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KINEMATICS OF MECHANISMS A brief discussion on links, joints and mechanisms
INTRODUCTION
Design of a mechanical system needs a proper understanding of two
aspects:
Geometric aspects of motion
Various forces involved in motion
The subject that deals only with geometric aspects of motion
without any consideration of forces is called ‘kinematics’ . The
word has been derived from the Greek word ‘kinema’ which means
motion.
A mechanism is a combination of rigid or restraining bodies so
shaped and connected that they move upon each other with a definite
relative motion.
A machine is a mechanism or collection of mechanisms which
transmits force from the source of power to the resistance(load) to be
overcome.
When the objective is only to transfer and transform motion without
any consideration of forces involved, it is a mechanism. On the other
hand, if the objective is to transfer mechanical energy only, it is a
machine.
MECHANISM VS. MACHINE
FOUR BAR MECHANISM: ROTARY TO OSCILLATORY
FOUR BAR MECHANISM: ROTARY TO ROTARY
BELL CRANK: RECIPROCATING TO RECIPROCATING
SLIDER CRANK: ROTARY TO RECIPROCATING
SCOTCH-YOKE MECHANISM
BOURKE ENGINE
(UTILIZING SCOTCH-YOKE)
WATT PARALLEL MOTION GENERATOR
PEAUCELLIER-LIPKIN LINKAGE
(STRAIGHT-LINE MOTION WITHOUT A GUIDE)
PANTOGRAPH
(PARALLEL MOTION TRANSFER)
CAMS
CAMS
GEARS
PAWL-RATCHET: INTERMITTENT MOTION
GENEVA WHEEL
QUICK RETURN MECHANISM
LINKS, JOINTS, KINEMATIC CHAINS Terminologies and Classifications
LINKS Link: A rigid member of a mechanism. Classification based on number of nodes
Singular: connected to one link
Binary: Connected to two other links
Ternary: Connected to three other links
Quaternary: Connected to four other links
And so on…………
NODE
It connects two links.
The type of joint determines the possible relative motion between the
connected links.
Basis of classification:
I. Type of contact: Lower and Higher Pairs
II. No. of Degrees of Freedom
III. Physical closure: Form or force closed
IV. No. of links joined: Order of the joint
V.
JOINTS OR KINEMATIC PAIRS
CLASSIFICATION BASED ON TYPE OF CONTACT
Lower Pair: connection through area of contact
Higher Pair: connection through line/point contact
Wrapping Pair: One of the links has one way rigidity
(Ex. Belt-pulley, chain-sprocket, rope-drum)
DOF
Degrees of Freedom of Joint: Connectivity Minimum number of independent co-ordinates needed to
completely specify the relative motion.
RELATIVE ROTATION (1-DOF)
RELATIVE TRANSLATION (1-DOF)
RELATIVE ROTATION AND TRANSLATION
(2-DOF)
Two Fundamental Joints
SPHERICAL JOINT
LOWER PAIRS 1
2
3
HIGHER PAIRS: LINE OR POINT CONTACT
HIGHER ORDER PIN JOINT
FORM CLOSED AND FORCED CLOSED JOINTS Form Closed: Geometry keeps the joint closed
Force Closed: A force is required the to close the joint
Spring Loaded Cam
CLASSIFICATION BASED ON DOF Maximum number of Joint DOF =5
Class I Joints
Class-II joints
Class-III joints
Class-IV joints
Class-V joints
Definitions
Kinematic Chain: An assembly of links and
joints to produce controlled output in response
to an input
Mechanism: A kinematic chain with at least one
link fixed or grounded
Machine: A mechanism that transform motion
while doing work
Definitions
Crank: Link that revolves 360o and pivoted to the ground
Rocker: Link that has oscillatory rotation and pivoted to the
ground
Coupler: Has complex motion and not connected to the ground
Ground: Frame or the fixed link
Types of Kinematic Chains
Closed If every link is
connected to two
other links
Open
Linkages
Mechanisms composed of rigid bodies and lower pairs are called linkages
KINEMATIC
INVERSIONS
KINEMATIC INVERSIONS
The process of obtaining different mechanisms by fixing
different links of the same kinematic chain is called kinematic
inversion.
Note that inversion does not change relative
motions between the links
INVERSIONS OF 4-BAR LINKAGE
INVERSIONS OF SLIDER-CRANK (OFFSET)
MECHANISM
Applications Reciprocating Engine
Reciprocating Compressor
Applications Whitworth Quick return mechanism
Rotary Engine
Applications Crank and slotted lever mechanism
Oscillating cylinder engine
Application: Hand Pump
INVERSIONS OF SCOTCH-YOKE
MECHANISM
ELLIPTIC TRAMMEL TO OLDHAM COUPLING
Animation1 Animation2