# Theory of Machines 1

Mechanics

Oct 31, 2013 (4 years and 6 months ago)

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Theory of Machines 1

RECOMMENDED TEXTS:

MECHANISMS AND DYNAMICS OF MACHINERY

Mabie & Reinholtz

MECHANICS OF MACHINERY

G. H. Martin

DEFINITIONS.

1.

STATICS

Science of bodies at rest or forces in equilibrium.

2.

DYNAMICS

Branch of mechani
cs that deals with motion, and the motion of bodies or
matter under the influence of forces.

3.

KINEMATICS

Science of pure motion, without reference to force or mass.

4.

KINETICS
-

Science of relations between the motions of bodies and

the forces acting
upon them.

This course is primarily about kinematics in that we are studying and analysing the motion of
machines and mechanisms in order to:

Analyse displacement

Differentiate this w.r.t. time in order to obtain component velocities

D
ifferentiate velocities w.r.t. time in order to obtain accelerations

generated due to acceleration

F=M.a, by finding a function for acceleration we can find
these for
ces.

Finally we wish to find the rate of change of acceleration or “jerk”

MECHANICS

STATICS

DYNAMICS
Branch of
mechanics that
deals with motion,
and the motion of
bodies or

matter
under the influence of
forces.

KINEMATICS

KINETICS

What are its constituents parts and how do they link together

Machine parts are known as “elements”

Two elements in rela
tive motion and in contact are known as a “pair”

The element joining pairs together is known as a “link”.

A group of links and elements that are joined together is a “kinematic chain”.

Fix one link of the kinematic chain and the chain becomes a “mecha
nism”

Apply force with the mechanism and it becomes a ”machine”

DEFINITIONS.

MECHANISM

Is an assemblage of (rigid) bodies formed and connected in such a manner that they
move upon each other with definite relative motion. (A chain/belt/cable

is non
-
rigid yet can be used in
a mechanism. Another example of this would be air or hydraulic fluid used in a pneumatic or hydraulic
system

they are not rigid in the true sense yet are used to transmit motion).

MACHINE
-

a mechanism, or collection o
f mechanisms which transmit force from the source of power
to the resistance to be overcome. Another definition is that a machine is a combination of resistant
bodies so arranged that by their means the mechanical forces of nature can be compelled to do wo
rk
accompanied by certain determinate motions.

NOTE

A mechanism is therefore kinematically described, its motion is what determines it as a mechanism. A
machine on the other hand is a mechanism which does work.

Rigid structure, truss, etc

Statics

Mecha
nism

Kinematics

Machine

Kinetics

EXAMPLES OF MECHANISMS:

CRANK LEVER RECIPROCATING DRIVE

Connected to piston pump

CRANK

Rotating element which may convert rotational motion into reciprocal or vice
-
versa

Diagram 1

SLIDER CRANK
-

ENGINE MECHANISM

Standard engine layout for two and four stroke internal combustion engines

Diagram 2

BELL CRANK

Used in motorcycle rear brakes

gives approximation to linear motion over short distances.

Diagram 3

PIVOTING PISTON CRANK

Used in
early steam engines. The valves opened and closed as the cylinder oscillated to allow steam
enter and exit the cylinder.

Diagram 4

Also known as a parall
ogram linkage. Used extensively to transmit motion from one crank to another
using a connecting rod. Motion may be reciprocal or fully rotational on the part of either crank

This is
dependent on the relationship between the crank lengths, connecting rod
length and the distance
between the two fixed centres.

Diagram 5

Changeover points or change points are shown below. This is where direction of rotation may be
rever
sed on one or other crank. On old railway locomotives the two sets of wheels on opposite sides of
-
-
of
-
phase by 90 degrees to ensure that no matter
what position the train stopped in there would be no dan
ger of wheel direction of rotation being
incorrect.

Diagram 6

If direction of rotation on one crank is opposite to that on the other then what is known as a butterfly
arr
angement will be obtained.

Diagram 7

MORE MECHANISM DEFINITIONS

Machine part or component of mechanism

assumed rigid (but not necessarily so for
example a chain,
belt, hydraulic fluid, cable, etc)

DRIVER

Input link or crank. Where the power comes from is typically a motor. Whether its an
AC, DC, diesel, petrol, etc. in 99% of cases input power or motion to a m
achine or a
mechanism is in the form of a rotating shaft.

CYCLE

When the parts of a mechanism or machine have passed through all the possible
positions the can assume and have returned to their original positions they have
completed a full cycle of mo
tion.

PERIOD

Time required for a full cycle of motion

typically 360 degrees rotation of the input
crank.

PHASE

The simultaneous relative position of the links at any instant during the cycle of
motion for the mechanism constitute a phase
.
Phase is t
he word used to describe
where the mechanism “is in its cycle of motion” at any moment in time. We use the
words “in
-
phase” to describe two systems whose positions are complimentary,
compatible or equivalent in some way at some specific moment in time.

PA
IRING ELEMENTS (Kinematic Pairs)

In order to transmit motion from the driver to the follower for example the

together in some manner. Connections between links are called Kinematic Pairs. Two bodies in contact
constitutes a pair.
Looking back at the mechanisms shown so far it is possible to see that most links are
joined to two other links and thus may be said to be part of not one but two pairs.

KINEMATIC CHAIN

A number of links connected by means of pairs makes a Kinematic Chai
n.

CONSTRAINED KINEMATIC CHAIN = MECHANISM

A constrained Kinematic chain is a mechanism as the constraint implies that a fixed link is present as a
frame of reference.e.g base or foundation. Without there being a fixed link whose position is defined
there

can be no frame of reference for the motion of the assembly of links. Without this ability to
absolutely define the motion of each element there is no mechanism.

CONSTRAINED CHAIN

Relative motion of the links always the same. In the figure below for the

same position “x” of link 5
there are two possible arrangements of links 3 and 4. Links 3 and 4 are unconstrained therefore this is
not a mechanism instead its an
Unconstrained Kinematic Chain

i.e. Were link s 2 and 4 to be directly
connected then it woul
d be a constrained chain.

Diagram. 8

LOCKED CHAIN

If no motion at all were possible then a
locked chain

is obtained

also known as a
structure

or
truss.

Diagram. 9

CLOSED CHAIN

Most mechanisms consist of closed chains wherein each link is connected to at least two others in the
system. AN example of this would be the early radial aircraft e
ngine type

OPEN CHAIN

An example of an open chain would be a pendulum

links with only one joint (but touches another

JOINT TYPES

More than two links may join at the same point and examples of these types of joint are given below:
A
ll these types of links may be used to form an open mechanism.

Diagram 10

PAIRS

ture of the
connection between the two links defines the pair type

i.e. the relative motion which the links are
permitted.

HIGHER AND LOWER KINEMATIC PAIRS:

LOWER PAIRING: ►

Two surfaces are in contact i.e. piston and cylinder, pivot etc.

slider.

HIGHER PAIRING ►

Contact is at a point, or along a line e.g. ball bearing, roller bearing, gear
teeth, cam surfaces

*Wear is higher at higher pairs.

WRAPPING PAIR ► Chain & sprocket, belt & pulley, cable/drum.

ANALYSIS

For the purposes o
f kinematic analysis we usually assumes a perfect fit occurs at a joint, i.e, no dead
band or clearance