THEORY OF MACHINES PDF
1. Definition. 2. Sub-divisions of Theory of Machines. undamental Units. 4. Derived Units. 5. Systems of Units. 6. C.G.S. Units. P.S. Units. 8. M.K.S. Units 9. 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, . Reference Books: ▫ John J. Uicker, Gordon R. Pennock, Joseph E. Shigley, Theory of Machines and Mechanisms. ▫ R.S. Khurmi, J.K. Gupta,Theory of Machines.
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Results 1 - 10 It is that branch of Theory of Machines which deals with the inertia forces which arise from Theory Theory of Machines by Rresourceone.info PDF | Introduction: mechanism and machines, kinematic links, kinematic pairs, kinematic chains, plane and space mechanism, kinematic. Meen DP Theory of Machines 3 Cr. Unit:I Introduction to mechanisms, velocity and acceleration analysis of mechanisms Introduction Mechanics: It is that.
In case the pulleys cannot be arranged, as shown in Fig. Belt drive with idler pulleys. A belt drive with an idler pulley, as shown in Fig.
This type of drive is provided to obtain high velocity ratio and when the required belt tension cannot be obtained by other means. When it is desired to transmit motion from one shaft to several shafts, all arranged in parallel, a belt drive with many idler pulleys, as shown in Fig. Compound belt drive. A compound belt drive, as shown in Fig. Stepped or cone pulley drive. A stepped or cone pulley drive, as shown in Fig, is used for changing the speed of the driven shaft while the main or driving shaft runs at constant speed.
This is accomplished by shifting the belt from one part of the steps to the other. Fast and loose pulley drive. A fast and loose pulley drive, as shown in Fig. A pulley which is keyed to the machine shaft is called fast pulley and runs at the same speed as that of machine shaft. A loose pulley runs freely over the machine shaft and is incapable of transmitting any power. When the driven shaft is required to be stopped, the belt is pushed on to the loose pulley by means of sliding bar having belt forks.
Velocity Ratio of Belt Drive It is the ratio between the velocities of the driver and the follower or driven. It may be expressed, mathematically, as discussed below: Velocity Ratio of a Compound Belt Drive Sometimes the power is transmitted from one shaft to another, through a number of pulleys, as shown in fig.
Consider a pulley 1 driving the pulley 2. Since the pulleys 2 and 3 are keyed to the same shaft, therefore the pulley 1 also drives the pulley 3 which, in turn, drives the pulley 4. We know that velocity ratio of pulleys 1 and 2, Similarly, velocity ratio of pulleys 3 and 4, Multiplying the above equations gives Prepared by Kiran Kumar.
Slip of Belt In the previous articles, we have discussed the motion of belts and shafts assuming a firm frictional grip between the belts and the shafts. But sometimes, the frictional grip becomes insufficient.
This may cause some forward motion of the driver without carrying the belt with it. This may also cause some forward motion of the belt without carrying the driven pulley with it.
This is called slip of the belt and is generally expressed as a percentage. The result of the belt slipping is to reduce the velocity ratio of the system. As the slipping of the belt is a common phenomenon, thus the belt should never be used where a definite velocity ratio is of importance.
Length of an open Belt Drive We have already discussed that in an open belt drive, both the pulleys rotate in the same direction as shown in Fig.
From the geometry of the figure, we find that O2 M will be perpendicular to O1 E. Length of a Cross Belt Drive We have already discussed that in a cross belt drive, both the pulleys rotate in opposite directions as shown in Fig. From the geometry of the figure, we find that O2M will be perpendicular to O1E. It is thus obvious that if sum of the radii of the two pulleys be constant, then length of the belt required will also remain constant, provided the distance between centres of the pulleys remain unchanged.
Power transmitted by a Belt Fig. We have already discussed that the driving pulley pulls the belt from one side and delivers the same to the other side.
It is thus obvious that the tension on the former side i. When the two pulleys of different diameters are connected by means of an open belt as shown in Fig. A little consideration will show that when the two pulleys are connected by means of a crossed belt as shown in Fig.
The tension caused by centrifugal force is called centrifugal tension. The engine pulley is mm diameter and the pulley on the line shaft being mm.
A mm diameter pulley on the line shaft drives a mm diameter pulley keyed to a dynamo shaft. Find the speed of the dynamo shaft, when 1.
Theory of machines notes -diploma engineering
When there is no slip 2. The coefficient of friction between the belt and the pulley is 0. The other end of the rope is pulled by a man. The coefficient of friction is 0. Determine 1. The force required by the man, and 2. The power to raise the casting. Since the rope makes 2. Power to raise the casting We know that velocity of the rope, 4 Two pulleys, one mm diameter and the other mm diameter are on parallel shafts 1.
Find the length of the belt required and the angle of contact between the belt and each pulley. We know that 5 A shaft rotating at r. The belt is mm wide and 10 mm thick.
The distance between the shafts is 4m. The smaller pulley is 0.
Theory of Machines
Calculate the stress in the belt, if it is 1. Stress in the belt for an open belt drive First of all, let us find out the diameter of larger pulley d1. We know that Prepared by Kiran Kumar. The diameter of the driving pulley of the motor is mm. The driven pulley runs at r. The maximum allowable stress in the leather is 2. The coefficient of friction between the leather and pulley is 0. Assume open belt drive and neglect the sag and slip of the belt. Where Cam — driver member Follower - driven member.
The cam and the follower have line contact and constitute a higher pair. In a cam - follower pair, the cam normally rotates at uniform speed by a shaft, while the follower may is predetermined, will translate or oscillate according to the shape of the cam. A familiar example is the camshaft of an automobile engine, where the cams drive the push rods the followers to open and close the valves in synchronization with the motion of the pistons. The cams are widely used for operating the inlet and exhaust valves of Internal combustion engines, automatic attachment of machineries, paper cutting machines, spinning and weaving textile machineries, feed mechanism of automatic lathes.
Mechanism and Machine Theory
Example of cam action Classification of Followers i Based on surface in contact. The lines of movement of in-line cam followers pass through the centers of the camshafts Fig.
For this type, the lines of movement are offset from the centers of the camshafts Fig. The disk or plate cam has an irregular contour to impart a specific motion to the follower.
The follower moves in a plane perpendicular to the axis of rotation of the camshaft and is held in contact with the cam by springs or gravity. The cylindrical cam has a groove cut along its cylindrical surface. The roller follows the groove, and the follower moves in a plane parallel to the axis of rotation of the cylinder. The translating cam is a contoured or grooved plate sliding on a guiding surface s. The follower may oscillate Fig. The contour or the shape of the groove is determined by the specified motion of the follower.
Terms Used in Radial Cams Fig. It is the angle between the direction of the follower motion and a normal to the pitch curve.
This angle is very important in designing a cam profile. If the angle is too large, a reciprocating follower will jam in its bearings. Base circle: It is the smallest circle that can be drawn to the cam profile. Trace point: It is the reference point on the follower and is used to generate the pitch curve. In the case of knife edge follower, the knife edge represents the trace point and the pitch curve corresponds to the cam profile. In the roller follower, the centre of the roller represents the trace point.
Pitch point: It is a point on the pitch curve having the maximum pressure angle. Pitch circle: It is a circle drawn from the centre of the cam through the pitch points.
Pitch curve: It is the curve generated by the trace point as the follower moves relative to the cam. For a knife edge follower, the pitch curve and the cam profile are same where as for a roller follower; they are separated by the radius of the follower. Prime circle: It is the smallest circle that can be drawn from the centre of the cam and tangent to the point. For a knife edge and a flat face follower, the prime circle and the base circle and the base circle are identical.
For a roller follower, the prime circle is larger than the base circle by the radius of the roller. Lift or stroke: It is the maximum travel of the follower from its lowest position to the topmost position. Motion of the Follower Cam follower systems are designed to achieve a desired oscillatory motion. Appropriate displacement patterns are to be selected for this purpose, before designing the cam surface.
The cam is assumed to rotate at a constant speed and the follower raises, dwells, returns to its original position and dwells again through specified angles of rotation of the cam, during each revolution of the cam. Some of the standard follower motions are as follows: They are, follower motion with, a Uniform velocity b Modified uniform velocity c Uniform acceleration and deceleration d Simple harmonic motion Displacement diagrams: In a cam follower system, the motion of the follower is very important.
The displacement, velocity and acceleration diagrams are plotted for one cycle of operation i. Displacement diagrams are basic requirements for the construction of cam profiles. Construction of displacement diagrams and calculation of velocities and accelerations of followers with different types of motions are discussed in the following sections.
Also, since the velocity changes from zero to a finite value, within no time, theoretically, the acceleration becomes infinite at the beginning and end of rise and fall. Accordingly, the velocity of the follower varies uniformly with respect to angular displacement of cam. The displacement, velocity and acceleration patterns are shown in fig.
Construction of Cam Profile for a Radial Cam In order to draw the cam profile for a radial cam, first of all the displacement diagram for the given motion of the follower is drawn. Then by constructing the follower in its proper position at each angular position, the profile of the working surface of the cam is drawn.
In constructing the cam profile, the principle of kinematic inversion is used, i. The construction of cam profiles for different types of follower with different types of motions are discussed in the following examples. Practise problems: Determine max. Displacement diagram: Draw the cam profile for the same operating conditions of problem 1 , with the follower off set by 10 mm to the left of cam center. Same as previous problem. Cam profile: Construction is same as previous case, except that the lines drawn from 1,2,3….
Draw the cam profile for conditions same as in 3 , with follower off set to right of cam center by 5mm and cam rotating counter clockwise. Same as previous case. The effect of slip is to reduce the velocity ratio of the drive. In precision machine, in which a definite velocity ratio is importance as in watch mechanism, special purpose machines..
Gears are machine elements that transmit motion by means of successively engaging teeth. The gear teeth act like small levers. Gears essentially allow positive engagement between teeth so high forces can be transmitted while still undergoing essentially rolling contact. Gears do not depend on friction and do best when friction is minimized.
Let the wheel A be keyed to the rotating shaft and the wheel B to the shaft, to be rotated. A little consideration will show, that when the wheel A is rotated by a rotating shaft, it will rotate the wheel B in the opposite direction as shown in Fig.
The wheel B will be rotated by the wheel A so long as the tangential force exerted by the wheel A does not exceed the maximum frictional resistance between the two wheels.
But when the tangential force P exceeds the frictional resistance F , slipping will take place between the two wheels. Thus the friction drive is not a positive drive. In order to avoid the slipping, a number of projections called teeth as shown in Fig.
A friction wheel with the teeth cut on it is known as toothed wheel or gear. The usual connection to show the toothed wheels is by their pitch circles. Advantages and Disadvantages of Gear Drive The following are the advantages and disadvantages of the gear drive as compared to belt, rope and chain drives: It transmits exact velocity ratio. It may be used to transmit large power. It has high efficiency. It has reliable service. It has compact layout. The manufacture of gears requires special tools and equipment.
The error in cutting teeth may cause vibrations and noise during operation. Classification of Toothed Wheels Gears may be classified according to the relative position of the axes of revolution. The axes may be 1. Gears for connecting parallel shafts, 2. Gears for connecting intersecting shafts, 3. Gears for neither parallel nor intersecting shafts.
Gears for connecting parallel shafts 1. Spur gears: Spur gears are the most common type of gears.
They have straight teeth, and are mounted on parallel shafts. Sometimes, many spur gears are used at once to create very large gear reductions.
Each time a gear tooth engages a tooth on the other gear, the teeth collide, and this impact makes a noise. It also increases the stress on the gear teeth.
To reduce the noise and stress in the gears, most of the gears in your car are External contact Internal contact Spur gears Spur gears are the most commonly used gear type. They are characterized by teeth, which are perpendicular to the face of the gear. Spur gears are most commonly available, and are generally the least expensive. Spur gears generally cannot be used when a direction change between the two shafts is required.
Spur gears are easy to find, inexpensive, and efficient. Parallel helical gears: The teeth on helical gears are cut at an angle to the face of the gear.
When two teeth on a helical gear system engage, the contact starts at one end of the tooth and gradually spreads as the gears rotate, until the two teeth are in full engagement. Helical gears Herringbone gears or double-helical gears This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears. For this reason, helical gears are used in almost all car transmission. Because of the angle of the teeth on helical gears, they create a thrust load on the gear when they mesh.
Devices that use helical gears have bearings that can support this thrust load. One interesting thing about helical gears is that if the angles of the gear teeth are correct, they can be mounted on perpendicular shafts, adjusting the rotation angle by 90 degrees.
Helical gears to have the following differences from spur gears of the same size: The rack is like a gear whose axis is at infinity mathematically but practically a gear of larger length. Racks are straight gears that are used to convert rotational motion to translational motion by means of a gear mesh. They are in theory a gear with an infinite pitch diameter. In theory, the torque and angular velocity of the pinion gear are related to the Force and the velocity of the rack by the radius of the pinion gear, as is shown.
Perhaps the most well-known application of a rack is the rack and pinion steering system used on many cars in the past. Gears for connecting intersecting shafts: Bevel gears are useful when the direction of a shaft's rotation needs to be changed. They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well. The teeth on bevel gears can be straight, spiral or hypoid. Straight bevel gear teeth actually have the same problem as straight spur gear teeth, as each tooth engages; it impacts the corresponding tooth all at once.
Just like with spur gears, the solution to this problem is to curve the gear teeth.
Theory Of Machines by R. S. Khurmi, J.K. Gupta
These spiral teeth engage just like helical teeth: Straight bevel gears Spiral bevel gears On straight and spiral bevel gears, the shafts must be perpendicular to each other, but they must also be in the same plane. The hypoid gear, can engage with the axes in different planes. This feature is used in many car differentials. The ring gear of the differential and the input pinion gear are both hypoid.
This allows the input pinion to be mounted lower than the axis of the ring gear. Figure shows the input pinion engaging the ring gear of the differential. Since the driveshaft of the car is connected to the input pinion, this also lowers Hypoid gears the driveshaft. This means that the driveshaft doesn't pass into the passenger compartment of the car as much, making more room for people and cargo.
Neither parallel nor intersecting shafts: Helical gears may be used to mesh two shafts that are not parallel, although they are still primarily use in parallel shaft applications. A special application in which helical gears are used is a crossed gear mesh, in which the two shafts are perpendicular to each other. Crossed-helical gears Worm and worm gear: Worm gears are used when large gear reductions are needed.
It is common for worm gears to have reductions of Many worm gears have an interesting property that no other gear set has: This is because the angle on the worm is so shallow that when the gear tries to spin it, the friction between the gear and the worm holds the worm in place.
This feature is useful for machines such as conveyor systems, in which the locking feature can act as a brake for the conveyor when the motor is not turning. One other very interesting usage of worm gears is in the Torsen differential, which is used on some high-performance cars and trucks. Terms Used in Gears Fig. The radial distance between the Pitch Circle and the top of the teeth.
The radial distance between the bottom of the tooth to pitch circle. Base Circle: The circle from which is generated the involute curve upon which the tooth profile is based. Center Distance: The distance between centers of two gears. Circular Pitch: Millimeter of Pitch Circle circumference per tooth. Circular Thickness: The thickness of the tooth measured along an arc following the Pitch Circle Clearance: The distance between the top of a tooth and the bottom of the space into which it fits on the meshing gear.
Contact Ratio: The ratio of the length of the Arc of Action to the Circular Pitch. Diametral Pitch: Teeth per mm of diameter.
The working surface of a gear tooth, located between the pitch diameter and the top of the tooth. Face Width: The width of the tooth measured parallel to the gear axis. The working surface of a gear tooth, located between the pitch diameter and the bottom of the teeth Gear: The larger of two meshed gears. If both gears are the same size, they are both called "gears". The top surface of the tooth. Line of Action: That line along which the point of contact between gear teeth travels, between the first point of contact and the last.
Millimeter of Pitch Diameter to Teeth. The smaller of two meshed gears. Pitch Circle: The circle, the radius of which is equal to the distance from the center of the gear to the pitch point. Diametral pitch: Teeth per millimeter of pitch diameter. Pitch Point: The point of tangency of the pitch circles of two meshing gears, where the Line of Centers crosses the pitch circles. Pressure Angle: Angle between the Line of Action and a line perpendicular to the Line of Centers.
Root Circle: The circle that passes through the bottom of the tooth spaces.
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Working Depth: The depth to which a tooth extends into the space between teeth on the mating gear. Although the two profiles have different velocities V1 and V2 at point K, their velocities along N1N2 are equal in both magnitude and direction. Otherwise the two tooth profiles would separate from each other. Pitch point divides the line between the line of centers and its position decides the velocity ratio of the two teeth.
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Your email address will not be published. Notify me of follow-up comments by email. Notify me of new posts by email. Table of Contents: Related Posts Fundamentals of Machining Processes: Conventional and Nonconventional Process.
Exact answers of the asked questions, without unnecessary description. Covers all points in syllabus. Also questions asked in recent exams. Simple and easy to remember formulas for the numerical problems. Numerical problems arranged from simpler to toughter for getting confidence in solving. Theory of machines notes-diploma engineering contain easy to reproduce diagrams. Screenshots from the Notes As shown in screen shot below the notes provide exact definitions with the underlined keywords.Helical gears Herringbone gears or double-helical gears This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears.
Find i Angular velocity of connecting rod and ii Velocity of slider.
The power of a governor is the work done at the sleeve for a given percentage change of speed. Straight bevel gears Spiral bevel gears On straight and spiral bevel gears, the shafts must be perpendicular to each other, but they must also be in the same plane. In general, the phenomenon, when the tip of tooth undercuts the root on its mating Wheel gear is known as interference.
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