Description depends on the Timing table ( Theoretical & Limited Practical)WeekIntroduction/ Theory of machines, Machine, Structure, Links, Kinematics pair, - Kinematics

chain1

Velocity in Mechanisms/ Velocity diagram, Relative velocity of two bodiesmoving in straight line, Relative velocity of point on link2

Relative velocity of slider crank mechanism, Relative velocity of Four-Bar mechanism and Rubbing velocity of a pin joint / Problems3

Acceleration in mechanisms/ Acceleration diagrams, Tangential component, Radial component, Coriolis component4

Acceleration diagrams/ Problems5Exam + Review of Exam6

Balancing of rotating masses/ Single mass rotating in same plane, Several masses rotating in sameplane, Mathematical solution, Graphical solution,

Masses rotating in different planes7

Balancing of rotating masses/ Problems8Balancing of reciprocating masses/ Reciprocating masses(balancing in piston)Exam +

Review of Exam9

Balancing of reciprocating masses/ Problems10Exam + Review of Exam11

Friction Belts/ Belt drive, Types of belts, Velocity ratio of belt, Power transmitted, Ratio of driving tension for flat belt, Ratio of driving tension for V- belt, Angle of contact, The effect

of centrifugal tension, The effect of initial tension12

Friction Belts/ Problems +Exam + Review of Exam13Disc clutch, cone clutch14

Centrifugal clutch15Clutches/ Problems16

Exam + Review of Exam17Flywheel/Turning moment diagram, Energy stored in flywheel, Dimensions of flywheel rim18

Flywheel/ Problems19Exam + Review of Exam20

Gear/ Pitch circle diameter, Condition for transmission ofconstant velocity ratio, Velocity of sliding, Path of contact, Arc of contact, Interference, Rack and pinion21

Gear Trains/ Simple gear trains, Compound gear trains, Simple epicycle gear trains, Compound epicycle gear trains, Torques on gear trains22

Problems23Exam + Review of Exam24

Speed governors/ Dead weight governors(Portor and Proell), Spring loaded governors(Hartnell)25

Governors /Problems26Exam + Review of Exam27

Gyroscope/The gyroscope effect on:airplane, shipandautomobile/ Problems 28Cams29

Cams/ Problems + Exam + Review of Exam30Final Exam Durations

Theory of Machine

Topics to be considered:

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References: 1- Mechanics of Machines:- By: J. Hannah and R.C. Stephens (Text Book).

2- Theory of Machine. By:- R.S. Khurmi and J. K. Gupta.

3- Theory of Machine. By:- Thomas Beven.

4- Kinematics and Dynamics of Machines. By: G.H. Martin

Introduction

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 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.Or defined as: the study of the relative motion between the parts of machine and the study of forces which act on those parts.

Sub- divisions of theory of Machines: They Theory of Machines may be sub- divided into the following four branches: 1- Kinematics: is that branch of theory of machines which is responsible to study the motion of bodies without reference to the forces which are cause this motion, i.e it’s relate the motion variables (displacement, velocity, acceleration) with the time.

2- Kinetics: is that branch of theory of machines which is responsible to relate the action of forces on bodies to their resulting motion.

3- Dynamics: is that branch of theory of machines which deals with the forces and their effects, while acting upon the machine parts in motion.

5- Statics: is that branch of theory of machines which deals with the forces and their effects, while the machine parts are rest.

DefinitionsLinks: are rigid bodies each having hinged holes or slot to be connected together by some means to constitute a mechanism which able to transmit motion or forces to some another locations.Types of LinksIn order to transmit motion, the driver and the follower may be connected by the following three types of links: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. 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.3. Fluid link. A fluid link is one which is formed by having a fluid in a receptacle and themotion is transmitted through the fluid by pressure or compression only, as in the case of hydraulicpresses, jacks and brakes.

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Mechanism: is a combination of rigid bodies which are formed and connected together by some means, so that they are moved to perform some functions, such as the crank- connecting rod mechanism of the I.C. engines, steering mechanisms of automobiles……. etc.Structure: is an assemblageofresistant bodies which are not kinematic links because there is no relative motion between the links. There is only straining action due to forces acting on them, for exampleroof truss. Machine frames etc., are the examples of a structure.Kinematic Pair: The two links or elements of a machine, when in contact with each other, are said to form apair. If the relative motion between them is completely or successfully constrained (i.e. in a definitedirection), the pair is known as kinematic pair.Kinematic Chain: When the kinematic pairs arecoupled in such a way that the last linkis joined to the first link to transmitdefinite motion (i.e. completely orsuccessfully constrained motion), it iscalled a kinematic chain. In otherwords, a kinematic chain may be definedas a combination of kinematicpairs, joined in such a way that eachlink forms a part of two pairs and therelative motion between the links orelements is completely or successfullyconstrained. For example, the crankshaftof an engine forms a kinematicpair with the bearings which are fixedin a pair, the connecting rod with thecrank forms a second kinematic pair,the piston with the connecting rod forms a third pair and the piston with the cylinder forms a fourthpair. The total combination of these links is a kinematic chain.

Note:

A mechanism with four links it iscalled a Simple Mechanism. A mechanism with more than four links it iscalled a Compound Mechanism.

Link

Binary Link

Ternary Link

Quaternary Link

Example:

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The connection of mechanism partsThe mechanism is a combination of rigid bodies which are connected together using different methods: Hinged part: The hinge connection may be used to connect the links together or connect a link to a fixed point, piston, disc ….. etc, the connection is achieved using pin, which is pass through the hinge holes

Sliding Parts: The sliding connection may be used to connect two links rotate about fixed points by means of slot, pin and hinge.

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Rolling without slipping parts:

Translated bodies: There are some bodies in the mechanism which are constrained to move in translation manner, such as the piston of crank- connecting rod mechanism, the body is used to be in translation motion, if any line remains in some configuration during motion; then all the points have the same absolute velocity and acceleration.

Velocity diagram: The motion is absolute, then select any fixed point such as o be as a reference point (i.e point of zero velocity).

Draw the path of translation.

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If vBis known, select a scale factor to draw the velocity diagram (denoted by SFv)

The draw a line ob=(vB)(SFv) in direction of vB parallel to the path of translation.

Then all points on the piston have the same velocity, such as point D, i.e on the velocity diagram, the point d coincide on the point b.

Acceleration diagram: ∵ the motion is absolute, and then select any fixed point such as o be as a

reference point (i.e point of zero acceleration). Draw the path of translation. If aB is known, select a scale factor to draw the acceleration diagram (denoted

by SFa)

In which ob=(aB)(SFa). Then all points on the piston have the same acceleration value. Note: the base (ref.) point o of vo =0, ao=0.

Bodies rotate about fixed point: Consider the link shown which is rotate about the fixed point o, the motion of this link can be analyzed using the principle of absolute motion as follow: If θ: angular displacement about fixed rotation center. ω: angular velocity about fixed rotation center. α: angular acceleration about fixed rotation center.

Velocity diagram: In order to analyze the velocity of any point we follow with one of following methods: 1- If ω is given:-

Draw the link by SFp (scale factor for position),

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2- If vAis given:-

Select SFv, specify reference point of zero velocity.

Draw oa of length (vA)(SFv) in the same direction given.

To find value and direction of ω:

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4-Bodies under general plane motion:- If a body under general plane motion, then it’s motion can be analyzed using the principle of relative motion.

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The motion of any point can be discretized into translation and rotation, if consider the link shown under general plane motion, the ends, B of absolute velocities vA, vB, and absolute accelerations aA, aB then:-

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Velocity diagram: Consider the shown link under general plane motion, to specify the velocity of any point, it’s required one of following:- 1- Absolute velocity of any point (value and direction).

Absolute velocity of other point (value or direction).

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2- Absolute velocity of any point (value and direction). Angular velocity of the link which is the same for all points.

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Acceleration diagram:

To draw the acceleration diagram it’s required one of following:- 1- ω or VBC; Absolute velocity of any point (value and direction).

2- αor aBC: Absolute acceleration of any point (value and direction) or Angular acceleration of the link.

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