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Kinematics of Mechanisms 5Velocity Analysis

Latifah Nurahmi

Latifah.nurahmi@gmail.com

Room C.250

Assignment 1

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The picture shows a cargo lift mechanism. At this instant, point A has a velocity of 12 in/s in

the direction shown. Point B has a velocity of 10.4 in/s. Determine:

- The angular velocity of the lower link/input link

- The velocity of point B relative to point A

mailto:Latifah.nurahmi@gmail.com

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Assignment 1

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O

C

OA = 20 inAB = 23 inBC = 16 in

Assignment 2

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A rock-crushing mechanism is used in a machine where large rock is placed in a vertical

hopper and falls into the crushing chamber. Determine the angular velocity of the crushing

ram when the crank rotates at 120 rpm clockwise

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Assignment 3

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The pictutre shows a primitive well pump that

is common in undeveloped areas. To

maximize water flow, the piston should travel

upward at 50 mm/s. In the position shown,

determine the angular velocity of the handle

to achieve the desired piston speed.

Assignment 3

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Assignment 4

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Heavy roofing materials can be transported on the conveyor to the roof. The conveyor is lifted

into place by extending the hydraulic cylinder. At this instant, the cylinder is extending at 8 ft/min.

Determine the rate that the conveyor is being lifted.

Assignment 4

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Instantaneous Center of Velocity

Instantaneous center of velocity

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Instantaneous center of velocity(ICV)

Any point on a rigid body or on itsextension that has zero velocity

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Given the velocity VA of point A on a rigid

body and the angular velocity.

Then the ICV is located perpendicular

from VA.

Finding ICV

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1. The lines intersect at one point

Finding ICV

VA … ?

VB … ?

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2. Parallel lines intersect at infinity

Finding ICV

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3. Two lines fall on top of each

other

Finding ICV

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Velocity of a point with ICV

Consider two points A and B on a rigid

link. Let vA and vB be the velocities of

points A and B at a given instant.

If vA is known in magnitude and

direction and vB in direction only, then

the magnitude of vB may be

determined by the instantaneous

centre method.

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Velocity of a point with ICV

Draw AI and BI perpendiculars to the

directions vA and vB respectively.

Let these lines intersect at I, which is

known as instantaneous centre or

virtual centre of the link.

The complete rigid link rotates about

the centre I at the given instant.

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Velocity of a point with ICV

The relations shown may be used to

determine the magnitude of the

velocity of point B.

IBB

IAAIAA

IAA

IAIA

rv

rvrv

rkv

rkvv

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Location of ICV

When the two links are connected by a pin joint (or pivot

joint), the instant center lies on the center of the pin as.

Such an instant center is of permanent nature. If one of the

links is fixed, the instant center will be of fixed type.

When the two links have a pure rolling contact (without

slipping), the instantaneous centre lies on their point of

contact, as this point will have the same velocity on both

links

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Location of ICV

When the two links have a sliding contact, the instant center lies at the center of curvature

of the path of contact.

This points lies at the common normal at the point of contact.

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ICV of Four bar mechanism

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ICV of Four bar mechanism

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Centrodes

As the link 3 moves, the ICV will also change. The locus of all ICV is called centrodes.

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ICV of Slider crank mechanism

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ICV of Slider crank mechanism

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Velocity analysis with ICV

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Four bar mechanism

ω2 is known.

The magnitude of the velocity of point

A can be computed as vA = ω2 O2A.

Its direction and sense can be

determined by inspection.

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Four bar mechanism

Note that point A is also instant center

and it has the same velocity as part of

link 2 and as part of link 3.

Since link 3 is effectively pivoting about

I13 at this instant, the angular velocity

ω3 can be found by ω3 = vA /AI13 .

Once ω3 is known, the magnitude of vB

can also be found from vB = ω3 AI13

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Four bar mechanism

Once vB is known, ω4 can also be found

from ω4 = vB /BO4 = vB /BO4 .

Finally, vC (or the velocity of any other

point on the coupler) can be found

from vC = ω3 CI13

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Freudenstein’s Theorem

Line connecting I13 and I24 is

called Collineation axis

Angular velocity ratio