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

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