Chapter 6Velocity in Mechanisms

(Instant Centre Method)

9/16/2016

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

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

2

Introduction

Instant center of a moving body:

center which keeps changing fromone 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

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

3

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.

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

4

Methods for Determining the

Velocity of a Point on a Link

1. Instant center method

2. Relative velocity method

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

5

Number of Instant Centers in a

Mechanism

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

6

Types of Instant Centers

a. Primary instant centers

1. Fixed instant centers

2. Permanent instant centers

b. Secondary instant centers

1. Neither fixed nor permanent instant

centers

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

7

Types of Instantaneous Centers

Fixed ICs, I12 & I14:same place for all

configurations of

mechanism

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

8

Types of Instantaneous Centers

I23 & I34, permanent

ICs: move whenmechanism moves,

but joints are of

permanent nature

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

9

Types of Instantaneous Centers

I13 & I24, neither

fixed nor

permanent ICs:vary with

configuration of

mechanism

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

10

Location of Instantaneous Centers

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

11

Aronhold Kennedy Theorem

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

straight line.

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

12

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

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

13

Links 1 2 3 4

Instantaneous

centers

12 23 34

13 24

14

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

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

14

Method of Locating Instantaneous

Centers in a Mechanism

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.

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

15

Method of Locating Instantaneous

Centers in a Mechanism

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

16

Example 6.1

The crank AB rotates uniformly at 100 rpm.

Locate all instantaneous centers and find

the angular velocity of link BC.

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

17

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

crank rotates cw with an angular velocity of 10

rad/s, find:

1. Velocity of slider A

2. Angular velocity of ConRod AB

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

18

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

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

19

Example 6.39/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

20

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.

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

21

Example 6.4

9/16/2016

Mohammad Suliman Abuhaiba,

Ph.D., PE

22

Example 6.5

The figure shows a sewing needle

bar mechanism O1ABO2CD

wherein the different dimensions

are as follows: 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 velocity of

needle at D for the given

configuration. Crank O1A rotates

at 400 rpm.

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

23

Example 6.5

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

24

Example 6.6The various dimensions of

a Whitworth quick return

motion mechanism are as

follows: OQ = 100 mm; OA

= 200 mm; QC = 150 mm;

and CD = 500 mm. The

crank OA rotates at 120

rpm cw. Locate all ICs

and find the velocity of

ram D.

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

25

Example 6.6

9/16/2016

Mohammad Suliman Abuhaiba, Ph.D., PE

26