Se impune schema cinematica a mecanismului plan tip [619801]

Byadmin

UNIVERSITATEA DIN ORADEA
FACULTATEA DE INGINERIE MANAGERIALĂ SI
TEHNOLOGICĂ
DEPARTAMENTUL DE INGINERIE MECANICĂ ȘI
AUTOVEHICULE RUTIERE

1

Proiect I
MECANISME II

Îndrumător: Prof. univ. dr.ing. Rus Alexandru

Student: [anonimizat]: 231 A

2019

2
APLICATIA I
Se impune schema cinematica a mecanismului plan tip
R-RRRTRT de clasa a II -a cu doua contururi inchise
independente.Conturul I este format din asamblarea la
MF)=(0,1) a lantului diadic LcD(2,3) tip RRR, iar conturul II
este obtinut prin legarea la elemente le 2 si 0 a lantului diadic
LcD(4,5) tip RTR. (fig.1)

Fig.1

1.1 Analiza strutcturala a mecanismului
Analiza geometrica a mecanismului implica definirea atat a
lungimilor constant (notate cu 𝑙𝑖) si a celor variabile ( notate cu 𝑠𝑖),
cat si a unghiurilor constant (notate cu ∝𝑖) si a celor variabile
(notate cu 𝜑𝑖)
Mecanismul este monomobil , ceea ce se verifica prin
calcularea gradului de mobilitate cu formula:
𝑀 = 3𝑛 − 2𝐶5 − 𝐶4 = 3𝑥2 − 2𝑥7 = 1
in care:

3
n=5, numarul de elemente mobile;
𝐶5=7,numarul de cuple cinemamatice de clasa a -V-a;
𝐶4 = 0,numarul de cuple cinematice de clasa a -IV-a;
Formula anterioara arata ca este sufficient o singura
deplasare unghiulara 𝜑𝑖
(ca parametru de intrare) pentru pozitionarea univocal a
tuturor elementelor cinematice din schema cinematica
considerata. Numarul ciclurilor independente se calculeaza
cu relatia:

Formula structural topologica a mecanismului motor MM se
obtine prin atasarea la mecanismul initial, denumit diadice in
ordinea LcD(2,3) si LcD(4,5);
𝑀𝑀 = 𝑀𝐹(0,1) + 𝐿𝑐𝐷(2,3) + 𝐿𝑐𝐷(4,5)

1.2 Geometria grafica a mecanismului
Analiza geometrica a mecanismului implica definirea atat a
lungimilor constant (notate cu 𝑙𝑖) si a celor variabile ( notate cu 𝑠𝑖),
cat si a unghiurilor constant (notate cu ∝𝑖) si a celor variabile
(notate cu 𝜑𝑖) Parametrii constant sunt:
𝐴0𝐵0 = 𝑙0𝑥 = 0, 0,253 [𝑚]; 𝐵𝐵0 = 𝑙0𝑦 = 0,098 [𝑚]; 𝐴0𝐷0 = 𝑙𝑑
= 0,112 [𝑚]; 𝐷0𝐷0 = 𝑙ℎ = 0,267 [𝑚]; 𝐶𝐷′ = 𝑙5
= 0,258 [𝑚]; 𝐴0𝐴 = 𝑙𝑖 = 0,122 [𝑚]; 𝐴𝐵 = 𝑙2
= 0,250 [𝑚]; 𝐵𝐵0 = 𝑙3 = 0,290 [𝑚]; 𝐵𝐴𝐶 =∝=
35° Pentru trasarea la scara a schemei cinematice se adopta
scara lungimilor constant sau variabile: 𝑘𝑙 = 𝑘𝑠 = 1/250
[m]/[mm]. In functie de scara aleasa se calculeaza lungim ile
constant pe desen cu formula:

4
Noile valori vor fi:
𝑙𝑜𝑥 𝑙𝑜𝑦 𝑙𝑑 𝑙ℎ 𝑙1 𝑙2 𝑙3 L4 𝑙5
𝑙𝑖[𝑚] 0,253 0,098 0,112 0,267 0,122 0,250 0,290 0.02 0,258
𝑙𝑖[mm] 63,25 24,5 28 66,75 30,5 62,5 72,5 5 64,5

Pentru trasarea la scara a schemei cinematice se parcurg
urmatoarele etape:
– Se alege, pe plansa, punctual fix 𝐴0 in partea stanga jos;
– Se pozitioneaza punctual fix 𝐵0 fata de 𝐴0 prin masurarea
coordonatelor carteziene 𝑥𝐵0 = 𝑙𝑜𝑥; 𝑦𝐵0 = −𝑙𝑜𝑦;
– Se pozitioneaza punctul fix 𝐷0 fata de 𝐴0 prin masurarea
coordonatelor carteziene 𝑥𝐷0 = −𝑙𝑑; 𝑦𝐷0 = 𝑙ℎ;
– Se masoara in sens trigonometric, fata de 𝐴0𝑋, unghiuli 𝜑1 =
330°si pe directia obtinuta se pozitioneaza punctul mobil A
prin masurarea lungimii ( 𝐴𝐴0) = (𝑙𝑙);
– Se construiesc arcel e de cerc Γ𝐵𝐵0cu central in 𝐵0 de raza 𝑙3
si Γ𝐵𝐴 cu central in A si raza l2;
– Cele doua arce de cerc se intersecteaza in punctele B si B’; se
allege punctual B din conditia de continuitate a miscarii, ceea
ce corespunde solutiei adoptate in pozitia initiala a manivelei
(𝜑1 = 0);
– Se masoara fata de AB unghiul constant ∝2= 35°; intersectia
dintre directia obtinuta si paralela prin 𝐷0 la axa 𝐴0𝑋,
punctual C, reprezinta centrul articulatiei dintre elementele 2
si 4;
– Pe aceasta plansa se masoara parametrii de pozitionare ai
elementelor cinematice conduse 𝑠2, 𝑠4, 𝑠5, 𝜑2, 𝜑3, 𝜑4;
Se realizeaza filmul miscarii mecanismului pe un ciclu
cinematic complet 𝜑1 = [0,2𝜋] repetand constructia grafica
mentionata anterior. Avand schema cinematic trasata in 24
poizitii successive se pot masra parametrii 𝑠2, 𝑠4, 𝑠5, 𝜑2, 𝜑3, 𝜑4

5
apoi se traseaza diagramele de variatie ale deplasarilor
unghiulare si liniare.

2
1.3. Calculul analitic al deplasarilor , vitezelor si acceleratiilor.
Se considera schema cinematica a mecanismului patrulater alaturi
decare s -au schitat cele doua contururui inchise ale vectorilor
asociati(fig.2)

6

Fig. 2

1.3.1 Calculul geometro -cinema tic al conturului I
Conturul vectorial I este asociat lantului cinematic inchis
[0,1,2,3,0], prin orientarea fiecarei laturi astfel incat unghiul
de pozitionare sa fie cat mai mic posibil.
Se scrie ecuatia vectoriala de inchidere a conturului I:
𝑙 1 + 𝑙 2 = 𝑙 0 𝑥 − 𝑙 𝑜𝑦 + 𝑙 3
Se scriu ecuatiile de proiectii pe axele de coordo nate:
𝑙2𝑐𝑜𝑠𝜑2 − 𝑙3𝑐𝑜𝑠𝜑3 = 𝑙𝑜𝑥 −
𝑙1𝑐𝑜𝑠𝜑1; 𝑙2𝑐𝑜𝑠𝜑2 − 𝑙3𝑐𝑜𝑠𝜑3 =
−𝑙𝑜𝑦 − 𝑙1𝑐𝑜𝑠𝜑1. Calculul
deplasarilor unghiulare
Sistemul de ecutatii de mai sus
se rezolva prin metoda

7
eliminarii uneia din cele doua
necunoscute .
𝑙2𝑐𝑜𝑠𝜑2 + 𝑏1(𝜑1) = 𝑙3𝑐𝑜𝑠𝜑3;
𝑙2𝑐𝑜𝑠𝜑2 + 𝑏2(𝜑2) = 𝑙3𝑐𝑜𝑠𝜑3.
Prin ridicarea la patrat a celor doua ecuatii, se ajunge in
final la forma
𝐴2𝑠𝑖𝑛𝜑2 + 𝐵2𝑐𝑜𝑠𝜑2 + 𝐶2
= 0; In care:
𝐴2 = 2𝑙2(𝑙0𝑦 + 𝑙1𝑠𝑖𝑛𝜑1); 𝐵2 = 2𝑙2(−𝑙0𝑥 + 𝑙1𝑐𝑜𝑠𝜑1);
𝐶2 = 𝑙02 + 𝑙12 + 𝑙22 − 𝑙32 + 2𝑙1(𝑙0𝑦𝑠𝑖𝑛𝜑1 −
𝑙0𝑥𝑐𝑜𝑠𝜑1). Solutia acestei ecuatii este de forma:
.
Pentru calculul lui 𝜑3 se procedeaza similar, prin izolare si
eliminarea lui 𝜑2 din sistemul de ecuatii neliniare initial
obinandu -se ecuatia:
𝐴3𝑠𝑖𝑛𝜑3 + 𝐵3𝑐𝑜𝑠𝜑3 + 𝐶3
= 0; In care:
𝐴3 = −2𝑙3(𝑙0𝑦 + 𝑙1𝑠𝑖𝑛𝜑1); 𝐵3 = −2𝑙3(−𝑙0𝑥 + 𝑙1𝑐𝑜𝑠𝜑1);
𝐶3 = 𝑙02 + 𝑙12 + 𝑙22 − 𝑙32 + 2𝑙1(𝑙0𝑦𝑠𝑖𝑛𝜑1 −
𝑙0𝑥𝑐𝑜𝑠𝜑1). Solutia acestei ecuatii este de forma:

Calculul vitezelor unghiulare.
Se deriveaza ecuatiile scalare de deplasare, in functie de
timp, obtinandu -se un sistem de doua ecuatii liniare de
forma:

8
(−𝑙2𝑠𝑖𝑛𝜑2)𝜑 2 + (𝑙3𝑠𝑖𝑛𝜑3)𝜑 3 = (𝑙1𝑠𝑖𝑛𝜑1)𝜑 1;
(𝑙2𝑐𝑜𝑠𝜑2)𝜑 2 + (−𝑙3𝑐𝑜𝑠𝜑3)𝜑 3 = (−𝑙1𝑠𝑖𝑛𝜑1)𝜑 1.
Rezolvand sistemul prin metoda reducerii, se obtine:
;

Calculul acceleratiilor unghiulare .
Se deriveaza ecuatiile scalare de viteza, in functie de timp
obtinanduse un sistem de doua ecuatii liniare de forma:
(𝑙2𝑐𝑜𝑠𝜑2)𝜑 2 + (−𝑙3𝑐𝑜𝑠𝜑3)𝜑 3
= (𝑙1𝑠𝑖𝑛𝜑1)𝜑 12 + (𝑙2𝑠𝑖𝑛𝜑2)𝜑 22 − (𝑙3𝑠𝑖𝑛𝜑3)𝜑 32
(−𝑙2𝑠𝑖𝑛𝜑2)𝜑 2 + (𝑙3𝑠𝑖𝑛𝜑3)𝜑 3
= (𝑙1𝑠𝑖𝑛𝜑1)𝜑 12 + (𝑙2𝑠𝑖𝑛𝜑2)𝜑 22 − (𝑙3𝑠𝑖𝑛𝜑3)𝜑 32
Rezolvand sistemul prin metoda reducerii, se obtine:

1.3.2 Calculul geometro -cinematic al conturului II
Conturul vectorial II este asociat lantului cinematic inchis
[0,1,2,4,5,0], prin orientarea fiecarei laturi astfel incat
unghiul de pozitionare sa fie cat mai mic posibil.
Se scrie ecuatia vectoriala de inchidere a conturului II:
𝑙1 + 𝑠4 − 𝑠5 = −𝑙𝑑 + 𝑙ℎ .
Se scriu ecuatiile de proiectii pe axele de coordonate:

9

Calculul deplasarilor liniare .
Sistemul de ecuatii partial neliniare, de mai sus, se
rezolva prin metoda elimina rii uneia din cele doua
necunoscute si ;

.

Calculul vitezelor liniare .
Se deriveaza ecuatiile scalare de deplasare, in functie de
timp, obtinandu -se un sistem de doua ecuatii liniare de
forma:
Rez
ulta:

Calculul acceleratiilor liniare .
Se deriveaza ecuatiile scalare de viteza, in functie de timp,
obtinanduse un sistem de doua ecuatii liniare de forma:
𝑠4 cos(∝ +𝜑2) − 2𝑠4 sin(𝛼 + 𝜑2) 𝜑 2 − 𝜑 2𝑠4 cos(𝛼 + 𝜑2)
+ 𝜑 2𝑠4 sin(𝛼 + 𝜑2) − 𝑠 5 = 𝜑 12𝑙1𝑐𝑜𝑠𝜑1

10
𝑠4 sin(∝ +𝜑2) + 2𝑠4 cos(𝛼 + 𝜑2) 𝜑 2 + 𝜑 2𝑠4 sin(𝛼 + 𝜑2)
− 𝜑 2𝑠4 sin(𝛼 + 𝜑2) = 𝜑 12𝑙1𝑐𝑜𝑠𝜑1

Rezulta:

ans =

Fi1 Fi2 Fi3
0 1.5536 -3.1308
0.0524 1.5522 -3.1319
0.1047 1.5507 -3.1329
0.1571 1.5494 -3.1337
0.2094 1.5480 -3.1345
0.2618 1.5467 -3.1351
0.3142 1.5454 -3.1357
0.3665 1.5442 -3.1363
0.4189 1.5431 -3.1367
0.4712 1.5421 -3.1371
0.5236 1.5411 -3.1375
0.5760 1.5403 -3.1378
0.6283 1.5395 -3.1381
0.6807 1.5388 -3.1384
0.7330 1.5382 -3.1386
0.7854 1.5377 -3.1388
0.8378 1.5373 -3.1390
0.8901 1.5370 -3.1391
0.9425 1.5367 -3.1392
0.9948 1.5365 -3.1394
1.0472 1.5364 -3.1394
1.0996 1.5363 -3.1395
1.1519 1.5363 -3.1395
1.2043 1.5363 -3.1396 1.2566 1.5364 -3.1396
1.3090 1.5366 -3.1396
1.3614 1.5367 -3.1396
1.4137 1.5369 -3.1395
1.4661 1.5372 -3.1395
1.5184 1.5374 -3.1394
1.5708 1.5377 -3.1394
1.6232 1.5380 -3.1393
1.6755 1.5384 -3.1392
1.7279 1.5387 -3.1391
1.7802 1.5391 -3.1389
1.8326 1.5395 -3.1388
1.8850 1.5399 -3.1386
1.9373 1.5403 -3.1384
1.9897 1.5407 -3.1382
2.0420 1.5411 -3.1380
2.0944 1.5416 -3.1377
2.1468 1.5420 -3.1375
2.1991 1.5425 -3.1372
2.2515 1.5429 -3.1369
2.3038 1.5434 -3.1365
2.3562 1.5438 -3.1361
2.4086 1.5443 -3.1357
2.4609 1.5448 -3.1353
2.5133 1.5452 -3.1348 2.5656 1.5457 -3.1343
2.6180 1.5462 -3.1337
2.6704 1.5467 -3.1331
2.7227 1.5472 -3.1324
2.7751 1.5476 -3.1317
2.8274 1.5481 -3.1309
2.8798 1.5486 -3.1300
2.9322 1.5491 -3.1290
2.9845 1.5496 -3.1279
3.0369 1.5501 -3.1266
3.0892 1.5506 -3.1252
3.1416 1.5511 -3.1237
3.1940 1.5516 -3.1219
3.2463 1.5520 -3.1199
3.2987 1.5525 -3.1176
3.3510 1.5530 -3.1149
3.4034 1.5535 -3.1118
3.4558 1.5540 -3.1081
3.5081 1.5545 -3.1037
3.5605 1.5550 -3.0983
3.6128 1.5555 -3.0917
3.6652 1.5561 -3.0833
3.7176 1.5566 -3.0724
3.7699 1.5571 -3.0577
3.8223 1.5576 -3.0370

11
3.8746 1.5581 -3.0060
3.9270 1.5586 -2.9552
3.9794 1.5591 -2.8608
4.0317 1.5596 -2.6553
4.0841 1.5601 -2.2106
4.1364 1.5606 -1.6336
4.1888 1.5611 -1.2031
4.2412 1.5616 -0.9322
4.2935 1.5621 -0.7590
4.3459 1.5625 -0.6425
4.3982 1.5630 -0.5606
4.4506 1.5635 -0.5009
4.5029 1.5640 -0.4564
4.5553 1.5644 -0.4229
4.6077 1.5649 -0.3976
4.6600 1.5653 -0.3789 4.7124 1.5657 -0.3658
4.7647 1.5661 -0.3577
4.8171 1.5665 -0.3545
4.8695 1.5668 -0.3562
4.9218 1.5671 -0.3636
4.9742 1.5674 -0.3780
5.0265 1.5677 -0.4016
5.0789 1.5679 -0.4386
5.1313 1.5681 -0.4972
5.1836 1.5682 -0.5940
5.2360 1.5683 -0.7696
5.2883 1.5683 -1.1372
5.3407 1.5683 -1.9350
5.3931 1.5682 -2.6639
5.4454 1.5680 -2.9007
5.4978 1.5677 -2.9900 5.5501 1.5674 -3.0347
5.6025 1.5670 -3.0611
5.6549 1.5665 -3.0783
5.7072 1.5659 -3.0904
5.7596 1.5651 -3.0993
5.8119 1.5643 -3.1060
5.8643 1.5634 -3.1113
5.9167 1.5625 -3.1155
5.9690 1.5614 -3.1190
6.0214 1.5602 -3.1218
6.0737 1.5590 -3.1242
6.1261 1.5577 -3.1263
6.1785 1.5564 -3.1280
6.2308 1.5550 -3.1295
6.2832 1.5536 -3.1308

fi1 s4 s5

ans =
Fi1 s4 s5
0 0.3221 0.0538
0.0524 0.3141 0.0585
0.1047 0.3061 0.0628 0.1571 0.2982 0.0667
0.2094 0.2904 0.0702
0.2618 0.2827 0.0733
0.3142 0.2751 0.0760 0.3665 0.2677 0.0782
0.4189 0.2604 0.0800
0.4712 0.2533 0.0814
0.5236 0.2465 0.0823
0 1 2 3 4 5 6 7-4-3-2-1012
fi1fi2, fi3Variatia Fi1 functie de fi2, fi3

12
0.5760 0.2398 0.0828
0.6283 0.2334 0.0829
0.6807 0.2273 0.0825
0.7330 0.2214 0.0817
0.7854 0.2158 0.0804
0.8378 0.2105 0.0788
0.8901 0.2055 0.0767
0.9425 0.2008 0.0742
0.9948 0.1964 0.0714
1.0472 0.1924 0.0681
1.0996 0.1888 0.0645
1.1519 0.1855 0.0605
1.2043 0.1826 0.0562
1.2566 0.1801 0.0515
1.3090 0.1779 0.0466
1.3614 0.1762 0.0413
1.4137 0.1748 0.0357
1.4661 0.1738 0.0299
1.5184 0.1733 0.0238
1.5708 0.1731 0.0175
1.6232 0.1733 0.0109
1.6755 0.1740 0.0041
1.7279 0.1750 -0.0028
1.7802 0.1764 -0.0099
1.8326 0.1783 -0.0172
1.8850 0.1805 -0.0246
1.9373 0.1831 -0.0321
1.9897 0.1861 -0.0397
2.0420 0.1894 -0.0474
2.0944 0.1931 -0.0551
2.1468 0.1971 -0.0628
2.1991 0.2015 -0.0706
2.2515 0.2063 -0.0783
2.3038 0.2113 -0.0860
2.3562 0.2166 -0.0937
2.4086 0.2222 -0.1013
2.4609 0.2281 -0.1088 2.5133 0.2343 -0.1161
2.5656 0.2407 -0.1234
2.6180 0.2473 -0.1305
2.6704 0.2541 -0.1374
2.7227 0.2611 -0.1441
2.7751 0.2683 -0.1507
2.8274 0.2756 -0.1570
2.8798 0.2831 -0.1630
2.9322 0.2906 -0.1688
2.9845 0.2983 -0.1744
3.0369 0.3060 -0.1796
3.0892 0.3138 -0.1846
3.1416 0.3216 -0.1892
3.1940 0.3294 -0.1935
3.2463 0.3371 -0.1975
3.2987 0.3449 -0.2011
3.3510 0.3526 -0.2044
3.4034 0.3602 -0.2073
3.4558 0.3677 -0.2099
3.5081 0.3751 -0.2120
3.5605 0.3824 -0.2138
3.6128 0.3894 -0.2152
3.6652 0.3964 -0.2162
3.7176 0.4031 -0.2168
3.7699 0.4096 -0.2170
3.8223 0.4159 -0.2168
3.8746 0.4219 -0.2162
3.9270 0.4276 -0.2152
3.9794 0.4331 -0.2139
4.0317 0.4383 -0.2121
4.0841 0.4431 -0.2100
4.1364 0.4477 -0.2075
4.1888 0.4519 -0.2046
4.2412 0.4557 -0.2013
4.2935 0.4592 -0.1977
4.3459 0.4623 -0.1938
4.3982 0.4651 -0.1895 4.4506 0.4674 -0.1849
4.5029 0.4694 -0.1800
4.5553 0.4710 -0.1747
4.6077 0.4721 -0.1692
4.6600 0.4729 -0.1635
4.7124 0.4732 -0.1574
4.7647 0.4731 -0.1512
4.8171 0.4726 -0.1447
4.8695 0.4717 -0.1379
4.9218 0.4704 -0.1310
4.9742 0.4687 -0.1240
5.0265 0.4666 -0.1167
5.0789 0.4641 -0.1094
5.1313 0.4611 -0.1018
5.1836 0.4578 -0.0942
5.2360 0.4541 -0.0866
5.2883 0.4501 -0.0788
5.3407 0.4457 -0.0710
5.3931 0.4409 -0.0632
5.4454 0.4358 -0.0553
5.4978 0.4303 -0.0475
5.5501 0.4246 -0.0397
5.6025 0.4186 -0.0320
5.6549 0.4122 -0.0243
5.7072 0.4057 -0.0167
5.7596 0.3988 -0.0093
5.8119 0.3918 -0.0019
5.8643 0.3846 0.0052
5.9167 0.3771 0.0122
5.9690 0.3696 0.0189
6.0214 0.3618 0.0254
6.0737 0.3540 0.0317
6.1261 0.3461 0.0377
6.1785 0.3381 0.0434
6.2308 0.3301 0.0488
6.2832 0.3221 0.0538

13

fi1 omega2 omega3

ans =
fi1 omega2 omega3
0 0.2881 -26.5802
0.0524 -1.1333 -26.5174
0.1047 -2.5477 -26.3780
0.1571 -3.9518 -26.1626
0.2094 -5.3422 -25.8718
0.2618 -6.7152 -25.5068
0.3142 -8.0675 -25.0688
0.3665 -9.3955 -24.5595
0.4189 -10.6959 -23.9806
0.4712 -11.9653 -23.3341
0.5236 -13.2003 -22.6223
0.5760 -14.3978 -21.8475
0.6283 -15.5544 -21.0122
0.6807 -16.6673 -20.1191
0.7330 -17.7335 -19.1711
0.7854 -18.7500 -18.1709
0.8378 -19.7144 -17.1216
0.8901 -20.6239 -16.0262
0.9425 -21.4761 -14.8879
0.9948 -22.2689 -13.7100
1.0472 -23.0001 -12.4957 1.0996 -23.6679 -11.2485
1.1519 -24.2703 -9.9717
1.2043 -24.8059 -8.6688
1.2566 -25.2733 -7.3435
1.3090 -25.6713 -5.9992
1.3614 -25.9987 -4.6396
1.4137 -26.2549 -3.2683
1.4661 -26.4391 -1.8889
1.5184 -26.5510 -0.5052
1.5708 -26.5902 0.8791
1.6232 -26.5567 2.2604
1.6755 -26.4508 3.6351
1.7279 -26.2727 4.9994
1.7802 -26.0231 6.3498
1.8326 -25.7026 7.6825
1.8850 -25.3122 8.9943
1.9373 -24.8530 10.2814
1.9897 -24.3264 11.5405
2.0420 -23.7339 12.7683
2.0944 -23.0773 13.9614
2.1468 -22.3582 15.1168
2.1991 -21.5790 16.2313 2.2515 -20.7416 17.3019
2.3038 -19.8486 18.3259
2.3562 -18.9025 19.3004
2.4086 -17.9060 20.2229
2.4609 -16.8618 21.0910
2.5133 -15.7731 21.9022
2.5656 -14.6429 22.6544
2.6180 -13.4745 23.3457
2.6704 -12.2711 23.9742
2.7227 -11.0363 24.5382
2.7751 -9.7737 25.0363
2.8274 -8.4869 25.4670
2.8798 -7.1798 25.8293
2.9322 -5.8561 26.1221
2.9845 -4.5198 26.3449
3.0369 -3.1750 26.4969
3.0892 -1.8257 26.5778
3.1416 -0.4763 26.5873
3.1940 0.8690 26.5257
3.2463 2.2057 26.3930
3.2987 3.5291 26.1897
3.3510 4.8345 25.9164
0 1 2 3 4 5 6 7-0.3-0.2-0.100.10.20.30.40.5Variatia fi1 functie de s4, s5
fi1s4, s5

14
3.4034 6.1167 25.5740
3.4558 7.3701 25.1637
3.5081 8.5886 24.6868
3.5605 9.7651 24.1451
3.6128 10.8909 23.5406
3.6652 11.9550 22.8761
3.7176 12.9420 22.1554
3.7699 13.8289 21.3839
3.8223 14.5771 20.5712
3.8746 15.1144 19.7369
3.9270 15.2836 18.9315
3.9794 14.6708 18.3270
4.0317 11.8831 18.7652
4.0841 0.5168 26.1541
4.1364 -248.3517 271.1593
4.1888 56.0899 -35.4433
4.2412 39.4398 -19.6292
4.2935 34.2461 -14.4851
4.3459 31.7419 -11.5683 4.3982 30.2814 -9.4179
4.4506 29.3173 -7.5971
4.5029 28.6103 -5.9371
4.5553 28.0372 -4.3623
4.6077 27.5264 -2.8353
4.6600 27.0321 -1.3365
4.7124 26.5222 0.1449
4.7647 25.9720 1.6153
4.8171 25.3597 3.0791
4.8695 24.6635 4.5403
4.9218 23.8575 6.0049
4.9742 22.9069 7.4831
5.0265 21.7574 8.9949
5.0789 20.3137 10.5838
5.1313 18.3841 12.3540
5.1836 15.5024 14.6062
5.2360 10.1151 18.5359
5.2883 -8.9299 34.3991
5.3407 62.8807 -44.2876 5.3931 29.3479 -18.9174
5.4454 24.1326 -18.3793
5.4978 21.6706 -19.0752
5.5501 19.9076 -19.9293
5.6025 18.3955 -20.7892
5.6549 16.9864 -21.6154
5.7072 15.6191 -22.3931
5.7596 14.2651 -23.1148
5.8119 12.9100 -23.7757
5.8643 11.5467 -24.3723
5.9167 10.1721 -24.9019
5.9690 8.7852 -25.3623
6.0214 7.3866 -25.7513
6.0737 5.9778 -26.0675
6.1261 4.5608 -26.3093
6.1785 3.1383 -26.4759
6.2308 1.7130 -26.5663
6.2832 0.2881 -26.5802

fi1 v4 v5

ans =
fi1 v4 v5
0 -7.9520 4.3713
0.0524 -8.2355 4.5448 0.1047 -8.4787 4.6763
0.1571 -8.6817 4.7664
0.2094 -8.8447 4.8162 0.2618 -8.9681 4.8267
0.3142 -9.0526 4.7995
0.3665 -9.0991 4.7363
0 1 2 3 4 5 6 7-300-200-1000100200300Variatia fi1 functie de omega2, omega3
fi1omega2, omega3

15
0.4189 -9.1085 4.6389
0.4712 -9.0820 4.5095
0.5236 -9.0209 4.3503
0.5760 -8.9264 4.1638
0.6283 -8.8001 3.9523
0.6807 -8.6435 3.7186
0.7330 -8.4582 3.4653
0.7854 -8.2459 3.1950
0.8378 -8.0082 2.9105
0.8901 -7.7470 2.6147
0.9425 -7.4639 2.3101
0.9948 -7.1608 1.9995
1.0472 -6.8396 1.6856
1.0996 -6.5019 1.3708
1.1519 -6.1495 1.0576
1.2043 -5.7843 0.7483
1.2566 -5.4078 0.4450
1.3090 -5.0217 0.1499
1.3614 -4.6277 -0.1354
1.4137 -4.2273 -0.4092
1.4661 -3.8218 -0.6701
1.5184 -3.4127 -0.9169
1.5708 -3.0011 -1.1487
1.6232 -2.5883 -1.3648
1.6755 -2.1753 -1.5647
1.7279 -1.7630 -1.7482
1.7802 -1.3524 -1.9153
1.8326 -0.9440 -2.0664
1.8850 -0.5385 -2.2018
1.9373 -0.1364 -2.3223
1.9897 0.2618 -2.4288
2.0420 0.6558 -2.5224
2.0944 1.0455 -2.6043
2.1468 1.4306 -2.6761
2.1991 1.8111 -2.7392
2.2515 2.1869 -2.7954
2.3038 2.5582 -2.8463
2.3562 2.9249 -2.8937 2.4086 3.2871 -2.9396
2.4609 3.6450 -2.9856
2.5133 3.9987 -3.0336
2.5656 4.3482 -3.0855
2.6180 4.6936 -3.1427
2.6704 5.0350 -3.2069
2.7227 5.3724 -3.2796
2.7751 5.7056 -3.3620
2.8274 6.0345 -3.4551
2.8798 6.3589 -3.5600
2.9322 6.6785 -3.6772
2.9845 6.9928 -3.8072
3.0369 7.3013 -3.9502
3.0892 7.6034 -4.1061
3.1416 7.8983 -4.2745
3.1940 8.1851 -4.4548
3.2463 8.4628 -4.6459
3.2987 8.7301 -4.8464
3.3510 8.9857 -5.0547
3.4034 9.2281 -5.2687
3.4558 9.4555 -5.4857
3.5081 9.6659 -5.7026
3.5605 9.8568 -5.9155
3.6128 10.0252 -6.1194
3.6652 10.1675 -6.3079
3.7176 10.2784 -6.4722
3.7699 10.3506 -6.5989
3.8223 10.3717 -6.6665
3.8746 10.3192 -6.6349
3.9270 10.1448 -6.4184
3.9794 9.7220 -5.7928
4.0317 8.6248 -4.0040
4.0841 4.8885 2.4248
4.1364 -71.7834 137.8629
4.1888 21.4105 -27.2584
4.2412 15.9983 -17.9533
4.2935 14.0870 -14.8703
4.3459 12.9862 -13.2488 4.3982 12.1916 -12.1954
4.4506 11.5356 -11.4129
4.5029 10.9454 -10.7715
4.5553 10.3837 -10.2042
4.6077 9.8291 -9.6722
4.6600 9.2685 -9.1509
4.7124 8.6926 -8.6232
4.7647 8.0951 -8.0763
4.8171 7.4702 -7.4991
4.8695 6.8126 -6.8807
4.9218 6.1156 -6.2081
4.9742 5.3699 -5.4637
5.0265 4.5605 -4.6196
5.0789 3.6596 -3.6256
5.1313 2.6094 -2.3793
5.1836 1.2671 -0.6291
5.2360 -0.8486 2.4689
5.2883 -7.2089 12.9899
5.3407 14.7588 -26.0558
5.3931 3.9151 -7.6927
5.4454 1.9038 -4.7820
5.4978 0.7652 -3.3949
5.5501 -0.1367 -2.4171
5.6025 -0.9384 -1.6078
5.6549 -1.6833 -0.8890
5.7072 -2.3883 -0.2297
5.7596 -3.0599 0.3836
5.8119 -3.7005 0.9569
5.8643 -4.3104 1.4925
5.9167 -4.8890 1.9908
5.9690 -5.4350 2.4514
6.0214 -5.9470 2.8733
6.0737 -6.4236 3.2556
6.1261 -6.8634 3.5972
6.1785 -7.2654 3.8974
6.2308 -7.6285 4.1555
6.2832 -7.9520 4.3713

16

fi1 epsilon2 epsilon3

ans =

1.0e+007 *

fi1 epsilon2 epsilon3
0 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001 0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0000
0.0000 -0.0002 -0.0000
0.0000 -0.0002 -0.0000
0.0000 -0.0002 -0.0000
0.0000 -0.0002 -0.0000
0.0000 -0.0002 -0.0000
0.0000 -0.0002 0.0000
0.0000 -0.0002 0.0000
0.0000 -0.0002 0.0000
0.0000 -0.0002 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001 0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0 1 2 3 4 5 6 7-100-50050100150Variatia fi1 functie de v4, v5
fi1v4, v5

17
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0001 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001
0.0000 0.0000 0.0001 0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0001 0.0001
0.0000 -0.0002 0.0001
0.0000 -0.0003 0.0002
0.0000 0.0001 0.0003
0.0000 -5.7879 0.2431
0.0000 0.0382 -0.0013
0.0000 0.0098 -0.0004
0.0000 0.0052 -0.0002
0.0000 0.0035 -0.0002
0.0000 0.0027 -0.0001
0.0000 0.0022 -0.0001
0.0000 0.0019 -0.0001
0.0000 0.0016 -0.0001
0.0000 0.0015 -0.0001
0.0000 0.0013 -0.0001
0.0000 0.0012 -0.0001
0.0000 0.0011 -0.0001
0.0000 0.0011 -0.0001
0.0000 0.0010 -0.0001
0.0000 0.0009 -0.0001
0.0000 0.0009 -0.0001
0.0000 0.0009 -0.0001 0.0000 0.0008 -0.0001
0.0000 0.0008 -0.0002
0.0000 0.0007 -0.0002
0.0000 0.0003 -0.0002
0.0000 0.0008 -0.0006
0.0000 -0.0506 0.0017
0.0000 -0.0022 0.0001
0.0000 -0.0008 -0.0000
0.0000 -0.0005 -0.0000
0.0000 -0.0004 -0.0000
0.0000 -0.0003 -0.0001
0.0000 -0.0003 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001
0.0000 -0.0002 -0.0001

fi1 a4 a5
0 1 2 3 4 5 6 7-6-5-4-3-2-101x 107Variatia fi1 functie epsilon2, epsilon3
fi1epsilon2, epsilon3

18

ans =

1.0e+007 *

fi1 a4 a5

0 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
0.0000 -0.0000 -0.0000
0.0000 -0.0000 -0.0000
0.0000 -0.0000 -0.0000
0.0000 -0.0000 -0.0000
0.0000 -0.0000 -0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0001 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0001
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 -0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0000 -0.0000
0.0000 1.7700 1.1343 0.0000 -0.0121 -0.0076
0.0000 -0.0032 -0.0020
0.0000 -0.0017 -0.0011
0.0000 -0.0012 -0.0007
0.0000 -0.0009 -0.0006
0.0000 -0.0007 -0.0005
0.0000 -0.0006 -0.0004
0.0000 -0.0006 -0.0004
0.0000 -0.0005 -0.0003
0.0000 -0.0005 -0.0003
0.0000 -0.0004 -0.0003
0.0000 -0.0004 -0.0003
0.0000 -0.0004 -0.0002
0.0000 -0.0003 -0.0002
0.0000 -0.0003 -0.0002
0.0000 -0.0003 -0.0002
0.0000 -0.0003 -0.0002
0.0000 -0.0003 -0.0002
0.0000 -0.0002 -0.0002
0.0000 -0.0002 -0.0002
0.0000 -0.0001 -0.0001
0.0000 -0.0002 -0.0002
0.0000 0.0154 0.0095
0.0000 0.0007 0.0004
0.0000 0.0002 0.0001
0.0000 0.0002 0.0001
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 0.0000
0.0000 0.0001 -0.0000
0.0000 0.0001 -0.0000
0.0000 0.0001 -0.0000
0.0000 0.0001 -0.0000
0.0000 0.0001 -0.0000
0.0000 0.0001 -0.0000
0.0000 0.0000 -0.0000

19

1.4 Calculul fortelor si momentelor de inertie
1.4.1 Calculul acceleratiilor centrelor de masa

Fig.3
0 1 2 3 4 5 6 7-2024681012141618x 106Variatia fi1 functie a4, a5
fi1a4, a5

20
Elementul 1 are centrul de masa in punctual 𝐺1 la distant
𝐴0𝐺1 = 𝑔1 = 0,5𝑙1. Componentele axiale sunt:
𝑥𝐺1 = 𝑔1 ∙ 𝑐𝑜𝑠𝜑1; 𝑦𝐺1 = 𝑔1 ∙ 𝑠𝑖𝑛𝜑1
𝑥 𝐺1 = −0,5𝑙1 ∙ 𝜑 12 ∙ 𝑐𝑜𝑠𝜑1; 𝑦 𝐺1 = −0,5𝑙1 ∙ 𝜑 12 ∙ 𝑠𝑖𝑛𝜑1
Elementul 2 are centrul de masa in punctual 𝐺2 la
distant 𝐴 0 𝐺 2 = 𝐴 0 𝐴 + 𝐴 𝐺 2 . Componentele axiale sunt:
𝑥𝐺2 = 𝑙1𝑐𝑜𝑠𝜑1 + 𝑔2𝑐𝑜𝑠𝜑2;
𝑦𝐺2 = 𝑙1𝑠𝑖𝑛𝜑1 + 𝑔2𝑠𝑖𝑛𝜑2
𝑔2 = 0,1𝑙2
𝑥 𝐺2 = −𝑙1𝜑 1𝑐𝑜𝑠𝜑1 − 0,1𝑙2(𝜑 22𝑐𝑜𝑠𝜑2 + 𝜑 2𝑠𝑖𝑛𝜑2);
𝑦 𝐺2 = −𝑙1𝜑 1𝑠𝑖𝑛𝜑1 − 0,1𝑙2(𝜑 22𝑠𝑖𝑛𝜑2 + 𝜑 2𝑐𝑜𝑠𝜑2);
Elementul 3 are centrul de masa in punctual 𝐺3 la
distant 𝐴 0 𝐺 3 = . Componentele
axiale sunt:
𝑔3 = 0,2𝑙3
𝑥𝐺3 = 𝑙0𝑥 + 𝑔3 ∙ 𝑐𝑜𝑠𝜑3; 𝑦𝐺3 = −𝑙0𝑦 + 𝑔3 ∙ 𝑠𝑖𝑛𝜑3
𝑥 𝐺3 = −0,2𝑙3(𝜑 32𝑐𝑜𝑠𝜑3 + 𝜑 3𝑠𝑖𝑛𝜑3);
𝑦 𝐺3 = −0,2𝑙3(𝜑 32𝑠𝑖𝑛𝜑3 + 𝜑 3𝑐𝑜𝑠𝜑3);
Elementul 4 are centrul de masa in punctual 𝐺4 la
distant 𝐴 0 𝐺 4 = . Componentele
axiale sunt:
𝑥𝐺4 = −𝑙𝑑 − 𝑠5; 𝑦𝐺4 = 𝑙ℎ
𝑥 𝐺4 = −𝑆5 ; 𝑦 𝐺4 = 0
Elementul 5 are centrul de masa in punctual 𝐺5 la
distant 𝐴 0 𝐺 5 = . Componentele
axiale sunt:

21
𝑔5 = 0,3𝑠5
𝑥𝐺5 = −𝑙𝑑 − 𝑔5; 𝑦𝐺5 = 𝑙ℎ
𝑥 𝐺5 = −0,3𝑠 5; 𝑦 𝐺4 = 0

1.4.2 Calculul fortelor si cuplurilor de inertie
Torsorul fortei de inertie al elementului cinematic j, cu
miscare plana, are trei component:
;
Aceste component se calculeaza pentru fiecare bara, a
carui masa se considera concentrate in centrul de masa:
Pentru manivela 1
= – m1 G1
= – m1 G1
= – JG1 1= 0
Pentru biela 2
= – m2 G2
= – m2 G2
= – JG2 2
Pentru balansierul 3
= – m3 G3

22
= – m3 G3
= – JG3 3
Pentru patina 4:
= – m4 G4
= – m4 G4
= – JG4 4
Pentru glisiera translanta 5:
= – m5 G5
= – m5 G5 = 0
= – JG5 5 =0

1.4.3 Valori calculate anal itic

fi1 Fi1x Fi1y

ans =

1.0e+003 *

fi1 Fi1x Fi1y
0 1.7792 0 0.0001 1.7767 0.0931
0.0001 1.7694 0.1860 0.0002 1.7573 0.2783
0.0002 1.7403 0.3699

23
0.0003 1.7185 0.4605
0.0003 1.6921 0.5498
0.0004 1.6610 0.6376
0.0004 1.6253 0.7236
0.0005 1.5852 0.8077
0.0005 1.5408 0.8896
0.0006 1.4921 0.9690
0.0006 1.4394 1.0458
0.0007 1.3827 1.1197
0.0007 1.3222 1.1905
0.0008 1.2581 1.2581
0.0008 1.1905 1.3222
0.0009 1.1197 1.3827
0.0009 1.0458 1.4394
0.0010 0.9690 1.4921
0.0010 0.8896 1.5408
0.0011 0.8077 1.5852
0.0012 0.7236 1.6253
0.0012 0.6376 1.6610
0.0013 0.5498 1.6921
0.0013 0.4605 1.7185
0.0014 0.3699 1.7403
0.0014 0.2783 1.7573
0.0015 0.1860 1.7694
0.0015 0.0931 1.7767
0.0016 0.0000 1.7792
0.0016 -0.0931 1.7767
0.0017 -0.1860 1.7694
0.0017 -0.2783 1.7573
0.0018 -0.3699 1.7403
0.0018 -0.4605 1.7185
0.0019 -0.5498 1.6921
0.0019 -0.6376 1.6610
0.0020 -0.7236 1.6253
0.0020 -0.8077 1.5852
0.0021 -0.8896 1.5408
0.0021 -0.9690 1.4921
0.0022 -1.0458 1.4394
0.0023 -1.1197 1.3827
0.0023 -1.1905 1.3222 0.0024 -1.2581 1.2581
0.0024 -1.3222 1.1905
0.0025 -1.3827 1.1197
0.0025 -1.4394 1.0458
0.0026 -1.4921 0.9690
0.0026 -1.5408 0.8896
0.0027 -1.5852 0.8077
0.0027 -1.6253 0.7236
0.0028 -1.6610 0.6376
0.0028 -1.6921 0.5498
0.0029 -1.7185 0.4605
0.0029 -1.7403 0.3699
0.0030 -1.7573 0.2783
0.0030 -1.7694 0.1860
0.0031 -1.7767 0.0931
0.0031 -1.7792 0.0000
0.0032 -1.7767 -0.0931
0.0032 -1.7694 -0.1860
0.0033 -1.7573 -0.2783
0.0034 -1.7403 -0.3699
0.0034 -1.7185 -0.4605
0.0035 -1.6921 -0.5498
0.0035 -1.6610 -0.6376
0.0036 -1.6253 -0.7236
0.0036 -1.5852 -0.8077
0.0037 -1.5408 -0.8896
0.0037 -1.4921 -0.9690
0.0038 -1.4394 -1.0458
0.0038 -1.3827 -1.1197
0.0039 -1.3222 -1.1905
0.0039 -1.2581 -1.2581
0.0040 -1.1905 -1.3222
0.0040 -1.1197 -1.3827
0.0041 -1.0458 -1.4394
0.0041 -0.9690 -1.4921
0.0042 -0.8896 -1.5408
0.0042 -0.8077 -1.5852
0.0043 -0.7236 -1.6253
0.0043 -0.6376 -1.6610
0.0044 -0.5498 -1.6921 0.0045 -0.4605 -1.7185
0.0045 -0.3699 -1.7403
0.0046 -0.2783 -1.7573
0.0046 -0.1860 -1.7694
0.0047 -0.0931 -1.7767
0.0047 -0.0000 -1.7792
0.0048 0.0931 -1.7767
0.0048 0.1860 -1.7694
0.0049 0.2783 -1.7573
0.0049 0.3699 -1.7403
0.0050 0.4605 -1.7185
0.0050 0.5498 -1.6921
0.0051 0.6376 -1.6610
0.0051 0.7236 -1.6253
0.0052 0.8077 -1.5852
0.0052 0.8896 -1.5408
0.0053 0.9690 -1.4921
0.0053 1.0458 -1.4394
0.0054 1.1197 -1.3827
0.0054 1.1905 -1.3222
0.0055 1.2581 -1.2581
0.0056 1.3222 -1.1905
0.0056 1.3827 -1.1197
0.0057 1.4394 -1.0458
0.0057 1.4921 -0.9690
0.0058 1.5408 -0.8896
0.0058 1.5852 -0.8077
0.0059 1.6253 -0.7236
0.0059 1.6610 -0.6376
0.0060 1.6921 -0.5498
0.0060 1.7185 -0.4605
0.0061 1.7403 -0.3699
0.0061 1.7573 -0.2783
0.0062 1.7694 -0.1860
0.0062 1.7767 -0.0931
0.0063 1.7792 -0.0000

24

fi1 Fi2x Fi2y
ans =
1.0e+007 *
fi1 Fi2x Fi2y
0 0.0219 0.0000
0.0000 0.0219 0.0008
0.0000 0.0219 0.0016
0.0000 0.0218 0.0023
0.0000 0.0217 0.0031
0.0000 0.0216 0.0039
0.0000 0.0214 0.0046
0.0000 0.0213 0.0054
0.0000 0.0211 0.0061
0.0000 0.0208 0.0069
0.0000 0.0206 0.0076
0.0000 0.0203 0.0083
0.0000 0.0200 0.0090
0.0000 0.0197 0.0097
0.0000 0.0193 0.0104
0.0000 0.0190 0.0111
0.0000 0.0186 0.0118
0.0000 0.0181 0.0124
0.0000 0.0177 0.0131
0.0000 0.0172 0.0137
0.0000 0.0167 0.0143 0.0000 0.0162 0.0149
0.0000 0.0157 0.0155
0.0000 0.0152 0.0160
0.0000 0.0146 0.0165
0.0000 0.0140 0.0170
0.0000 0.0134 0.0175
0.0000 0.0128 0.0180
0.0000 0.0122 0.0185
0.0000 0.0115 0.0189
0.0000 0.0109 0.0193
0.0000 0.0102 0.0197
0.0000 0.0095 0.0200
0.0000 0.0088 0.0203
0.0000 0.0081 0.0206
0.0000 0.0074 0.0209
0.0000 0.0067 0.0212
0.0000 0.0059 0.0214
0.0000 0.0052 0.0216
0.0000 0.0044 0.0218
0.0000 0.0037 0.0219
0.0000 0.0029 0.0221
0.0000 0.0022 0.0221 0.0000 0.0014 0.0222
0.0000 0.0006 0.0223
0.0000 -0.0001 0.0223
0.0000 -0.0009 0.0223
0.0000 -0.0017 0.0222
0.0000 -0.0024 0.0221
0.0000 -0.0032 0.0221
0.0000 -0.0040 0.0219
0.0000 -0.0047 0.0218
0.0000 -0.0055 0.0216
0.0000 -0.0062 0.0214
0.0000 -0.0069 0.0212
0.0000 -0.0077 0.0209
0.0000 -0.0084 0.0206
0.0000 -0.0091 0.0203
0.0000 -0.0098 0.0200
0.0000 -0.0105 0.0197
0.0000 -0.0111 0.0193
0.0000 -0.0118 0.0189
0.0000 -0.0124 0.0184
0.0000 -0.0131 0.0180
0.0000 -0.0137 0.0175
0 1 2 3 4 5 6 7-2000-1500-1000-5000500100015002000Variatia fi1 functie de fi1x, fi1y
fi1fi1x, fi1y

25
0.0000 -0.0143 0.0170
0.0000 -0.0148 0.0165
0.0000 -0.0154 0.0160
0.0000 -0.0159 0.0154
0.0000 -0.0165 0.0149
0.0000 -0.0170 0.0143
0.0000 -0.0175 0.0137
0.0000 -0.0179 0.0131
0.0000 -0.0184 0.0124
0.0000 -0.0188 0.0118
0.0000 -0.0192 0.0111
0.0000 -0.0195 0.0104
0.0000 -0.0199 0.0097
0.0000 -0.0202 0.0090
0.0000 -0.0205 0.0083
0.0000 -0.0208 0.0076
0.0000 -0.0210 0.0069
0.0000 -0.0213 0.0061
0.0000 -0.0215 0.0054
0.0000 -0.0216 0.0046
0.0000 -0.0218 0.0039
0.0000 -0.0219 0.0031
0.0000 -0.0220 0.0023
0.0000 -0.0221 0.0015
0.0000 -0.0221 0.0008
0.0000 -0.0221 -0.0000
0.0000 -0.0221 -0.0008
0.0000 -0.0221 -0.0015
0.0000 -0.0220 -0.0023
0.0000 -0.0219 -0.0031
0.0000 -0.0218 -0.0039
0.0000 -0.0216 -0.0046
0.0000 -0.0215 -0.0054
0.0000 -0.0213 -0.0061
0.0000 -0.0210 -0.0068
0.0000 -0.0208 -0.0076
0.0000 -0.0205 -0.0083
0.0000 -0.0202 -0.0090
0.0000 -0.0199 -0.0097
0.0000 -0.0196 -0.0104 0.0000 -0.0192 -0.0111
0.0000 -0.0188 -0.0117
0.0000 -0.0184 -0.0124
0.0000 -0.0180 -0.0130
0.0000 -0.0175 -0.0136
0.0000 -0.0171 -0.0142
0.0000 -0.0166 -0.0148
0.0000 -0.0161 -0.0154
0.0000 -0.0156 -0.0159
0.0000 -0.0151 -0.0165
0.0000 -0.0146 -0.0170
0.0000 -0.0139 -0.0175
0.0000 -0.0129 -0.0179
0.0000 -0.0493 -0.0178
0.0000 1.0972 -0.0274
0.0000 0.0348 -0.0193
0.0000 0.0059 -0.0195
0.0000 -0.0006 -0.0199
0.0000 -0.0028 -0.0202
0.0000 -0.0036 -0.0205
0.0000 -0.0038 -0.0208
0.0000 -0.0036 -0.0210
0.0000 -0.0033 -0.0212
0.0000 -0.0029 -0.0214
0.0000 -0.0024 -0.0216
0.0000 -0.0018 -0.0218
0.0000 -0.0012 -0.0219
0.0000 -0.0006 -0.0220
0.0000 0.0001 -0.0220
0.0000 0.0008 -0.0221
0.0000 0.0015 -0.0221
0.0000 0.0022 -0.0221
0.0000 0.0029 -0.0221
0.0000 0.0036 -0.0220
0.0000 0.0043 -0.0219
0.0000 0.0050 -0.0218
0.0000 0.0058 -0.0216
0.0000 0.0065 -0.0215
0.0000 0.0072 -0.0213
0.0000 0.0079 -0.0210 0.0000 0.0086 -0.0208
0.0000 0.0093 -0.0205
0.0000 0.0099 -0.0202
0.0000 0.0106 -0.0199
0.0000 0.0111 -0.0196
0.0000 0.0115 -0.0192
0.0000 0.0116 -0.0188
0.0000 0.0593 -0.0183
0.0000 -0.0477 -0.0173
0.0000 0.0087 -0.0173
0.0000 0.0125 -0.0169
0.0000 0.0139 -0.0164
0.0000 0.0147 -0.0159
0.0000 0.0154 -0.0154
0.0000 0.0161 -0.0148
0.0000 0.0166 -0.0142
0.0000 0.0171 -0.0136
0.0000 0.0176 -0.0130
0.0000 0.0181 -0.0124
0.0000 0.0185 -0.0117
0.0000 0.0189 -0.0111
0.0000 0.0193 -0.0104
0.0000 0.0197 -0.0097
0.0000 0.0200 -0.0090
0.0000 0.0203 -0.0083
0.0000 0.0206 -0.0076
0.0000 0.0208 -0.0068
0.0000 0.0211 -0.0061
0.0000 0.0213 -0.0054
0.0000 0.0214 -0.0046
0.0000 0.0216 -0.0038
0.0000 0.0217 -0.0031
0.0000 0.0218 -0.0023
0.0000 0.0219 -0.0015
0.0000 0.0219 -0.0008
0.0000 0.0219 0.0000

26

fi1 Fi3x Fi3y

ans =

1.0e+006 *

fi1 Fi3x Fi3y

0 -0.0090 -0.0161
0.0000 -0.0090 -0.0160
0.0000 -0.0090 -0.0160
0.0000 -0.0089 -0.0159
0.0000 -0.0088 -0.0158
0.0000 -0.0087 -0.0156
0.0000 -0.0086 -0.0154
0.0000 -0.0084 -0.0151
0.0000 -0.0083 -0.0148
0.0000 -0.0081 -0.0145
0.0000 -0.0079 -0.0142
0.0000 -0.0077 -0.0138
0.0000 -0.0074 -0.0134
0.0000 -0.0072 -0.0129
0.0000 -0.0069 -0.0124
0.0000 -0.0066 -0.0119
0.0000 -0.0063 -0.0114
0.0000 -0.0060 -0.0108
0.0000 -0.0057 -0.0103
0.0000 -0.0054 -0.0097
0.0000 -0.0051 -0.0090
0.0000 -0.0048 -0.0084
0.0000 -0.0044 -0.0078
0.0000 -0.0041 -0.0071 0.0000 -0.0038 -0.0064
0.0000 -0.0035 -0.0057
0.0000 -0.0032 -0.0050
0.0000 -0.0029 -0.0043
0.0000 -0.0026 -0.0036
0.0000 -0.0023 -0.0029
0.0000 -0.0020 -0.0021
0.0000 -0.0018 -0.0014
0.0000 -0.0015 -0.0007
0.0000 -0.0013 0.0000
0.0000 -0.0011 0.0007
0.0000 -0.0009 0.0014
0.0000 -0.0007 0.0021
0.0000 -0.0005 0.0028
0.0000 -0.0004 0.0035
0.0000 -0.0003 0.0042
0.0000 -0.0002 0.0048
0.0000 -0.0001 0.0055
0.0000 -0.0001 0.0061
0.0000 -0.0000 0.0067
0.0000 -0.0000 0.0073
0.0000 -0.0000 0.0079
0.0000 -0.0001 0.0085
0.0000 -0.0001 0.0090
0.0000 -0.0002 0.0095 0.0000 -0.0003 0.0100
0.0000 -0.0004 0.0105
0.0000 -0.0006 0.0109
0.0000 -0.0007 0.0114
0.0000 -0.0009 0.0118
0.0000 -0.0011 0.0122
0.0000 -0.0013 0.0126
0.0000 -0.0015 0.0129
0.0000 -0.0018 0.0132
0.0000 -0.0020 0.0135
0.0000 -0.0023 0.0138
0.0000 -0.0026 0.0141
0.0000 -0.0029 0.0144
0.0000 -0.0032 0.0146
0.0000 -0.0035 0.0148
0.0000 -0.0038 0.0150
0.0000 -0.0041 0.0152
0.0000 -0.0044 0.0153
0.0000 -0.0048 0.0155
0.0000 -0.0051 0.0156
0.0000 -0.0054 0.0157
0.0000 -0.0057 0.0158
0.0000 -0.0060 0.0159
0.0000 -0.0063 0.0160
0.0000 -0.0066 0.0161
0 1 2 3 4 5 6 7-2024681012x 106Variatia fi1 functie de fi2x, fi2y
fi1fi2x, fi2y

27
0.0000 -0.0069 0.0161
0.0000 -0.0072 0.0162
0.0000 -0.0075 0.0162
0.0000 -0.0077 0.0163
0.0000 -0.0080 0.0163
0.0000 -0.0082 0.0163
0.0000 -0.0084 0.0164
0.0000 -0.0086 0.0164
0.0000 -0.0088 0.0164
0.0000 -0.0089 0.0164
0.0000 -0.0091 0.0164
0.0000 -0.0092 0.0164
0.0000 -0.0093 0.0164
0.0000 -0.0094 0.0164
0.0000 -0.0094 0.0164
0.0000 -0.0095 0.0164
0.0000 -0.0095 0.0164
0.0000 -0.0095 0.0164
0.0000 -0.0095 0.0164
0.0000 -0.0094 0.0164
0.0000 -0.0094 0.0164
0.0000 -0.0093 0.0164
0.0000 -0.0092 0.0164
0.0000 -0.0091 0.0164
0.0000 -0.0089 0.0164
0.0000 -0.0088 0.0163
0.0000 -0.0086 0.0163
0.0000 -0.0085 0.0163
0.0000 -0.0083 0.0163
0.0000 -0.0081 0.0163
0.0000 -0.0079 0.0162
0.0000 -0.0078 0.0162
0.0000 -0.0076 0.0162
0.0000 -0.0074 0.0161
0.0000 -0.0073 0.0161
0.0000 -0.0072 0.0161 0.0000 -0.0072 0.0161
0.0000 -0.0073 0.0161
0.0000 -0.0076 0.0161
0.0000 -0.0081 0.0161
0.0000 -0.0092 0.0163
0.0000 -0.0117 0.0165
0.0000 -0.0177 0.0167
0.0000 -0.0372 0.0166
0.0000 -0.3474 0.0354
0.0000 4.0291 0.2110
0.0000 0.1594 0.0439
0.0000 0.0569 0.0279
0.0000 0.0317 0.0217
0.0000 0.0212 0.0184
0.0000 0.0157 0.0163
0.0000 0.0124 0.0150
0.0000 0.0102 0.0142
0.0000 0.0088 0.0136
0.0000 0.0077 0.0133
0.0000 0.0069 0.0131
0.0000 0.0064 0.0130
0.0000 0.0059 0.0131
0.0000 0.0056 0.0131
0.0000 0.0054 0.0133
0.0000 0.0053 0.0135
0.0000 0.0052 0.0137
0.0000 0.0052 0.0139
0.0000 0.0053 0.0141
0.0000 0.0054 0.0144
0.0000 0.0057 0.0146
0.0000 0.0059 0.0149
0.0000 0.0063 0.0151
0.0000 0.0067 0.0154
0.0000 0.0072 0.0157
0.0000 0.0079 0.0159
0.0000 0.0087 0.0162 0.0000 0.0098 0.0164
0.0000 0.0113 0.0166
0.0000 0.0133 0.0168
0.0000 0.0165 0.0169
0.0000 0.0224 0.0167
0.0000 0.0390 0.0161
0.0000 0.4054 0.0343
0.0000 -0.2124 0.0537
0.0000 -0.0161 0.0122
0.0000 -0.0058 0.0029
0.0000 -0.0042 -0.0011
0.0000 -0.0041 -0.0035
0.0000 -0.0042 -0.0051
0.0000 -0.0045 -0.0064
0.0000 -0.0048 -0.0074
0.0000 -0.0052 -0.0084
0.0000 -0.0055 -0.0092
0.0000 -0.0058 -0.0100
0.0000 -0.0062 -0.0107
0.0000 -0.0065 -0.0114
0.0000 -0.0068 -0.0120
0.0000 -0.0071 -0.0125
0.0000 -0.0073 -0.0131
0.0000 -0.0076 -0.0135
0.0000 -0.0078 -0.0140
0.0000 -0.0080 -0.0144
0.0000 -0.0082 -0.0147
0.0000 -0.0084 -0.0150
0.0000 -0.0086 -0.0153
0.0000 -0.0087 -0.0155
0.0000 -0.0088 -0.0157
0.0000 -0.0089 -0.0159
0.0000 -0.0090 -0.0160
0.0000 -0.0090 -0.0160
0.0000 -0.0090 -0.0161

0 1 2 3 4 5 6 7-0.500.511.522.533.544.5x 106variatia fi1 functie de fi3x, fi3y
fi1fi3x, fi3y

28
fi1 Fi4x

ans =

1.0e+006 *

fi1 Fi4x

0 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002 0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005 0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0002
0.0000 0.0002
0.0000 0.0003
0.0000 0.0004

29
0.0000 0.0005
0.0000 0.0004
0.0000 -0.0002
0.0000 0.0603
0.0000 -1.8166
0.0000 -0.0758
0.0000 -0.0271
0.0000 -0.0154
0.0000 -0.0106
0.0000 -0.0081
0.0000 -0.0066
0.0000 -0.0056
0.0000 -0.0049
0.0000 -0.0044
0.0000 -0.0040
0.0000 -0.0037
0.0000 -0.0034
0.0000 -0.0032
0.0000 -0.0030
0.0000 -0.0029
0.0000 -0.0027
0.0000 -0.0026 0.0000 -0.0025
0.0000 -0.0024
0.0000 -0.0023
0.0000 -0.0023
0.0000 -0.0022
0.0000 -0.0021
0.0000 -0.0021
0.0000 -0.0020
0.0000 -0.0020
0.0000 -0.0019
0.0000 -0.0018
0.0000 -0.0017
0.0000 -0.0015
0.0000 -0.0010
0.0000 -0.0002
0.0000 -0.0747
0.0000 0.0950
0.0000 0.0074
0.0000 0.0024
0.0000 0.0012
0.0000 0.0007
0.0000 0.0004 0.0000 0.0003
0.0000 0.0002
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000

fi1 Fi5x

ans =

1.0e+006 *
0 1 2 3 4 5 6 7-20-15-10-505x 105Variatia fi1 functie de Fi4x
fi1fi4x

30

fi1 Fi5x

0 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0006
0.0000 0.0006
0.0000 0.0006
0.0000 0.0007
0.0000 0.0007
0.0000 0.0007 0.0000 0.0008
0.0000 0.0008
0.0000 0.0008
0.0000 0.0009
0.0000 0.0009
0.0000 0.0009
0.0000 0.0010
0.0000 0.0010
0.0000 0.0010
0.0000 0.0010
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0010
0.0000 0.0010
0.0000 0.0010
0.0000 0.0010
0.0000 0.0009
0.0000 0.0009
0.0000 0.0009
0.0000 0.0008
0.0000 0.0008
0.0000 0.0008
0.0000 0.0007
0.0000 0.0007
0.0000 0.0007
0.0000 0.0006
0.0000 0.0006
0.0000 0.0005
0.0000 0.0005 0.0000 0.0005
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0002
0.0000 0.0003
0.0000 0.0003
0.0000 0.0004
0.0000 0.0005
0.0000 0.0007
0.0000 0.0009
0.0000 0.0011
0.0000 0.0009
0.0000 -0.0005
0.0000 0.1357
0.0000 -4.0873
0.0000 -0.1705
0.0000 -0.0610
0.0000 -0.0346
0.0000 -0.0239
0.0000 -0.0183
0.0000 -0.0149
0.0000 -0.0126
0.0000 -0.0111
0.0000 -0.0099
0.0000 -0.0090
0.0000 -0.0083
0.0000 -0.0077
0.0000 -0.0072
0.0000 -0.0068
0.0000 -0.0064
0.0000 -0.0061
0.0000 -0.0059
0.0000 -0.0056
0.0000 -0.0054
0.0000 -0.0053
0.0000 -0.0051
0.0000 -0.0049

31
0.0000 -0.0048
0.0000 -0.0047
0.0000 -0.0046
0.0000 -0.0044
0.0000 -0.0043
0.0000 -0.0041
0.0000 -0.0038
0.0000 -0.0033
0.0000 -0.0023
0.0000 -0.0004
0.0000 -0.1680
0.0000 0.2138
0.0000 0.0166 0.0000 0.0053
0.0000 0.0026
0.0000 0.0015
0.0000 0.0010
0.0000 0.0007
0.0000 0.0005
0.0000 0.0003
0.0000 0.0002
0.0000 0.0002
0.0000 0.0001
0.0000 0.0001
0.0000 0.0001
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0000
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001
0.0000 -0.0001

fi1 Mi2 Mi3 Mi4

ans =

1.0e+005 *

fi1 Mi2 Mi3 Mi4

0 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000 0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0004 0.0000
0.0000 0.0008 0.0003 0.0000
0.0000 0.0008 0.0003 0.0000
0.0000 0.0008 0.0003 0.0000
0.0000 0.0008 0.0003 0.0000
0.0000 0.0007 0.0003 0.0000
0.0000 0.0007 0.0003 0.0000
0.0000 0.0007 0.0003 0.0000
0 1 2 3 4 5 6 7-4.5-4-3.5-3-2.5-2-1.5-1-0.500.5x 106Variatia fi1 functie de fi5x
Fi1Fi5x

32
0.0000 0.0007 0.0002 0.0000
0.0000 0.0007 0.0002 0.0000
0.0000 0.0007 0.0002 0.0000
0.0000 0.0007 0.0002 0.0000
0.0000 0.0007 0.0002 0.0000
0.0000 0.0007 0.0002 0.0000
0.0000 0.0007 0.0001 0.0000
0.0000 0.0007 0.0001 0.0000
0.0000 0.0007 0.0001 0.0000
0.0000 0.0007 0.0001 0.0000
0.0000 0.0007 0.0001 0.0000
0.0000 0.0006 0.0000 0.0000
0.0000 0.0006 0.0000 0.0000
0.0000 0.0006 -0.0000 0.0000
0.0000 0.0006 -0.0000 0.0000
0.0000 0.0006 -0.0000 0.0000
0.0000 0.0006 -0.0001 0.0000
0.0000 0.0006 -0.0001 0.0000
0.0000 0.0005 -0.0001 0.0000
0.0000 0.0005 -0.0001 0.0000
0.0000 0.0005 -0.0001 0.0000
0.0000 0.0005 -0.0001 0.0000
0.0000 0.0005 -0.0002 0.0000
0.0000 0.0005 -0.0002 0.0000
0.0000 0.0004 -0.0002 0.0000
0.0000 0.0004 -0.0002 0.0000
0.0000 0.0004 -0.0002 0.0000
0.0000 0.0004 -0.0002 0.0000
0.0000 0.0004 -0.0003 0.0000
0.0000 0.0003 -0.0003 0.0000
0.0000 0.0003 -0.0003 0.0000
0.0000 0.0003 -0.0003 0.0000
0.0000 0.0003 -0.0003 0.0000
0.0000 0.0003 -0.0003 0.0000
0.0000 0.0002 -0.0003 0.0000
0.0000 0.0002 -0.0003 0.0000
0.0000 0.0002 -0.0003 0.0000
0.0000 0.0002 -0.0004 0.0000
0.0000 0.0002 -0.0004 0.0000
0.0000 0.0001 -0.0004 0.0000
0.0000 0.0001 -0.0004 0.0000
0.0000 0.0001 -0.0004 0.0000
0.0000 0.0001 -0.0004 0.0000
0.0000 0.0001 -0.0004 0.0000
0.0000 0.0000 -0.0004 0.0000
0.0000 0.0000 -0.0004 0.0000
0.0000 0.0000 -0.0004 0.0000
0.0000 -0.0000 -0.0004 -0.0000
0.0000 -0.0000 -0.0004 -0.0000
0.0000 -0.0000 -0.0004 -0.0000 0.0000 -0.0000 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0002 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0001 -0.0004 -0.0000
0.0000 -0.0000 -0.0004 -0.0000
0.0000 0.0000 -0.0004 0.0000
0.0000 0.0001 -0.0004 0.0000
0.0000 0.0001 -0.0005 0.0000
0.0000 0.0002 -0.0005 0.0000
0.0000 0.0003 -0.0005 0.0000
0.0000 0.0004 -0.0005 0.0000
0.0000 0.0006 -0.0005 0.0000
0.0000 0.0008 -0.0005 0.0000
0.0000 0.0009 -0.0005 0.0000
0.0000 0.0007 -0.0006 0.0000
0.0000 -0.0004 -0.0011 -0.0000
0.0000 0.1090 -0.0093 0.0001
0.0000 -3.2731 0.1086 -0.0031

33
0.0000 -0.1354 0.0044 -0.0001
0.0000 -0.0480 0.0017 -0.0000
0.0000 -0.0270 0.0010 -0.0000
0.0000 -0.0185 0.0008 -0.0000
0.0000 -0.0140 0.0006 -0.0000
0.0000 -0.0113 0.0005 -0.0000
0.0000 -0.0095 0.0005 -0.0000
0.0000 -0.0083 0.0004 -0.0000
0.0000 -0.0073 0.0004 -0.0000
0.0000 -0.0066 0.0004 -0.0000
0.0000 -0.0060 0.0004 -0.0000
0.0000 -0.0056 0.0004 -0.0000
0.0000 -0.0052 0.0004 -0.0000
0.0000 -0.0048 0.0004 -0.0000
0.0000 -0.0046 0.0004 -0.0000
0.0000 -0.0043 0.0004 -0.0000
0.0000 -0.0041 0.0004 -0.0000
0.0000 -0.0039 0.0004 -0.0000
0.0000 -0.0038 0.0004 -0.0000
0.0000 -0.0036 0.0004 -0.0000
0.0000 -0.0035 0.0004 -0.0000
0.0000 -0.0034 0.0004 -0.0000
0.0000 -0.0033 0.0005 -0.0000
0.0000 -0.0032 0.0005 -0.0000
0.0001 -0.0031 0.0005 -0.0000
0.0001 -0.0030 0.0005 -0.0000
0.0001 -0.0029 0.0005 -0.0000
0.0001 -0.0027 0.0005 -0.0000
0.0001 -0.0025 0.0006 -0.0000
0.0001 -0.0021 0.0006 -0.0000
0.0001 -0.0012 0.0007 -0.0000 0.0001 0.0004 0.0011 0.0000
0.0001 -0.1384 0.0109 -0.0001
0.0001 0.1791 -0.0059 0.0002
0.0001 0.0145 -0.0005 0.0000
0.0001 0.0051 -0.0001 0.0000
0.0001 0.0029 0.0000 0.0000
0.0001 0.0020 0.0001 0.0000
0.0001 0.0015 0.0001 0.0000
0.0001 0.0013 0.0002 0.0000
0.0001 0.0011 0.0002 0.0000
0.0001 0.0010 0.0002 0.0000
0.0001 0.0009 0.0002 0.0000
0.0001 0.0009 0.0003 0.0000
0.0001 0.0008 0.0003 0.0000
0.0001 0.0008 0.0003 0.0000
0.0001 0.0008 0.0003 0.0000
0.0001 0.0008 0.0003 0.0000
0.0001 0.0008 0.0003 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000
0.0001 0.0008 0.0004 0.0000

1.5 Cinetostatica mecanismului cu bare
Cinetostatica mecanismului cu bare urmareste: calculul
reactiunilor din cuplele cinematice fara frecare, calculul
fortelor momentului motor ca moment de echilibru dinamic.
0 1 2 3 4 5 6 7-3.5-3-2.5-2-1.5-1-0.500.5x 105Varita fi1 functie de Mi2, Mi3, Mi4
fi1Mi2, Mi3, Mi4

34
Se cunosc fortele de greutate, forta de rezistenta tehnologica,
precut si fortele/c uplurile de intertie.
Forta de rezistenta tehnologica se calculeaza, observand diagram
din fig.4:

Fig.4
1.5.1 Calculul reactiunilor din cuplele cinematice (fara frecare)
Formula structural -topologica a mecanismului este:
MM=MF(0,1)+LD(2,3)+LD(4,5)
Deoarece forta de rezistenta tehnologica 𝐹𝑟5 actioneaza pe
elemental cinematic condus 5, iar LD este static determinat,
calculul cinetostatic se efectueaza in ordinea invers celui
cinematic.

35

Fig.5

Fig.6

36

Fig.7
Cinetostatica LD(4,5)
Se considera schema cinematic a LD (4,5) ca structura
izolata, aflata in echilibru cinetostatic, incarcata cu toate
fortele exterioare(greutate,forta de rezistenta tehnologica,
fortele/cuplurile de inertie) si cu reactiunile din cuple.
Se scriu ectuatiile de echilibru cinetostatic (doua de proiectii
si una de moment) pentru unul din cele doua elemente 4 sau
5 si pentru intreaga grupa:
∑(𝐹𝑥)𝑔𝑟 = 0 ; 𝑅24 sin(∝ +𝜑2) + 𝐹𝑖𝑥4 + 𝐹𝑖𝑥5 + 𝐹𝑟 = 0;
∑(𝐹𝑦)𝑔𝑟 = 0;
𝑅24 cos(∝ +𝜑2) + 𝑅05 + 𝐹𝑖𝑥4 + 𝐹𝑖𝑥5 − 𝐺4 − 𝐺5 = 0;
∑(𝐹𝑥)5 = 0 ; −𝑅54𝑥 + 𝐹𝑖𝑥5 + 𝐹𝑟 =
0 ∑(𝐹𝑦)5 = 0 ; 𝑅05 − 𝑅54𝑥 − 𝐺5 =
0

37
∑(𝑀𝑐)4 = 0 ; 𝑅24ℎ4 + 𝑀𝑖𝑧4 = 0
∑(𝑀𝑐)5 = 0 ; −𝑅05ℎ5 + 𝐺5𝑔5 = 0

Sistemul de 6 ecuatii liniare cu 6 necunoscute se paote
rezolva, fie cu metoda Cramer, fie prin decuplarea unor
ecuatii prin metoda substitutiei.
Rezulta:

Cinetostatica LD(2,3)
Prin izolarea lantului cinematic dyadic format din elementele
2 si 3 se introduce in punctual C reactiunea 𝑅24 calculata
anterior, iar in punctele A si 𝐵0 (reprezentand cuplele
potentiale) se introduce componentele reactiunilor dinspre
elementele 1 respe ctiv 0. Ecuatiile de echilibru cinetostatic
pentru fiecare din cele doua elemente cinematice 2 si 3 sunt
doua de proiectii si una de momente:
∑(𝐹𝑥)2 = 0 ; 𝑅12𝑥 + 𝐹𝑖𝑥2 − 𝑅24 sin(∝ +𝜑2) + 𝑅32𝑥 = 0
∑(𝐹𝑦)2 = 0 ; 𝑅12𝑦 + 𝐹𝑖𝑦2 − 𝐺2 + 𝑅24 cos(∝ +𝜑2) + 𝑅32𝑥 = 0
∑(𝑀𝐴)2 = 0;

38
𝐹𝑖𝑥2 ∙ 𝑔2 ∙ sin(𝜑2) − (𝐹𝑖𝑦2 − 𝐺2)𝑔2 ∙ cos(𝜑2) + 𝑀𝑖𝑧2 − 𝑅24 ∙ 𝑙4 +
𝑅32𝑥
∙ 𝑙2 sin 𝜑2 − 𝑅32𝑦 ∙ 𝑙2𝑐𝑜𝑠𝜑2 = 0
∑(𝐹𝑥3)3 = 0 ; 𝑅03𝑥 + 𝐹𝑖𝑥3 − 𝑅32𝑥 = 0
∑(𝐹𝑦3)3 = 0 ; 𝑅03𝑦 − 𝑅32𝑦 + 𝐹𝑖𝑦3 − 𝐺3 = 0
∑(𝑀𝐵)3 = 0;
𝐹𝑖𝑥3 ∙ 𝑔3 ∙ sin(𝜑3) − (𝐹𝑖𝑦3 − 𝐺3)𝑔3 ∙ cos(𝜑3) + 𝑀𝑖𝑧3 − 𝑅32𝑥 ∙ 𝑙3
sin 𝜑3
+ 𝑅32𝑦 ∙ 𝑙3𝑐𝑜𝑠𝜑3 = 0
Sistemul format de cele 6 ecuatii liniare se rezolva prin
decuplarea unor ecuatii prin metoda substitutiei. Rezulta:

Unde:
A=

𝑠4
𝐵 = 𝐹𝑖𝑥3 ∙ 0,2 ∙ 𝑙3 sin(𝜑3) − (𝐹𝑖𝑦3 − 𝐺3)0,2 ∙ 𝑙3cos(𝜑3) + 𝑀𝑖3
𝑅12𝑥 = −𝐹𝑖𝑥2 + 𝑅24 sin(∝ +𝜑2) − 𝑅32𝑥
𝑅12𝑦 = −𝐹𝑖𝑦2 − 𝑅24 cos(∝ +𝜑2) − 𝑅32𝑦 + 𝐺2
𝑅03𝑥 = −𝐹𝑖𝑥3 + 𝑅32𝑥
𝑅03𝑦 = −𝐹𝑖𝑦3 + 𝑅32𝑦 + 𝐺3

39

Cinetostatica manivelei 1
Se izoleaza manivela 1 si se introduce componentele
reactiunii necunoscute din articulatia 𝐴0 ale reac tiunii
cunoscute din articulatia A, precum si cuplul necunoscut de
echilibru cinetostatic ce actioneaza asuprea elementului
conducator.
Ecuatiile de echilibru cinetostatic al barei 1 sunt:
∑ 𝐹𝑥1 = 0 ; 𝑅01𝑥 − 𝑅12𝑥 + 𝐹𝑖𝑥1 = 0
𝑅01𝑥 = 𝑅12𝑥 − 𝐹𝑖𝑥1
∑ 𝐹𝑦1 = 0 ; 𝑅01𝑦 − 𝑅12𝑦 + 𝐹𝑖𝑦1 = 0
𝑅01𝑥 = 𝑅12𝑦 − 𝐹𝑖𝑦1
𝑀𝑒1 = 𝑅12𝑥 ∙ 𝑙1 sin 𝜑1 + 𝑅12𝑦 ∙ 𝑙1𝑐𝑜𝑠𝜑1 − 𝐺1 ∙ 𝑎1 ∙ sin 𝜑1

1.6. Valorile calculate analitic:

fi1 R24

ans =

1.0e+006 *

fi1 R24

0 -0.0004
0.0000 -0.0004
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003 0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0003
0.0000 -0.0004
0.0000 -0.0004
0.0000 -0.0004 0.0000 -0.0004
0.0000 -0.0004
0.0000 -0.0005
0.0000 -0.0005
0.0000 -0.0005
0.0000 -0.0006
0.0000 -0.0006
0.0000 -0.0006
0.0000 -0.0007
0.0000 -0.0007

40
0.0000 -0.0008
0.0000 -0.0008
0.0000 -0.0009
0.0000 -0.0009
0.0000 -0.0010
0.0000 -0.0010
0.0000 -0.0011
0.0000 -0.0011
0.0000 -0.0012
0.0000 -0.0013
0.0000 -0.0013
0.0000 -0.0014
0.0000 -0.0014
0.0000 -0.0015
0.0000 -0.0016
0.0000 -0.0016
0.0000 -0.0017
0.0000 -0.0018
0.0000 -0.0018
0.0000 -0.0019
0.0000 -0.0019
0.0000 -0.0020
0.0000 -0.0020
0.0000 -0.0021
0.0000 -0.0021
0.0000 -0.0022
0.0000 -0.0022
0.0000 -0.0023
0.0000 -0.0023
0.0000 -0.0023
0.0000 -0.0024
0.0000 -0.0024
0.0000 -0.0024
0.0000 -0.0024
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0025
0.0000 -0.0024
0.0000 -0.0024
0.0000 -0.0024
0.0000 -0.0024
0.0000 -0.0023
0.0000 -0.0023 0.0000 -0.0022
0.0000 -0.0022
0.0000 -0.0021
0.0000 -0.0021
0.0000 -0.0020
0.0000 -0.0020
0.0000 -0.0019
0.0000 -0.0019
0.0000 -0.0018
0.0000 -0.0017
0.0000 -0.0017
0.0000 -0.0016
0.0000 -0.0016
0.0000 -0.0015
0.0000 -0.0014
0.0000 -0.0014
0.0000 -0.0013
0.0000 -0.0012
0.0000 -0.0012
0.0000 -0.0011
0.0000 -0.0010
0.0000 -0.0010
0.0000 -0.0009
0.0000 -0.0009
0.0000 -0.0009
0.0000 -0.0008
0.0000 -0.0008
0.0000 -0.0008
0.0000 -0.0008
0.0000 -0.0008
0.0000 -0.0009
0.0000 -0.0009
0.0000 -0.0010
0.0000 -0.0012
0.0000 -0.0014
0.0000 -0.0017
0.0000 -0.0021
0.0000 -0.0024
0.0000 -0.0020
0.0000 0.0003
0.0000 -0.2381
0.0000 7.1568
0.0000 0.2981
0.0000 0.1063
0.0000 0.0602
0.0000 0.0414
0.0000 0.0315
0.0000 0.0256
0.0000 0.0217
0.0000 0.0189 0.0000 0.0169
0.0000 0.0153
0.0000 0.0140
0.0000 0.0130
0.0000 0.0122
0.0000 0.0115
0.0000 0.0108
0.0000 0.0103
0.0000 0.0098
0.0000 0.0094
0.0000 0.0091
0.0000 0.0088
0.0000 0.0085
0.0000 0.0082
0.0000 0.0080
0.0000 0.0077
0.0000 0.0075
0.0000 0.0073
0.0000 0.0071
0.0000 0.0067
0.0000 0.0063
0.0000 0.0054
0.0000 0.0035
0.0000 0.0003
0.0000 0.2952
0.0000 -0.3769
0.0000 -0.0297
0.0000 -0.0098
0.0000 -0.0051
0.0000 -0.0032
0.0000 -0.0022
0.0000 -0.0017
0.0000 -0.0013
0.0000 -0.0011
0.0000 -0.0009
0.0000 -0.0008
0.0000 -0.0007
0.0000 -0.0006
0.0000 -0.0006
0.0000 -0.0006
0.0000 -0.0005
0.0000 -0.0005
0.0000 -0.0005
0.0000 -0.0005
0.0000 -0.0005
0.0000 -0.0004
0.0000 -0.0004
0.0000 -0.0004
0.0000 -0.0004
0.0000 -0.0004

41
0.0000 -0.0004 0.0000 -0.0004 0.0000 -0.0004

fi1 R05
1.0e+006 *

fi1 R05

0 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0004
0.0000 0.0004 0.0000 0.0004
0.0000 0.0004
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0006
0.0000 0.0006
0.0000 0.0006
0.0000 0.0006
0.0000 0.0007
0.0000 0.0007
0.0000 0.0007
0.0000 0.0008
0.0000 0.0008
0.0000 0.0008
0.0000 0.0009
0.0000 0.0009
0.0000 0.0009
0.0000 0.0010
0.0000 0.0010
0.0000 0.0010
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0012 0.0000 0.0012
0.0000 0.0012
0.0000 0.0013
0.0000 0.0013
0.0000 0.0013
0.0000 0.0013
0.0000 0.0013
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0015
0.0000 0.0015
0.0000 0.0015
0.0000 0.0015
0.0000 0.0015
0.0000 0.0015
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0.0000 0.0014
0 1 2 3 4 5 6 7-1012345678x 106Variatia fi1 functie de R24
fi1R24

42
0.0000 0.0014
0.0000 0.0013
0.0000 0.0013
0.0000 0.0013
0.0000 0.0013
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0012
0.0000 0.0011
0.0000 0.0011
0.0000 0.0011
0.0000 0.0010
0.0000 0.0010
0.0000 0.0009
0.0000 0.0009
0.0000 0.0009
0.0000 0.0008
0.0000 0.0008
0.0000 0.0008
0.0000 0.0007
0.0000 0.0007
0.0000 0.0007
0.0000 0.0006
0.0000 0.0006
0.0000 0.0006
0.0000 0.0006
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0005
0.0000 0.0006
0.0000 0.0006
0.0000 0.0007
0.0000 0.0008 0.0000 0.0009
0.0000 0.0011
0.0000 0.0013
0.0000 0.0014
0.0000 0.0012
0.0000 -0.0001
0.0000 0.1346
0.0000 -4.0458
0.0000 -0.1685
0.0000 -0.0601
0.0000 -0.0340
0.0000 -0.0234
0.0000 -0.0178
0.0000 -0.0144
0.0000 -0.0122
0.0000 -0.0107
0.0000 -0.0095
0.0000 -0.0086
0.0000 -0.0079
0.0000 -0.0073
0.0000 -0.0068
0.0000 -0.0064
0.0000 -0.0061
0.0000 -0.0058
0.0000 -0.0055
0.0000 -0.0053
0.0000 -0.0051
0.0000 -0.0049
0.0000 -0.0047
0.0000 -0.0046
0.0000 -0.0045
0.0000 -0.0043
0.0000 -0.0042
0.0000 -0.0041
0.0000 -0.0039
0.0000 -0.0038 0.0000 -0.0035
0.0000 -0.0030
0.0000 -0.0019
0.0000 -0.0001
0.0000 -0.1686
0.0000 0.2155
0.0000 0.0171
0.0000 0.0057
0.0000 0.0030
0.0000 0.0019
0.0000 0.0013
0.0000 0.0010
0.0000 0.0008
0.0000 0.0007
0.0000 0.0006
0.0000 0.0005
0.0000 0.0005
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0004
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003
0.0000 0.0003

0 1 2 3 4 5 6 7-4.5-4-3.5-3-2.5-2-1.5-1-0.500.5x 106Variatia fi1 functie de R05
fi1R05

43
fi1 R54x R54y

ans =

1.0e+006 *

fi1 R54x R54y
0 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0004 0.0002
0.0000 0.0004 0.0002
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0005 0.0003
0.0000 0.0005 0.0004
0.0000 0.0005 0.0004
0.0000 0.0005 0.0004
0.0000 0.0006 0.0004
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0007 0.0005
0.0000 0.0007 0.0005
0.0000 0.0007 0.0006
0.0000 0.0008 0.0006
0.0000 0.0008 0.0006
0.0000 0.0008 0.0007
0.0000 0.0009 0.0007 0.0000 0.0009 0.0007
0.0000 0.0009 0.0008
0.0000 0.0010 0.0008
0.0000 0.0010 0.0008
0.0000 0.0010 0.0009
0.0000 0.0011 0.0009
0.0000 0.0011 0.0009
0.0000 0.0011 0.0010
0.0000 0.0012 0.0010
0.0000 0.0012 0.0010
0.0000 0.0012 0.0011
0.0000 0.0013 0.0011
0.0000 0.0013 0.0011
0.0000 0.0013 0.0012
0.0000 0.0014 0.0012
0.0000 0.0014 0.0012
0.0000 0.0014 0.0012
0.0000 0.0014 0.0013
0.0000 0.0015 0.0013
0.0000 0.0015 0.0013
0.0000 0.0015 0.0013
0.0000 0.0015 0.0013
0.0000 0.0015 0.0013
0.0000 0.0015 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0016 0.0014
0.0000 0.0015 0.0014
0.0000 0.0015 0.0014
0.0000 0.0015 0.0013
0.0000 0.0015 0.0013
0.0000 0.0015 0.0013
0.0000 0.0015 0.0013 0.0000 0.0014 0.0013
0.0000 0.0014 0.0013
0.0000 0.0014 0.0012
0.0000 0.0014 0.0012
0.0000 0.0013 0.0012
0.0000 0.0013 0.0011
0.0000 0.0013 0.0011
0.0000 0.0012 0.0011
0.0000 0.0012 0.0011
0.0000 0.0012 0.0010
0.0000 0.0011 0.0010
0.0000 0.0011 0.0009
0.0000 0.0011 0.0009
0.0000 0.0010 0.0009
0.0000 0.0010 0.0008
0.0000 0.0009 0.0008
0.0000 0.0009 0.0008
0.0000 0.0009 0.0007
0.0000 0.0008 0.0007
0.0000 0.0008 0.0007
0.0000 0.0008 0.0006
0.0000 0.0007 0.0006
0.0000 0.0007 0.0006
0.0000 0.0007 0.0005
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0007 0.0005
0.0000 0.0007 0.0006
0.0000 0.0008 0.0007
0.0000 0.0009 0.0008
0.0000 0.0011 0.0010
0.0000 0.0013 0.0012
0.0000 0.0015 0.0014

44
0.0000 0.0013 0.0011
0.0000 -0.0001 -0.0002
0.0000 0.1361 0.1345
0.0000 -4.0869 -4.0459
0.0000 -0.1701 -0.1686
0.0000 -0.0606 -0.0602
0.0000 -0.0342 -0.0341
0.0000 -0.0235 -0.0234
0.0000 -0.0179 -0.0179
0.0000 -0.0145 -0.0145
0.0000 -0.0122 -0.0123
0.0000 -0.0107 -0.0107
0.0000 -0.0095 -0.0096
0.0000 -0.0086 -0.0087
0.0000 -0.0079 -0.0080
0.0000 -0.0073 -0.0074
0.0000 -0.0068 -0.0069
0.0000 -0.0064 -0.0065
0.0000 -0.0060 -0.0062
0.0000 -0.0057 -0.0059
0.0000 -0.0055 -0.0056
0.0000 -0.0052 -0.0054 0.0000 -0.0050 -0.0052
0.0000 -0.0049 -0.0050
0.0000 -0.0047 -0.0048
0.0000 -0.0045 -0.0047
0.0000 -0.0044 -0.0045
0.0000 -0.0043 -0.0044
0.0000 -0.0042 -0.0043
0.0000 -0.0040 -0.0042
0.0000 -0.0039 -0.0040
0.0000 -0.0037 -0.0038
0.0000 -0.0034 -0.0036
0.0000 -0.0029 -0.0031
0.0000 -0.0019 -0.0020
0.0000 -0.0000 -0.0001
0.0000 -0.1676 -0.1687
0.0000 0.2142 0.2154
0.0000 0.0170 0.0170
0.0000 0.0057 0.0056
0.0000 0.0030 0.0029
0.0000 0.0019 0.0018
0.0000 0.0014 0.0013
0.0000 0.0011 0.0010 0.0000 0.0009 0.0008
0.0000 0.0007 0.0006
0.0000 0.0006 0.0005
0.0000 0.0006 0.0005
0.0000 0.0005 0.0004
0.0000 0.0005 0.0004
0.0000 0.0005 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0003
0.0000 0.0004 0.0002
0.0000 0.0004 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002
0.0000 0.0003 0.0002

fi1 R32x R32y
ans =
1.0e+007 *
fi1 R32x R32y

0 0.3712 0.0581
0.0000 0.3708 0.0577
0.0000 0.3699 0.0573
0.0000 0.3685 0.0567
0.0000 0.3667 0.0561
0.0000 0.3643 0.0553
0.0000 0.3615 0.0544 0.0000 0.3582 0.0534
0.0000 0.3545 0.0523
0.0000 0.3503 0.0510
0.0000 0.3456 0.0497
0.0000 0.3405 0.0483
0.0000 0.3350 0.0468
0.0000 0.3290 0.0451
0.0000 0.3226 0.0434
0.0000 0.3158 0.0416 0.0000 0.3087 0.0397
0.0000 0.3011 0.0378
0.0000 0.2931 0.0357
0.0000 0.2848 0.0336
0.0000 0.2761 0.0315
0.0000 0.2671 0.0293
0.0000 0.2578 0.0270
0.0000 0.2481 0.0247
0.0000 0.2382 0.0223
0 1 2 3 4 5 6 7-4.5-4-3.5-3-2.5-2-1.5-1-0.500.5x 106Variatia fi1 functie de R54x, R54y
fi1R54x, R54y

45
0.0000 0.2279 0.0200
0.0000 0.2174 0.0176
0.0000 0.2066 0.0151
0.0000 0.1956 0.0127
0.0000 0.1844 0.0102
0.0000 0.1729 0.0077
0.0000 0.1612 0.0053
0.0000 0.1493 0.0028
0.0000 0.1373 0.0004
0.0000 0.1251 -0.0021
0.0000 0.1128 -0.0045
0.0000 0.1003 -0.0069
0.0000 0.0877 -0.0092
0.0000 0.0750 -0.0115
0.0000 0.0623 -0.0138
0.0000 0.0494 -0.0161
0.0000 0.0365 -0.0182
0.0000 0.0236 -0.0204
0.0000 0.0107 -0.0225
0.0000 -0.0023 -0.0245
0.0000 -0.0152 -0.0265
0.0000 -0.0281 -0.0284
0.0000 -0.0410 -0.0302
0.0000 -0.0538 -0.0320
0.0000 -0.0666 -0.0338
0.0000 -0.0792 -0.0354
0.0000 -0.0918 -0.0370
0.0000 -0.1043 -0.0385
0.0000 -0.1166 -0.0399
0.0000 -0.1288 -0.0413
0.0000 -0.1408 -0.0426
0.0000 -0.1527 -0.0439
0.0000 -0.1644 -0.0451
0.0000 -0.1758 -0.0462
0.0000 -0.1871 -0.0472
0.0000 -0.1981 -0.0482
0.0000 -0.2089 -0.0491
0.0000 -0.2195 -0.0500
0.0000 -0.2298 -0.0508
0.0000 -0.2398 -0.0516
0.0000 -0.2495 -0.0523
0.0000 -0.2590 -0.0529
0.0000 -0.2681 -0.0536
0.0000 -0.2769 -0.0541
0.0000 -0.2854 -0.0547
0.0000 -0.2935 -0.0552
0.0000 -0.3013 -0.0556
0.0000 -0.3088 -0.0561
0.0000 -0.3158 -0.0565
0.0000 -0.3225 -0.0569 0.0000 -0.3288 -0.0572
0.0000 -0.3347 -0.0576
0.0000 -0.3403 -0.0579
0.0000 -0.3454 -0.0583
0.0000 -0.3501 -0.0586
0.0000 -0.3544 -0.0589
0.0000 -0.3583 -0.0592
0.0000 -0.3617 -0.0595
0.0000 -0.3647 -0.0599
0.0000 -0.3673 -0.0602
0.0000 -0.3695 -0.0605
0.0000 -0.3712 -0.0609
0.0000 -0.3724 -0.0612
0.0000 -0.3733 -0.0616
0.0000 -0.3737 -0.0620
0.0000 -0.3736 -0.0624
0.0000 -0.3731 -0.0629
0.0000 -0.3722 -0.0633
0.0000 -0.3708 -0.0638
0.0000 -0.3689 -0.0644
0.0000 -0.3667 -0.0649
0.0000 -0.3640 -0.0655
0.0000 -0.3608 -0.0662
0.0000 -0.3573 -0.0669
0.0000 -0.3532 -0.0677
0.0000 -0.3488 -0.0685
0.0000 -0.3440 -0.0695
0.0000 -0.3387 -0.0705
0.0000 -0.3330 -0.0717
0.0000 -0.3269 -0.0730
0.0000 -0.3204 -0.0745
0.0000 -0.3135 -0.0763
0.0000 -0.3062 -0.0784
0.0000 -0.2984 -0.0809
0.0000 -0.2901 -0.0840
0.0000 -0.2812 -0.0880
0.0000 -0.2716 -0.0932
0.0000 -0.2608 -0.1003
0.0000 -0.2481 -0.1104
0.0000 -0.2313 -0.1252
0.0000 -0.2049 -0.1469
0.0000 -0.1558 -0.1724
0.0000 -0.0764 -0.1805
0.0000 -0.0410 -0.4249
0.0000 0.1388 -3.0267
0.0000 0.0487 -0.3362
0.0000 0.0068 -0.1274
0.0000 -0.0216 -0.0599
0.0000 -0.0394 -0.0320
0.0000 -0.0493 -0.0204 0.0000 -0.0536 -0.0165
0.0000 -0.0538 -0.0164
0.0000 -0.0511 -0.0185
0.0000 -0.0462 -0.0217
0.0000 -0.0397 -0.0256
0.0000 -0.0320 -0.0298
0.0000 -0.0234 -0.0342
0.0000 -0.0141 -0.0387
0.0000 -0.0043 -0.0432
0.0000 0.0060 -0.0478
0.0000 0.0165 -0.0525
0.0000 0.0272 -0.0572
0.0000 0.0380 -0.0619
0.0000 0.0489 -0.0668
0.0000 0.0597 -0.0718
0.0000 0.0704 -0.0770
0.0000 0.0808 -0.0825
0.0000 0.0909 -0.0883
0.0000 0.1005 -0.0946
0.0000 0.1093 -0.1016
0.0000 0.1171 -0.1093
0.0000 0.1232 -0.1181
0.0000 0.1268 -0.1282
0.0000 0.1263 -0.1396
0.0000 0.1189 -0.1521
0.0000 0.0994 -0.1634
0.0000 0.0612 -0.1695
0.0000 0.0393 -0.4817
0.0000 -0.0691 -0.4396
0.0000 0.1073 0.0288
0.0000 0.1907 0.0585
0.0000 0.2250 0.0557
0.0000 0.2445 0.0521
0.0000 0.2586 0.0499
0.0000 0.2703 0.0488
0.0000 0.2805 0.0484
0.0000 0.2898 0.0485
0.0000 0.2984 0.0489
0.0000 0.3065 0.0496
0.0000 0.3140 0.0503
0.0000 0.3210 0.0511
0.0000 0.3276 0.0520
0.0000 0.3337 0.0529
0.0000 0.3393 0.0537
0.0000 0.3445 0.0545
0.0000 0.3493 0.0553
0.0000 0.3536 0.0560
0.0000 0.3574 0.0566
0.0000 0.3608 0.0572
0.0000 0.3637 0.0576

46
0.0000 0.3662 0.0579
0.0000 0.3681 0.0582 0.0000 0.3696 0.0583
0.0000 0.3706 0.0583 0.0000 0.3712 0.0583
0.0000 0.3712 0.0581

fi1 R03x R03y

ans =

1.0e+007 *

fi1 R03x R03y

0 0.3721 0.0597
0.0000 0.3717 0.0593
0.0000 0.3708 0.0589
0.0000 0.3694 0.0583
0.0000 0.3675 0.0577
0.0000 0.3652 0.0569
0.0000 0.3624 0.0559
0.0000 0.3591 0.0549
0.0000 0.3553 0.0538
0.0000 0.3511 0.0525
0.0000 0.3464 0.0511
0.0000 0.3413 0.0497
0.0000 0.3357 0.0481
0.0000 0.3297 0.0464
0.0000 0.3233 0.0447
0.0000 0.3165 0.0428
0.0000 0.3093 0.0409
0.0000 0.3017 0.0389
0.0000 0.2937 0.0368
0.0000 0.2853 0.0346
0.0000 0.2766 0.0324 0.0000 0.2676 0.0301
0.0000 0.2582 0.0278
0.0000 0.2485 0.0254
0.0000 0.2386 0.0230
0.0000 0.2283 0.0205
0.0000 0.2177 0.0181
0.0000 0.2069 0.0156
0.0000 0.1959 0.0130
0.0000 0.1846 0.0105
0.0000 0.1731 0.0080
0.0000 0.1614 0.0054
0.0000 0.1495 0.0029
0.0000 0.1374 0.0004
0.0000 0.1252 -0.0021
0.0000 0.1129 -0.0046
0.0000 0.1004 -0.0071
0.0000 0.0878 -0.0095
0.0000 0.0751 -0.0119
0.0000 0.0623 -0.0142
0.0000 0.0495 -0.0165
0.0000 0.0366 -0.0188
0.0000 0.0236 -0.0210
0.0000 0.0107 -0.0231 0.0000 -0.0023 -0.0252
0.0000 -0.0152 -0.0273
0.0000 -0.0281 -0.0292
0.0000 -0.0410 -0.0311
0.0000 -0.0538 -0.0330
0.0000 -0.0666 -0.0347
0.0000 -0.0792 -0.0364
0.0000 -0.0918 -0.0381
0.0000 -0.1042 -0.0396
0.0000 -0.1165 -0.0411
0.0000 -0.1287 -0.0425
0.0000 -0.1407 -0.0439
0.0000 -0.1525 -0.0452
0.0000 -0.1642 -0.0464
0.0000 -0.1756 -0.0475
0.0000 -0.1869 -0.0486
0.0000 -0.1979 -0.0496
0.0000 -0.2087 -0.0506
0.0000 -0.2192 -0.0515
0.0000 -0.2294 -0.0523
0.0000 -0.2394 -0.0531
0.0000 -0.2491 -0.0538
0.0000 -0.2585 -0.0545
0 1 2 3 4 5 6 7-3.5-3-2.5-2-1.5-1-0.500.5x 107Variatia fi1 functie de R32x, R32y
fi1R32x, R32y

47
0.0000 -0.2676 -0.0551
0.0000 -0.2764 -0.0557
0.0000 -0.2848 -0.0562
0.0000 -0.2930 -0.0567
0.0000 -0.3007 -0.0572
0.0000 -0.3081 -0.0577
0.0000 -0.3152 -0.0581
0.0000 -0.3218 -0.0585
0.0000 -0.3281 -0.0589
0.0000 -0.3340 -0.0592
0.0000 -0.3395 -0.0596
0.0000 -0.3446 -0.0599
0.0000 -0.3493 -0.0602
0.0000 -0.3535 -0.0605
0.0000 -0.3574 -0.0608
0.0000 -0.3608 -0.0612
0.0000 -0.3638 -0.0615
0.0000 -0.3664 -0.0618
0.0000 -0.3685 -0.0622
0.0000 -0.3702 -0.0625
0.0000 -0.3715 -0.0629
0.0000 -0.3723 -0.0632
0.0000 -0.3727 -0.0636
0.0000 -0.3727 -0.0641
0.0000 -0.3722 -0.0645
0.0000 -0.3712 -0.0650
0.0000 -0.3698 -0.0655
0.0000 -0.3680 -0.0660
0.0000 -0.3657 -0.0666
0.0000 -0.3630 -0.0672
0.0000 -0.3599 -0.0678
0.0000 -0.3564 -0.0686
0.0000 -0.3524 -0.0693
0.0000 -0.3480 -0.0702
0.0000 -0.3431 -0.0711
0.0000 -0.3379 -0.0721
0.0000 -0.3322 -0.0733
0.0000 -0.3262 -0.0746
0.0000 -0.3197 -0.0761 0.0000 -0.3128 -0.0779
0.0000 -0.3054 -0.0800
0.0000 -0.2976 -0.0825
0.0000 -0.2893 -0.0856
0.0000 -0.2805 -0.0896
0.0000 -0.2708 -0.0948
0.0000 -0.2601 -0.1019
0.0000 -0.2473 -0.1120
0.0000 -0.2304 -0.1269
0.0000 -0.2038 -0.1485
0.0000 -0.1540 -0.1740
0.0000 -0.0727 -0.1822
0.0000 -0.0063 -0.4285
0.0000 -0.2641 -3.0478
0.0000 0.0327 -0.3406
0.0000 0.0011 -0.1302
0.0000 -0.0247 -0.0620
0.0000 -0.0415 -0.0339
0.0000 -0.0509 -0.0221
0.0000 -0.0549 -0.0180
0.0000 -0.0548 -0.0178
0.0000 -0.0520 -0.0199
0.0000 -0.0470 -0.0230
0.0000 -0.0404 -0.0269
0.0000 -0.0326 -0.0311
0.0000 -0.0240 -0.0355
0.0000 -0.0146 -0.0400
0.0000 -0.0048 -0.0446
0.0000 0.0054 -0.0492
0.0000 0.0160 -0.0538
0.0000 0.0267 -0.0585
0.0000 0.0375 -0.0633
0.0000 0.0483 -0.0682
0.0000 0.0591 -0.0732
0.0000 0.0698 -0.0785
0.0000 0.0802 -0.0840
0.0000 0.0903 -0.0898
0.0000 0.0998 -0.0962
0.0000 0.1085 -0.1032 0.0000 0.1162 -0.1110
0.0000 0.1222 -0.1198
0.0000 0.1257 -0.1298
0.0000 0.1250 -0.1413
0.0000 0.1173 -0.1538
0.0000 0.0972 -0.1651
0.0000 0.0573 -0.1712
0.0000 -0.0012 -0.4851
0.0000 -0.0478 -0.4449
0.0000 0.1089 0.0275
0.0000 0.1913 0.0582
0.0000 0.2255 0.0558
0.0000 0.2449 0.0525
0.0000 0.2590 0.0504
0.0000 0.2707 0.0494
0.0000 0.2810 0.0492
0.0000 0.2903 0.0494
0.0000 0.2990 0.0499
0.0000 0.3071 0.0506
0.0000 0.3146 0.0514
0.0000 0.3217 0.0523
0.0000 0.3283 0.0532
0.0000 0.3344 0.0541
0.0000 0.3401 0.0550
0.0000 0.3453 0.0559
0.0000 0.3501 0.0567
0.0000 0.3544 0.0574
0.0000 0.3582 0.0581
0.0000 0.3616 0.0587
0.0000 0.3646 0.0591
0.0000 0.3670 0.0595
0.0000 0.3690 0.0598
0.0000 0.3705 0.0599
0.0000 0.3715 0.0599
0.0000 0.3721 0.0599
0.0000 0.3721 0.0597

48

fi1 R01x R01y

ans =

1.0e+007 *

fi1 R01x R01y

0 -0.3934 -0.0581
0.0000 -0.3929 -0.0585
0.0000 -0.3920 -0.0589
0.0000 -0.3905 -0.0591
0.0000 -0.3886 -0.0592
0.0000 -0.3861 -0.0592
0.0000 -0.3831 -0.0591
0.0000 -0.3797 -0.0588
0.0000 -0.3757 -0.0585
0.0000 -0.3713 -0.0580
0.0000 -0.3664 -0.0574
0.0000 -0.3610 -0.0567
0.0000 -0.3552 -0.0559
0.0000 -0.3489 -0.0550
0.0000 -0.3421 -0.0540
0.0000 -0.3350 -0.0528
0.0000 -0.3274 -0.0516
0.0000 -0.3194 -0.0503
0.0000 -0.3110 -0.0489
0.0000 -0.3022 -0.0475
0.0000 -0.2931 -0.0459
0.0000 -0.2835 -0.0443
0.0000 -0.2737 -0.0426
0.0000 -0.2635 -0.0409 0.0000 -0.2530 -0.0391
0.0000 -0.2421 -0.0372
0.0000 -0.2310 -0.0353
0.0000 -0.2196 -0.0333
0.0000 -0.2080 -0.0313
0.0000 -0.1961 -0.0293
0.0000 -0.1839 -0.0272
0.0000 -0.1716 -0.0251
0.0000 -0.1590 -0.0230
0.0000 -0.1463 -0.0209
0.0000 -0.1334 -0.0188
0.0000 -0.1203 -0.0167
0.0000 -0.1071 -0.0146
0.0000 -0.0938 -0.0124
0.0000 -0.0804 -0.0103
0.0000 -0.0669 -0.0082
0.0000 -0.0533 -0.0061
0.0000 -0.0396 -0.0041
0.0000 -0.0259 -0.0020
0.0000 -0.0122 -0.0000
0.0000 0.0015 0.0020
0.0000 0.0152 0.0039
0.0000 0.0289 0.0059
0.0000 0.0425 0.0078
0.0000 0.0561 0.0096 0.0000 0.0696 0.0114
0.0000 0.0831 0.0132
0.0000 0.0964 0.0149
0.0000 0.1096 0.0166
0.0000 0.1227 0.0183
0.0000 0.1356 0.0199
0.0000 0.1484 0.0214
0.0000 0.1609 0.0229
0.0000 0.1733 0.0244
0.0000 0.1855 0.0259
0.0000 0.1974 0.0273
0.0000 0.2092 0.0286
0.0000 0.2206 0.0300
0.0000 0.2318 0.0313
0.0000 0.2427 0.0325
0.0000 0.2534 0.0338
0.0000 0.2637 0.0350
0.0000 0.2737 0.0361
0.0000 0.2834 0.0373
0.0000 0.2928 0.0384
0.0000 0.3018 0.0395
0.0000 0.3104 0.0406
0.0000 0.3187 0.0417
0.0000 0.3266 0.0428
0.0000 0.3341 0.0438
0 1 2 3 4 5 6 7-3.5-3-2.5-2-1.5-1-0.500.5x 107Variatia fi1 functie de R03x, R03y
fi1R03x, R03y

49
0.0000 0.3412 0.0449
0.0000 0.3479 0.0459
0.0000 0.3542 0.0470
0.0000 0.3601 0.0480
0.0000 0.3656 0.0490
0.0000 0.3706 0.0501
0.0000 0.3752 0.0511
0.0000 0.3793 0.0522
0.0000 0.3830 0.0533
0.0000 0.3862 0.0543
0.0000 0.3890 0.0554
0.0000 0.3913 0.0565
0.0000 0.3931 0.0577
0.0000 0.3945 0.0588
0.0000 0.3954 0.0600
0.0000 0.3958 0.0611
0.0000 0.3958 0.0623
0.0000 0.3952 0.0636
0.0000 0.3943 0.0648
0.0000 0.3928 0.0661
0.0000 0.3909 0.0674
0.0000 0.3885 0.0687
0.0000 0.3857 0.0701
0.0000 0.3824 0.0716
0.0000 0.3786 0.0730
0.0000 0.3744 0.0745
0.0000 0.3697 0.0761
0.0000 0.3646 0.0778
0.0000 0.3590 0.0795
0.0000 0.3530 0.0814
0.0000 0.3466 0.0834
0.0000 0.3397 0.0856
0.0000 0.3324 0.0881
0.0000 0.3246 0.0908
0.0000 0.3164 0.0940
0.0000 0.3077 0.0977 0.0000 0.2983 0.1023
0.0000 0.2882 0.1081
0.0000 0.2769 0.1158
0.0000 0.2637 0.1264
0.0000 0.2464 0.1417
0.0000 0.2194 0.1639
0.0000 0.1696 0.1899
0.0000 0.0894 0.1986
0.0000 0.0708 0.4295
0.0000 -0.6456 3.4589
0.0000 -0.0588 0.3725
0.0000 -0.0038 0.1531
0.0000 0.0272 0.0833
0.0000 0.0456 0.0547
0.0000 0.0556 0.0429
0.0000 0.0595 0.0388
0.0000 0.0593 0.0388
0.0000 0.0560 0.0410
0.0000 0.0505 0.0443
0.0000 0.0434 0.0482
0.0000 0.0350 0.0525
0.0000 0.0257 0.0570
0.0000 0.0157 0.0615
0.0000 0.0051 0.0661
0.0000 -0.0058 0.0707
0.0000 -0.0171 0.0753
0.0000 -0.0286 0.0800
0.0000 -0.0401 0.0847
0.0000 -0.0517 0.0894
0.0000 -0.0633 0.0943
0.0000 -0.0747 0.0994
0.0000 -0.0859 0.1047
0.0000 -0.0968 0.1104
0.0000 -0.1071 0.1165
0.0000 -0.1167 0.1232
0.0000 -0.1251 0.1307 0.0000 -0.1320 0.1392
0.0000 -0.1363 0.1490
0.0000 -0.1365 0.1601
0.0000 -0.1297 0.1721
0.0000 -0.1107 0.1830
0.0000 -0.0729 0.1885
0.0000 -0.0745 0.5170
0.0000 0.0857 0.4355
0.0000 -0.1186 -0.0130
0.0000 -0.2042 -0.0420
0.0000 -0.2394 -0.0394
0.0000 -0.2596 -0.0363
0.0000 -0.2744 -0.0346
0.0000 -0.2866 -0.0340
0.0000 -0.2974 -0.0342
0.0000 -0.3072 -0.0349
0.0000 -0.3163 -0.0359
0.0000 -0.3248 -0.0371
0.0000 -0.3327 -0.0385
0.0000 -0.3402 -0.0400
0.0000 -0.3471 -0.0416
0.0000 -0.3536 -0.0431
0.0000 -0.3595 -0.0447
0.0000 -0.3650 -0.0462
0.0000 -0.3701 -0.0477
0.0000 -0.3746 -0.0491
0.0000 -0.3787 -0.0505
0.0000 -0.3823 -0.0518
0.0000 -0.3853 -0.0530
0.0000 -0.3879 -0.0541
0.0000 -0.3900 -0.0551
0.0000 -0.3916 -0.0560
0.0000 -0.3927 -0.0568
0.0000 -0.3933 -0.0575
0.0000 -0.3934 -0.0581

0 1 2 3 4 5 6 7-1-0.500.511.522.533.5x 107Variatia fi1 functie de R01x, R01y
fi1R01x, R01y

50
fi1 Me1
ans =
1.0e+008

fi1 Me1

0 -0.0639
0.0000 -0.0794
0.0000 -0.0947
0.0000 -0.1095
0.0000 -0.1239
0.0000 -0.1378
0.0000 -0.1511
0.0000 -0.1637
0.0000 -0.1756
0.0000 -0.1868
0.0000 -0.1970
0.0000 -0.2064
0.0000 -0.2149
0.0000 -0.2224
0.0000 -0.2289
0.0000 -0.2344
0.0000 -0.2388
0.0000 -0.2422
0.0000 -0.2445
0.0000 -0.2456
0.0000 -0.2457
0.0000 -0.2447
0.0000 -0.2426
0.0000 -0.2395
0.0000 -0.2353
0.0000 -0.2301
0.0000 -0.2239
0.0000 -0.2168
0.0000 -0.2087
0.0000 -0.1998
0.0000 -0.1900
0.0000 -0.1795
0.0000 -0.1682
0.0000 -0.1562
0.0000 -0.1436
0.0000 -0.1305
0.0000 -0.1169
0.0000 -0.1028
0.0000 -0.0884
0.0000 -0.0737 0.0000 -0.0588
0.0000 -0.0437
0.0000 -0.0286
0.0000 -0.0134
0.0000 0.0017
0.0000 0.0167
0.0000 0.0315
0.0000 0.0460
0.0000 0.0603
0.0000 0.0741
0.0000 0.0874
0.0000 0.1002
0.0000 0.1125
0.0000 0.1241
0.0000 0.1350
0.0000 0.1452
0.0000 0.1545
0.0000 0.1631
0.0000 0.1708
0.0000 0.1775
0.0000 0.1833
0.0000 0.1882
0.0000 0.1920
0.0000 0.1948
0.0000 0.1966
0.0000 0.1973
0.0000 0.1970
0.0000 0.1956
0.0000 0.1931
0.0000 0.1896
0.0000 0.1851
0.0000 0.1795
0.0000 0.1729
0.0000 0.1654
0.0000 0.1569
0.0000 0.1475
0.0000 0.1372
0.0000 0.1261
0.0000 0.1141
0.0000 0.1015
0.0000 0.0882
0.0000 0.0742 0.0000 0.0597
0.0000 0.0447
0.0000 0.0292
0.0000 0.0134
0.0000 -0.0027
0.0000 -0.0190
0.0000 -0.0355
0.0000 -0.0520
0.0000 -0.0686
0.0000 -0.0850
0.0000 -0.1013
0.0000 -0.1174
0.0000 -0.1332
0.0000 -0.1486
0.0000 -0.1636
0.0000 -0.1780
0.0000 -0.1919
0.0000 -0.2051
0.0000 -0.2177
0.0000 -0.2294
0.0000 -0.2404
0.0000 -0.2506
0.0000 -0.2599
0.0000 -0.2682
0.0000 -0.2757
0.0000 -0.2823
0.0000 -0.2880
0.0000 -0.2929
0.0000 -0.2969
0.0000 -0.3003
0.0000 -0.3030
0.0000 -0.3050
0.0000 -0.3055
0.0000 -0.3006
0.0000 -0.2754
0.0000 -0.2078
0.0000 -0.3286
0.0000 -1.4138
0.0000 -0.1487
0.0000 -0.0752
0.0000 -0.0669
0.0000 -0.0702

51
0.0000 -0.0742
0.0000 -0.0760
0.0000 -0.0751
0.0000 -0.0715
0.0000 -0.0656
0.0000 -0.0576
0.0000 -0.0479
0.0000 -0.0366
0.0000 -0.0242
0.0000 -0.0107
0.0000 0.0037
0.0000 0.0188
0.0000 0.0345
0.0000 0.0505
0.0000 0.0669
0.0000 0.0834
0.0000 0.0999
0.0000 0.1163
0.0000 0.1326 0.0000 0.1485
0.0000 0.1638
0.0000 0.1784
0.0000 0.1918
0.0000 0.2034
0.0000 0.2120
0.0000 0.2147
0.0000 0.2059
0.0000 0.1777
0.0000 0.3858
0.0000 0.2051
0.0000 0.0938
0.0000 0.1422
0.0000 0.1665
0.0000 0.1775
0.0000 0.1821
0.0000 0.1830
0.0000 0.1813
0.0000 0.1776 0.0000 0.1724
0.0000 0.1657
0.0000 0.1578
0.0000 0.1488
0.0000 0.1387
0.0000 0.1277
0.0000 0.1158
0.0000 0.1032
0.0000 0.0898
0.0000 0.0758
0.0000 0.0613
0.0000 0.0464
0.0000 0.0310
0.0000 0.0154
0.0000 -0.0004
0.0000 -0.0163
0.0000 -0.0322
0.0000 -0.0481
0.0000 -0.0639

1.6 Program de calcul

Programul de calcul cinematic si dinamic s -a
intocmit un program de calcul in mediul Matlab –
Simulink. Programul se scrie cu ajutorul editorului
Matlab editor se salveaza in:

C: ̸Matlab/bin/mecanismeA1.m si ruleaza in work space.

l1=input('introduceti l1=');
l2=input('introduceti l2=');
l3=input('introduceti l3=');
ld=input('introduceti ld=');
0 1 2 3 4 5 6 7-16-14-12-10-8-6-4-2024x 107Variatia fi1 functie de Me1
fi1Me1

52
lh=input('introduceti lh=');
l0x=input('introduceti l0x=');
l0y=input('introduceti l0y=');
omega1=input('Introduceti
omega1=');
alfa=input('Introduceti alfa=');
p=input('introduceti pasul
p='); fi1=0:p:2*pi;
a2=2.*l2.*(l0y+l1.*sin(fi1));
b2=2*l2*(l1.*cos(fi1) -l0x);
c2=l0x*l0x+l0y*l0y+l1*l1+l2*l2 -l3*l3+2*l1*(l0y.*sin(fi1) -l0x.*cos(fi1));
d2=(a2 -sqrt(a2.*a2+b2.*b2 -c2.*c2))./(b2 -c2);
fi2=2*atan(d 2);

a3=-2*l3*(l0y+l1.*sin(fi1)); b3= –
2*l3*(l1.*cos(fi1) -l0x);
c3=l0x*l0x+l0y*l0y+l1*l1 -l2*l2+l3*l3+2*l1*(l0y.*sin(fi1) -l0x.*cos(fi1));
d3=(a3 -sqrt(a3.*a3+b3.*b3 -c3.*c3))./(b3 -c3);

fi3=2*ata
n(d3);
%if fi3<0,
%fi3=pi+fi3 ;

omega2=omega1.*l1.*sin(fi1 -fi3)./(l2.*sin(fi3 -fi2));
omega3=omega1.*l1.*sin(fi1 -fi2)./(l2.*sin(fi3 -fi2));

epsilon2=(l1.*omega1.*omega1.*cos(fi1 -fi3)+l2.*omega2.*omega2.*cos(fi3 –
fi2)-
…
l3.*omega3.*omega3)./(l2.*sin(fi3 -fi2));
epsilon3=(l1.*omega1.*omega1.*cos(fi1 -fi3)-
l3.*omega3.*omega3.*cos(fi3fi2)+…
l2.*omega2.*omega2)./(l3.*sin(fi3 -fi2));

s4=(lh -l1.*sin(fi1))./sin(alfa+fi2);
s5=((lh -l1.*sin(fi1))./tan(alfa+fi2))+ld+l1.*cos(fi1);

v4=-(omega2.*s4.*cos(alfa+fi2)+omega1.*l1.*cos(fi1))./sin(alfa+fi2); v5= –
omega1.*l1.*sin(fi1)+v4.*cos(alfa+fi2) -omega2.*s4.*sin(alfa+fi2);

a4=(2*v4.*omega2.*cos(alfa+fi2)+epsilo n2.*s4.*cos(alfa+fi2) -…
omega2.*omega2.*s4.*sin(alfa+fi2) –

53
omega1.*omega1.*l1.*sin(fi1))./sin(alfa+fi2); a5= –
omega1.*omega1.*l1.*cos(fi1)+a4.*cos(alfa+fi2) -…
omega2.*(2*v4.*sin(alfa+fi2) -s4.*cos(alfa+fi2)) -epsilon2.*s4.*sin(alfa+fi2);

disp(' fi1 fi2 fi3' )
[fi1',fi2
',fi3']
pause;
plot(fi1
,fi2,
fi1,fi3)
pause;
disp(' fi1 s4 s5' )
[fi1',s
4',s5']
pause;
plot(fi
1,s4,
fi1,s5
)
pause;
disp(' fi1 omega2 omega3' )
[fi1',omega2',omega3']
plot(fi1,omega2,
fi1,omega3) pause;
disp(' fi1 v4 v5' )
[fi1',v4',v5']
plot(fi1,v4,
fi1,v5)
pause;
disp(' fi1 epsilon2 epsilon3' )
[fi1',epsilon2',epsilon3']
plot(fi1,epsilon2,
fi1,epsilon3) pause;
disp(' fi1 a4 a5' )
[fi1',a4',a5']
plot(fi1,a4,
fi1,a5)

>>APLICATIA 1
introduceti l1=0.122
introduceti l2=0.250

54
introduceti l3=0.290
introduceti ld=0.112
introduceti lh=0.267
introduceti l0x=0.253
introduceti l0y=0.098
introduceti m1=1.2
introduceti m2=6.8
introduceti m3=5
introduceti m4=1
introduceti m5=7.5
introduceti J2=(m2*l2^2)/12
introduceti J3=(m3*l3^2)/12
introduceti j4=(m4*(0.02)^2)/12
introduceti g=9.81
Introduceti omega1=(pi*520)/30
Introduceti alfa=(35*pi)/180
introduceti pasul p=(3*pi)/180

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