BASICS OF MECHANISMS
Introduction:
Definitions :
Link or Element, Pairing of Elements with degrees of freedom, Grubler‟s
criterion (without derivation), Kinematic chain, Mechanism, Mobility of
Mechanism, Inversions, Machine.
Kinematic Chains and Inversions
:
Kinematic chain with three lower pairs, Four bar chain,
Single slider crank chainand Double slider crank chain andtheir inversions.
.
Terminology and
Definitions-Degree of Freedom, Mobility
Kinematics:
The study of motion (position, velocity, acceleration). A
majorgoal of understanding kinematics is to develop the ability to design a
systemthat will satisfy specified motion requirements. This will be the
emphasis of this class.
Kinetics:
The effect of forces
on moving bodies. Good kinematic designshould produce good kinetics.
Mechanism:
A system design to transmit motion. (low forces)
Machine:
A system designed to transmit motion and energy. (forces
involved)
Basic Mechanisms:
Includes geared systems, cam-follower systems and linkages
(rigid links connected by sliding or rotating joints). A mechanism has multiple
moving parts (for example, a simple hinged door does not qualifyas a
mechanism).
Examples of
mechanisms:
Tin snips, vise grips, car suspension, backhoe ,piston engine,
folding chair, windshield wiper drive system, etc.
Key concepts:Degrees
of freedom:
The number of inputs required to completely control asystem.
Examples:
A simple rotating link. A two link system. A
four-barlinkage. A five-bar linkage.
Types of motion:
Mechanisms may produce motions that are pure rotation,pure
translation, or a combination of the two. We reduce the degrees of freedom of a
mechanism by restraining the ability of the mechanism to movein translation
(x-y directions for a 2D mechanism) or in rotation (about the z-axis for a 2-D
mechanism).
Link:
A rigid body with two or more nodes (joints) that are used
to connect toother rigid bodies. (WM examples: binary link, ternary link (3
joints),quaternary link (4 joints))
Joint:
A connection between two links that allows motion between
the links.The motion allowed may be rotational (revolute joint), translational
(sliding orprismatic joint), or a combination of the two (roll-slide joint).
Kinematic chain:
An assembly of links and joints used to coordinate anoutput
motion with an input motion.
Link or element:
A mechanism is made of a number of resistant bodies out of
which some may have motions relative to the others. A resistant body or a group
of resistant bodies with rigid connections preventing their relative movement
is known as a link.
A link may also be defined as a member or a combination of
members of a mechanism, connecting other members and having motion relative to
them, thus a link may consist of one or more resistant bodies. A link is also
known as Kinematic link or an element. Links
can be classified into 1) Binary, 2) Ternary, 3) Quarternary, etc.
Kinematic Pair:
A Kinematic Pair or simply a pair is a joint of two links having
relative motion between them.
Example:
In the above given Slider crank mechanism, link 2 rotates
relative to link 1 and constitutes a revolute or turning pair. Similarly, links
2, 3 and 3, 4 constitute turning pairs. Link 4 (Slider) reciprocates relative
to link 1 and its a sliding pair.
Types of Kinematic
Pairs:
Kinematic pairs can be classified according toi) Nature of
contact.ii) Nature of mechanical constraint.iii) Nature of relative motion.
i) Kinematic pairs
according to nature of contact :
a) Lower Pair: A pair of links having surface or area
contact between the members isknown as a lower pair. The contact surfaces of
the two links are similar. Examples: Nut turning on a screw, shaft rotating in
a bearing, all pairs of a slider-crank mechanism, universal joint. b) Higher Pair: When a pair has a point
or line contact between the links, it is knowna s a higher pair. The contact
surfaces of the two links are dissimilar. Examples: Wheel rolling on a surface
cam and follower pair, tooth gears, ball and roller bearings, etc.
ii) Kinematic pairs
according to nature of mechanical constraint.
a) Closed pair: When the elements of a pair are held
together mechanically, it is known as a closed pair. The contact between the
two can only be broken only by the destruction of at least one of the members.
All the lower pairs and some of the higher pairs are closed pairs.
b) Unclosed pair: When two links of a pair are in contact
either due to force of gravity or some spring action, they constitute an unclosed
pair. In this the links are not held together mechanically. Ex.: Cam and
follower pair.
iii) Kinematic pairs
according to nature of relative motion.
a) Sliding pair: If two links have a sliding motion relative
to each other, they form asliding pair. A rectangular rod in a rectangular hole
in a prism is an example of asliding pair.b) Turning Pair: When on link has a
turning or revolving motion relative to the other,they constitute a turning
pair or revolving pair.c) Rolling pair: When the links of a pair have a rolling
motion relative to each other,they form a rolling pair. A rolling wheel on a
flat surface, ball ad roller bearings, etc.are some of the examples for a
Rolling pair.d) Screw pair (Helical Pair): if two mating links have a turning
as well as slidingmotion between them, they form a screw pair. This is achieved
by cutting matchingthreads on the two links.The lead screw and the nut of a
lathe is a screw Paire) Spherical pair: When one link in the form of a sphere
turns inside a fixed link, it isa spherical pair. The ball and socket joint is
a spherical pair.
Degrees of Freedom:
An unconstrained rigid body moving in space can describe the
following independentmotions.1. Translational Motions along any three mutually
perpendicular axes x, y and z,2. Rotational motions along these axes. Thus a
rigid body possesses six degrees of freedom. The connection of a link with another
imposes certain constraints on their relative motion. The number of restraints can
never be zero (joint is disconnected) or six (joint becomes solid).Degrees of
freedom of a pair is defined as the number of independent relative motions,
both translational and rotational, a pair can have. Degrees of freedom = 6
–
no. of restraints. To find the number of degrees of freedom
for a plane mechanism we have an equation known as
Grubler’s equation and is given by F = 3 ( n –
1 )
–
2 j1
–
j2
F = Mobility or number of degrees of freedom n = Number of
links including frame. j1 = Joints with single (one) degree of freedom.J2 = Joints
with two degrees of freedom. If F > 0, results in
a mechanism with „F‟ degrees of freedom.
F = 0, results in a
statically determinate structure. F < 0, results in a statically
indeterminate structure.
Kinematic Chain:
A Kinematic chain is an assembly of links in which the
relative motions of the links is possible and the motion of each relative to
the others is definite (fig. a, b, and c.)
