Chapter 6site.iugaza.edu.ps/mhaiba/files/2013/09/CH6-Velocity-in-Mechanisms-ICM-2015.pdfMethod of Locating Instantaneous Centers in a Mechanism 3. Locate fixed & permanent ICs by inspection

Chapter 6Velocity in Mechanisms

(Instant Centre Method)

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Mohammad Suliman Abuhaiba, Ph.D., PE1

Introduction

Combined motion of rotation & translation of

link AB: pure rotation about some center I,

instant center of rotation

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Introduction

Instantaneous center of a moving

body: center which keeps changing

from one instant to another.

Centrode: locus of all such ICs

instantaneous axis: A line through anIC & perpendicular to plane of

motion

Axode: Locus of this axis

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Space and Body Centrodes

IC: a point in the body which may be

considered fixed at any particular moment

Space centrode: locus of IC in space

during a definite motion of the body

Body centrode: locus of IC relative to bodyitself

Body centrode rolls without slipping over

space centrode.

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Kinematics with MicroStation - Ch03L Centrodes.mp4

Methods for Determining the

Velocity of a Point on a Link

1. Instantaneous center method

2. Relative velocity method

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Velocity of a Point on a Link by

IC Method

vA is known in magnitude

& direction & vB in direction

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Number of Instantaneous Centers

in a Mechanism

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Types of Instantaneous Centers

a. Primary instantaneous centers

1. Fixed instant centers

2. Permanent instant centers

b. Secondary instantaneous centers

1. Neither fixed nor permanent instant

centers

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Fixed ICs, I12 & I14:same place for all

configurations of

mechanism

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I23 & I34, permanent

ICs: move whenmechanism moves,

but joints are of

permanent nature

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I13 & I24, neither

fixed nor

permanent ICs:vary with

configuration of

mechanism

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Location of Instantaneous Centers

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Aronhold Kennedy Theorem

If 3 bodies move relative to eachother, they have 3 ICs that lie on a

straight line.

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permanent Ics: Iab & Iac

3rd IC Ibc must lie on line joining Iab & Iac

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Kinematics with MicroStation - Ch03 I Instantaneous Centers II.flv


Let Ibc lies outside line

joining Iab & IaC

Ibc belongs to links B & C

If Ibc is on B. Its velocity vBC

must be perpendicular to

line joining Iab & Ibc

If Ibc is on C. Its velocity

vBC must be

perpendicular to line

joining Iac & Ibc

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Velocity of Ibc cannot be

perpendicular to both

lines Iab Ibc & IacIbc unless

Ibc lies on line Iab Iac.

Iab, Iac and Ibc must lie on

same straight line.

Exact location of Ibc on

line Iab Iac depends upon

directions & magnitudes

of the angular velocities

of B & C relative to A.

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Method of Locating ICs in a Mechanism

Fig. 6.8 (a)

1. Determine number of ICs (N)

2. Make a list of all instantaneous centers

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Links 1 2 3 4

Instantaneous

centers

12 23 34

13 24

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Method of Locating Instantaneous

Centers in a Mechanism

3. Locate fixed & permanent ICs by

inspection.

I12 & I14 are fixed Ics

I23 & I34 are permanent IC

The four bar mechanism has:

four turning pairs

four primary (fixed and permanent) ICs

located at centers of the pin joints

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4. Locate remaining neither fixed nor

permanent ICs (secondary centers) by

Kennedy’s theorem

Circle diagram Fig. 6.8 (b)

Mark points on a circle equal to number

of links in a mechanism.

5. Join points by solid lines to show that

these centers are already found.

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Example 6.1

In a pin jointed four bar mechanism, AB = 300

mm, BC = CD = 360 mm, and AD = 600 mm. The

angle BAD = 60°. The crank AB rotates uniformly

at 100 rpm. Locate all instantaneous centers and

find the angular velocity of link BC.

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Example 6.1

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Example 6.2Locate all ICs of the slider crank mechanism. The

lengths of crank OB & connecting rod AB are 100

mm & 400 mm respectively. If the crank rotates cw

with an angular velocity of 10 rad/s, find:

1. Velocity of slider A

2. Angular velocity of connecting rod AB

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Example 6.2

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Example 6.3

A mechanism has the following dimensions:

OA = 200 mm; AB = 1500 mm; BC = 600 mm;

CD = 500 mm and BE = 400 mm. Locate all

ICs. If crank OA rotates uniformly at 120 rpm

cw, find:

1. velocity of B, C and D

2. angular velocity of links AB, BC and CD

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Example 6.39/26/2015


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Example 6.4The mechanism of a wrapping machine has the

following dimensions : O1A = 100 mm; AC = 700 mm;

BC = 200 mm; O3C = 200 mm; O2E = 400 mm; O2D =

200 mm and BD = 150 mm. The crank O1A rotates at

a uniform speed of 100 rad/s. Find the velocity of

point E of the bell crank lever by IC method.

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Example 6.4

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Example 6.5

Fig. 6.21 shows a sewing needle

bar mechanism O1ABO2CD

wherein the different dimensions

are as follows: Crank O1A = 16 mm;

b = 45°; Vertical distance between

O1 & O2 = 40 mm; Horizontal

distance between O1 & O2 = 13

mm; O2B = 23 mm; AB = 35 mm;

O2BC = 90°; BC = 16 mm; CD = 40

mm. D lies vertically below O1. Find

the velocity of needle at D for the

given configuration. The crank O1A

rotates at 400 rpm.

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Example 6.5

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Example 6.6The various dimensions of

a Whitworth quick return

motion mechanis are as

follows: OQ = 100 mm; OA

= 200 mm; QC = 150 mm;

and CD = 500 mm. The

crank OA makes an angle

of 60° with the vertical &

rotates at 120 rpm cw.

Locate all ICs and find the

velocity of ram D.

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../Videos/Detail Animation of Whitworth Quick return mechanism with Description..flv

Example 6.6

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Documents

Chapter 6site.iugaza.edu.ps/mhaiba/files/2013/09/CH6-Velocity-in-Mechanisms-ICM-2015.pdfMethod of Locating Instantaneous Centers in a Mechanism 3. Locate fixed & permanent ICs by inspection