28-02-2013, 03:18 PM
Simple Mechanisms
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Introduction
We have already discussed that a machine is a device
which receives energy and transforms it into some useful
work. A machine consists of a number of parts or bodies.
In this chapter, we shall study the mechanisms of the various
parts or bodies from which the machine is assembled. This is
done by making one of the parts as fixed, and the relative
motion of other parts is determined with respect to the fixed
part.
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. For example, in a reciprocating steam engine,
as shown in Fig. 5.1, piston, piston rod and crosshead constitute
one link ; connecting rod with big and small end bearings
constitute a second link ; crank, crank shaft and flywheel
a third link and the cylinder, engine frame and main bearings
a fourth link.
Types of Links
In order to transmit motion, the driver
and the follower may be connected by the following three types of links :
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.
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.
Structure
It is an assemblage of a number of resistant bodies (known as members) having no relative
motion between them and meant for carrying loads having straining action. A railway bridge, a roof
truss, machine frames etc., are the examples of a structure.
Difference Between a Machine and a Structure
The following differences between a machine and a structure are important from the subject
point of view :
1. The parts of a machine move relative to one another, whereas the members of a structure
do not move relative to one another.
2. A machine transforms the available energy into some useful work, whereas in a structure
no energy is transformed into useful work.
3. The links of a machine may transmit both power and motion, while the members of a
structure transmit forces only.
Classification of Kinematic Pairs
The kinematic pairs may be classified according to the following considerations :
1. 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.
© 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.
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.
Number of Degrees of Freedom for Plane Mechanisms
In the design or analysis of a mechanism, one of the most important concern is the number of
degrees of freedom (also called movability) of the mechanism. It is defined as the number of input
parameters (usually pair variables) which must be independently controlled in order to bring the
mechanism into a useful engineering purpose. It is possible to determine the number of degrees of
freedom of a mechanism directly from the number of links and the number and types of joints which
it includes.