Introduction(1)

Introduction to the study of mechanisms

Theory of Machines is defined as branch of Engineering-science which deals the study of relative motion between the different parts of machine and forces which applied on them.

The Theory of Machines can be sub-divided into following four branches

Kinematics: It is the branch of Theory of Machines which deals with the relative motion between the different parts of the machines.

Dynamics: It is the branch of Theory of Machines which deals with the forces and their effects when acting upon the machine parts in motion.

Kinetics: It is the branch of Theory of Machines which deals the inertia forces which comes from combined effect of mass and motion of machine parts.

Statics: It is branch of Theory of Machines which deals with forces and their effects when the machine parts are at rest.

Basic definitions & descriptions

Mechanism: The term mechanism is applied to combination of geometrical bodies that constitute a machine or part of machine. A mechanism therefore defined as a combination of rigid or resistant bodies which formed and connected so that they move with definite relative motions with respect to one another. When one of links of a kinematic chain is fixed then the chain is known as the mechanism. It may be used for transmitting motion. A mechanism with four links is known as a simple mechanism and the mechanism with more than four links is known as a compound mechanism.

Machine: A machine is device which receives energy in some available type and utilizes it to do some type of work. A machine has two functions i.e. transmitting definite relative motion and transmitting force also. These functions which require strength and rigidity to transmit the forces.

Machine Design: The suitable combination of subjects, mechanism, machine theory and machine material give rise to machine design.

Mechanical Design: The creation of scheme for the construction and assembly of a machine is mechanical design.

The similarity in machines and mechanisms is that,

• They are both combinations of rigid bodies
• The relative motion of the rigid bodies is definite.

The difference between machine and mechanism is that machines transform energy to do the work while mechanisms is so not necessarily perform this function. The term machinery generally means machines and mechanisms.

Mechanism configurations, links, chains, inversions

Kinematic Link

Each part of a machine that moves relative to other part is known as a kinematic link (or simply link) or element. A link consist of several parts that are rigidly fastened together so that they do not move relative to one another. For example in a reciprocating steam engine which is shown in fig below the piston, piston rod, and crosshead constitute one link with connecting rod with big and small end bearings form a second link then crank, crank shaft and flywheel a third link and cylinder, engine frame with main bearings a fourth link. A link or element need not to be a rigid body but it must be resistant body. A body is known to be a resistant body if it is capable of transmitting required forces with negligible deformation. So a link should have the following two characteristics.

• It should have relative motion, and
• It must be a resistant body.

Types of link

Rigid link.: A rigid link is one which does not undergo any type of deformation when transmitting motion. Strictly rigid links do not exist. However as the deformation of a connecting rod, crank of a reciprocating steam engine is not appreciable. They can be considered as rigid link.

Flexible link.: A flexible link is one that is partly deformed in such that not to affect the transmission of motion. For e.g. belts, chains, ropes and wires are flexible links and transmitted tensile forces only.

Fluid link:. A fluid link is one that is formed by having a fluid in receptacle and motion is transmitted through fluid by pressure or compression only as in case of hydraulic presses, jacks and brakes.

Difference Between a Machine and a Structure

• The parts of a machine move relative to one another whereas members of a structure do not move relative to other.
• A machine transforms available energy into some useful work whereas in structure no energy is transformed into useful work.
• The links of a machine can transmit both power and motion while the members of structure transmit forces only.

Kinematic Pair

The two links or elements of a machine, when in contact with each other then they are said to form a pair. If relative motion between them is successfully constrained (i.e. in a definite direction), the pair is known as the kinematic pair.

Classification of Kinematic Pairs

According to the type of relative motion between elements. The kinematic pairs according to the type of relative motion between the elements can be classified as below.

(a) Sliding pair

When two elements of a pair are connected in such a way that one can only slide relative to the other then the pair is known as a sliding pair. The piston and cylinder, cross-head and guides of a reciprocating steam engine and its guides in shaper with tail stock on lathe bed etc. are the examples of a sliding pair. A little supposition will show that the sliding pair has sucessfully constrained motion.

(b) Turning pair

When two elements of a pair which connected in that way that one can only turn or revolve about the fixed axis of another link then the pair known as turning pair. The shaft with collars at both ends fitted into a circular hole and the crankshaft in a journal bearing in engine, lathe spindle supported in the head stock, cycle wheels turning over their own axles etc. are the examples of turning pair. A turning pair also has a completely constrained motion.

(c) Rolling pair

When the two elements of pair are connected in that way that one rolls over another fixed link then the pair is known to rolling pair. Ball and roller bearings are the examples of rolling pair.

(d) Screw pair

When the two elements of pair ar connected in such a way that one element can turn about the other by screw threads then the pair is known screw pair. The lead screw of a lathe with nut and bolt are examples of screw pair.

(e) Spherical pair

When the two elements of pair are connected in that way that one element with spherical shape turns or swivels about the other fixed element the pair formed is called spherical pair.

References:
1. H.H. Mabie and C. F. Reinholtz, “Mechanism and Dynamics of Machinery”, Wiley.
2. J.S. Rao & R.V. Dukkipati Mechanisms and Machine Theory, New Age International (P) Limited..
3. J.E. Shigley and J.J. Uicker, Jr., “ Theory of Machines and Mechanisms”, McGraw Hill.
4. B. Paul, “Kinematics and Dynamics of Planar Machinery”, Prentice Hall.
5. C. E. Wilson, J.P. Sadler and W.J. Michels, “Kinematics and Dynamics of Machinery”, Harper Row.