Displacement diagrams

Displacement diagrams: In a cam follower system, the motion of the follower is very important. Its displacement can be plotted against the angular displacement θ of the cam and it is called as the displacement diagram. The displacement of the follower is plotted along the y-axis and angular displacement θ of the cam is plotted along x-axis. From the displacement diagram, velocity and acceleration of the follower can also be plotted for different angular displacements θ of the cam. The displacement, velocity and acceleration diagrams are plotted for one cycle of operation i.e., one rotation of the cam. 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

(a) Follower motion with Uniform velocity:

(b) Follower motion with modified uniform velocity:

(c) Follower motion with uniform acceleration and retardation (UARM):

(d) Simple Harmonic Motion:

(e) Cycloidal motion:

Types of follower motion

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
(e) Cycloidal motion

CAMS

CAMS
INTRODUCTION A cam is a mechanical device used to transmit motion to a follower by direct contact. The driver is called the cam and the driven member is called the follower. In a cam follower pair, the cam normally rotates while the follower may translate or oscillate. 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. Types of cams Cams can be classified based on their physical shape. a) Disk or plate cam: 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.
b) Cylindrical cam : 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.
c) Translating cam The translating cam is a contoured or grooved plate sliding on a guiding surface(s). The follower may oscillate or reciprocate . The contour or the shape of the groove is determined by the specified motion of the follower.
Types of followers:
(i) Based on surface in contact.
(a) Knife edge follower
(b) Roller follower
(c) Flat faced follower
(d) Spherical follower
(ii) Based on type of motion:
(a) Oscillating follower
(b) Translating follower
(iii) Based on line of motion:
(a) Radial follower: The lines of movement of in-line cam followers pass through the centers of the camshafts.
(b) Off-set follower: For this type, the lines of movement are offset from the centers of the camshafts.

Quick return motion mechanisms

Quick return mechanisms are used in machine tools such as shapers and power driven saws for the purpose of giving the reciprocating cutting tool a slow cutting stroke and a quick return stroke with a constant angular velocity of the driving crank. Some of the common types of quick return motion mechanisms are discussed below. The ratio of time required for the cutting stroke to the time required for the return stroke is called the time ratio and is greater than unity.

Kinematic chain

Kinematic chain: A kinematic chain is a group of links either joined together or arranged in a manner that permits them to move relative to one another. If the links are connected in such a way that no motion is possible, it results in a locked chain or structure.

Constrained motion

Constrained motion: In a kinematic pair, if one element has got only one definite motion relative to the other, then the motion is called constrained motion.

(a) Completely constrained motion. If the constrained motion is achieved by the pairing elements themselves, then it is called completely constrained motion.

(b) Successfully constrained motion. If constrained motion is not achieved by the pairing elements themselves, but by some other means, then, it is called successfully constrained motion. Eg. Foot step bearing, where shaft is constrained from moving upwards, by its self weight.

(c) Incompletely constrained motion. When relative motion between pairing elements takes place in more than one direction, it is called incompletely constrained motion. Eg. Shaft in a circular hole.

Types of kinematic pairs

1)Based on nature of contact between elements:

(a) Lower pair. If the joint by which two members are connected has surface contact, the pair is known as lower pair
(b) Higher pair. If the contact between the pairing elements takes place at a point or along a line, such as in a ball bearing or between two gear teeth in contact, it is known as a higher pair.

2) Based on relative motion between pairing elements:
(a) Siding pair. Sliding pair is constituted by two elements so connected that one is constrained to have a sliding motion relative to the other. DOF = 1
(b) Turning pair (revolute pair). When connections of the two elements are such that only a constrained motion of rotation of one element with respect to the other is possible, the pair constitutes a turning pair. DOF = 1
(c) Cylindrical pair. If the relative motion between the pairing elements is the combination of turning and sliding, then it is called as cylindrical pair. DOF = 2
(d) Rolling pair. When the pairing elements have rolling contact, the pair formed is called rolling pair. Eg. Bearings, Belt and pulley. DOF = 1
(e) Spherical pair. A spherical pair will have surface contact and three degrees of freedom. Eg. Ball and socket joint. DOF = 3
(f) Helical pair or screw pair. When the nature of contact between the elements of a pair is such that one element can turn about the other by screw threads, it is known as screw pair. Eg. Nut and bolt. DOF = 1

3) Based on the nature of mechanical constraint.
a) Closed pair. Elements of pairs held together mechanically due to their geometry constitute a closed pair. They are also called form-closed or self-closed pair.
(b) Unclosed or force closed pair. Elements of pairs held together by the action of external forces constitute unclosed or force closed pair .Eg. Cam and follower.

Basics of Fluid Mechanics

Mechanics: It is that branch of scientific analysis which deals with motion, time and force.
Kinematics is the study of motion, without considering the forces which produce that motion. Kinematics of machines deals with the study of the relative motion of machine parts. It involves the study of position, displacement, velocity and acceleration of machine parts.

Dynamics of machines involves the study of forces acting on the machine parts and the motions resulting from these forces.

Plane motion: A body has plane motion, if all its points move in planes which are parallel to some reference plane. A body with plane motion will have only three degrees of freedom. I.e., linear along two axes parallel to the reference plane and rotational/angular about the axis perpendicular to the reference plane. (eg. linear along X and Z and rotational about Y.)The reference plane is called plane of motion. Plane motion can be of three types. 1) Translation 2) rotation and 3) combination of translation and rotation.
Translation: A body has translation if it moves so that all straight lines in the body move to parallel positions. Rectilinear translation is a motion wherein all points of the body move in straight lie paths.

Rotation: In rotation, all points in a body remain at fixed distances from a line which is perpendicular to the plane of rotation.

Translation and rotation: It is the combination of both translation and rotation which is exhibited by many machine parts.

Binary link: Link which is connected to other links at two points.

Ternary link: Link which is connected to other links at three points.

Quaternary link: Link which is connected to other links at four points.

Pairing elements: the geometrical forms by which two members of a mechanism are joined together, so that the relative motion between these two is consistent are known as pairing elements and the pair so formed is called kinematic pair. Each individual link of a mechanism forms a pairing element.

Degrees of freedom (DOF): It is the number of independent coordinates required to describe the position of a body in space.

Second law of thermodynamics:

1. Heat cannot by itself pass from a cold to a hot body.

2. All spontaneous processes are to some extent irreversible and are accompanied by degradation of energy.

3. It is impossible to construct a heat engine that operates continuously in a cycle to produce no effect other than conversion of heat supplied completely into work. This is called Kelvin – Planck statement.

4. It is impossible to construct a heat pump (reverse heat engine) that operates continuously to produce no effect other than transfer of heat from low temperature body to a high temperature body.

Heat capacity

Heat capacity:

Heat capacity of a substance is defined as the heat transfer necessary to bring about a change in the temperature of unit amount of substance by one degree centigrade. Since it is heat transfer which is a path function, it depends upon the way heating is done. For example gases can be heated to increase the temperature by two different methods. The unit quantity of gas taken in container with rigid wall, when heated its volume remains constant. Another method is to have the wall which is flexible. If the piston is movable in the piston and cylinder arrangement, gas when heated pushes piston and pressure will be constant. Even if we take unit amount of gas in both these heating methods, it is observed the heat transfer is not the same.

Thermodynamics Process

Thermodynamic process:

A system in thermodynamic equilibrium is disturbed by imposing some driving force; it undergoes changes to attain a state of new equilibrium. Whatever is happening to the system between these two equilibrium state is called a process. It may be represented by a path which is the locus all the states in between on a p-V diagram as shown in the figure above.

For a system of gas in piston and cylinder arrangement which is in equilibrium, altering pressure on the piston may be driving force which triggers a process shown above in which the volume decreases and pressure increases. This happens until the increasing pressure of the gas equalizes that of the surroundings. If we locate the values of all intermediate states, we get the path on a p-V diagram.

Equilibriums of Thermodynamics

Equilibrium state:

A system is said to be in thermodynamic equilibrium if it satisfies the condition for thermal equilibrium, mechanical equilibrium and also chemical equilibrium. If it is in equilibrium, there are no changes occurring or there is no process taking place.

Thermal equilibrium:

There should not be any temperature difference between different regions or locations within the system. If there are, then there is no way a process of heat transfer does not take place. Uniformity of temperature throughout the system is the requirement for a system to be in thermal equilibrium.

Surroundings and the system may be at different temperatures and still system may be in thermal equilibrium.

Mechanical equilibrium:

There should not be any pressure difference between different regions or locations within the system. If there are, then there is no way a process of work transfer does not take place. Uniformity of pressure throughout the system is the requirement for a system to be in mechanical equilibrium.

Surroundings and the system may be at pressures and still system may be in mechanical equilibrium.

Chemical equilibrium:

There should not be any chemical reaction taking place anywhere in the system, then it is said to be in chemical equilibrium. Uniformity of chemical potential throughout the system is the requirement for a system to be in chemical equilibrium.

Surroundings and the system may have different chemical potential and still system may be in chemical equilibrium.