View
5
Download
0
Category
Preview:
Citation preview
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
Recommended