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MECHANICS

Science dealing with motion

DIVISIONS OF MECHANICS

Statics – Deals with systems which are not changing with time.

Dynamics – Deals with systems which are changing with time.

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DIVISIONS OF DYNAMICS

KINEMATICS – Deals with Motion and Time

(Kinema – Greek Word – Motion)

KINETICS – Deals with Motion, Time and

Forces.

Statics Kinematics Kinetics

STRUCTURE MECHANISM MACHINE

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Some Definitions

Machine – device to transfer or transform energy to do useful work.

Mechanism – device to transfer or transform given input motion to specified output motion

Structure – a single body with no motion / combination of bodies with no relative motion

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Classification of Mechanisms

Based on the nature of output speed

Uniform motion mechanism
Non-uniform motion mechanism

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Uniform Motion Mechanisms

Uniform Motion – Equal Displacement For

Equal Time Interval

Examples : All Gear Drives

All Chain Drives

Belt Drives without slip

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Non-Uniform Motion Mechanisms

Non-Uniform Motion – Unequal Displacement

For Equal Time Interval

Examples : Linkage Mechanisms

Cam Mechanisms

Geneva Wheel

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Classification of mechanisms

Based on mobility (D.O.F) of the mechanism

1. Considering the D.O.F. of output only

a) Constrained Mechanism

b) Unconstrained Mechanism

2. Considering the sum of the D.O.F. Of

input and output motions

a) Single (one) d.o.f. mechanism

b) Multi-d.o.f. mechanism

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Constrained Mechanism

One independent output motion. Output member is constrained to move in a particular manner only.

Example: Four-bar mechanism

Slider Crank Mechanism

Five-bar mechanism with two

inputs

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Unconstrained mechanism

Output motion has more than one D.O.F.

Example: Automobile Differential during

turning the vehicle on a curve

Five-bar mechanism with one

input

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Single D.O.F Mechanism

Sum of the input and output D.O.F. is two.

Single D.O.F. Motion - One Independent

Input motion and one independent

output motion

Examples : Four-Bar Mechanism

Cam-Follower Mechanism

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Multi D.O.F. Mechanism

Sum of the input and output motion D.O.F. is more than two.

Multi D.O.F. Motion – More than one

Independent Output / Input Motions Examples : Automobile Differential

3-D Cam Mechanism

(Camoid)

Five-Bar Mechanism

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Classification of Mechanisms

Based on position occupied in space

Planar Mechanism
Spherical Mechanism
Spatial Mechanism

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Planar Mechanism

Planar Motion – Particles/Points of Members

move in parallel planes

Examples : Planar Four-Bar Mechanism

Slider Crank Mechanism

Cam-Follower Mechanism

Spur/Helical Gear Drives

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Four-bar Crank Rocker and Coupler Curve

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Two Stroke Engine

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Spherical Mechanism�

Spherical Motion – Points maintain Constant

Distance w.r.t. a Common Centre Point

in any position during motion.

Examples : Universal Joint

Bevel Gear Drive

Spherical Four-Bar Mechanism

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Spatial Mechanism

Spatial Motion – Points can occupy any
Position in space

Examples : Spatial Four-Bar Mechanism
Worm Gear Drive
Serial Manipulators

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Classification of mechanisms

Based on the connection of the output member

Open mechanism
Closed mechanism

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Open Mechanism

Output member not connected to the fixed link / frame

Robot arms
Arms of earth movers

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Closed Mechanism

Output member connected to the frame.

Four-bar mechanism
Slider-crank mechanism
Cam follower mechanism

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Components of Mechanisms

Link / element

Kinematic pairs / joints

Kinematic chain

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Link / Element

A single resistant body / combination of resistant bodies having relative motion with another resistant body / combination of resistant bodies.

Rigid Body Flexible Body Liquid

A

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Link with one Node : Unary Link
Link with two Nodes : Binary Link (a)
Link with three Nodes : Ternary Link (b)
Link with four Nodes : Quaternary Link (c)

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Kinematic Pairs / Joints

Combination of two links kept in permanent contact permitting particular kind(s) of relative motion(s) between them

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Classification of Pairs

BASED ON NATURE OF CONTACT BETWEEN LINKS:

1. Lower Pairs -- Surface Contact

2. Higher Pairs – Point or Line Contact

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BASED ON HOW THE CONTACT IS MAINTAINED:

1. Self / Form Closed Pairs – Shape/Form of the links maintain the contact. No external force.

2. Force Closed Pairs – External forces like gravitational force, spring force etc., required to maintain the contact.

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BASED ON THE DEGREE OF FREEDOM

1. Type I / Class I – One D.O.F

2. Type II / Class II – Two D.O.F

3. Type III / Class III – Three D.O.F

4. Type IV / Class IV – Four D.O.F

5. Type V / Class V – Five D.O.F

BASED ON THE NATURE OF CONSTRAINT

1. (Completely) Constrained Pair - 1 D.O.F

2. Unconstrained Pair – More than 1 D.O.F

3. Successfully Constrained pair – Unconstrained

pair converted as Constrained pair by some

means.

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Completely Constrained Pair

Successfully

Unconstrained Pair Constrained Pair

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BASED ON THE POSSIBLE MOTIONS (Few Important Types only)

Name of Pair Letter Symbol D.O.F

1. Revolute / Turning Pair R 1

2. Prismatic / Sliding Pair P 1

3. Helical / Screw Pair H 1

4. Cylindrical Pair C 2

5. Spherical / Globular Pair S (or) G 3

6. Flat / Planar Pair E 3

7. Cylindric Plane Pair Cp 4

8. Spheric Plane Pair Sp 5

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Kinematic Chain

Assembly of links and pairs to produce required / specified output motion(s) for given input motion(s)

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Mechanism

A kinematic chain with one link fixed / stationary

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Mobility / D.O.F of Mechanism

No. of inputs required to get a constrained mechanism (or) no. of position variables needed to sketch the mechanism with all link lengths known.

KUTZBACH CRITERION FOR PLANAR MECHANISM
F = 3(n-1)-2P₁-1P₂
F – D.O.F n – No. of links
P₁– No. of kinematic pairs with 1 D.O.F.
P₂– No. of kinematic pairs with 2 D.O.F.

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DETERMINATION OF D.O.F

n = 3
P₁= 3
P₂ = 0
F=3 x(3 – 1) – 2 x2 – 1x 0
= 6 – 6 – 0 = 0

This is a STRUCTURE

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n = 4
P₁= 4
P₂= 0
F = 3x(4 – 1) – 2x4 – 1x0
= 9 – 8 – 0
= 1

This is a Constrained Mechanism.

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n = 5
P₁= 5
P₂= 0
F =3 x (5 – 1) – 2x5 – 1x0
= 12 – 10 – 0
= 2

This is an Unconstrained Mechanism.

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n = 6
P₁= 7
P₂= 0
F =3 x (6 – 1) – 2x7– 1x0
= 15– 14 – 0
= 1

This is a Constrained Mechanism.

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n = 6
P₁= 7
P₂= 0
F =3 x (6 – 1) – 2x7 – 1x0
= 15 – 14 – 0
= 1

This is a Constrained Mechanism.

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n = 11
P₁= 15
P₂= 0
F =3 x (11 – 1) – 2x15 – 1x0
= 30 – 30 – 0
= 0
There are two pairs between Links (2,4,5); (3,4,6);
(5,7,8); (8,10,11)

This is a Structure.

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Gruebler’s Criterion

This criterion is used to find out whether an assembly of links with 1 d.o.f. lower pairs is a constrained mechanism or not.

3n – 2l – 4 = 0
n – no. of links l – no.of lower pairs with

one d.o.f

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F < 0 Pre-loaded structure

Super structure

F = 0 Structure

F = 1 Constrained Mechanism

F > 1 Unconstrained Mechanism

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Constrained Mechanism

Unconstrained Mechanism

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LINK / ELEMENT

KINEMATIC PAIR / JOINT

KINEMATIC CHAIN

MECHANISM

MACHINE

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Link / Element – A resistant body which has relative motion with another resistant body of a system.
Kinematic Pair / Joint - Combination / Assembly of two links kept in permanent contact, permitting particular kind(s) of definite relative motion(s) between them.

Kinematic Chain – Combination / Assembly of links and pairs such that each link has minimum two pairs, permitting controlled definite output motion for a specified input motion.

Mechanism – A kinematic chain with one link fixed / stationary.

Machine – A device, which has one or more mechanisms, transferring / transforming motion and energy to do required useful work easily.

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MOBILITY OR DEGREE OF FREEDOM

For a Link – Six in spatial motion, three in planar motion.

For a Kinematic Pair – Number of independent co-ordinates/pair variables to specify the position of one link with another link (OR) number of independent relative motions possible between the links. Maximum five and minimum one in spatial motion. Maximum two and minimum one in planar motion.

For a Kinematic Chain/Mechanism – Number of independent position variables to sketch the configuration with known link lengths (OR) number of input motions required to get a constrained output motion

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Spatial D.O.F. Planar D.O.F.

R – Pair P – Pair C - Pair

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Kinematic Inversions

Process of obtaining different mechanisms from the same kinematic chain, by fixing different links in turn, is known as

kinematic inversion.

Four inversions are possible from four-bar

kinematic chain.

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Formation of four-bar mechanism

No. of links – 4, No. of pairs – 4.
All the pairs are revolute pairs.
Links are :1. Fixed link or Frame
2. Input Link
3. Coupler
4. Output link or Follower

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Assembly Condition

Lengths of links: Longest link - l

Shortest link - s

Intermediate links – p, q

l < s + p + q

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Grashofian four-bar mechanism

Atleast one link will have full rotation if

S + l ≤ p + q

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GRASHOF’ S LAW

In a planar four bar revolute pair kinematic chain if the sum of the lengths of the shortest and the longest links is less than or equal to the sum of the lengths of the other two intermediate links at least one link will have full rotation.

Mechanisms obtained from the kinematic chain satisfying these conditions are known as Grashofian Mechanisms.

Mechanisms obtained from the kinematic chain which are not obeying these conditions are known as Non-Grashofian Mechanisms.

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�

Inversions of four bar Mechanisms are named based on the motions of input link and output link.

Crank - Link with 360 degree rotation

Rocker/Lever – Link with less than 360 degree

rotation

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Four- bar Inversions

Crank – Rocker Mechanisms (Two)
Drag Link / Double Crank Mechanism
Double – Rocker Mechanism
Above are Grashofian Inversions

All four non-Grashofian inversions are Double – Rocker mechanisms

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Rockers of Grashofian Mechanisms will have less than 180 degree rotation.

Rockers of Non-Grashofian Mechanisms can have greater than 180 degree rotation.

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