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Tehnica mecanica

Tehnica mecanica

Qdidactic » stiinta & tehnica » tehnica mecanica
Mecanism cu bare

Mecanism cu bare

Mecanism cu bare

APLICATIA 2

Se considera schema cinematica a unui mecanism plan cu bare din componenta unei masini-unealta.

Lungimile caracteristice ale mecanismului plan cu bare sunt:

; ; ; ;

Turatia elementului conducator este

Masele barelor au valorile numerice:

1. Geometria grafica a mecanismului

Geometria grafica a mecanismului se refera la construirea schemei cinematice. La o scara a lungimilor . Cunoscand lungimile caracteristice reale in se calculeaza lungimile corespunzatoare pe desen in cu formula :

Noile valori ale lungimilor sunt date in tabelul de mai jos :

Constructia grafica incepe prin alegerea punctului ca origine a sistemului de axe cartezian . Fata de la care se masoara coordonatele punctelor fixe , si

Se construieste un cerc cu centrul in O_lsi raza

Ca pozitie initiala a articulatiei mobile A, se considera punctul de pe axa . Alegand pasul unghiular si imparte in 24 de parti cercul descris de punctul A, astfel ca

Constructia grafica a schemei cinematice implica parcurgerea urmatoarelor etape succesive :

- se uneste punctul cu si pe directia obtinuta se masoara se pozitioneaza articulatia dintre elementele 3 si 4 ;

-in punctul , , se deseneaza cate un dreptunghi, reprezentand patina glisor 2, respectiv 4, avand latura mare pe directia barei 3, reprezentand cupla de translatie dintre elementele 2 si 3, respectiv 3 si 4 ;

-se pozitioneaza punctul C pe axa y, la distanta :

si se construieste o dreapta //, ca loc geometric pentru cupla de translatie C ;

-se pozitioneaza punctul C' pe dreapta , la distanta :

CC' =174,86 mm

-in punctele se ridica verticale pana la intersectia cu , rezultand punctele de pe bara 5, a carei miscare este de translatie rectilinie ;

- pozitiile extreme ale elementului condus 5 corespund pozitiilor extreme ale barei 3, aceste pozitii se obtin ca directii tangente, duse din , la cercul descris de punctul A fata de punctul fix .

Pe aceasta plansa se pot masura , cu rigla si raportorul, deplasarile liniare si unghiulare ale elementelor cinematice.

Schema cinematica a unui lant cinematic, evidentiaza numarul si natura cuplelor cinematice, modul in care acestea se leaga intre ele, pozitia relativa a zonelor de contact ale cuplelor cinematice si forma geometrica a acestora.

2. Analiza cinematica

Analiza cinematica are drept scop determinarea pozitiilor, traiectoriilor, vitezelor si acceleratiilor liniare si unghiulare ale elementelor si diferitelor puncte ale mecanismului. Analiza se face progresiv, pornind de la pozitiile, vitezele si acceleratiile cunoscute ale elementelor conducataare.

Metodele folosite pentru analiza cinematica pot fi : grafice, grafo-analitice si analitice

Metoda grafo-analitica

Etapele de lucru specifice analizei cinematice ale mecanismelor, sunt urmatoarele :

- Desenarea mecanismului in 24 pozitii si stabilirea traiectoriei punctului studiat.

Metoda analitica

In functie de pozitia impusa a elementului conducator l, se vor deduce expresiile analitice pentru deplasarile, vitezele si acceleratiile elementelor cinematice conduse. In ordinea 2,3,4 si 5.

Ecuatiile vectoriale de inchidere ale contururilor I. II. sunt :

In care s-a folosit notatia l_h=l_o+l

Ecuatiile scalare in sistemul cartezian zy se obtin din cele vectoriale. mentinand semnele din fata fiecarui termen:

2.1. Calculul deplasarilor

Prin rezolvarea sistemelor de ecuatii scalare de mai sus partial neliniare. Se deduc formulele de calcul analitic al deplasarilor liniare si unghiulare ca parametri variabili necunoscuti :

= = arctg

sl. sin

2.2. Calculul vitezelor

Ecuatiile de viteze (liniare si unghiulare) se obtin prin derivarea in functie de timp a ecuatiilor de deplasare :

Rezulta:

2.3. Calculul acceleratiilor

Ecuatiile de acceleratii (liniare si unghiulare) se obtin prin derivarea in functie de timp a ecuatiilor de viteze :

= = -

Tabel 1

fi1 fi3 s2 s5

0 0 21.0000 0

0.0436 0.0228 20.9950 0.2969

0.0872 0.0457 20.9801 0.5936

0.1308 0.0685 20.9552 0.8900

0.1744 0.0914 20.9204 1.1861

0.2180 0.1142 20.8757 1.4815

0.2616 0.1371 20.8210 1.7763

0.3052 0.1599 20.7565 2.0702

0.3488 0.1828 20.6822 2.3631

0.3924 0.2057 20.5980 2.6548

0.4360 0.2285 20.5041 2.9453

0.4796 0.2514 20.4005 3.2344

0.5232 0.2743 20.2872 3.5220

0.5668 0.2973 20.1643 3.8078

0.6104 0.3202 20.0318 4.0918

0.6540 0.3431 19.8898 4.3739

0.6976 0.3661 19.7384 4.6539

0.7412 0.3891 19.5777 4.9316

0.7848 0.4121 19.4076 5.2070

0.8284 0.4351 19.2284 5.4799

0.8720 0.4582 19.0401 5.7501

0.9156 0.4813 18.8428 6.0176

0.9592 0.5044 18.6365 6.2822

1.0028 0.5275 18.4214 6.5438

1.0464 0.5507 18.1976 6.8023

1.0900 0.5739 17.9652 7.0574

1.1336 0.5971 17.7242 7.3092

1.1772 0.6204 17.4749 7.5574

1.2208 0.6437 17.2173 7.8020

1.2644 0.6671 16.9516 8.0429

fi1 fi3 s2 s5

1.3080 0.6905 16.6779 8.2798

1.3516 0.7140 16.3963 8.5128

1.3952 0.7375 16.1069 8.7416

1.4388 0.7611 15.8100 8.9662

1.4824 0.7848 15.5055 9.1865

1.5260 0.8085 15.1938 9.4023

1.5696 0.8323 14.8749 9.6135

1.6132 0.8562 14.5490 9.8200

1.6568 0.8803 14.2163 10.0217

1.7004 0.9044 13.8768 10.2185

1.7440 0.9286 13.5309 10.4103

1.7876 0.9530 13.1786 10.5969

1.8312 0.9775 12.8202 10.7783

1.8748 1.0022 12.4557 10.9542

1.9184 1.0270 12.0854 11.1247

1.9620 1.0520 11.7096 11.2896

2.0056 1.0773 11.3282 11.4488

2.0492 1.1028 10.9417 11.6020

2.0928 1.1285 10.5501 11.7493

2.1364 1.1546 10.1536 11.8903

2.1800 1.1810 9.7526 12.0250

2.2236 1.2079 9.3471 12.1532

2.2672 1.2351 8.9375 12.2745

2.3108 1.2629 8.5239 12.3888

2.3544 1.2914 8.1065 12.4958

2.3980 1.3205 7.6858 12.5950

2.4416 1.3505 7.2618 12.6859

2.4852 1.3815 6.8349 12.7679

2.5288 1.4138 6.4055 12.8401

2.5724 1.4476 5.9738 12.9014

2.6160 1.4832 5.5402 12.9502

2.6596 1.5212 5.1053 12.9840

2.7032 1.5622 4.6695 12.9995

2.7468 -1.5345 4.2336 -12.9914

2.7904 -1.4842 3.7984 -12.9513

2.8340 -1.4266 3.3654 -12.8650

2.8776 -1.3584 2.9363 -12.7079

2.9212 -1.2746 2.5142 -12.4338

2.9648 -1.1662 2.1046 -11.9502

3.0084 -1.0173 1.7171 -11.0593

3.0520 -0.8000 1.3720 -9.3256

3.0956 -0.4730 1.1102 -5.9218

3.1392 -0.0263 1.0003 -0.3420

3.1828 0.4290 1.0894 5.4076

3.2264 0.7702 1.3382 9.0519

3.2700 0.9975 1.6767 10.9215

3.3136 1.1522 2.0607 11.8775

3.3572 1.2641 2.4686 12.3933

3.4008 1.3501 2.8895 12.6847

3.4444 1.4197 3.3180 12.8518

3.4880 1.4783 3.7508 12.9444

3.5316 1.5292 4.1858 12.9888

3.5752 -1.5669 4.6217 -12.9999

3.6188 -1.5255 5.0575 -12.9867

3.6624 -1.4872 5.4925 -12.9546

3.7060 -1.4514 5.9263 -12.9074

3.7496 -1.4174 6.3582 -12.8474

3.7932 -1.3850 6.7879 -12.7763

3.8368 -1.3539 7.2151 -12.6953

3.8804 -1.3238 7.6394 -12.6054

3.9240 -1.2945 8.0605 -12.5071

3.9676 -1.2660 8.4782 -12.4009

4.0112 -1.2382 8.8923 -12.2874

4.0548 -1.2108 9.3023 -12.1668

4.0984 -1.1840 9.7083 -12.0394

4.1420 -1.1575 10.1098 -11.9054

4.1856 -1.1314 10.5068 -11.7650

4.2292 -1.1056 10.8989 -11.6185

4.2728 -1.0801 11.2861 -11.4659

4.3164 -1.0548 11.6680 -11.3074

4.3600 -1.0297 12.0445 -11.1431

4.4036 -1.0049 12.4153 -10.9732

4.4472 -0.9802 12.7804 -10.7978

4.4908 -0.9557 13.1396 -10.6171

4.5344 -0.9313 13.4925 -10.4310

4.5780 -0.9070 13.8392 -10.2398

4.6216 -0.8829 14.1793 -10.0436

4.6652 -0.8589 14.5128 -9.8424

4.7088 -0.8349 14.8395 -9.6364

4.7524 -0.8111 15.1592 -9.4257

4.7960 -0.7874 15.4717 -9.2104

4.8396 -0.7637 15.7769 -8.9906

4.8832 -0.7401 16.0747 -8.7665

4.9268 -0.7165 16.3649 -8.5381

4.9704 -0.6931 16.6474 -8.3056

5.0140 -0.6696 16.9220 -8.0691

5.0576 -0.6463 17.1886 -7.8287

5.1012 -0.6229 17.4470 -7.5845

5.1448 -0.5997 17.6973 -7.3366

5.1884 -0.5764 17.9391 -7.0852

5.2320 -0.5532 18.1725 -6.8304

5.2756 -0.5300 18.3973 -6.5723

5.3192 -0.5069 18.6133 -6.3111

5.3628 -0.4838 18.8205 -6.0468

5.4064 -0.4607 19.0189 -5.7796

5.4500 -0.4377 19.2082 -5.5097

5.4936 -0.4146 19.3884 -5.2371

5.5372 -0.3916 19.5595 -4.9620

5.5808 -0.3686 19.7212 -4.6845

5.6244 -0.3457 19.8737 -4.4047

5.6680 -0.3227 20.0167 -4.1229

5.7116 -0.2998 20.1502 -3.8391

5.7552 -0.2769 20.2742 -3.5534

5.7988 -0.2540 20.3885 -3.2661

5.8424 -0.2311 20.4932 -2.9771

5.8860 -0.2082 20.5882 -2.6868

5.9296 -0.1853 20.6734 -2.3951

5.9732 -0.1624 20.7488 -2.1024

6.0168 -0.1396 20.8144 -1.8086

6.0604 -0.1167 20.8701 -1.5139

6.1040 -0.0939 20.9160 -1.2185

6.1476 -0.0710 20.9519 -0.9226

6.1912 -0.0482 20.9778 -0.6262

6.2348 -0.0253 20.9939 -0.3294

6.2784 -0.0025 20.9999 -0.0326

Tabel 2

fi1 omega3 v2 v5

0 2.0833 0 -27.0835

0.0436 2.0834 -0.9083 -27.0770

0.0872 2.0835 -1.8161 -27.0576

0.1308 2.0838 -2.7231 -27.0252

0.1744 2.0841 -3.6287 -26.9799

0.2180 2.0845 -4.5326 -26.9217

0.2616 2.0850 -5.4344 -26.8506

0.3052 2.0856 -6.3336 -26.7666

0.3488 2.0863 -7.2297 -26.6698

0.3924 2.0871 -8.1223 -26.5602

0.4360 2.0880 -9.0111 -26.4379

0.4796 2.0890 -9.8956 -26.3030

0.5232 2.0901 -10.7753 -26.1554

0.5668 2.0914 -11.6499 -25.9952

0.6104 2.0927 -12.5188 -25.8226

0.6540 2.0942 -13.3818 -25.6376

0.6976 2.0958 -14.2384 -25.4402

0.7412 2.0976 -15.0881 -25.2306

fi1 omega3 v2 v5

0.7848 2.0995 -15.9306 -25.0088

0.8284 2.1016 -16.7655 -24.7749

0.8720 2.1038 -17.5923 -24.5291

0.9156 2.1063 -18.4107 -24.2714

0.9592 2.1089 -19.2203 -24.0019

1.0028 2.1117 -20.0206 -23.7207

1.0464 2.1148 -20.8112 -23.4280

1.0900 2.1180 -21.5919 -23.1238

1.1336 2.1216 -22.3622 -22.8084

1.1772 2.1254 -23.1217 -22.4816

1.2208 2.1295 -23.8701 -22.1438

1.2644 2.1340 -24.6069 -21.7950

1.3080 2.1388 -25.3319 -21.4353

1.3516 2.1440 -26.0446 -21.0649

1.3952 2.1496 -26.7447 -20.6838

1.4388 2.1557 -27.4319 -20.2921

1.4824 2.1624 -28.1057 -19.8899

1.5260 2.1696 -28.7659 -19.4773

1.5696 2.1774 -29.4121 -19.0545

1.6132 2.1859 -30.0439 -18.6213

1.6568 2.1953 -30.6611 -18.1779

1.7004 2.2055 -31.2631 -17.7242

1.7440 2.2167 -31.8498 -17.2602

1.7876 2.2291 -32.4208 -16.7859

1.8312 2.2427 -32.9757 -16.3011

1.8748 2.2578 -33.5141 -15.8055

1.9184 2.2746 -34.0357 -15.2990

1.9620 2.2932 -34.5402 -14.7810

2.0056 2.3141 -35.0270 -14.2510

2.0492 2.3375 -35.4959 -13.7083

2.0928 2.3639 -35.9464 -13.1518

2.1364 2.3937 -36.3780 -12.5803

2.1800 2.4277 -36.7901 -11.9919

2.2236 2.4666 -37.1821 -11.3842

2.2672 2.5115 -37.5534 -10.7543

2.3108 2.5634 -37.9032 -10.0977

2.3544 2.6241 -38.2304 -9.4086

2.3980 2.6956 -38.5338 -8.6792

2.4416 2.7806 -38.8120 -7.8982

2.4852 2.8826 -39.0629 -7.0497

2.5288 3.0065 -39.2839 -6.1109

2.5724 3.1589 -39.4714 -5.0478

2.6160 3.3492 -39.6205 -3.8092

2.6596 3.5909 -39.7241 -2.3152

2.7032 3.9039 -39.7715 -0.4371

2.7468 -4.3187 39.7467 2.0401

2.7904 -4.8831 39.6239 5.4915

2.8340 -5.6760 39.3600 10.6058

2.8776 -6.8324 38.8794 18.7220

2.9212 -8.5950 38.0407 32.6164

2.9648 -11.4174 36.5611 58.4338

3.0084 -16.1521 33.8355 110.3699

3.0520 -24.1744 28.5312 218.9535

3.0956 -35.8684 18.1175 415.1018

3.1392 -43.7240 1.0465 568.2155

3.1828 -37.1783 -16.5444 439.5189

3.2264 -25.3104 -27.6940 236.1647

3.2700 -16.8439 -33.4140 118.7710

3.3136 -11.8230 -36.3386 62.4786

3.3572 -8.8419 -37.9169 34.7043

3.4008 -6.9904 -38.8084 19.8928

3.4444 -5.7820 -39.3197 11.3163

3.4880 -4.9571 -39.6028 5.9547

3.5316 -4.3722 -39.7386 2.3623

3.5752 3.9438 39.7727 -0.1995

3.6188 3.6214 39.7322 -2.1308

3.6624 3.3729 39.6342 -3.6596

3.7060 3.1777 39.4897 -4.9216

3.7496 3.0217 39.3061 -6.0010

3.7932 2.8950 39.0886 -6.9516

3.8368 2.7909 38.8409 -7.8087

3.8804 2.7042 38.5656 -8.5962

3.9240 2.6314 38.2649 -9.3307

3.9676 2.5696 37.9402 -10.0238

4.0112 2.5168 37.5929 -10.6836

4.0548 2.4713 37.2239 -11.3163

4.0984 2.4317 36.8341 -11.9262

4.1420 2.3972 36.4241 -12.5165

4.1856 2.3670 35.9947 -13.0898

4.2292 2.3402 35.5463 -13.6479

4.2728 2.3165 35.0794 -14.1921

4.3164 2.2954 34.5945 -14.7234

4.3600 2.2765 34.0919 -15.2427

4.4036 2.2596 33.5722 -15.7505

4.4472 2.2443 33.0356 -16.2472

4.4908 2.2305 32.4825 -16.7332

4.5344 2.2180 31.9133 -17.2087

4.5780 2.2067 31.3283 -17.6738

4.6216 2.1964 30.7279 -18.1286

4.6652 2.1869 30.1124 -18.5731

4.7088 2.1783 29.4822 -19.0074

4.7524 2.1704 28.8375 -19.4314

4.7960 2.1631 28.1789 -19.8451

4.8396 2.1564 27.5065 -20.2484

4.8832 2.1503 26.8208 -20.6413

4.9268 2.1446 26.1221 -21.0236

4.9704 2.1393 25.4107 -21.3952

5.0140 2.1345 24.6871 -21.7561

5.0576 2.1300 23.9515 -22.1061

5.1012 2.1258 23.2044 -22.4451

5.1448 2.1220 22.4461 -22.7730

5.1884 2.1184 21.6770 -23.0898

5.2320 2.1151 20.8974 -23.3952

5.2756 2.1120 20.1078 -23.6892

5.3192 2.1092 19.3085 -23.9716

5.3628 2.1065 18.5000 -24.2424

5.4064 2.1041 17.6826 -24.5014

5.4500 2.1018 16.8567 -24.7485

5.4936 2.0997 16.0227 -24.9837

5.5372 2.0978 15.1810 -25.2068

5.5808 2.0960 14.3320 -25.4178

5.6244 2.0944 13.4762 -25.6165

Referat: Clasificarea constructiilor

Referat: PROIECT ATESTAT Constructii-lucrari publice - instalatii de incalzire

5.6680 2.0929 12.6139 -25.8029

5.7116 2.0915 11.7455 -25.9769

5.7552 2.0902 10.8715 -26.1384

5.7988 2.0891 9.9924 -26.2874

5.8424 2.0881 9.1084 -26.4238

5.8860 2.0872 8.2201 -26.5474

5.9296 2.0864 7.3278 -26.6584

5.9732 2.0857 6.4321 -26.7566

6.0168 2.0850 5.5332 -26.8420

6.0604 2.0845 4.6317 -26.9145

6.1040 2.0841 3.7280 -26.9741

6.1476 2.0838 2.8225 -27.0209

6.1912 2.0835 1.9157 -27.0547

6.2348 2.0834 1.0079 -27.0755

6.2784 2.0833 0.0997 -27.0834

Tabel 3

fi1 epsilon3 a2 a5

0 0 -0.0083 0

0.0000 0.0000 -0.0083 -0.0001

0.0000 0.0000 -0.0083 -0.0002

0.0000 0.0000 -0.0083 -0.0004

0.0000 0.0000 -0.0083 -0.0005

fi1 epsilon3 a2 a5

0.0000 0.0000 -0.0082 -0.0006

0.0000 0.0000 -0.0082 -0.0007

0.0000 0.0000 -0.0082 -0.0008

0.0000 0.0000 -0.0082 -0.0009

0.0000 0.0000 -0.0081 -0.0011

0.0000 0.0000 -0.0081 -0.0012

0.0000 0.0000 -0.0080 -0.0013

0.0001 0.0000 -0.0080 -0.0014

0.0001 0.0000 -0.0080 -0.0015

0.0001 0.0000 -0.0079 -0.0016

0.0001 0.0000 -0.0078 -0.0017

0.0001 0.0000 -0.0078 -0.0019

0.0001 0.0000 -0.0077 -0.0020

0.0001 0.0000 -0.0077 -0.0021

0.0001 0.0000 -0.0076 -0.0022

0.0001 0.0000 -0.0075 -0.0023

0.0001 0.0000 -0.0074 -0.0024

0.0001 0.0000 -0.0073 -0.0025

0.0001 0.0000 -0.0073 -0.0026

0.0001 0.0000 -0.0072 -0.0027

0.0001 0.0000 -0.0071 -0.0028

0.0001 0.0000 -0.0070 -0.0029

0.0001 0.0000 -0.0069 -0.0030

0.0001 0.0000 -0.0068 -0.0031

0.0001 0.0000 -0.0067 -0.0032

0.0001 0.0000 -0.0066 -0.0033

0.0001 0.0000 -0.0064 -0.0034

0.0001 0.0001 -0.0063 -0.0035

0.0001 0.0001 -0.0062 -0.0036

0.0001 0.0001 -0.0061 -0.0037

0.0002 0.0001 -0.0060 -0.0038

0.0002 0.0001 -0.0058 -0.0039

0.0002 0.0001 -0.0057 -0.0040

0.0002 0.0001 -0.0056 -0.0041

0.0002 0.0001 -0.0054 -0.0042

0.0002 0.0001 -0.0053 -0.0043

0.0002 0.0001 -0.0051 -0.0044

0.0002 0.0001 -0.0050 -0.0045

0.0002 0.0001 -0.0048 -0.0046

0.0002 0.0002 -0.0047 -0.0047

0.0002 0.0002 -0.0045 -0.0048

0.0002 0.0002 -0.0044 -0.0049

0.0002 0.0002 -0.0042 -0.0050

0.0002 0.0003 -0.0040 -0.0051

0.0002 0.0003 -0.0038 -0.0053

0.0002 0.0003 -0.0037 -0.0055

0.0002 0.0004 -0.0035 -0.0056

0.0002 0.0004 -0.0033 -0.0059

0.0002 0.0005 -0.0031 -0.0061

0.0002 0.0006 -0.0029 -0.0065

0.0002 0.0007 -0.0027 -0.0069

0.0002 0.0008 -0.0024 -0.0074

0.0002 0.0010 -0.0022 -0.0081

0.0003 0.0012 -0.0019 -0.0091

0.0003 0.0015 -0.0015 -0.0104

0.0003 0.0019 -0.0012 -0.0123

0.0003 0.0025 -0.0007 -0.0151

0.0003 0.0033 -0.0001 -0.0194

0.0003 0.0118 0.0152 0.0298

0.0003 0.0143 0.0164 0.0470

0.0003 0.0179 0.0184 0.0749

0.0003 0.0234 0.0217 0.1233

0.0003 0.0320 0.0272 0.2134

0.0003 0.0466 0.0370 0.3942

0.0003 0.0715 0.0558 0.7770

0.0003 0.1088 0.0934 1.5306

0.0003 0.1236 0.1587 2.1917

0.0003 0.0096 0.2086 0.1897

0.0003 -0.1190 0.1667 -2.1539

0.0003 -0.1130 0.0992 -1.6342

0.0003 -0.0751 0.0588 -0.8391

0.0003 -0.0487 0.0385 -0.4234

0.0003 -0.0333 0.0280 -0.2275

0.0003 -0.0241 0.0222 -0.1306

0.0003 -0.0184 0.0187 -0.0790

0.0003 -0.0147 0.0166 -0.0494

0.0004 -0.0121 0.0153 -0.0314

0.0004 -0.0034 -0.0001 0.0200

0.0004 -0.0026 -0.0007 0.0155

0.0004 -0.0020 -0.0011 0.0126

0.0004 -0.0016 -0.0015 0.0106

0.0004 -0.0013 -0.0018 0.0092

0.0004 -0.0010 -0.0021 0.0082

0.0004 -0.0009 -0.0024 0.0075

0.0004 -0.0007 -0.0026 0.0069

0.0004 -0.0006 -0.0029 0.0065

0.0004 -0.0005 -0.0031 0.0062

0.0004 -0.0004 -0.0033 0.0059

0.0004 -0.0004 -0.0035 0.0057

0.0004 -0.0003 -0.0036 0.0055

0.0004 -0.0003 -0.0038 0.0053

0.0004 -0.0003 -0.0040 0.0052

0.0004 -0.0002 -0.0042 0.0050

0.0004 -0.0002 -0.0043 0.0049

0.0004 -0.0002 -0.0045 0.0048

0.0004 -0.0002 -0.0047 0.0047

0.0004 -0.0001 -0.0048 0.0046

0.0004 -0.0001 -0.0050 0.0045

0.0004 -0.0001 -0.0051 0.0044

0.0005 -0.0001 -0.0053 0.0043

0.0005 -0.0001 -0.0054 0.0042

0.0005 -0.0001 -0.0055 0.0041

0.0005 -0.0001 -0.0057 0.0040

0.0005 -0.0001 -0.0058 0.0039

0.0005 -0.0001 -0.0059 0.0038

0.0005 -0.0001 -0.0061 0.0037

0.0005 -0.0001 -0.0062 0.0036

0.0005 -0.0001 -0.0063 0.0035

0.0005 -0.0000 -0.0064 0.0034

0.0005 -0.0000 -0.0065 0.0033

0.0005 -0.0000 -0.0067 0.0032

0.0005 -0.0000 -0.0068 0.0031

0.0005 -0.0000 -0.0069 0.0030

0.0005 -0.0000 -0.0070 0.0029

0.0005 -0.0000 -0.0071 0.0028

0.0005 -0.0000 -0.0072 0.0027

0.0005 -0.0000 -0.0072 0.0026

0.0005 -0.0000 -0.0073 0.0025

0.0005 -0.0000 -0.0074 0.0024

0.0005 -0.0000 -0.0075 0.0023

0.0005 -0.0000 -0.0076 0.0022

0.0005 -0.0000 -0.0076 0.0021

0.0006 -0.0000 -0.0077 0.0020

0.0006 -0.0000 -0.0078 0.0019

0.0006 -0.0000 -0.0078 0.0018

0.0006 -0.0000 -0.0079 0.0016

0.0006 -0.0000 -0.0079 0.0015

0.0006 -0.0000 -0.0080 0.0014

0.0006 -0.0000 -0.0080 0.0013

0.0006 -0.0000 -0.0081 0.0012

0.0006 -0.0000 -0.0081 0.0011

0.0006 -0.0000 -0.0082 0.0010

0.0006 -0.0000 -0.0082 0.0008

0.0006 -0.0000 -0.0082 0.0007

0.0006 -0.0000 -0.0082 0.0006

0.0006 -0.0000 -0.0083 0.0005

0.0006 -0.0000 -0.0083 0.0004

0.0006 -0.0000 -0.0083 0.0002

0.0006 -0.0000 -0.0083 0.0001

0.0006 -0.0000 -0.0083 0.0000

2.4. Program de calcul

Pentru calculul cinematic si dinamic s-a intocmit un program de calcul in mediul Matlab-Simulink.

l0=input ('Introduceti l

l1=input ('Introduceti l1=');

l3=input ('Introduceti l3=');

lh=input ('Introduceti lh=');

m1=input ('Introduceti m1=');

m2=input ('Introduceti m2=');

m3=input ('Introduceti m3=');

m4=input ('Introduceti m4=');

m5=input ('Introduceti m5=');

g=input ('Introduceti g=');

Jg1=input ('Introduceti Jg1=');

Jg3=input ('Introduceti Jg3=');

Fr=input ('Introduceti Fr=');

omega1=input ('introduceti omega1=');

p=input ('Introduceti pasul p=');

fi1=0:p:2*pi;

fi3=atan ((11.*sin(fi1))./(10+11.*cos(fi1)));

s2=sqrt(10.*10+11.*11+2.*10.*11.*cos(fi1));

s5=13.*sin(fi3);

v2=-11.*omega1.*sin(fi1-fi3);

omega3=(11.*omega1.*cos(fi1-fi3))./s2;

v5=-13.*omega3.*cos(fi3);

a2=-11.*omega1.*omega1.*cos(fi1-fi3)+s2.*omega3.*omega3;

epsilon3=-(11.*omega1.*omega1.*sin(fi1-fi3)+2.*v2.*omega3)./s2;

a5=-13.*omega3.*omega3.*sin(fi3)+13.*epsilon3.*cos(fi3);

disp(' fi1 fi3 s2 s5' )

[fi1',fi3',s2',s5']

pause;

plot(fi1,fi3,fi1,s2,fi1,s5)

pause;

disp(' fi1 omega3 v2 v5' )

[fi1',omega3',v2',v5']

pause;

plot(fi1,omega3,fi1,v2,fi1,v5)

pause;

disp(' fi1 epsilon3 a2 a5' )

[fi1',epsilon3',a2',a5']

pause;

plot(fi1,epsilon3,fi1,a2,fi1,a5)

pause;

ag1x=-0.5.*l1.*omega1.*omega1.*sin(fi1);

ag1y=-0.5.*l1.*omega1.*omega1.*cos(fi1);

ag2x=-l1.*omega1.*omega1.*sin(fi1);

ag2y=-l1.*omega1.*omega1.*cos(fi1);

ag3x=-0.5.*l3.*(omega3.*omega3.*sin(fi3)-epsilon3.*cos(fi3));

ag3y=-0.5.*l3.*(omega3.*omega3.*cos(fi3)-epsilon3.*sin(fi3));

ag4x=2.*ag3x;

ag4y=2.*ag3y;

ag5x=a5;

Fi1x=-m1.*ag1x;

Fi1y=-m1.*ag1y;

Fi2x=-m2.*ag2x;

Fi2y=-m2.*ag2y;

Fi3x=-m3.*ag3x;

Fi3y=-m3.*ag3y;

Fi4x=-m4.*ag4x;

Fi4y=-m4.*ag4y;

Fi5x=-m5.*ag5x;

Mi3=-Jg3.*epsilon3;

G1=m1.*g;

G2=m2.*g;

G3=m3.*g;

G4=m4.*g;

G5=m5.*g;

R54=-Fi5x+Fr;

R05=G5;

R34x=-R54-Fi4x;

R34y=-Fi4y+G4;

R32=(R34x.*l3.*cos(fi3)+R34y.*l3.*sin(fi3)+0.5.*Fi3x.*l3.*cos(fi3)+0.5.*(Fi3y-G3).*l3.*sin(fi3)-Mi3)./s2;

R12x=-R32.*cos(fi3)-Fi2x;

R12y=-R32.*sin(fi3)-Fi2y+G2;

R03x=-Fi3x+R34x+R32.*cos(fi3);

R03y=R34y-Fi3y+G3+R32.*sin(fi3);

R01x=R12x-Fi1x;

R01y=R12y-Fi1y-G1;

Me1=l1.*R12x.*cos(fi1)+l1.*R12y.*sin(fi1)-0.5.*l1*G1.*sin(fi1);

disp(' fi1 R54' )

[fi1',R54']

pause;

plot(fi1,R54)

pause;

disp(' fi1 R34x R34y')

[fi1',R34x',R34y']

pause;

plot(fi1,R34x,fi1,R34y)

pause;

disp(' fi1 R32')

[fi1',R32']

pause;

disp(' fi1 R03x R03y' )

[fi1',R03x',R03y']

pause;

plot(fi1,R03x,fi1,R03y)

pause;

disp(' fi1 R12x R12y' )

[fi1',R12x',R12y']

pause;

plot(fi1,R12x,fi1,R12y)

pause;

disp(' fi1 R01x R01y')

[fi1',R01x',R01y']

pause;

plot(fi1,R01x,fi1,R01y)

pause;

disp(' fi1 Me1')

[fi1',Me1']

pause;

plot(fi1,Me1)

pause;

3. Calculul fortelor si momentelor de inertie

Se aleg maesle pentru fiecare element:

Se calculeaza fortele de greutate:

Metoda analitica

Calculul acceleratiilor centrelor de masa

-Elementul 1 are centrul de masa in punctul la distanta . Componentele axiale sunt:

-Elementul 2 are centrul de masa in punctul la distanta . Componentele axiale sunt:

-Elementul 3 are centrul de masa in punctul la distanta . Componentele axiale sunt:

-Elementul 4 are centrul de masa in punctul la distanta . Componentele axiale sunt:

-Elementul 5 are centrul de masa in punctul la distanta Componentele axiale sunt:

3. Calculul fortelor si cuplurilor de inertie

Torsorul fortei de inertie al elementului cinematic j, cu miscare plana, are trei componente:

Aceste componente se calculeaza pentru fiecare bara, a carui masa se considera concentrata in centrul de masa :

Pentru manivela 1 :

Pentru patina 2 :

Pentru balansierul 3 :

Pentru biela 4 :

Pentru glisiera translanta 5 (sanie portcutit):

Calculul reactiunilor in cuplele cinematice

Cinetostatica mecanismului cu bare urmareste : calculul reactiunilor din cuplele cinematice fara frecare, calculul fortelor si cuplurilor de frecare din cuplele cinematice si calculul momentului motor ca moment de echilibru dinamic. Se cunosc fortele de greutate, forta de rezistenta tehnologica, precum si fortele/ cuplurile de inertie.

4.Metoda analitica

4.1. Calculul reactiunilor din cuplele cinematice

Formula structural-topologica a mecanismului este MM=MF(0,1)+LD(2,3)+LD(4,5)

Deoarece forta de rezistenta tehnologica F_maxactioneaza pe elementul cinematic condus 5, iar LD este static determinat, calculul cinetostatic se efectueaza in ordinea inversa celui cinematic.

Cinetostatica LD (4,5)

Se considera schema cinematica a LD(4,5) ca structura izolata, aflata in echuilibru cinetostatic, incarcata cu toate fortele exterioare (greutate, forta de reyistenta tehnologica, fortele / cuplurile de inertie ) si cu reactiunile din cuple.

Se scriu ecuatiile de echilibru cinetostatic (doua de proiectii si una de momente) pentru fiecare din cele doua elemente 4 si 5 :

Cinetostatica LD(2,3)

Prin izolarea lantului cinematic diadic format din elementele 2 si 3 se introduc in punctul B componentele reactiunii calculate anterior, iar in punctele A si (reprezentind cuplele potentiale) se introduc componentele reactiunilor dinspre elementele 1 respectiv 0.

Reactiunea din cupla interioara (translanta) s-a introdus in punctul A prin forta perpendicular ape ghidajul comun si momentul

Ecuatiile de echilibru cinetostatic pentru fiecare din cele doua elemente cinematice 2 si 3 sunt doua de proectii si una de momente:

Sistemul format de cele 6 ecuatii liniare se rezolva prin decuplarea unor ecuatii si prin metoda substitutiei.

4.2. Cinetostatica manivelei l

Se izoleaza manivela l si se introduc componentele reactiunii necunoscute din articulatia , ale reactiunii

cunoscute din articulatia A, precum si cuplul necunoscut de echilibru cinetostatic, ce actioneaza asupra elementului conducator.

Ecuatiile de echilibru cinetostatic al barei l sunt:

Tabel 4

fi1 R54

0 0.0022

0.0000 0.0022

0.0000 0.0021

0.0000 0.0020

0.0000 0.0019

0.0000 0.0018

0.0000 0.0017

0.0000 0.0016

0.0000 0.0015

0.0000 0.0014

0.0000 0.0013

0.0000 0.0012

0.0000 0.0011

0.0000 0.0010

0.0000 0.0009

0.0000 0.0008

0.0000 0.0007

0.0000 0.0006

0.0000 0.0005

0.0000 0.0004

0.0000 0.0003

0.0000 0.0002

0.0000 0.0001

0.0000 0.0000

0.0000 -0.0000

0.0000 -0.0001

0.0000 -0.0002

0.0000 -0.0003

0.0000 -0.0004

0.0000 -0.0005

0.0000 -0.0006

0.0000 -0.0007

0.0000 -0.0008

0.0000 -0.0009

0.0000 -0.0010

0.0000 -0.0011

0.0000 -0.0013

0.0000 -0.0015

0.0000 -0.0018

0.0000 -0.0022

0.0000 -0.0027

0.0000 -0.0035

0.0000 -0.0045

0.0000 -0.0061

0.0000 -0.0085

0.0000 0.0186

0.0000 0.0281

0.0000 0.0435

0.0000 0.0701

0.0000 0.1196

0.0000 0.2190

0.0000 0.4296

0.0000 0.8440

0.0000 1.2077

0.0000 0.1066

0.0000 -1.1824

0.0000 -0.8966

0.0000 -0.4593

0.0000 -0.2307

0.0000 -0.1229

0.0000 -0.0696

0.0000 -0.0412

0.0000 -0.0249

0.0000 -0.0150

0.0000 0.0133

0.0000 0.0108

0.0000 0.0092

0.0000 0.0081

0.0000 0.0073

0.0000 0.0068

0.0000 0.0063

0.0000 0.0060

0.0000 0.0058

0.0000 0.0056

0.0000 0.0055

0.0000 0.0054

0.0000 0.0052

0.0000 0.0051

0.0000 0.0050

0.0000 0.0049

0.0000 0.0048

0.0000 0.0047

0.0000 0.0046

0.0000 0.0045

0.0000 0.0044

0.0000 0.0043

0.0000 0.0042

0.0000 0.0041

0.0001 0.0040

0.0001 0.0039

0.0001 0.0038

0.0001 0.0037

0.0001 0.0036

0.0001 0.0035

0.0001 0.0034

0.0001 0.0033

0.0001 0.0032

0.0001 0.0031

0.0001 0.0030

0.0001 0.0029

0.0001 0.0028

0.0001 0.0027

0.0001 0.0026

0.0001 0.0025

0.0001 0.0024

0.0001 0.0023

0.0001 0.0022

Tabel 5

fi1 R34x R34y

0 -0.0022 0.0001

0.0000 -0.0022 0.0001

0.0000 -0.0021 0.0001

0.0000 -0.0020 0.0001

0.0000 -0.0019 0.0001

0.0000 -0.0018 0.0001

0.0000 -0.0017 0.0001

0.0000 -0.0016 0.0001

0.0000 -0.0015 0.0001

0.0000 -0.0014 0.0001

0.0000 -0.0013 0.0001

0.0000 -0.0012 0.0001

0.0000 -0.0011 0.0001

0.0000 -0.0010 0.0001

0.0000 -0.0009 0.0001

0.0000 -0.0008 0.0001

0.0000 -0.0007 0.0001

0.0000 -0.0006 0.0001

0.0000 -0.0005 0.0001

0.0000 -0.0004 0.0001

0.0000 -0.0003 0.0001

0.0000 -0.0002 0.0001

0.0000 -0.0001 0.0001

0.0000 -0.0000 0.0001

0.0000 0.0000 0.0001

0.0000 0.0001 0.0001

0.0000 0.0002 0.0001

0.0000 0.0003 0.0001

0.0000 0.0004 0.0001

0.0000 0.0005 0.0001

0.0000 0.0006 0.0001

0.0000 0.0007 0.0001

0.0000 0.0008 0.0001

0.0000 0.0010 0.0001

0.0000 0.0011 0.0001

0.0000 0.0013 0.0001

0.0000 0.0015 0.0001

0.0000 0.0018 0.0001

0.0000 0.0022 0.0001

0.0000 0.0027 0.0001

0.0000 0.0035 0.0001

0.0000 0.0045 0.0001

0.0000 0.0061 0.0001

0.0000 0.0084 0.0002

0.0000 -0.0186 -0.0002

0.0000 -0.0280 -0.0003

0.0000 -0.0433 -0.0004

0.0000 -0.0698 -0.0006

0.0000 -0.1192 -0.0008

0.0000 -0.2182 -0.0012

0.0000 -0.4280 -0.0019

0.0000 -0.8408 -0.0032

0.0000 -1.2031 -0.0046

0.0000 -0.1062 -0.0051

0.0000 1.1779 -0.0047

0.0000 0.8931 -0.0033

0.0000 0.4575 -0.0021

0.0000 0.2298 -0.0013

0.0000 0.1224 -0.0008

0.0000 0.0693 -0.0006

0.0000 0.0411 -0.0004

0.0000 0.0248 -0.0003

0.0000 0.0149 -0.0003

0.0000 -0.0132 0.0002

0.0000 -0.0107 0.0001

0.0000 -0.0091 0.0001

0.0000 -0.0080 0.0001

0.0000 -0.0073 0.0001

0.0000 -0.0067 0.0001

0.0000 -0.0063 0.0001

0.0000 -0.0060 0.0001

0.0000 -0.0058 0.0001

0.0000 -0.0056 0.0001

0.0000 -0.0055 0.0001

0.0000 -0.0053 0.0001

0.0000 -0.0052 0.0001

0.0000 -0.0051 0.0001

0.0000 -0.0050 0.0001

0.0000 -0.0049 0.0001

0.0000 -0.0048 0.0001

0.0000 -0.0047 0.0001

0.0000 -0.0046 0.0001

0.0000 -0.0045 0.0001

0.0000 -0.0044 0.0001

0.0000 -0.0043 0.0001

0.0000 -0.0042 0.0001

0.0000 -0.0041 0.0001

0.0001 -0.0040 0.0001

0.0001 -0.0039 0.0001

0.0001 -0.0038 0.0001

0.0001 -0.0037 0.0001

0.0001 -0.0036 0.0001

0.0001 -0.0035 0.0001

0.0001 -0.0034 0.0001

0.0001 -0.0033 0.0001

0.0001 -0.0032 0.0001

0.0001 -0.0031 0.0001

0.0001 -0.0030 0.0001

0.0001 -0.0029 0.0001

0.0001 -0.0028 0.0001

0.0001 -0.0027 0.0001

0.0001 -0.0026 0.0001

0.0001 -0.0025 0.0001

0.0001 -0.0024 0.0001

0.0001 -0.0023 0.0001

0.0001 -0.0022 0.0001

Tabel 6

fi1 R32

0 -0.0004

0.0000 -0.0004

0.0000 -0.0003

0.0001 -0.0002

0.0001 -0.0001

0.0002 -0.0001

0.0002 -0.0000

0.0002 0.0000

0.0002 0.0001

0.0003 0.0001

0.0003 0.0000

0.0003 -0.0001

0.0003 -0.0004

0.0003 -0.0021

0.0003 -0.0062

0.0003 -0.0171

0.0003 -0.0474

0.0003 -0.1399

0.0003 -0.4488

0.0003 -1.4622

0.0003 -3.3023

0.0003 -0.3631

0.0003 3.3658

0.0003 1.6405

0.0003 0.5071

0.0003 0.1553

0.0003 0.0513

0.0003 0.0179

0.0003 0.0063

0.0003 0.0020

0.0004 0.0004

0.0004 0.0001

0.0004 -0.0002

0.0004 -0.0003

0.0004 -0.0004

0.0004 -0.0005

0.0004 -0.0006

0.0004 -0.0007

0.0005 -0.0007

0.0005 -0.0006

0.0005 -0.0005

0.0006 -0.0005

0.0006 -0.0004

Tabel 7

fi1 R03x R03y

0 -0.0023 0.0006

0.0000 -0.0022 0.0006

0.0000 -0.0021 0.0006

0.0000 -0.0020 0.0006

0.0000 -0.0019 0.0006

0.0000 -0.0018 0.0006

0.0000 -0.0017 0.0006

0.0000 -0.0016 0.0006

0.0000 -0.0015 0.0006

0.0000 -0.0014 0.0006

0.0000 -0.0013 0.0006

0.0000 -0.0012 0.0006

0.0000 -0.0011 0.0006

0.0000 -0.0010 0.0006

0.0000 -0.0009 0.0006

0.0000 -0.0008 0.0006

0.0000 -0.0007 0.0006

0.0000 -0.0006 0.0006

0.0000 -0.0005 0.0006

0.0000 -0.0004 0.0006

0.0000 -0.0003 0.0006

0.0000 -0.0002 0.0006

0.0000 -0.0001 0.0006

0.0000 -0.0000 0.0006

0.0000 0.0000 0.0006

0.0000 0.0001 0.0006

0.0000 0.0002 0.0006

0.0000 0.0003 0.0007

0.0000 0.0004 0.0007

0.0000 0.0005 0.0007

0.0000 0.0006 0.0007

0.0000 0.0007 0.0007

0.0000 0.0008 0.0007

0.0000 0.0009 0.0007

0.0000 0.0011 0.0007

0.0000 0.0012 0.0007

0.0000 0.0015 0.0007

0.0000 0.0018 0.0008

0.0000 0.0021 0.0008

0.0000 0.0027 0.0008

0.0000 0.0034 0.0009

0.0000 0.0044 0.0009

0.0000 0.0059 0.0010

0.0000 0.0083 0.0011

0.0000 -0.0183 -0.0008

0.0000 -0.0276 -0.0010

0.0000 -0.0428 -0.0011

0.0000 -0.0692 -0.0007

0.0000 -0.1189 0.0010

0.0000 -0.2206 0.0073

0.0000 -0.4455 0.0292

0.0000 -0.9307 0.0902

0.0000 -1.4799 0.1290

0.0000 -0.1410 -0.0231

0.0000 1.4671 0.1180

0.0000 0.9981 0.0988

0.0000 0.4785 0.0331

0.0000 0.2328 0.0084

0.0000 0.1222 0.0012

0.0000 0.0687 -0.0008

0.0000 0.0405 -0.0011

0.0000 0.0245 -0.0011

0.0000 0.0147 -0.0009

0.0000 -0.0131 0.0011

0.0000 -0.0106 0.0010

0.0000 -0.0090 0.0009

0.0000 -0.0080 0.0009

0.0000 -0.0072 0.0009

0.0000 -0.0067 0.0008

0.0000 -0.0063 0.0008

0.0000 -0.0060 0.0008

0.0000 -0.0058 0.0008

0.0000 -0.0056 0.0008

0.0000 -0.0054 0.0008

0.0000 -0.0053 0.0007

0.0000 -0.0052 0.0007

0.0000 -0.0051 0.0007

0.0000 -0.0050 0.0007

0.0000 -0.0049 0.0007

0.0000 -0.0048 0.0007

0.0000 -0.0047 0.0007

0.0000 -0.0046 0.0007

0.0000 -0.0045 0.0007

0.0000 -0.0044 0.0007

0.0000 -0.0043 0.0007

0.0000 -0.0042 0.0007

0.0000 -0.0041 0.0007

0.0001 -0.0040 0.0007

0.0001 -0.0039 0.0007

0.0001 -0.0038 0.0007

0.0001 -0.0037 0.0006

0.0001 -0.0036 0.0006

0.0001 -0.0035 0.0006

0.0001 -0.0034 0.0006

0.0001 -0.0033 0.0006

0.0001 -0.0032 0.0006

0.0001 -0.0031 0.0006

0.0001 -0.0030 0.0006

0.0001 -0.0029 0.0006

0.0001 -0.0028 0.0006

0.0001 -0.0027 0.0006

0.0001 -0.0026 0.0006

0.0001 -0.0025 0.0006

0.0001 -0.0024 0.0006

0.0001 -0.0023 0.0006

Tabel 8

fi1 R12x R12y

0 0.0004 0.0068

0.0000 0.0003 0.0068

0.0000 0.0002 0.0068

0.0000 0.0001 0.0068

0.0000 0.0000 0.0068

0.0000 -0.0000 0.0069

0.0000 -0.0001 0.0069

0.0000 -0.0002 0.0069

0.0000 -0.0003 0.0069

0.0001 -0.0003 0.0070

0.0001 -0.0004 0.0070

0.0001 -0.0005 0.0071

0.0001 -0.0006 0.0071

0.0001 -0.0006 0.0072

0.0001 -0.0007 0.0072

0.0001 -0.0007 0.0073

0.0001 -0.0008 0.0073

0.0001 -0.0008 0.0074

0.0001 -0.0009 0.0074

0.0001 -0.0009 0.0075

0.0001 -0.0010 0.0076

0.0001 -0.0010 0.0077

0.0001 -0.0010 0.0078

0.0002 -0.0010 0.0078

0.0002 -0.0011 0.0079

0.0002 -0.0011 0.0080

0.0002 -0.0011 0.0081

0.0002 -0.0010 0.0081

0.0002 -0.0010 0.0082

0.0002 -0.0010 0.0083

0.0002 -0.0010 0.0084

0.0002 -0.0009 0.0084

0.0002 -0.0009 0.0085

0.0002 -0.0008 0.0085

0.0002 -0.0008 0.0086

0.0002 -0.0007 0.0086

0.0003 -0.0006 0.0086

0.0003 -0.0006 0.0087

0.0003 -0.0005 0.0088

0.0003 -0.0005 0.0090

0.0003 -0.0004 0.0084

0.0003 -0.0002 0.0068

0.0003 0.0006 0.0027

0.0003 0.0033 -0.0078

0.0003 0.0136 -0.0364

0.0003 0.0549 -0.1196

0.0003 0.2358 -0.3729

0.0003 1.0186 -1.0400

0.0003 2.9397 -1.4953

0.0003 0.3630 -0.0006

0.0003 -3.0608 -1.3912

0.0003 -1.1774 -1.1333

0.0003 -0.2749 -0.4171

0.0003 -0.0630 -0.1330

0.0003 -0.0152 -0.0400

0.0003 -0.0036 -0.0086

0.0003 -0.0006 0.0027

0.0003 0.0002 0.0069

0.0004 0.0004 0.0085

0.0004 0.0005 0.0090

0.0004 0.0005 0.0086

0.0004 0.0006 0.0085

0.0004 0.0006 0.0083

0.0004 0.0007 0.0083

0.0004 0.0008 0.0082

0.0004 0.0009 0.0081

0.0004 0.0010 0.0080

0.0004 0.0011 0.0079

0.0004 0.0012 0.0079

0.0004 0.0012 0.0078

0.0004 0.0013 0.0078

0.0004 0.0013 0.0077

0.0004 0.0014 0.0077

0.0004 0.0014 0.0076

0.0005 0.0015 0.0075

0.0005 0.0015 0.0074

0.0005 0.0015 0.0073

0.0005 0.0015 0.0072

0.0005 0.0015 0.0071

0.0005 0.0015 0.0070

0.0005 0.0014 0.0070

0.0005 0.0014 0.0069

0.0005 0.0013 0.0069

0.0006 0.0012 0.0068

0.0006 0.0011 0.0068

0.0006 0.0010 0.0068

0.0006 0.0009 0.0068

0.0006 0.0008 0.0067

0.0006 0.0007 0.0067

0.0006 0.0006 0.0067

0.0006 0.0005 0.0067

0.0006 0.0004 0.0068

Tabel 9

fi1 R01x R01y

0 0.0004 0.0060

0.0000 0.0003 0.0060

0.0000 0.0002 0.0060

0.0000 0.0001 0.0060

0.0000 0.0000 0.0061

0.0000 -0.0001 0.0061

0.0000 -0.0002 0.0061

0.0000 -0.0003 0.0062

0.0001 -0.0003 0.0062

0.0001 -0.0004 0.0062

0.0001 -0.0004 0.0063

0.0001 -0.0005 0.0063

0.0001 -0.0006 0.0063

0.0001 -0.0006 0.0064

0.0001 -0.0007 0.0064

0.0001 -0.0007 0.0065

0.0001 -0.0008 0.0065

0.0001 -0.0008 0.0066

0.0001 -0.0009 0.0066

0.0001 -0.0009 0.0067

0.0001 -0.0010 0.0067

0.0001 -0.0010 0.0068

0.0001 -0.0010 0.0069

0.0001 -0.0011 0.0070

0.0001 -0.0011 0.0071

0.0002 -0.0011 0.0071

0.0002 -0.0011 0.0072

0.0002 -0.0011 0.0073

0.0002 -0.0011 0.0074

0.0002 -0.0011 0.0075

0.0002 -0.0010 0.0076

0.0002 -0.0010 0.0077

0.0002 -0.0009 0.0077

0.0002 -0.0009 0.0078

0.0002 -0.0008 0.0079

0.0002 -0.0007 0.0079

0.0003 -0.0007 0.0079

0.0003 -0.0006 0.0080

0.0003 -0.0005 0.0081

0.0003 -0.0005 0.0083

0.0003 -0.0004 0.0077

0.0003 -0.0002 0.0061

0.0003 0.0006 0.0020

0.0003 0.0033 -0.0085

0.0003 0.0136 -0.0371

0.0003 0.0549 -0.1203

0.0003 0.2358 -0.3736

0.0003 1.0186 -1.0407

0.0003 2.9397 -1.4960

0.0003 0.3630 -0.0013

0.0003 -3.0608 -1.3918

0.0003 -1.1774 -1.1340

0.0003 -0.2749 -0.4178

0.0003 -0.0629 -0.1337

0.0003 -0.0152 -0.0407

0.0003 -0.0036 -0.0093

0.0003 -0.0006 0.0020

0.0003 0.0002 0.0062

0.0004 0.0004 0.0078

0.0004 0.0005 0.0083

0.0004 0.0005 0.0080

0.0004 0.0006 0.0078

0.0004 0.0007 0.0077

0.0004 0.0007 0.0076

0.0004 0.0008 0.0075

0.0004 0.0009 0.0074

0.0004 0.0010 0.0074

0.0004 0.0010 0.0073

0.0004 0.0011 0.0073

0.0004 0.0011 0.0072

0.0004 0.0012 0.0072

0.0004 0.0012 0.0071

0.0004 0.0013 0.0071

0.0004 0.0013 0.0070

0.0004 0.0014 0.0070

0.0004 0.0014 0.0069

0.0004 0.0015 0.0069

0.0004 0.0015 0.0068

0.0005 0.0015 0.0068

0.0005 0.0015 0.0067

0.0005 0.0016 0.0067

0.0005 0.0016 0.0066

0.0005 0.0016 0.0065

0.0005 0.0016 0.0064

0.0005 0.0015 0.0063

0.0005 0.0015 0.0062

0.0005 0.0014 0.0062

0.0005 0.0014 0.0061

0.0005 0.0013 0.0061

0.0006 0.0013 0.0061

0.0006 0.0012 0.0061

0.0006 0.0012 0.0060

0.0006 0.0011 0.0060

0.0006 0.0010 0.0060

0.0006 0.0009 0.0060

0.0006 0.0008 0.0060

0.0006 0.0007 0.0060

0.0006 0.0006 0.0060

0.0006 0.0005 0.0060

0.0006 0.0004 0.0060

Tabel 10

fi1 Me1

0 0.0003

0.0000 0.0005

0.0001 0.0007

0.0001 0.0009

0.0002 0.0011

0.0002 0.0013

0.0003 0.0015

0.0003 0.0016

0.0003 0.0018

0.0004 0.0020

0.0004 0.0022

0.0005 0.0024

0.0005 0.0026

0.0006 0.0028

0.0006 0.0030

0.0007 0.0032

0.0007 0.0034

0.0007 0.0036

0.0008 0.0038

0.0008 0.0040

0.0009 0.0041

0.0009 0.0043

0.0010 0.0045

0.0010 0.0047

0.0010 0.0049

0.0011 0.0050

0.0011 0.0052

0.0012 0.0054

0.0012 0.0055

0.0013 0.0057

0.0013 0.0058

0.0014 0.0059

0.0014 0.0061

0.0014 0.0062

0.0015 0.0063

0.0015 0.0064

0.0016 0.0065

0.0017 0.0066

0.0017 0.0067

0.0018 0.0067

0.0019 0.0067

0.0019 0.0066

0.0020 0.0066

0.0020 0.0065

0.0021 0.0064

0.0021 0.0063

0.0022 0.0061

0.0022 0.0060

0.0023 0.0058

0.0023 0.0057

0.0024 0.0055

0.0024 0.0053

0.0024 0.0050

0.0025 0.0048

0.0025 0.0045

0.0026 0.0043

0.0026 0.0040

0.0027 0.0037

0.0027 0.0035

0.0027 0.0030

0.0028 0.0021

0.0028 0.0001

0.0029 -0.0046

0.0029 -0.0183

0.0030 -0.0646

0.0030 -0.2436

0.0031 -0.9525

0.0031 -2.5846

0.0031 -0.3122

0.0032 2.6793

0.0032 1.0915

0.0033 0.2804

0.0033 0.0730

0.0034 0.0202

0.0034 0.0050

0.0034 -0.0001

0.0035 -0.0021

0.0035 -0.0030

0.0036 -0.0035

0.0036 -0.0037

0.0037 -0.0039

0.0037 -0.0041

0.0037 -0.0044

0.0038 -0.0046

0.0038 -0.0048

0.0039 -0.0050

0.0039 -0.0052

0.0040 -0.0054

0.0040 -0.0056

0.0041 -0.0057

0.0041 -0.0058

0.0041 -0.0060

0.0042 -0.0061

0.0043 -0.0062

0.0043 -0.0063

0.0044 -0.0063

0.0045 -0.0063

0.0046 -0.0062

0.0047 -0.0061

0.0047 -0.0060

0.0048 -0.0059

0.0048 -0.0058

0.0048 -0.0057

0.0049 -0.0056

0.0049 -0.0055

0.0050 -0.0053

0.0050 -0.0052

0.0051 -0.0050

0.0051 -0.0049

0.0051 -0.0047

0.0052 -0.0045

0.0052 -0.0043

0.0053 -0.0042

0.0053 -0.0040

0.0054 -0.0038

0.0054 -0.0036

0.0054 -0.0034

0.0055 -0.0032

0.0055 -0.0030

0.0056 -0.0028

0.0056 -0.0026

0.0057 -0.0024

0.0057 -0.0022

0.0058 -0.0020

0.0058 -0.0018

0.0058 -0.0016

0.0059 -0.0014

0.0059 -0.0012

0.0060 -0.0011

0.0060 -0.0009

0.0061 -0.0007

0.0061 -0.0005

0.0061 -0.0003

0.0062 -0.0001

0.0062 0.0001

0.0063 0.0003

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