MECHANIKA - Zadání práce z kinematiky

MECHANIKA

1. Zadání práce z kinematiky

Vypočítejte a graficky znázorněte – průběh polohy, rychlosti a zrychlení bodu L.

Hnacím členem je člen 2.

Dáno: ω₂₁ = 100 s^-1 = konst. a rozměry mechanismu (viz obr.)

r = 0,2 m

|AB| = 0,7 m

e = 0,3 m

|CL| = 1,2 m

Odevzdané řešení bude obsahovat:

1. Zadání

2. Algoritmus řešení (vztahy)

3. Vývojový diagram

4. Program

5. Číselné výsledky

6. Grafické zpracování výsledků

2. Algoritmus řešení (vztahy)

Průběh polohy

Rychlost bodu L

Zrychlení bodu L

3. Vývojový diagram

Cyklus

fd = mopen ('e:homerychl.txt','w');

mfprintf (fd,'vlxtt vlytt vln');

fd1=mopen ('e:homepoloha.txt','w');

mfprintf (fd1,'rxtt rytt rn');

n:=1 .. 360

fi=n*%pi/180;

pom1=r^2+l^2-2*r*l*cos(fi);

pom2=h*cos(asin(e/sqrt(pom1))-asin(r*sin(fi)/sqrt(pom1)));

pom3=h*sin(asin(e/sqrt(pom1))-asin((r*sin(fi))/sqrt(pom1)));

rx(n)=r*cos(fi)+pom2;

ry(n)=r*sin(fi)+pom3;

vly(n)=(r*cos(fi)+pom2*(1/sqrt(1-(e^2/pom1)))*(-e/sqrt(pom1^3)*r*l*sin(fi))-

(1/sqrt(1-(sin(fi)*r)^2/pom1))*(cos(fi)*r*sqrt(pom1)-((sin(fi)*r)/

(2*sqrt(pom1)))/pom1)*2*r*l*sin(fi))*w;

vlx(n)=(-r*sin(fi)-pom3*(1/sqrt(1-e^2/(pom1)))*(-e*r*l*sin(fi)/sqrt(pom1^3))-

(1/sqrt(1-(sin(fi)*r)^2/pom1))*((r*cos(fi)*sqrt(pom1)-r*sin(fi)/

(2*sqrt(pom1)))/pom1)*2*r*l*sin(fi))*w;

vl(n)=sqrt(vlx(n)^2+vly(n)^2);

mfprintf (fd,'%ft %f t %fn', vlx(n), vly(n), vl(n));

rv(n)=sqrt(rx(n)^2+ry(n)^2);

mfprintf (fd1,'%ft %f t %fn', rx(n), ry(n), rv(n));

Cyklus

4. Program

//scilab file

// omega

w=100;

r=0.2;

l=0.7;

h=1.2;

e=0.3;

vly=ones(360,1);

vlx=ones(360,1);

vl=ones(360,1);

fd = mopen('e:homerychl.txt','w');

mfprintf(fd,'vlxtt vlytt vln');

fd1=mopen('e:homepoloha.txt','w');

mfprintf(fd1,'rxtt rytt rn');

for n=1:1:360,

fi=n*%pi/180;

pom1=r^2+l^2-2*r*l*cos(fi);

pom2=h*cos(asin(e/sqrt(pom1))-asin(r*sin(fi)/sqrt(pom1)));

pom3=h*sin(asin(e/sqrt(pom1))-asin((r*sin(fi))/sqrt(pom1)));

rx(n)=r*cos(fi)+pom3;

ry(n)=r*sin(fi)+pom2;

vly(n)=(r*cos(fi)+pom2*(1/sqrt(1-(e^2/pom1)))*(-e/sqrt(pom1^3)*r*l*sin(fi))-(1/sqrt(1- (sin(fi)*r)^2/pom1))*(cos(fi)*r*sqrt(pom1)-((sin(fi)*r)/(2*sqrt(pom1)))/pom1)*2*r*l*sin(fi))*w;

vlx(n)=(-r*sin(fi)-pom3*(1/sqrt(1-e^2/(pom1)))*(-e*r*l*sin(fi)/sqrt(pom1^3))-(1/sqrt(1-(sin(fi)*r)^2/pom1))*((r*cos(fi)*sqrt(pom1)-r*sin(fi)/(2*sqrt(pom1)))/pom1)*2*r*l*sin(fi))*w;

vl(n)=sqrt(vlx(n)^2+vly(n)^2);

mfprintf(fd,'%ft %f t %fn', vlx(n), vly(n), vl(n));

rv(n)=sqrt(rx(n)^2+ry(n)^2);

mfprintf(fd1,'%ft %f t %fn', rx(n), ry(n), rv(n));

end;

x=1:360;

mclose(fd);

mclose(fd1);

f1=scf(1);

f2=scf(2);

f3=scf(3);

f4=scf(4);

scf(f1);

plot(x,vlx,'Stupně', 'Rychlost Vlx [m/s]');

xtitle('Závislost rychlosti Vlx na natočení');

xgrid(1);

scf(f2);

plot(x,vly,'Stupně', 'Rychlost Vly [m/s]');

xtitle('Závislost rychlosti Vly na natočení');

xgrid(1);

scf(f3);

plot(x,rx,'Stupně','Poloha rx [m]');

xtitle('Závislost polohy rx na natočení');

xgrid(1);

scf(f4);

plot(x,ry,'Stupně','Poloha ry [m]');

xtitle('Závislost polohy ry na natočení');

xgrid(1);

disp('Computing finish');

5. Číselné výsledky

Průběh polohy <1°;360°>

rx ry r rx ry r

0.968539 1.331158

0.977115 1.332623

0.985720 1.334059

0.994348 1.335466

1.002989 1.336846

1.011636 1.338199

1.020280 1.339528

1.028914 1.340832

1.037530 1.342114

1.046120 1.343375

1.054676 1.344615

1.063191 1.345836

1.071658 1.347038

1.080070 1.348223

1.088419 1.349392

1.096699 1.350546

1.104903 1.351686

1.113026 1.352812

1.121062 1.353926

1.129006 1.355028

1.136851 1.356119

1.144593 1.357200

1.152229 1.358271

1.159753 1.359334

1.167162 1.360387

1.174452 1.361433

1.181620 1.362472

1.188663 1.363503

1.195580 1.364527

1.202366 1.365545

1.209022 1.366556

1.215544 1.367561

1.221932 1.368561

1.228184 1.369553

1.234300 1.370540

1.240280 1.371521

1.246122 1.372495

1.251827 1.373463

1.257395 1.374424

1.262827 1.375377

1.268122 1.376324

1.273281 1.377263

1.278305 1.378193

1.283195 1.379115

1.287952 1.380027

1.292577 1.380930

1.297072 1.381822

1.301437 1.382703

1.305674 1.383573

1.309784 1.384430

1.313769 1.385274

1.317631 1.386103

1.321371 1.386919

1.324990 1.387718

1.328491 1.388502

1.331874 1.389268

1.335142 1.390016

1.338295 1.390744

1.341336 1.391453

1.344267 1.392141

1.347088 1.392807

1.349801 1.393450

1.352408 1.394069

1.354911 1.394664

1.357310 1.395232

1.359607 1.395774

1.361804 1.396288

1.363901 1.396773

1.365901 1.397228

1.367804 1.397652

1.369611 1.398045

1.371325 1.398404

1.372945 1.398730

1.374473 1.399021

1.375910 1.399276

1.377258 1.399494

1.378516 1.399675

1.379687 1.399817

1.380770 1.399919

1.381767 1.399980

1.382679 1.400000

1.383506 1.399977

1.384249 1.399911

1.384908 1.399801

1.385486 1.399646

1.385981 1.399445

1.386395 1.399197

1.386729 1.398901

1.386983 1.398557

1.387157 1.398164

1.387252 1.397721

1.387268 1.397227

1.387207 1.396683

1.387068 1.396086

1.386852 1.395436

1.386559 1.394733

1.386190 1.393977

1.385745 1.393165

1.385225 1.392299

1.384630 1.391377

1.383960 1.390400

1.383215 1.389365

1.382397 1.388274

1.381505 1.387125

1.380539 1.385919

1.379501 1.384654

1.378390 1.383331

1.377207 1.381949

1.375951 1.380507

1.374624 1.379007

1.373226 1.377447

1.371757 1.375827

1.370217 1.374148

1.368606 1.372408

1.366926 1.370609

1.365176 1.368749

1.363356 1.366829

1.361468 1.364849

1.359511 1.362809

1.357486 1.360709

1.355393 1.358548

1.353232 1.356328

1.351004 1.354049

1.348710 1.351710

1.346349 1.349312

1.343923 1.346855

1.341431 1.344340

1.338874 1.341766

1.336252 1.339134

1.333567 1.336446

1.330818 1.333700

1.328005 1.330897

1.325130 1.328039

1.322193 1.325126

1.319194 1.322158

1.316134 1.319135

1.313014 1.316059

1.309833 1.312931

1.306594 1.309750

1.303295 1.306519

1.299938 1.303237

1.296524 1.299905

1.293052 1.296525

1.289524 1.293097

1.285940 1.289622

1.282302 1.286102

1.278609 1.282537

1.274862 1.278929

1.271062 1.275278

1.267210 1.271586

1.263306 1.267854

1.259352 1.264083

1.255348 1.260274

1.251294 1.256429

1.247191 1.252549

1.243041 1.248636

1.238844 1.244691

1.234601 1.240715

1.230313 1.236709

1.225980 1.232677

1.221603 1.228618

1.217184 1.224535

1.212723 1.220429

1.208220 1.216302

1.203678 1.212156

1.199097 1.207992

1.194477 1.203812

1.189820 1.199618

1.185126 1.195412

1.180397 1.191196

1.175634 1.186972

1.170837 1.182741

1.166007 1.178506

1.161146 1.174269

1.156254 1.170031

1.151332 1.165795

1.146382 1.161563

1.141405 1.157337

1.136401 1.153120

1.131371 1.148913

1.126317 1.144718

1.121239 1.140538

1.116139 1.136376

1.111018 1.132233

1.105877 1.128112

1.100716 1.124015

1.095538 1.119944

1.090342 1.115902

1.085130 1.111892

1.079904 1.107914

1.074664 1.103973

1.069412 1.100071

1.064148 1.096209

1.058873 1.092390

1.053590 1.088617

1.048298 1.084892

1.043000 1.081218

1.037695 1.077596

1.032386 1.074030

1.027073 1.070521

1.021758 1.067073

1.016442 1.063687

1.011126 1.060365

1.005810 1.057111

1.000497 1.053926

0.995187 1.050813

0.989882 1.047774

0.984582 1.044811

0.979290 1.041927

0.974005 1.039123

0.968729 1.036401

0.963464 1.033764

0.958210 1.031214

0.952968 1.028752

0.947741 1.026381

0.942529 1.024102

0.937332 1.021917

0.932153 1.019827

0.926993 1.017835

0.921852 1.015942

0.916732 1.014149

0.911633 1.012458

0.906558 1.010871

0.901508 1.009387

0.896482 1.008009

0.891483 1.006738

0.886513 1.005574

0.881571 1.004519

0.876659 1.003573

0.871778 1.002737

0.866930 1.002011

0.862115 1.001396

0.857335 1.000893

0.852591 1.000502

0.847884 1.000223

0.843215 1.000055

0.838586 1.000000

0.833997 1.000057

0.829449 1.000225

0.824945 1.000505

0.820484 1.000895

0.816069 1.001397

0.811699 1.002008

0.807378 1.002728

0.803104 1.003556

0.798881 1.004492

0.794708 1.005535

0.790588 1.006683

0.786520 1.007934

0.782507 1.009289

0.778549 1.010746

0.774648 1.012302

0.770805 1.013957

0.767021 1.015709

0.763297 1.017556

0.759634 1.019497

0.756034 1.021530

0.752498 1.023652

0.749026 1.025863

0.745620 1.028159

0.742282 1.030539

0.739011 1.033001

0.735811 1.035543

0.732681 1.038162

0.729624 1.040857

0.726639 1.043624

0.723729 1.046462

0.720895 1.049368

0.718138 1.052340

0.715458 1.055375

0.712859 1.058472

0.710340 1.061627

0.707903 1.064838

0.705549 1.068103

0.703279 1.071418

0.701096 1.074783

0.699000 1.078194

0.696992 1.081648

0.695074 1.085144

0.693248 1.088678

0.691514 1.092248

0.689874 1.095852

0.688329 1.099487

0.686881 1.103150

0.685531 1.106840

0.684281 1.110554

0.683133 1.114289

0.682086 1.118043

0.681144 1.121813

0.680307 1.125598

0.679578 1.129394

0.678957 1.133200

0.678447 1.137013

0.678048 1.140831

0.677763 1.144652

0.677592 1.148474

0.677538 1.152294

0.677603 1.156110

0.677787 1.159920

0.678093 1.163723

0.678523 1.167516

0.679077 1.171297

0.679758 1.175064

0.680567 1.178816

0.681506 1.182550

0.682577 1.186265

0.683781 1.189959

0.685120 1.193630

0.686597 1.197277

0.688211 1.200898

0.689966 1.204491

0.691863 1.208056

0.693904 1.211589

0.696089 1.215091

0.698422 1.218560

0.700903 1.221994

0.703533 1.225392

0.706315 1.228753

0.709250 1.232076

0.712339 1.235360

0.715583 1.238604

0.718984 1.241806

0.722542 1.244966

0.726260 1.248084

0.730137 1.251157

0.734175 1.254186

0.738373 1.257170

0.742734 1.260108

0.747257 1.263000

0.751943 1.265845

0.756791 1.268642

0.761801 1.271393

0.766974 1.274095

0.772309 1.276750

0.777805 1.279356

0.783460 1.281914

0.789275 1.284423

0.795248 1.286885

0.801376 1.289298

0.807658 1.291663

0.814092 1.293980

0.820676 1.296250

0.827405 1.298473

0.834278 1.300649

0.841291 1.302779

0.848440 1.304863

0.855722 1.306902

0.863131 1.308896

0.870663 1.310847

0.878313 1.312754

0.886075 1.314620

0.893945 1.316444

0.901917 1.318227

0.909983 1.319971

0.918138 1.321677

0.926375 1.323344

0.934687 1.324976

0.943066 1.326572

0.951507 1.328133

0.960000 1.329662

Rychlost bodu L <1°;360°>

vlx  vly vl

19.247744 19.247750

18.497095 18.497115

17.749467 17.749507

17.006256 17.006322

16.268833 16.268935

15.538538 15.538692

14.816671 14.816903

14.104487 14.104838

13.403183 13.403723

12.713900 12.714734

12.037711 12.039002

11.375616 11.377610

10.728539 10.731601

10.097324 10.101980

9.482728 9.489731

8.885422 8.895825

8.305987 8.321249

7.744913 7.767023

7.202597 7.234238

6.679349 6.724099

6.175383 6.237974

5.690828 5.777452

5.225726 5.344420

4.780034 4.941131

4.353631 4.570274

3.946318 4.235009

3.557824 3.938945

3.187812 3.685984

2.835882 3.480005

2.501578 3.324325

2.184391 3.221026

1.883767 3.170309

1.599110 3.170144

1.329790 3.216394

1.075148 3.303397

0.834498 3.424749

0.607137 3.574050

0.392347 3.745410

0.189399 3.933714

-0.002438 4.134694

-0.183900 4.344873

-0.355717 4.561468

-0.518613 4.782271

-0.673304 5.005538

-0.820490 5.229895

-0.960859 5.454257

-1.095078 5.677768

-1.223796 5.899747

-1.347639 6.119658

-1.467211 6.337070

-1.583090 6.551644

-1.695829 6.763108

-1.805955 6.971247

-1.913968 7.175891

-2.020341 7.376911

-2.125518 7.574205

-2.229919 7.767700

-2.333934 7.957346

-2.437927 8.143111

-2.542235 8.324982

vlx  vly vl

-2.647171 8.502960

-2.753022 8.677062

-2.860049 8.847314

-2.968492 9.013758

-3.078565 9.176442

-3.190463 9.335427

-3.304358 9.490781

-3.420404 9.642581

-3.538734 9.790912

-3.659464 9.935863

-3.782692 10.077533

-3.908500 10.216026

-4.036956 10.351449

-4.168114 10.483916

-4.302011 10.613544

-4.438677 10.740453

-4.578126 10.864767

-4.720365 10.986613

-4.865387 11.106119

-10.041567 -5.013180 11.223415

-10.094579 -5.163722 11.338631

-10.142766 -5.316983 11.451899

-10.186177 -5.472926 11.563352

-10.224864 -5.631509 11.673121

-10.258884 -5.792684 11.781336

-10.288291 -5.956396 11.888128

-10.313145 -6.122588 11.993625

-10.333505 -6.291198 12.097954

-10.349432 -6.462160 12.201240

-10.360990 -6.635405 12.303605

-10.368240 -6.810860 12.405169

-10.371247 -6.988453 12.506048

-10.370075 -7.168107 12.606356

-10.364790 -7.349743 12.706203

-10.355456 -7.533282 12.805695

-10.342140 -7.718643 12.904933

-10.324905 -7.905744 13.004017

-10.303819 -8.094502 13.103040

-10.278945 -8.284833 13.202090

-10.250350 -8.476653 13.301253

-10.218097 -8.669877 13.400608

-10.182252 -8.864420 13.500229

-10.142876 -9.060196 13.600187

-10.100035 -9.257120 13.700546

-10.053789 -9.455105 13.801366

-10.004201 -9.654066 13.902699

-9.853916 14.004595

-10.054569 14.107096

-10.255938 14.210241

-10.457937 14.314061

-10.660478 14.418583

-10.863474 14.523828

-11.066839 14.629811

-11.270484 14.736542

-11.474321 14.844024

-11.678261 14.952258

-11.882216 15.061236

-12.086096 15.170945

-12.289810 15.281368

-12.493268 15.392483

-12.696378 15.504260

-12.899046 15.616666

-13.101180 15.729662

-13.302686 15.843204

-13.503466 15.957243

-13.703425 16.071724

-13.902464 16.186590

-14.100484 16.301777

-14.297384 16.417215

-14.493062 16.532832

-14.687415 16.648550

-14.880338 16.764289

-15.071723 16.879960

-15.261463 16.995475

-15.449447 17.110739

-15.635564 17.225653

-15.819700 17.340115

-16.001741 17.454021

-16.181570 17.567259

-16.359067 17.679719

-16.534113 17.791283

-16.706585 17.901833

-16.876359 18.011246

-17.043309 18.119398

-17.207309 18.226162

-17.368228 18.331406

-17.525935 18.434998

-17.680299 18.536805

-17.831185 18.636688

-17.978456 18.734510

-18.121976 18.830129

-18.261606 18.923405

-18.397205 19.014194

-18.528633 19.102351

-18.655746 19.187731

-18.778399 19.270188

-18.896449 19.349575

-19.009750 19.425745

-19.118153 19.498550

-19.221512 19.567844

-19.319677 19.633479

-19.412501 19.695309

-19.499833 19.753188

-19.581524 19.806972

-19.657424 19.856515

-19.727383 19.901677

-19.791250 19.942316

-19.848877 19.978294

-19.900113 20.009475

-19.944809 20.035725

-19.982819 20.056912

-20.013992 20.072910

-20.038185 20.083594

-20.055250 20.088842

-20.065043 20.088539

-20.067422 20.082572

-20.062246 20.070834

-20.049375 20.053222

-20.028672 20.029641

-20.000000 20.000000

-19.963227 19.964214

-19.918222 19.922207

-19.864857 19.873907

-19.803006 19.819254

-19.732547 19.758194

-19.653360 19.690681

-19.565328 19.616680

-19.468340 19.536167

-19.362285 19.449127

-19.247059 19.355557

-19.122559 19.255466

-18.988688 19.148877

-18.845353 19.035825

-18.692465 18.916363

-18.529939 18.790556

-18.357696 18.658488

-18.175661 18.520261

-17.983765 18.375995

-17.781941 18.225831

-17.570132 18.069931

-17.348283 17.908482

-17.116345 17.741694

-16.874277 17.569804

-16.622040 17.393077

-16.359603 17.211811

-16.086943 17.026332

-15.804039 16.837005

-15.510880 16.644228

-15.207459 16.448441

-14.893776 16.250125

-14.569839 16.049807

-14.235660 15.848060

-13.891261 15.645506

-13.536667 15.442822

-13.171913 15.240740

-12.797041 15.040049

-12.412097 14.841598

-12.017137 14.646297

-11.612224 14.455119

-11.197426 14.269099

-10.772820 14.089333

-10.338491 13.916978

-9.894530 13.753243

-9.441035 13.599390

-8.978113 13.456719

-8.505876 13.326565

-8.024446 13.210278

-7.533951 13.109214

-7.034526 13.024713

-6.526315 12.958084

-6.009469 12.910577

-5.484144 12.883369

-4.950507 12.877534

-4.408730 12.894027

-3.858993 12.933662

-3.301484 12.997099

-2.736397 13.084827

-2.163934 13.197160

-1.584304 13.334232

-0.997723 13.496001

-0.404415 13.682255

0.195390 13.892621

0.801454 14.126582

1.413534 14.383494

2.031377 14.662601

2.654726 14.963055

3.283317 15.283935

3.916876 15.624262

4.555128 15.983017

5.197786 16.359156

5.844560 16.751617

6.495152 17.159336

7.149259 17.581254

7.806570 18.016321

8.466771 18.463504

9.129537 18.921792

9.794543 19.390194

10.461453 19.867745

11.129928 20.353507

11.799623 20.846566

12.470187 21.346034

13.141264 21.851051

13.812491 22.360780

14.483503 22.874406

15.153927 23.391141

15.823386 23.910216

16.491497 24.430882

17.157874 24.952413

17.822126 25.474097

18.483855 25.995244

19.142661 26.515178

19.798139 27.033238

20.449880 27.548780

21.097469 28.061173

21.740489 28.569800

22.378519 29.074057

23.011134 29.573352

23.637904 30.067106

24.258397 30.554751

24.872177 31.035731

25.478807 31.509501

26.077843 31.975528

26.668842 32.433289

27.251356 32.882273

27.824937 33.321979

28.389131 33.751919

28.943485 34.171614

29.487544 34.580597

30.020850 34.978413

30.542945 35.364618

31.053371 35.738779

31.551666 36.100475

32.037369 36.449299

32.510022 36.784853

32.969162 37.106753

33.414331 37.414628

33.845069 37.708117

34.260920 37.986874

34.661427 38.250563

35.046137 38.498864

35.414600 38.731467

35.766368 38.948075

36.100999 39.148403

36.418052 39.332181

36.717094 39.499146

36.997697 39.649051

37.259438 39.781659

37.501901 39.896743

37.724681 39.994089

37.927377 40.073491

38.109600 40.134754

38.270972 40.177691

38.411124 40.202124

38.529699 40.207884

38.626356 40.194809

38.700766 40.162743

38.752615 40.111537

38.781607 40.041050

38.787464 39.951144

38.769925 39.841687

38.728750 39.712554

38.663723 39.563623

38.574649 39.394780

38.461358 39.205916

38.323708 38.996928

38.161584 38.767722

37.974900 38.518211

37.763602 38.248319

37.527672 37.957983

37.267123 37.647153

36.982009 37.315796

36.672421 36.963896

36.338490 36.591463

35.980394 36.198529

35.598353 35.785157

35.192635 35.351442

34.763556 34.897514

34.311485 34.423546

33.836840 33.929755

33.340098 33.416406

32.821786 32.883817

32.282493 32.332364

31.722863 31.762481

31.143599 31.174666

30.545465 30.569483

29.929283 29.947564

29.295936 29.309613

28.646363 28.656402

27.981563 27.988775

27.302590 27.307647

26.610555 26.614002

25.906617 25.908891

25.191984 25.193427

24.467913 24.468785

23.735697 23.736191

22.996668 22.996925

22.252187 22.252304

21.503643 21.503685

20.752441 20.752450

20.000000 20.000000

6. Grafické zpracování výsledků