# Velocity diagram theory of machines

Cam Profile: The contour of the working surface of the cam. Tracer Point: The point at the knife edge of a follower, or the center of a roller, or the center of a spherical face.

## The Geometry of Gears

Base Circle: The smallest circle drawn, tangential to the cam profile, with its center on the axis of the camshaft. The size of the base circle determines the size of the cam. Prime Circle: The smallest circle drawn, tangential to the pitch curve, with its center on the axis of the camshaft. Pressure Angle: The angle between the normal to the pitch curve and the direction of motion of the follower at the point of contact.

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.

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. It is observed in the displacement diagrams of the follower with uniform velocity that the acceleration of the follower becomes infinite at the beginning and ending of rise and return strokes.

In order to prevent this, the displacement diagrams are slightly modified. In the modified form, the velocity of the follower changes uniformly during the beginning and end of each stroke.

Accordingly, the displacement of the follower varies parabolically during these periods. With this modification, the acceleration becomes constant during these periods, instead of being infinite as in the uniform velocity type of motion.

The displacement, velocity and acceleration patterns are shown in fig. Here, the displacement of the follower varies parabolically with respect to angular displacement of cam. Accordingly, the velocity of the follower varies uniformly with respect to angular displacement of cam.

Similarly Max. Similarly, Max. The motion executed by the follower here, is similar to that of the projection of a point moving along a cyloidal curve on a vertical line as shown in figure 7. The construction of displacement diagram and the standard patterns of velocity and acceleration diagrams are shown in fig. Compared to all other follower motions, cycloidal motion results in smooth operation of the follower.

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Very simple and clear presentation. Easily understandable by the students. Could you kindly work out a few problems based on these profiles? Pls giv solution for it. Got exam on Design a cam with the base circle diameter of 40mm and width of 18mm.

The valve moves with uniform acceleration and deacceleration for each half of the lift. Draw the cam profile with the above dimensions using design software.

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If the scale used for displacement diagram is different than that of constructing cam,does it wrong? Sir I need a solution for this question How to draw the answer i. A circular cam of diameter mm has an eccentric axis of rotation which is offset 30mm from the centre.V a is perpendicular to OA. So we know the direction and magnitude of V a. The velocity of slider B is along OB. The configuration and velocity diagram for this problem is given below.

Step 1. Step 2. From a draw a vector ab perpendicular to the line AB. Step 3.

### 300+ TOP THEORY of MACHINES – Mechanical Engineering Multiple choice Questions and Answers

The velocity of slider B is along the line of stroke OB, from o draw a line parallel to OB which will intersect vector ab at b. The vector ob represent the velocity of slider B V B. The velocity of any point C on the connecting rod can be determined by the help of relation:.

The point c can be located on the velocity diagram. Join o with c. Example 3. Angular velocity of link O 1 A. Velocity of slider at B.

The velocity of A with respect to O 2. In the configuration diagram let us take a point C on the link O 1 B. The velocity diagram can be drawn as explain below. O 1 and O 2 are fixed points on the configuration diagram so they are taken as single point o 1, o 2 on the velocity diagram. This will contain point c. Then from o 1 draw a vector o 1 c representing V CO1 this will intersect ac at point c. Step 4. Locate the point b corresponding to point B such that.

A rigid body undergoing in plane motion, there always exist a point in the plane of motion at which the velocity is zero at that particular instant. This point is called instantaneous centre of rotation or I-centre.

It may or may not lie on the body. If the location of this point is determined then we can simplify the velocity analysis. To locate the I-centre, we use the fact that the velocity of a point on a body is always perpendicular to the position vector from I-centre to that point. If the velocity at two points A and B are known, I-centre will lie at the intersection of the perpendiculars to the velocity vectors through A and B.New Modules Updated Modules.

The geometry of both Cycloid and Involute gears. An analysis of the motion between two teeth and the calculation of the path of contact. View other versions 5. Introduction It is difficult to imagine machines which do not include some sort of toothed gear system. These are used for the transmission of motion or of power. The systems include Spur gearing in which the axes of the shafts connected are parallel Note Helical Gearing is the name given to a type of spur gearing in which, although the axes of the shafts are parallel, the teeth are cut on helices instead of straight across the wheel parallel to the axes.

Bevel Gearing in which the axes of the shafts intersect and Skew or Spiral Gearing in which the axes are both non parallel and non intersecting. Velocity Ratio is defined by Classical mechanics as the distance that the point of Effort moved, divided by the distance that the point of Load moved as given from here.

A constant velocity ratio between the shafts without any possibility of slippage. The ability to transmit large torques from the driving to the driven shaft. Definitions Before considering the Theory of gear teeth in detail a few necessary definitions are given. These terms are generally used in connection with toothed gearing. The Pitch Circle Diameter is the diameter of a circle which by a pure rolling action would transmit the same motion as the actual gear wheel.

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It should be noted that in the case of wheels which connect non-parallel shafts, the pitch circle diameter is different for each cross section of the wheel normal to the axis of rotation.

The Pitch Point is the point of contact of two pitch circles. The Pitch Line is the line of contact of two Pitch surfaces. The Circular Pitch, is the length of arc round the pitch circle between corresponding points on adjacent teeth. The Module The Path of Contact on the diagram is the path traced out by the point of contact between a pair of teeth.

This may be divided into "Approach" and "Recess". The Arc of Contact is the arc traced out along the pitch circle whilst one pair of teeth is in contact. Again this can be divided into "Approach" and Recess".

It can be shown that the arc of contact since the path of contact represents a distance round the bases circle. The Addendum is the radial length of a tooth from the pitch circle to the tip of the tooth. This is normally constant for a set of gears and the standard value is The Dedendum is the radial length of a tooth from the pitch circle to the root of the tooth.

The Pressure Angle or Angle of Obliquity is the angle between the common normal and the tangent at the pitch point. The normal pressure between teeth acts along. A Pinion is the smaller of two mating gear wheels. The Motion Transmitted Between Two Teeth The diagram shows two gear wheels with centers at andwith the mating teeth in contact at.Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising.

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Submit Search. Home Explore. Successfully reported this slideshow. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime. Upcoming SlideShare. Like this document? Why not share! Velocity and acceleration of mechan Embed Size px.

Start on. Show related SlideShares at end.Which of the following disciplines provides study of inertia forces arising from the combined effect of the mass and the motion of the parts a theory of machines b applied mechanics c mechanisms d kinetics e kinematics.

Helpful example on Velocity and Acceleration diagram 2

Ans: d. Which of the following disciplines provides study of relative motion between the parts of a machine a theory of machines b applied mechanics c mechanisms d kinetics e kinematics. Ans: e. Which of the following disciplines provides study of the relative motion between the parts of a machine and the forces acting on the parts a theory of machines b applied mechanics c mechanisms d kinetics e kinematics.

Ans: a. The type of pair formed by two elements which are so connected that one is constrained to turn or revolve about a fixed axis of another element is known as a turning pair b rolling pair c sliding pair d spherical pair e lower pair, Ans: a. Which of the following is a lower pair a ball and socket i b piston and cylinder c cam and follower d a and b above e belt drive.

If two moving elements have surface contact in motion, such pair is known as a sliding pair b rolling pair c surface pair d lower pair e higher pair. The example of lower pair is a shaft revolving in a bearing b straight line motion mechanisms c automobile steering gear d all of the above e none of the above. Pulley in a belt drive acts as a cylindrical pair b turning pair c rolling pair d sliding pair e surface pair. Ans: c. The example of rolling pair is a bolt and nut b lead screw of a lathe c ball and socket joint d ball bearing and roller bearing e all of the above.

Any point on a link connecting double slider crank chain will trace a a straight line b circle c ellipse d parabola e hyperbola. The purpose of a link is to a transmit motion b guide other links c act as a support d all of the above e none of the above. A universal joint is an example of a higher pair b lower pair c rolling pair d sliding pair e turning pair. Ans: b.

Rectilinear motion of piston is converted into rotary by a cross head b slider crank c connecting rod d gudgeon pin e four bar chain mechanism. Pitch point on a cam is a any point on pitch curve b the point on cam pitch curve having the maximum pressure angle c any point on pitch circle d the point on cam pitch curve having the minimum pressure angle e none of the above.

The values of velocity and acceleration of piston at near dead center for a slider-crank mechanism will be a 0, and more than co2r b 0, and less than coV c 0, 0 d cor, 0 e none of the above. The example of spherical pair is a bolt and nut b lead screw of a lathe c ball and socket joint d ball bearing and roller bearing e none of the above.

Cross head and guides form a a lower pair b higher pair c turning pair d rolling pair e sliding pair.Theory of Machines is an applied science of the relationships between geometry and relative motion of the parts of the machine, and concerns to the forces which act on those parts. It involves analysis as well as synthesis. It will also be helpful for students in preparing them for their Engineering Syllabus. Himanshu Vasishta holds a B.

Tech in Mechanical Engineering from Chitkara University. He is a Marine Engineering and Automotive Engineering enthusiast.

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An e-learning professional, Himanshu has been training Mechanical Engineering students and graduates since the last 8 years.

Included in Premium Package. Add to Cart. Theory of Machines Created by Er. Course Content Mechanisms. Kinematic Pairs. Constrained Motion. Kinematic Chain. Degree of Freedom. Numerical on Degree of Freedom.

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Kinematics of Mechanisms. Concept of Relative Velocity. Relative Velocity of Points on Same Link. Velocity Analysis of 4 Bar Mechanism. Instantaneous Centre Method.

Types of Instantaneous Centres.Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising.

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We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime. Velocity and acceleration of mechanisms. Upcoming SlideShare. Like this presentation? Why not share! Embed Size px. Start on. Show related SlideShares at end. WordPress Shortcode. Published in: EngineeringTechnology. Full Name Comment goes here.