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LECTURE 13- accel & F2 ~ dyn, Cor

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1

Acceleration and Force Analysis (cont.)

Forces and Torques

2

now the forces and torque can be found

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3

Same FBDas static

case

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4

Same FBD

as static

case

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5

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6

SOLVING

FG2X = -5260. N

FG2Y = -1369. N

FAX = 5260. N

FAY = -1369. N

TSH = 193.8 N-m

FG4X = 832.3 N

FG4Y = -4566. NFN = 832.3 N

for directions consult the FBDs

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7

in this case, a static analysis does not give a good

approximation for the dynamic analysis

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8

BUT

If accelerations, masses or moments of inertia are small, the

static analysis could be very close to the dynamic analysis

AND IT IS

easier to obtain !

easier to change in an iterative design process !

See PS3 Q1 for a dynamic analysis that can be done by hand,

including solving a matrix by algebraic substitution.

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9

THE NEXT LEVEL OF COMPLEXITY IN KINEMATICS

what ifa body 1 is connected to a slider which moves in a

slot and this slot is in a body 2 which is rotating and

translating

often convenient to use a rotating frame of reference

which involves a specification of the Coriolis

acceleration (that you learned all about in ME 212)

consider the following example....

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absolute angularvelocity and absolute

angular acceleration of

BODY 2 and of the xy

coordinate axes (or xy

frame)

10

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11

The midterm covers up to here. The

Specific Design Project is also based on

material up to here. Together they form

40% of the evaluation for ME 321. This

first part of the course will NOT be

directly evaluated again. Be sure to study

for the midterm with more care than

usual. It is essentially a mini final exam.

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ME 321

Simulating a Four-bar

Mechanism in

ADAMS - View

Prepared by John Medley

1

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Mohsen Azimi

John McPhee

Adel Izadbakhsh

Acknowledgements

2

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A fairly simple problem (find TD)

O2A and AB O4B

a = 4 mm a = 10 mm

b = 8 mm b = 20 mm

At all pin joints, each link extends a

distance of b/2 as shown in the

sketch on the right. The pins are all

located at the midpoint of the width

of each link. The centres of massare located at the midpoint of the

link lengths

NOT TO SCALE

[oscillates through 60o]

[in this case ~ NOT

the same as the

SDS Project!]

3

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Where to find ADAMS?

ADAMS should be installed in these labs

1. Fulcrum

2. Helix

3. Lever 4. WEEF

5. Wheel

4

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To start ADAMS View

Programs

Engineering

MSC.ADAMS

Aview

ADAMS - View

5

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Operational steps involve 1. ADAMS interface specifications

2. Link geometries and positions

3. Link mass and mass-moment of

inertia

4. Pin joints5. Load torque

6. Crank angular velocity

7. Run a simulation for 1 cycle of crank

8. Finding TD (driving torque)

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1. ADAMS interface specifications

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To create a new model

Give a model name

Select where to save your model

Select units as

When everything above

is done, Click OK

8

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and get the starting interface

9

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To input an appropriate grid

Settings

Working Grid

10

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make these changes

by left clicking on the

box, selecting text and

inputting values using

your keyboard

Hit OK

Hit Apply

11

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It looks a little weird so

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To get a better fit use

- zoom: hit z and hold left button of mouseand move mouse up and down

- pan: hit t and hold left button of mouseand move mouse around

13

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and mess about until you get something like

this (can re-adjust later using z and t again)

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2. Link geometries and positions

(Note: In the example that I am doing in this tutorial, I refer to values

calculate in an Excel file. This file is not provided and you would be

expected to develop it yourself or simply calculate the required

values using your calculator. The present tutorial just indicates how

an Excel value can be easily inserted into ADAMS.)

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To add ground link

Left click here

Left click and select

On Ground

Left click

Paste in length from

Excel as follows:

(1.18050836506990E-01m)

for my chosen case (can use Ctrl c to

copy and Ctrl v to paste then

backspace once to see values in box). Can also use your

calculator to get the value and just type in using the keyboard!16

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Move cursor to

drawing area

(watching the

command line

for feedback),

left click on

starting point

(origin) and drag

to the right

17

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If you make a mistake(at any time) left click

here and do it again (but

colours and icons may

change) OR left click on

the link then right click

on it and select delete

from the menu and do it

again.

18

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To add crank

Left click here

Left click

Type in as follows:

(0.03m)

Repeat the above two steps

for Width and Depth(not reallynecessary but avoids a

Warning later)19

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Left click and

drag as done

previously with

the ground,

placing the crank

in the 90o

position as

shown

20

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Create the

Coupler and

Output Rockerlinks guessing at

their orientation

(note that there

is a gap between

them and that

the output link

has a different

Width andDepth)

21

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3. Link mass & mass-moment

of interia

(Note: In the example that I am doing in this tutorial, I

refer to values calculate in an Excel file. This file is not

provided and you would be expected to develop it

yourself or simply calculate the required values using

your calculator. The present tutorial just indicates how

an Excel value can be easily inserted into ADAMS.)

22

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To add mass and mass-moment

of inertia

Double left click on the Input Crank

then left click

here and

select User

Input

23

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Left click hereand paste in from

Excel (or use

calculator and

type in)

Left click

on Apply

Last step: left

click on OK24

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Repeat instructions of the last two slides for

the Coupler and the Output Rocker.

Note that Ixx + Iyy Izz in all cases and this is

important because, if it is not true, ADAMS may

inexplicably give incorrect results. Also, for the

values of the present case, the TD values are not

very sensitive to Izz variations. However, if the

input speed were higher or the TL value lower, Izzvariations would change TD more significantly.

25

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4. Pin joints

26

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To add pin joints

Left click here

(or if revolute joint

is not there, right clickon lower left corner

of the button and select

the revolute joint)

27

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Left click on

the crank (Part 2) toselect the First

Body (again

watching the

command line for

feedback) then left

click on the ground

and finally on the

joint itself (Wigglethe cursor around

to get the correct

selections ~ the

screen will give a

message to tell you

which body or joint

you are on!) 28

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Repeat the

process for the

second jointbetween crank

and coupler

selecting Part 3 as

the First Body and

Part 2 as the

Second Body

29

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Repeat the

process for the

third joint BUT

select 2 Bod-2 Loc

here

30

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For the third joint

between coupler

and output link,select Part 4 as

the First Body and

Part 3 as the

Second Body and

the First Location

on Part 4 and the

Second Location

on Part 3

31

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Repeat the

process for the

fourth joint BUT

select 2 Bod-1 Loc

here

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For the fourth

joint select Part 4

as the First Body

and ground as

the Second Body

33

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5. Load torque

34

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To add the load torque (TL)

Right click on the

lower right cornerof the Spring

button and left

click on the torque

arrow to select it

Left click

Left click on box

and type in -157 35

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Move cursor to

work area,

select the

body (Part 4)

and the point

of application

(ground.MARK

ER_2)

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6. Crank angular velocity

37

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To add the crank angular velocity

Left click

Left click on box and from

Excel paste in the angular

velocity of the crank in deg/s

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Left click onthe arrow for

joint 1 (crank

to ground

joint) to add

the angular

velocity to

your model

39

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To modify the

ridiculous

large motion

arrow, right

click on it and

selectAppearance

40

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Then

do all

this

41

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Do the same

thing for the

torque arrow

(typing in

0.020) and get

this appearance(much nicer!)

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7. Run a simulation for

1 cycle of crank

43

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To run a simulation

2. Enter time for 1

cycle from Excel or

your calculator

3. Enter 200 steps

4. Hit run!

1. Hit this

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You could get this

kind of crap from

ADAMS. It means

you must start over

and do everything

again very carefully!

Fortunately, I have a

previous model that

ran and I will now exit

ADAMS and insert my

previous model (by

selecting) Opening anexisting database in

the first menu of

ADAMS.45

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A simulation that ends

like this will occur. AWarning box may appear

and ruin the simulation

but select it and shrink it

so it is out of the way.

Then, hit the Reset

Arrow button just below

Simulation in the Toolbox

and then the forwardarrow to run it again.

Left click on the

workspace to get nicer

colours. Always hit the

Reset Arrow before the

Run button.

Hit Tools Purge

Cache Files to keep

space available on your

computer. Also, log out

and in again if ADAMS

does not want to run.46

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8. Finding TD (driving torque)

47

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To find the driving torque (TD)

Left click

here

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1. Left click

and select

Result Sets

4. Then hit this

2. Select 3. Hit this

5. And move cursor here

6. to get answer of 76.1966 Nm

for TD.

7. To return

to simulation

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You are done but read

on one more slide ...

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With a little effort, you can construct complex graphs like

this to verify the load torque and crank angular velocity

(but this was not required for the project).

51

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END(finally)

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LECTURE 14Cams 1 ~ intro,

graphical

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1

cams transmit motion to a follower

motion - depends directly on cam shape

- can be rolling and/or sliding

advantage compared with bar & bar-slider mechs- specific output displacement (easy to achieve)

common type rotating disc cam withreciprocating or oscillating follower

CAMS

2

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[from Design of Machinery, 2nd Ed, Norton]

3

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4

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in ME 321 will consider

disc cams with reciprocating followers

specified follower displacement with

low accelerations so that dynamic

effects are avoided

5

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Some Notation and Advice

large pressure angle causes significant side thrust

- thus usually keep below 30o

keep profile smooth to avoid vibration and impact problems6

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A Graphical Design Method

disc cam with flat-faced follower

1. start at the minimum follower displacement (r = rB)

2. rotate follower about the cam in the opposite direction to

the cam rotation

3. move the followerradially outward to the specified position

4. draw the cam tangent to the polygon formed by the followerfaces

7

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Givenr

rB 0o

r1 1r2 2r3 3etc.

Start like this

8

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(face half width)

cam

profile

follower

face

base circle

cam rotation

...and eventually get

part of the cam profile

9

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Extension to a Roller Follower

now drawcam profile

tangent to

followers

circular face

10

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LECTURE 15Cams 2 ~ analytical,

guidelines

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1

An Analytical Method

for a disc cam with a flat-faced follower

2

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Given: r = C + f ( ) .... (1) where C = constantFind: cam profile coordinates (x, y) and face half-width ( l max )

Soln:

let f f ( ) and from the geometry note that

3

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From the geometry, note that

x = r cos - l sin .... (3)

y = r sin + l cos .... (4)

4

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DISCUSSION OF GENERAL PRINCIPLES IN CAM DESIGN

[some examples of the issues involved

in cam selection and design]

FOR all but very slow speeds

follower displacement, velocity and acceleration

should be continuous

also jerk (time rate of change of acceleration)

should be finite

5

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If you want

you must live with piecewise functions "patched"

together in a continuous fashion.

often simply want a number of specific positions ~ can fit

profile curves together to minimize shock loading6

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Linear Reciprocating or Oscillating Follower?

reciprocating with linear motion of follower often required but

the linear bearings needed for this follower are more complex

and expensive than those of the pin of the oscillating follower

SO could try to approximate straight linemotion with a long oscillating follower

7

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if a roller is used for the contact with the cam, the linear

reciprocating follower must be prevented from rotating BUT the pin of the oscillating follower already

provides this constraint

if a roller is used for the contact with the cam, the linear

reciprocating follower must be prevented from rotating

BUT the pin of the oscillating followeralreadyprovides this constraint

if a flat-faced follower is used, the linear reciprocating action

allows placing the follower axis slightly out-of-plane which

allows friction to cause slow rotation about the follower axis

distribute wearover the face

ADVANTAGE COMPARED TO OSCILLATING FOLLOWER!8

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Spring-loaded Follower or Face Cam?

face cam expensive and may have friction and wear

problems along with cross-over shock (impact when

contact force moves from one side of the track to theother) causing vibration and additional wear problems.

BUT eliminates follower jump

spring can act to reduce shock loads by allowing

compliance in the system

BUT may allow some follower jump

9

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Roller or Flat-Faced Follower?

roller allows concave regions of the cam

roller easy to replace

roller friction lowerBUT more space needed and high temperatures

may "cook" the oil (degrade and leave hard deposits)

in the axle of the roller

AS A RESULT flat-faced followers more common

in internal combustion engines10

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To Dwell or Not to Dwell?

- dwell is a period in one revolution of the cam

when the follower does not move

yes!! an easy follower motion to implement that may be

required in a machine design

if dwell is not required should consider using a bar or

bar-slider mechanism (rather than a cam-follower

system ) which would be cheaper and be less likely to

have wear problems

11

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To Grind of Not to Grind?

ground cam usually has smoother operation and

less wearthan an as-milled cam

BUT increases the cost

sometimes a good boundary lubricant (one with

molecules that "stick" to the surface) will allow run-in of a milled cam WHICH may be a cheaper

alternative to grinding

12

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To Lubricate or Not to Lubricate?

yes! unless application prevents you (for example,

camera cam and linkages cannot have liquid lubricant

unless sealing is perfect)

recommend generous supply of clean oil of type usedfor hypoid gears (powerful boundary lubricant

additives)

lubricant also removes

heat and high

temperatures that often

increase wear

13

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END OF CAMS

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