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.