double slider crank chain are important from the subject
point of view:
9.6.1. Elliptical trammels. It is an instrument used for drawing ellipses. This inversion is
obtained by fixing the Slotted plate (link. 4), as shown .A. The fixed plate or link 4 has two
Straight grooves cut in it, at right angles to each other. The link 1 and link 3, are known as
sliders and form sliding pairs with link 4. The link AB (link 2) is a bar which forms turning pair
with links 1 and 3. When the links 1 and 3 slide along their respective grooves, any point on the
link 2 such as P traces out an ellipse on the surface of link 4, as shown below. A little
consideration will show that AP and BP are the semi-major axis and semi-minor axis of the
ellipse respectively.
Elliptical trammels
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Scotch yoke mechanism
9.6.2. Scotch yoke mechanism This mechanism is used for converting rotary motion into a
reciprocating motion. The inversion is obtained by fixing either the link 1 or link 3. The link 1 is
fixed. In this mechanism, when the link 2 (which corresponds to crank) rotates about B as
centre, the link 4 (which corresponds to a frame) reciprocates. The fixed link 1 guides the
frame.
9.6.3. Oldham's coupling An Oldham’s coupling is used for connecting two parallel shafts
whose axes are at a small distance apart. The shafts are coupled in such a way that if one shaft
rotates, the other shaft also rotates at the same speed. This inversion is obtained by fixing the
link 2, as shown below. The shafts to be connected have two flanges (link 1 and link 3) rigidly
fastened at their ends by forging.
Oldham's coupling
The link 1 and link 3 form turning pairs with link 2. These flanges have diametrical slots
cut in their inner faces, as shown in Fig. (b). The intermediate piece (link 4) which is a
circular disc, have two tongues (i.e. diametrical projections) T1 and T2 on each face at
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right angles to each other, as shown in Fig (c). The tongues on the link 4 closely fit into
the slots in the two flanges (link 1 and link 3). The link 4 can slide or reciprocate in the
slots in the flanges.
When the driving shaft A is rotated, the flange C (link 1) causes the intermediate piece
(link 4) to rotate at the same angle through which the flange has rotated, and it further
rotates the flange D (link 3) at the same angle and thus the shaft B rotates. Hence links
1, 3 and 4 have the same angular velocity at every instant. A little consideration will
show, that there is a sliding motion between the link 4 and each of the other links 1 and
3.
If the distance between the axes of the shafts is constant, the centre of intermediate
piece will describe a circle of radius equal to the distance between the axes of the two
shafts. Therefore, the maximum sliding speed of each tongue along its slot is equal to
the peripheral velocity of the centre of the disc along its circular path.
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right angles to each other, as shown in Fig (c). The tongues on the link 4 closely fit into
the slots in the two flanges (link 1 and link 3). The link 4 can slide or reciprocate in the
slots in the flanges.
When the driving shaft A is rotated, the flange C (link 1) causes the intermediate piece
(link 4) to rotate at the same angle through which the flange has rotated, and it further
rotates the flange D (link 3) at the same angle and thus the shaft B rotates. Hence links
1, 3 and 4 have the same angular velocity at every instant. A little consideration will
show, that there is a sliding motion between the link 4 and each of the other links 1 and
3.
If the distance between the axes of the shafts is constant, the centre of intermediate
piece will describe a circle of radius equal to the distance between the axes of the two
shafts. Therefore, the maximum sliding speed of each tongue along its slot is equal to
the peripheral velocity of the centre of the disc along its circular path.
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right angles to each other, as shown in Fig (c). The tongues on the link 4 closely fit into
the slots in the two flanges (link 1 and link 3). The link 4 can slide or reciprocate in the
slots in the flanges.
When the driving shaft A is rotated, the flange C (link 1) causes the intermediate piece
(link 4) to rotate at the same angle through which the flange has rotated, and it further
rotates the flange D (link 3) at the same angle and thus the shaft B rotates. Hence links
1, 3 and 4 have the same angular velocity at every instant. A little consideration will
show, that there is a sliding motion between the link 4 and each of the other links 1 and
3.
If the distance between the axes of the shafts is constant, the centre of intermediate
piece will describe a circle of radius equal to the distance between the axes of the two
shafts. Therefore, the maximum sliding speed of each tongue along its slot is equal to
the peripheral velocity of the centre of the disc along its circular path.
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