5633245080

Ver. 5/14/13. UW Madison, EMA 545, spring 2013. by Nasser M. Abbasi

- InI x |L

select modę

r 1 c 2    3

max time <		d 30
slow <			► | fast

mass and stiffness k1

_>]0.5 jJ 0.5 jJ

modę	1	2	3
	0.577	0.707	+ 0.408
0i	0.577	+ 0.000	0.816
Oz	0.577	+ 0.707	+ 0.408
f(hz)	0.352	0.370	0.403
UJ	2.214	2.324	2.530

±

k2

0.5

m1 <

-0.5

m2 <

m3 <P

inital position (angles. in degree) thetal    45

-1.5

theta2

theta3 <

-1    0    1    2    3    4    5    6

timc = 2.83 sec max= 30.00 sec

axistypę [norma!

0i{t) = 0.262 * eo.s(2.21 * /) + 0.393 * co.s(2.32 * t) + 0.131 * co.s(2.53 * t) 0₂{t) = 0.262 * eo.s(2.21 * /) - 0.262 * cos(2.53 * t) _p 0₃(t) = 0.262 * cos(2.21 *t) - 0.393 * co.s(2.32 *t)+ 0.131 * co.s(2.53 * t)

0    12    3    4

= 2.94 sec max= 30.

1    2    3

3.16 sec max

1-1-1-1-L_

12    3    4

3.26 scc max= 30.

12    3    4

3.37 sec max= 30.

0    12    3    4

= 3.48 sec max= 30.

0    12    3    4

= 3.59 sec max= 30.

12    3    4

3.81 sec max= 30.

2    3

scc max=

0    12    3

ic = 4.03 sec max= 30.

0    12    3

ic = 4.13 sec max= 30.

0    12    3

ic = 4.35 sec ma.x= 30.

stop	reset
me <|	J30
A	i	4 fast
d stiffness
JZ	► | 0.5 1 |
_L	► | 0.5 1 |
	_J^1 _u
	_J^1 _u
	01 ii

sition (angles, in degree)    -1

"2	0.577	+ 0.000
Oz	0.577	+ 0.707
f(hz)	0.352	0.370
UJ	2.214	2.324

-1.5 -j-j-j-j-j-j|

-2-101234

45

o

stop

le <|    |    >| 30

<|    |    ► | fast \ ₅

łiffness

0₂    -    0.577    + 0.000

03    -    0.577    + 0.707

f(hz)    0.352    0.370

u    2.214    2.324

1

0.5

0

-0.5

J0.5 jJ 0.5 jJ

-1.5 -j-j-j-j-j-j|

-2-101234

time = 4.68 sec max= 30.

jJ’ _J

ion (angles, in degree)    -1

45

►1°

stop

irr~

-i r

^►J 30 J fast

0₂    -    0.577    + 0.000

0₃    -    0.577    + 0.707

f(hz)    0.352    0.370

u    2.214    2.324

j0.5 jJ 0.5 jJ

A' _d

45

on (angles, in degree)

-1.5

stop

reset

* 'l~l •!³⁰

.|    | >|fasl 15

iffness

0₂    -    0.577    + 0.000

03    -    0.577    + 0.707

f(hz)    0.352    0.370

u    2.214    2.324

J0.5 jJ 0.5 jJ

jJ’ _J

sn (angles, in degree)    -1

45

-1.5

1

0.5

0

-0.5

stop

— u. /u/

ty

reset

■l~l •!³⁰

.|    | >|fasl 15

ffness

—    U.OU

0₂    -    0.577    +    0.000

0₃    -    0.577    +    0.707

f(hz)    0.352    0.370

u    2.214    2.324

J0.5 jJ 0.5 jJ

1

0.5

0

-0.5

in (angles, in degree)    -1

⁴⁵    _o|

jJ°

stop

reset

■l~l •!³⁰

¹    | >|fasl 15

fness

Ol	U.oYY	- U.YUY
02	0.577	+ 0.000
Oz	0.577	+ 0.707
f(hz)	0.352	0.370
UJ	2.214	2.324

J0.5 jJ 0.5 jJ

jJ’ _J

i (angles, in degree)    -1

45

-1.5

1

0.5

0

-0.5

stop

reset

■l~l •!³⁰

¹    | .|fast 15

fness

01	0.577	- 0.707
#2	0.577	+ 0.000
03	0.577	+ 0.707
f(hz)	0.352	0.370
UJ	2.214	2.324

1

0.5

0

-0.5

J0.5 jJ 0.5 jJ

jJ’ _J

i (angles, in degree)    -1

%

stop

JZI

_►] 30

|    >| fast

	0.577	- 0.707
02	0.577	+ 0.000
dz	0.577	+ 0.707
f(hz)	0.352	0.370
UJ	2.214	2.324

(angles, in degree) 45

j0.5 jJ

0.5 jJ

i|1 _J

2|1 _J

O⁰ si

o

stop

JZI

_►] 30

|    >| fast

	0.577	- 0.707
02	0.577	+ 0.000
dz	0.577	+ 0.707
f(hz)	0.352	0.370
UJ	2.214	2.324

j0.5 jJ

0.5 jJ

i|1 _J

2|1 _J

(angles, in degree) 45

reset

4~j ń³⁰

<|    |    ► | fast 1.5

1

0.5

0

-0.5

0₂    -    0.577    + 0.000

03    -    0.577    + 0.707

f(hz)    0.352    0.370

u    2.214    2.324

JO.5 jJ jJ 0.5 jJ

jJ 1 jJ

(angles, in degree)    -1

⁴⁵ t]

XJ' A

Al	J	► | 30
A	I	► I fast
ss
	► | 0.5
	► | 0.5
	_d^1

angles, in degree)

0₂    -    0.577    + 0.000

0₃    -    0.577    + 0.707

f(hz)    0.352    0.370

u    2.214    2.324

⁴⁵    _o|

~JZi1°

reset

O		► | 30
<]	I	► I fast
s	► | 0.5 jJ
	► | O.^5 jJ
	J^1
	J^1
	jJl

lgles, in degree)    -1

45

0₃    - 0.577    + 0.707

f(hz) 0.352    0.370

u 2.214    2.324

-1.5

J~J ń³⁰

«|    I    ► I fast !.5

- U.OYY f(hz) 0.352 w 2.214

+ U.YUY

0.370

2.324

Jo.5 1 | >| 0.5    1 |

ZZ^

lgles, in degree)

45

1 ■ 0.5 ■ 0 ■ ■0.5 ■ -1 ■

-1.5 ^L -2

-1 0 1

timc = 6.09

2    3    4

: max= 30.

ts

(73    — U.OU    -tU./Ul

f(hz) 0.352    0.370

JZI

_►] 30

|    >| fast

2.214

2.324

lgles, in degree) 45

j0.5 jJ 0.5 jJ

i|1 _J 2|1 _J

O⁰ si

I~I •!³⁰

|    |    >| fast

w    \j.u ii    i \j. i i

f(hz)    0.352    0.370

u    2.214    2.324

► | 0.5	_lI
► | 0.5
J^1
J^1
_
gles, in degree)
45

-0.5

-1.5

1.5

1

0.5

o

1    2    3

6.42 sec max= 30.'

run

reset

03

f(hz)

max time slow

30

fast

0.577

0.352

2.214

+ 0.707 0.370 2.324

1.5

ass and stiffness

<[ ► | 0.5
< ► 0.5
< ► 1	jJ
< ► 1	i|
i_^	jJ

1 ■

0.5 '

nital position (angles, in degree)

thetal

theta2

45

A o

-1.5 -j-j-j-j-j-*—

-2-101234

time = 6.64 sec max= 30.(

1    2    3

6.75 sec max= 30.1

reset

<l~ I -I ³⁰

<|    |    ► | fast i.s

“2	u.o/ /	1 u.uuu
dz	0.577	+ 0.707
f(hz)	0.352	0.370
UJ	2.214	2.324

JO.5 jJ jJ 0.5 jJ

jJ’ _J

1

0.5

0

-0.5

ingles, in degree)    -1

⁴⁵    _o|

~n-i° a

-1.5

run

stop

&

(? 1 r 2

-1.5 -j-j-j-j-j-j-

-2-101234

timc = 0.00 sec max= 30.0(

axistypę [norma! ¹

0    12    3    4

= 0.22 sec max= 30.0¹

0    12    3    4

= 0.33 sec max= 30.0

0    12    3    4

= 0.44 sec max= 30.C

1    2    3

0.65 sec max= 30.(

0    12    3    4

= 0.76 sec max= 30.

0    12    3    4

= 0.87 sec ma.x= 30.

0    12    3    4

= 0.98 sec max= 30.

0    12    3

= 1.09 sec max= 30.

1    2    3

1.20 sec max= 30.

1    2    3

1.31 sec max

1    2    3

1.41 sec max

0    12    3    4

i = 1.52 sec ma.x= 30.

0    12    3    4

= 1.74 sec max= 30.

0    12    3    4

= 1.96 sec max= 30.

0    12    3    4

= 2.39 sec max= 30.C

1    2    3

2.50 sec max= 30.0

mm

1    2    3

2.83 sec max= 30.0

0    12    3    4

= 2.94 sec ma.x= 30.0

0    12    3    4

= 3.05 sec max= 30.0

1    2    3

3.26 sec max= 30.C

1    2    3

3.37 sec max

12    3    4

3.48 sec max= 30.

0    12    3    4

= 3.59 sec max= 30.

0    12    3    4

= 3.81 sec ma.x= 30.

0    12    3    4

= 3.92 sec max= 30.

0    12    3    4

= 4.03 sec max= 30.

0    12    3    4

= 4.13 sec max= 30.

0    12    3    4

= 4.24 sec max= 30.

0    12    3    4

= 4.35 sec ma.x= 30.

ax time Iow

30

fast

1.5

f(hz)

UJ

and stiffness

<r	►I
<	►
<	►
<	►
±	A

0.5

0.5

1

1

1

0.5 ■

O ■ -0.5 ■

1 ■

-1.5 -j-j-j-j-j-j|

-2-101234

time = 4.57 sec max= 30.

I position (angles, in degree)    -1 ■

tal	45	0
ta2 <	>| o	0

=il

ctime

w

30

fast

1.5

f{hz)

UJ

ind stiffness

r	►I
	►
	►
	►
L	A

0.5

0.5

1

1

1

0.5 ■

0 ■ -0.5 ■

-1.5 -j-j-j-j-j-j|

-2-101234

time = 4.68 sec max= 30.

nosition (angles, in degree)    -1 ■

i1	45	0
>2 <	►I ^0	0

—

4JZ.CZ
J_1_

30

fast

j0.5    1 |

JO.5

J¹

f(hz)

UJ

A' _d

45

(angles, in degree)

-1.5

-2-101234

time = 4.90 sec max= 30.

^ —'
i	r		► | 30
		i	► I fast
iSS
		► | 0.5	_lI
		► | 0.5	_lI
		J^1
		J^1
		J1
angles. in degree) 45
		J°

1.5 '

1 ■

0.5 '

0 ■

-0.5 ■

-1 '

-1.5 --2

-1 o 1

time = 5.00

2    3    4

: max= 30.1

^ —'
iC J	► | 30
A J	► I fast
ss
► | 0.5	_lI
► | 0.5
J^1
J^1
_J^1
angles, in degree)
45
O L

-1.5

-10    12    3    4

time = 5.22 sec max= 30.(

d_I		► | 30
A	I	► I fast
ss
	>| 0.5 jJ
	"I^0-^5 _lI
	J^1
	J^1
	jji

angles, in degree)    -1

-2-101234

time = 5.33 sec max= 30.C

JZI		► | 30
A	I	► I fast
ss
	>| 0.5 jJ
	"I^0-^5 _lI
	J^1
	J^1
	jji

ingles, in degree)    -1

-2-101234

time = 5.44 sec max= 30.C

0    12    3    4

= 5.55 sec max= 30.C

run		stop	reset
		N..........

max time slow

				30
i		>\
i			►	fast

1.5

0₃    - 0.577

f(hz) 0.352 u 2.214

+ 0.707 0.370 2.324

ass and stiffness

<[ >| 0.5
< ► 0.5
< ► 1	jJ
4 ► 1	i|
i_^	jJ

1 ■ 0.5 '

nital position (angles, in degree)

thetal

theta2

45

► I 0

-1.5 -j-j-j-j-j-■—

-2-101234

time = 5.77 sec max= 30.C

0    12    3    4

= 5.88 sec max= 30.(

stop	reset

<l~ I -1³⁰

<| I    ► I fast 1.5

0₃    - 0.577    + 0.707

f(hz) 0.352    0.370

u 2.214    2.324

Jo.5 jJ jJ 0.5 jJ

1

0.5

0

-0.5

(angles, in degree)    -1

-1.5

⁴⁵    _o|

IQ° iJ

KM

<| I jjfast 1.5

J0.5 jJ jJ 0.5 jJ

1

0.5

o

■0.5

mgles, in degree)    -1

-2-101234

time = 6.09 sec max= 30.

te

o  

stop

&

L>

3

r?

2

K

te

te

o

r 1

0.393 * cos(2.32 * t) + 0.131 * cos(2.53 * t) -0.262 * cos(2.53 * t)

0.131 * cos(2.53 *t)~ 0.393 * cos(2.32 * t)

0    12    3    4

= 0.22 sec max= 30.

0    12    3    4

= 0.33 sec max= 30.

1    2    3

0.44 sec max= 30.

1    2    3

0.65 scc max

0    12    3    4

= 0.76 sec max= 30.

0    12    3    4

= 0.87 sec ma.x= 30.

1    2    3

0.98 sec max= 30.i

1    2    3

1.09 sec max= 30.(

12    3    4

1.20 sec max= 30.(

1    2    3

4

1.31 sec max= 30.C

12    3    4

1.52 sec max= 30.C

1    2    3

1.63 sec max= 30.C

1    2    3

1.85 sec max= 30.(

0    12    3    4

= 1.96 sec max= 30.1

1    2    3

2.07 sec max= 30.

0    12    3    4

= 2.28 sec max= 30.

1-1-1-1-L_

12    3    4

2.39 sec max= 30.

0    12    3    4

= 2.50 sec max= 30.

0    12    3    4

= 2.61 sec max= 30.

= 2.72 sec max= 30.

0    12    3    4

= 2.94 sec max= 30.

0    12    3    4

= 3.05 sec max= 30.

1    2    3

3.16 sec max= 30.

1    2    3

3.26 scc max= 30.

0    12    3    4

= 3.37 sec max= 30.

0    12    3    4

= 3.48 sec max= 30.

0    12    3    4

= 3.59 sec max= 30.

1    2    3

3.70 sec max= 30.'

1    2    3

3.81 sec max= 30.(

12    3    4

3.92 sec max= 30.C

12    3    4

4.13 sec max= 30.0

12    3    4

4.24 sec max= 30.0

_l

mls^ <

				30
i		>\
i			►	fast

fihz)

0.352

2.214

0.370

2.324

1.5

and stiffness

a1	45	0
a2 <	►I ^0	0

-1.5 -j-j-j-j-j-j—

-2-101234

time = 4.35 sec max= 30.0

o

O

O

45

-1.5 -j-j-j-j-j-j—

-2-101234

timc = 4.46 sec max= 30.0

-10    12    3

time = 4.57 sec max= 30.C

	► | ras	1.Sr
J0.5	_u	1 -
J0.5		0.5 ■
^J^1
		u ■
^J^1		-0.5 -
Jegree)		-1 '
45	_^J
ń°		“ 1.0 -2

\y-	► | ras	1.5
jJ 0.5		1 -
0.5		0.5 ■
J^1
J^1		u ■
J^1		-0.5 -
legree)		-1 '
45	_^J
		“ I .O -2

	1.5 ’
jj0.5 jJ	1 -
0.5 jJ	0.5 ■
J^1 _J	u ■
	-0.5 -
egree)	-1 '
^45 _oJ
ll° ij	“ 1.0 -2

o—^

1.5

r j icłoi

1.0

1    2    3

5.88 sec max= 30.

run

stop

reset

max time slow

30

fast

1.5

0_:i    - 0.577    + 0.707

f(hz) 0.352    0.370

u 2.214    2.324

ass and stiffness <1 <

<2

n1 <

n2 <

n3 <P

►J 0.5 jJ 0.5 _j_| ^1 1

0.5

-0.5

nital position (angles, in degree) thetal    45

theta2

► 0

-1.5

-2-101234

time = 6.20 sec max= 30.

-5

1.5

0    12    3    4

= 6.75 sec max= 30.0

1.5

1    2    3

7.40 sec max= 30.C

1    2    3

7.51 sec max= 30J

0    12    3    4

= 7.62 sec rnax= 30.

0    12    3    4

= 7.78 sec ma.x= 30.

0    12    3    4

= 7.94 sec max= 30.

0    12    3    4

= 8.10 sec max= 30.

0    12    3    4

= 8.26 sec max= 30.

0    12    3    4

= 8.43 sec max= 30.

1    2    3

8.59 sec max= 30.

0    12    3    4

= 8.75 sec ma.x= 30.

0    12    3    4

= 8.91 sec max= 30.

1    2    3

9.07 sec max= 30.i

1    2    3

9.40 sec max= 30.Ol

1-1-1-1-1-

12    3    4

9.56 sec max= 30.0(

0    12    3    4

= 9.72 sec max= 30.0(

0    12    3    4

= 9.88 sec max= 30.0(

-1    0    1    2    3    4    5

time = 10.05 sec max= 30.00 sec

1    2    3

10.21 sec max= 30.

1    2    3

10.37 sec max= 30

W

o

12    3    4

10.53 sec max= 30

► fast

1.5

2.214    2.324

0    12    3    4

= 10.69 sec max= 30

y —I

~.l    -1³⁰

__> | fast !.5

f(hz)

0.352

2.214

0.370

2.324

j0.5 jJ J0.5 jJ

5S, in degree)

⁴⁵ y zj° y

1

0.5

0

-0.5

-1.5

-10    12    3    4

time = 10.86 sec max= 30

&J ——j    f{hz)

0.352

2.214

0.370

2.324

~ I    >| 30    ^U

__[_ _►] fast 1.5 r

► | 0.5	_u
► | 0.5
: ^
les. in degree)
45
Q°

1

0.5

0

-0.5

-1.5

-10    12    3    4

time = 11.02 sec max= 30

reset

id		► | 30
	4 fast
iess
	► | 0.5 1 |
► | 0.5 1 |
		z
	>r	z
	_Z^1	z

(angles, in degree)    -1

0₃    - 0.577    + 0.707

f(hz) 0.352    0.370

u 2.214    2.324

-1.5

⁴⁵    _o|

l -1° iJ

1    2    3

11.34 sec max= 30

reset

id		► | 30
	4 fast
iess
	► | 0.5 1 |
► | 0.5 1 |
		z
		z
	_Z^1	z

(angles, in degree)    -1

0₃    - 0.577    + 0.707

f(hz) 0.352    0.370

u 2.214    2.324

-1.5 -j-j-j-j-j-j|

-2-101234

time = 11.50 sec max= 30

⁴⁵    _o|

l -1° iJ

0    12    3    4

= 11.67 sec ma.x= 30

in degree)

-1

time = 11.61

r 1 c 2    3

run stop reset

modę	1	2	3
	0.577	- 0.707	+ 0.408
#2	0.577	+ 0.000	- 0.816
03	0.577	+ 0.707	+ 0.408
f(U~\	n o co		n /ino

1

0.131 *cos(2.53 *t) - 0.262 * cos(2.53 * t) I 0.131 *cos(2.53