Theory of Machines simply called TOM is another important subject in Mechanical Engineering; it deals with the motions and their responsible forces of a body. In the theory of machines, we are going to study different types of Machine Elements, Laws, Components, Transmitters, Balancing of automobiles, etc. It is the combination of the topics Kinematics and Dynamics of Machines.
For example, let us consider the shaping machine (you can read about the shaper machine very soon on this website). A shaper is a machine tool used to cut, groove the materials using cutting tools whereas “cutting material will stay still without any motion (fixed) and the cutting tool will be moved to and fro directions“.
Internal Mechanism of a Shaper
So, the movement of to and fro is achieved with the help of the internal mechanism which is to convert the rotary motion (developed by the motor) into the reciprocating motion. So such conversion is possible only when we are aware of the links, kinematics, devices, and parts that are responsible for the conversion of motions (like gears, gear trains), etc.
Kinematics :
It deals with the relative motions of different parts of a mechanism without taking into consideration the forces producing the motions. Thus, it is the study, from a geometric point of view, to know the displacement, velocity and acceleration of a part of a mechanism.
Dynamics :
It involves the calculations of forces impressed upon different parts of a mechanism. The forces can be either static or dynamic. Dynamics is further subdivided into kinetics and statics. Kinetics is the study of forces when the body is in motion whereas statics deals with forces when the body is stationary.
Table of Contents
- Mechanisms
- Kinematics and Dynamics Analysis of Planar Mechanisms.
- Governors.
- Balancing.
- Gears.
- Gear Trains.
- Vibrations.
Mechanism
Mechanisms or Machine:
A machine is a mechanism or a combination of mechanisms which, apart from imparting definite motions to the parts, also transmits and modifies the available mechanical energy into some kind of desired work. It is neither a source of energy nor a producer of work but helps in proper utilization of the same. The motive
power has to be derived from external sources.
Types of Constrained Motion :
There are three types of constrained motion are following :
1. Completely Constrained Motion
When the motion between two elements of a pair is in a definite direction irrespective of the direction of the force applied, it is known as completely constrained motion. The constrained motion may be linear e or rotary.
The sliding pair and turning pair are the example of the completely constrained motion. In sliding pair, the inner prism can only slide inside the hollow prism. In case of turning pair, the inner shaft can have only rotary motion due to collars at the ends. In each case the force has be applied in a particular direction for the required motion.
2. Incompletely Constrained Motion :
When the motion between two elements of a pair is possible in more than one direction and depends upon the direction of the force applied, it is known as incompletely constrained motion.
For example, if the turning pair does not have collars, the inner shaft may have sliding or rotary motion depending upon the direction of the force applied. Each motion is independent of the other.
3. Successfully Constrained Motion
When the motion between two elements of a pair is possible in more than one direction but is made to have motion only in one direction by using some external means, it is a successfully constrained motion.
For example, a shaft in a footstep bearing may have vertical motion apart from rotary motion. But due to load applied on the shaft it is constrained to move in that direction and thus is a successfully constrained motion. Similarly, a piston in a cylinder of an internal combustion engine is made to have only reciprocating motion and no rotary motion due to constrain of the piston pin. Also, the valve of an IC engine is kept on the seat by the force of a spring and thus has successfully constrained motion.
Kinematic Link or Element :
Each part of a machine, which moves relative to some other part, is known as a kinematic link (or simply link) or element. A link may consist of several parts, which are rigidly fastened together, so that they do not move relative to one another.
A link or element need not to be a rigid body, but it must be a resistant body. A body is said to be a resistant body if it is capable of transmitting the required forces with negligible deformation. Thus a link should have the following two characteristics:
- It should have relative motion
- It must be a resistant body
Types of Links
In order to transmit motion, the driver and the follower may be connected by the following three types of links are :
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 the motion is transmitted through the fluid by pressure or compression only, as in the case of hydraulic presses, jacks and brakes.
Kinematic Pair:
The two links or elements of a machine, when in contact with each other, are said to form a pair. If the relative motion between them is completely or successfully constrained (i.e. in a definite direction), the pair is known as kinematic pair
Classification of Kinematic Pair :
The kinematic pairs may be classified according to the following considerations :
According to the type of relative motion between the elements. The kinematic pairs according to type of relative motion between the elements may be classified as discussed below:
(a) Sliding Pair : When the two elements of a pair are connected in such a way that one can only slide relative to the other, the pair is known as a sliding pair. The piston and cylinder, cross-head and guides of a reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed etc. are the examples of a sliding pair. A little consideration will show, that a sliding pair has a completely constrained motion.
(b) Turning Pair :When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their axles etc. are the examples of a turning pair. A turning pair also has a completely constrained motion.
(c) Rolling Pair : When the two elements of a pair are connected in such a way that one rolls
over another fixed link, the pair is known as rolling pair. Ball and roller bearings are examples of
rolling pair.
(d) Screw Pair : When the two elements of a pair are connected in such a way that one element
can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe
with nut, and bolt with a nut are examples of a screw pair.
(e) Spherical Pair : When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair. The ball and socket joint, attachment of a car mirror, pen stand etc., are the examples of a spherical pair.
According to the type of contact between the elements. The kinematic pairs according to
the type of contact between the elements may be classified as discussed below :
(a) Lower Pair : When the two elements of a pair have a surface contact when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs.
(b) Higher Pair :When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, then the pair is known as higher pair. A pair of friction discs, toothed gearing, belt and rope drives, ball and roller bearings and cam and follower are the examples of higher pairs.
According to the type of closure. The kinematic pairs according to the type of closure
between the elements may be classified as discussed below :
(a) Self Closed Pair : When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair.
(b) Force – Closed Pair : When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.
Kinematic Chain :
When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion (i.e. completely or successfully constrained motion), it is called a kinematic chain. In other words, a kinematic chain may be defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained. For example, the crankshaft of an engine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rod with the crank forms a second kinematic pair, the piston with the connecting rod forms a third pair and the piston with the cylinder forms a fourth pair. The total combination of these links is a kinematic chain.
Types of Joints
The usual types of joints in a chain are :
• Binary joint
• Ternary joint
• Quaternary joint
Binary Joint: If two links are joined at the same connection, it is called a binary joint.
Ternary Joint : If three links are joined at a connection, it is known as a ternary joint. It is considered equivalent
to two binary joints since fixing of any one link constitutes two binary joints with each of the other two
links.
Quaternary Joint : If four links are joined at a connection, it is known as a quaternary joint. It is considered
equivalent to three binary joints since fixing of any one link constitutes three binary joints. In general, if n number of links are connected at a joint, it is equivalent to (n – 1) binary joint