├── CAD
├── Legolas
│ ├── V1
│ │ ├── Full_Assembly.SLDASM
│ │ └── Legolas_v1.SLDASM
│ ├── V2
│ │ ├── Foot.SLDPRT
│ │ ├── Foreleg.SLDPRT
│ │ ├── Full Assembly.SLDASM
│ │ ├── Hip Pitch.SLDPRT
│ │ ├── Hip Roll.SLDPRT
│ │ ├── Hip Yaw.SLDPRT
│ │ ├── Legolas V2 Left Leg.SLDASM
│ │ ├── M4 Linkage 1.SLDASM
│ │ ├── M4 Linkage 2.SLDASM
│ │ ├── STLs
│ │ │ ├── Foot.STL
│ │ │ ├── Foreleg A.STL
│ │ │ ├── Foreleg B.STL
│ │ │ ├── Foreleg C.STL
│ │ │ ├── Hip 1 A.STL
│ │ │ ├── Hip 1 B.STL
│ │ │ ├── Hip 2.STL
│ │ │ ├── Hip Pitch A.STL
│ │ │ ├── Hip Pitch B.STL
│ │ │ ├── Ma Shues.zip
│ │ │ ├── Main body ADC Mount.STL
│ │ │ ├── Main body Wire Connector Container.STL
│ │ │ ├── Main body cover.STL
│ │ │ ├── Main body.STL
│ │ │ ├── Servo Cover.STL
│ │ │ ├── Shin.STL
│ │ │ ├── Shoe A.STL
│ │ │ ├── Shoe B.STL
│ │ │ ├── Test bench adaptor.STL
│ │ │ ├── Thigh Inner.STL
│ │ │ └── Thigh Outer.STL
│ │ ├── Servo Cover.SLDPRT
│ │ ├── Shin.SLDPRT
│ │ ├── Thigh Inner.SLDPRT
│ │ ├── Thigh Outer.SLDPRT
│ │ ├── Thrust Bearing.SLDASM
│ │ └── right_leg_redundant
│ │ │ ├── Legolas V2 Right Leg.SLDASM
│ │ │ ├── MirrorFoot.SLDPRT
│ │ │ ├── MirrorForeleg.SLDPRT
│ │ │ ├── MirrorHip Pitch.SLDPRT
│ │ │ ├── MirrorHip Roll.SLDPRT
│ │ │ ├── MirrorHip Yaw.SLDPRT
│ │ │ ├── MirrorM4 Linkage 1.SLDASM
│ │ │ ├── MirrorM4 Linkage 2.SLDASM
│ │ │ ├── MirrorServo Cover.SLDPRT
│ │ │ ├── MirrorShin.SLDPRT
│ │ │ ├── MirrorThigh Inner.SLDPRT
│ │ │ └── MirrorThigh Outer.SLDPRT
│ └── V3
│ │ ├── Foot v3.SLDPRT
│ │ ├── Foreleg v3.SLDPRT
│ │ ├── Servo Cover v3.SLDPRT
│ │ └── Shin v3.SLDPRT
├── Servo and electronics
│ ├── 40 kg Servo Arm.SLDPRT
│ ├── 40 kg Servo.SLDPRT
│ ├── 80kg_servo.SLDPRT
│ ├── 80kg_servo_arm.SLDPRT
│ ├── ADS1115.SLDPRT
│ ├── M4 Ball Joint Rod End.SLDPRT
│ ├── M4 Connecting Rod.SLDPRT
│ ├── M5 Ball Joint Rod End.SLDPRT
│ ├── M5 Connecting Rod.SLDPRT
│ ├── MPU 6050 IMU.SLDPRT
│ ├── Mirror40 kg Servo Arm.SLDPRT
│ ├── Mirror40 kg Servo.SLDPRT
│ ├── Mirror80kg_servo.SLDPRT
│ ├── Mirror80kg_servo_arm.SLDPRT
│ ├── Raspberry Pi 4 Model B.SLDPRT
│ ├── pca9685.SLDPRT
│ ├── servo driver pca9685.SLDPRT
│ ├── servo.SLDASM
│ ├── ~$Mirror40 kg Servo Arm.SLDPRT
│ ├── ~$Mirror40 kg Servo.SLDPRT
│ ├── ~$Mirror80kg_servo.SLDPRT
│ └── ~$Mirror80kg_servo_arm.SLDPRT
└── Test_Bench
│ └── Test_Bench_Mk2.SLDASM
├── LICENSE
├── Mujoco xml
├── Documentation for Solidworks to Mujoco.docx
├── References
│ └── agility_cassie
│ │ ├── LICENSE
│ │ ├── README.md
│ │ ├── assets
│ │ ├── achilles-rod.obj
│ │ ├── cassie-texture.png
│ │ ├── foot-crank.obj
│ │ ├── foot.obj
│ │ ├── heel-spring.obj
│ │ ├── hip-pitch.obj
│ │ ├── hip-roll.obj
│ │ ├── hip-yaw.obj
│ │ ├── knee-spring.obj
│ │ ├── knee.obj
│ │ ├── pelvis.obj
│ │ ├── plantar-rod.obj
│ │ ├── shin.obj
│ │ └── tarsus.obj
│ │ ├── cassie.png
│ │ ├── cassie.xml
│ │ └── scene.xml
└── Working Mk 5 - Old model - Demo only
│ ├── CMU Mk 5.xml
│ └── meshes
│ ├── L_Foot.STL
│ ├── L_Foot_collision.STL
│ ├── L_Foreleg.STL
│ ├── L_Hip_1.STL
│ ├── L_Hip_2.STL
│ ├── L_Linkage.STL
│ ├── L_Servo.STL
│ ├── L_Servo_Link.STL
│ ├── L_Servo_collision.STL
│ ├── L_Shin.STL
│ ├── L_Thigh.STL
│ ├── R_Foot.STL
│ ├── R_Foot_collision.STL
│ ├── R_Foreleg.STL
│ ├── R_Hip_1.STL
│ ├── R_Hip_2.STL
│ ├── R_Linkage.STL
│ ├── R_Servo.STL
│ ├── R_Servo_Link.STL
│ ├── R_Servo_collision.STL
│ ├── R_Shin.STL
│ ├── R_Thigh.STL
│ ├── base_link.STL
│ └── base_link_collision.STL
├── README.md
├── assets
├── Walking_Test_3.gif
├── Walking_Test_3.mp4
├── cover_image_back.jpg
└── cover_image_front.jpg
└── static_analysis
└── Leg_Static_Analysis.ipynb
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/LICENSE:
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1 | MIT License
2 |
3 | Copyright (c) 2023 David Ho
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 |
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/Mujoco xml/References/agility_cassie/LICENSE:
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1 | Copyright (c) 2022 Agility Robotics
2 |
3 | Permission is hereby granted, free of charge, to any person obtaining a copy
4 | of this software and associated documentation files (the "Software"), to
5 | deal in the Software without restriction, including without limitation the
6 | rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
7 | sell copies of the Software, and to permit persons to whom the Software is
8 | furnished to do so, subject to the following conditions:
9 |
10 | The above copyright notice and this permission notice shall be included in
11 | all copies or substantial portions of the Software.
12 |
13 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
14 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
15 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
16 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
17 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
18 | FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
19 | IN THE SOFTWARE.
20 |
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/Mujoco xml/References/agility_cassie/README.md:
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1 | # Agility Cassie Description (MJCF)
2 |
3 | ## Overview
4 |
5 | This package contains a simplified robot description (MJCF) of the Cassie
6 | bipedal robot. The original MJCF and assets were provided directly by
7 | [Agility Robotics](http://www.agilityrobotics.com/) under an
8 | [MIT License](LICENSE).
9 |
10 |
11 | 
12 |
13 |
14 | ## Modifications made to the original model
15 |
16 | 1. Replaced single quotes with double quotes.
17 | 2. Made collision geoms visible, put them in hidden group 3.
18 | 3. Removed `nuser_actuator` and `nuser_sensor` (automatically inferred since
19 | MuJoCo 2.1.2).
20 | 4. Changed solver from PGS to Newton.
21 | 5. Removed `` clause.
22 | 6. Removed attribute specs which are already default.
23 | 7. Improved collision geometry.
24 | 8. Added `scene.xml` which includes the robot, with a textured groundplane, skybox, and haze.
25 |
26 | ## License
27 |
28 | This model is released under an [MIT License](LICENSE).
29 |
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1 | # Blender v3.0.1 OBJ File: 'cassie-meshes.blend'
2 | # www.blender.org
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304 | v 0.003607 0.007500 -0.016862
305 | v 0.005711 0.007500 -0.017912
306 | v -0.005671 0.008999 -0.019404
307 | v -0.006870 0.008945 -0.016572
308 | v -0.004485 0.008996 -0.015203
309 | v -0.002956 0.008998 -0.018704
310 | v -0.002492 0.008923 -0.016667
311 | v -0.005924 0.006422 -0.018115
312 | v -0.006640 0.006499 -0.016990
313 | v -0.005967 0.006536 -0.019296
314 | v -0.003859 0.006424 -0.018584
315 | v -0.002771 0.006554 -0.018914
316 | v -0.003579 0.006413 -0.016356
317 | v -0.002926 0.006563 -0.015911
318 | v -0.005271 0.006560 -0.015160
319 | v -0.004621 0.007500 -0.018277
320 | v -0.004800 0.007500 -0.016203
321 | v -0.010589 0.008999 -0.013104
322 | v -0.012584 0.008937 -0.015118
323 | v -0.014867 0.009008 -0.013178
324 | v -0.013828 0.008919 -0.010646
325 | v -0.011545 0.009010 -0.010977
326 | v -0.013919 0.006385 -0.011721
327 | v -0.013668 0.006548 -0.010532
328 | v -0.014971 0.006548 -0.013289
329 | v -0.012792 0.006407 -0.014239
330 | v -0.012507 0.006551 -0.015105
331 | v -0.011326 0.006408 -0.012258
332 | v -0.010334 0.006546 -0.012114
333 | v -0.013709 0.007500 -0.013377
334 | v -0.011747 0.007500 -0.012079
335 | v -0.019474 0.008989 -0.005331
336 | v -0.018391 0.008955 -0.002484
337 | v -0.016290 0.009007 -0.002784
338 | v -0.015303 0.009005 -0.005116
339 | v -0.017243 0.008939 -0.007048
340 | v -0.018769 0.006424 -0.004256
341 | v -0.019168 0.006497 -0.003353
342 | v -0.019260 0.006570 -0.006011
343 | v -0.017451 0.006407 -0.006170
344 | v -0.016774 0.006560 -0.006886
345 | v -0.015985 0.006408 -0.004189
346 | v -0.015040 0.006557 -0.004645
347 | v -0.016779 0.006571 -0.002430
348 | v -0.016213 0.007500 -0.004587
349 | v -0.018560 0.007500 -0.004730
350 | v 0.059855 -0.015745 0.000714
351 | v 0.056740 -0.015760 -0.000579
352 | v 0.057468 -0.015697 -0.004239
353 | v 0.051237 -0.015757 0.002934
354 | v 0.055407 -0.015749 0.001924
355 | v 0.055933 -0.015763 0.004819
356 | v 0.055444 -0.015801 -0.001806
357 | v 0.053155 -0.015743 -0.004352
358 | v 0.053620 -0.015815 -0.001255
359 | v 0.050382 -0.015747 -0.001445
360 | v 0.053260 -0.015761 0.000585
361 | v 0.050731 -0.012675 0.002687
362 | v 0.056517 -0.012675 0.004901
363 | v 0.060040 -0.012675 -0.000192
364 | v 0.056136 -0.012675 -0.005003
365 | v 0.050826 -0.012675 -0.002695
366 | v 0.057466 -0.012675 0.002558
367 | v 0.057462 -0.012675 -0.002375
368 | v 0.052534 -0.012675 -0.002558
369 | v 0.052539 -0.012675 0.002375
370 | v 0.052136 0.003073 0.001708
371 | v 0.055533 0.003118 0.003061
372 | v 0.057850 0.003065 0.001528
373 | v 0.057772 0.003060 -0.001413
374 | v 0.055501 0.003048 -0.003197
375 | v 0.052574 0.003103 -0.001978
376 | v 0.054255 -0.014263 -0.001752
377 | v 0.055745 -0.014263 0.001752
378 | vt 0.750000 0.250000
379 | vt 0.750000 0.250000
380 | vt 0.750000 0.250000
381 | vt 0.750000 0.250000
382 | vt 0.750000 0.250000
383 | vt 0.750000 0.250000
384 | vt 0.750000 0.250000
385 | vt 0.750000 0.250000
386 | vt 0.750000 0.250000
387 | vt 0.750000 0.250000
388 | vt 0.750000 0.250000
389 | vt 0.750000 0.250000
390 | vt 0.750000 0.250000
391 | vt 0.750000 0.250000
392 | vt 0.750000 0.250000
393 | vt 0.750000 0.250000
394 | vt 0.750000 0.250000
395 | vt 0.750000 0.250000
396 | vt 0.750000 0.250000
397 | vt 0.750000 0.250000
398 | vt 0.750000 0.250000
399 | vt 0.750000 0.250000
400 | vt 0.750000 0.250000
401 | vt 0.750000 0.250000
402 | vt 0.750000 0.250000
403 | vt 0.750000 0.250000
404 | vt 0.750000 0.250000
405 | vt 0.750000 0.250000
406 | vt 0.750000 0.250000
407 | vt 0.750000 0.250000
408 | vt 0.750000 0.250000
409 | vt 0.750000 0.250000
410 | vt 0.750000 0.250000
411 | vt 0.750000 0.250000
412 | vt 0.750000 0.250000
413 | vt 0.750000 0.250000
414 | vt 0.750000 0.250000
415 | vt 0.750000 0.250000
416 | vt 0.750000 0.250000
417 | vt 0.750000 0.250000
418 | vt 0.750000 0.250000
419 | vt 0.750000 0.250000
420 | vt 0.750000 0.250000
421 | vt 0.750000 0.250000
422 | vt 0.750000 0.250000
423 | vt 0.750000 0.250000
424 | vt 0.750000 0.250000
425 | vt 0.750000 0.250000
426 | vt 0.750000 0.250000
427 | vt 0.750000 0.250000
428 | vt 0.750000 0.250000
429 | vt 0.750000 0.250000
430 | vt 0.750000 0.250000
431 | vt 0.750000 0.250000
432 | vt 0.750000 0.250000
433 | vt 0.750000 0.250000
434 | vt 0.750000 0.250000
435 | vt 0.750000 0.250000
436 | vt 0.750000 0.250000
437 | vt 0.750000 0.250000
438 | vt 0.750000 0.250000
439 | vt 0.750000 0.250000
440 | vt 0.750000 0.250000
441 | vt 0.750000 0.250000
442 | vt 0.750000 0.250000
443 | vt 0.750000 0.250000
444 | vt 0.750000 0.250000
445 | vt 0.750000 0.250000
446 | vt 0.750000 0.250000
447 | vt 0.750000 0.250000
448 | vt 0.750000 0.250000
449 | vt 0.750000 0.250000
450 | vt 0.750000 0.250000
451 | vt 0.750000 0.250000
452 | vt 0.750000 0.250000
453 | vt 0.750000 0.250000
454 | vt 0.750000 0.250000
455 | vt 0.750000 0.250000
456 | vt 0.750000 0.250000
457 | vt 0.750000 0.250000
458 | vt 0.750000 0.250000
459 | vt 0.750000 0.250000
460 | vt 0.750000 0.250000
461 | vt 0.750000 0.250000
462 | vt 0.750000 0.250000
463 | vt 0.750000 0.250000
464 | vt 0.750000 0.250000
465 | vt 0.750000 0.250000
466 | vt 0.750000 0.250000
467 | vt 0.750000 0.250000
468 | vt 0.750000 0.250000
469 | vt 0.750000 0.250000
470 | vt 0.750000 0.250000
471 | vt 0.750000 0.250000
472 | vt 0.750000 0.250000
473 | vt 0.750000 0.250000
474 | vt 0.750000 0.250000
475 | vt 0.750000 0.250000
476 | vt 0.750000 0.250000
477 | vt 0.750000 0.250000
478 | vt 0.750000 0.250000
479 | vt 0.750000 0.250000
480 | vt 0.750000 0.250000
481 | vt 0.750000 0.250000
482 | vt 0.750000 0.250000
483 | vt 0.750000 0.250000
484 | vt 0.750000 0.250000
485 | vt 0.750000 0.250000
486 | vt 0.750000 0.250000
487 | vt 0.750000 0.250000
488 | vt 0.750000 0.250000
489 | vt 0.750000 0.250000
490 | vt 0.750000 0.250000
491 | vt 0.750000 0.250000
492 | vt 0.750000 0.250000
493 | vt 0.750000 0.250000
494 | vt 0.750000 0.250000
495 | vt 0.750000 0.250000
496 | vt 0.750000 0.250000
497 | vt 0.750000 0.250000
498 | vt 0.750000 0.250000
499 | vt 0.750000 0.250000
500 | vt 0.750000 0.250000
501 | vt 0.750000 0.250000
502 | vt 0.750000 0.250000
503 | vt 0.750000 0.250000
504 | vt 0.750000 0.250000
505 | vt 0.750000 0.250000
506 | vt 0.750000 0.250000
507 | vt 0.750000 0.250000
508 | vt 0.750000 0.250000
509 | vt 0.750000 0.250000
510 | vt 0.750000 0.250000
511 | vt 0.750000 0.250000
512 | vt 0.750000 0.250000
513 | vt 0.750000 0.250000
514 | vt 0.750000 0.250000
515 | vt 0.750000 0.250000
516 | vt 0.750000 0.250000
517 | vt 0.750000 0.250000
518 | vt 0.750000 0.250000
519 | vt 0.750000 0.250000
520 | vt 0.750000 0.250000
521 | vt 0.750000 0.250000
522 | vt 0.750000 0.250000
523 | vt 0.750000 0.250000
524 | vt 0.750000 0.250000
525 | vt 0.750000 0.250000
526 | vt 0.750000 0.250000
527 | vt 0.750000 0.250000
528 | vt 0.750000 0.250000
529 | vt 0.750000 0.250000
530 | vt 0.750000 0.250000
531 | vt 0.750000 0.250000
532 | vt 0.750000 0.250000
533 | vt 0.750000 0.250000
534 | vt 0.750000 0.250000
535 | vt 0.750000 0.250000
536 | vt 0.750000 0.250000
537 | vt 0.750000 0.250000
538 | vt 0.750000 0.250000
539 | vt 0.750000 0.250000
540 | vt 0.750000 0.250000
541 | vt 0.750000 0.250000
542 | vt 0.750000 0.250000
543 | vt 0.750000 0.250000
544 | vt 0.750000 0.250000
545 | vt 0.250000 0.250000
546 | vt 0.250000 0.250000
547 | vt 0.250000 0.250000
548 | vt 0.250000 0.250000
549 | vt 0.250000 0.250000
550 | vt 0.250000 0.250000
551 | vt 0.250000 0.250000
552 | vt 0.250000 0.250000
553 | vt 0.250000 0.250000
554 | vt 0.250000 0.250000
555 | vt 0.250000 0.250000
556 | vt 0.250000 0.250000
557 | vt 0.250000 0.250000
558 | vt 0.250000 0.250000
559 | vt 0.250000 0.250000
560 | vt 0.250000 0.250000
561 | vt 0.250000 0.250000
562 | vt 0.250000 0.250000
563 | vt 0.250000 0.250000
564 | vt 0.250000 0.250000
565 | vt 0.250000 0.250000
566 | vt 0.250000 0.250000
567 | vt 0.250000 0.250000
568 | vt 0.250000 0.250000
569 | vt 0.250000 0.250000
570 | vt 0.250000 0.250000
571 | vt 0.250000 0.250000
572 | vt 0.250000 0.250000
573 | vt 0.250000 0.250000
574 | vt 0.250000 0.250000
575 | vt 0.250000 0.250000
576 | vt 0.250000 0.250000
577 | vt 0.250000 0.250000
578 | vt 0.250000 0.250000
579 | vt 0.250000 0.250000
580 | vt 0.250000 0.250000
581 | vt 0.250000 0.250000
582 | vt 0.250000 0.250000
583 | vt 0.250000 0.250000
584 | vt 0.250000 0.250000
585 | vt 0.250000 0.250000
586 | vt 0.250000 0.250000
587 | vt 0.250000 0.250000
588 | vt 0.250000 0.250000
589 | vt 0.250000 0.250000
590 | vt 0.250000 0.250000
591 | vt 0.250000 0.250000
592 | vt 0.250000 0.250000
593 | vt 0.250000 0.250000
594 | vt 0.250000 0.250000
595 | vt 0.250000 0.250000
596 | vt 0.250000 0.250000
597 | vt 0.250000 0.250000
598 | vt 0.250000 0.250000
599 | vt 0.250000 0.250000
600 | vt 0.250000 0.250000
601 | vt 0.250000 0.250000
602 | vt 0.250000 0.250000
603 | vt 0.250000 0.250000
604 | vt 0.250000 0.250000
605 | vt 0.250000 0.250000
606 | vt 0.250000 0.250000
607 | vt 0.250000 0.250000
608 | vt 0.250000 0.250000
609 | vt 0.250000 0.250000
610 | vt 0.250000 0.250000
611 | vt 0.250000 0.250000
612 | vt 0.250000 0.250000
613 | vt 0.250000 0.250000
614 | vt 0.250000 0.250000
615 | vt 0.250000 0.250000
616 | vt 0.250000 0.250000
617 | vt 0.250000 0.250000
618 | vt 0.250000 0.250000
619 | vt 0.250000 0.250000
620 | vt 0.250000 0.250000
621 | vt 0.250000 0.250000
622 | vt 0.250000 0.250000
623 | vt 0.250000 0.250000
624 | vt 0.250000 0.250000
625 | vt 0.250000 0.250000
626 | vt 0.250000 0.250000
627 | vt 0.250000 0.250000
628 | vt 0.250000 0.250000
629 | vt 0.250000 0.250000
630 | vt 0.250000 0.250000
631 | vt 0.250000 0.250000
632 | vt 0.250000 0.250000
633 | vt 0.250000 0.250000
634 | vt 0.250000 0.250000
635 | vt 0.250000 0.250000
636 | vt 0.250000 0.250000
637 | vt 0.250000 0.250000
638 | vt 0.250000 0.250000
639 | vt 0.250000 0.250000
640 | vt 0.250000 0.250000
641 | vt 0.250000 0.250000
642 | vt 0.250000 0.250000
643 | vt 0.250000 0.250000
644 | vt 0.250000 0.250000
645 | vt 0.250000 0.250000
646 | vt 0.250000 0.250000
647 | vt 0.250000 0.250000
648 | vt 0.250000 0.250000
649 | vt 0.250000 0.250000
650 | vt 0.250000 0.250000
651 | vt 0.250000 0.250000
652 | vt 0.250000 0.250000
653 | vt 0.250000 0.250000
654 | vt 0.250000 0.250000
655 | vt 0.250000 0.250000
656 | vt 0.250000 0.250000
657 | vt 0.250000 0.250000
658 | vt 0.250000 0.250000
659 | vt 0.250000 0.250000
660 | vt 0.250000 0.250000
661 | vt 0.250000 0.250000
662 | vt 0.250000 0.250000
663 | vt 0.250000 0.250000
664 | vt 0.250000 0.250000
665 | vt 0.250000 0.250000
666 | vt 0.250000 0.250000
667 | vt 0.250000 0.250000
668 | vt 0.250000 0.250000
669 | vt 0.250000 0.250000
670 | vt 0.250000 0.250000
671 | vt 0.250000 0.250000
672 | vt 0.250000 0.250000
673 | vt 0.250000 0.250000
674 | vt 0.250000 0.250000
675 | vt 0.250000 0.250000
676 | vt 0.250000 0.250000
677 | vt 0.250000 0.250000
678 | vt 0.250000 0.250000
679 | vt 0.250000 0.250000
680 | vt 0.250000 0.250000
681 | vt 0.250000 0.250000
682 | vt 0.250000 0.250000
683 | vt 0.250000 0.250000
684 | vt 0.250000 0.250000
685 | vt 0.250000 0.250000
686 | vt 0.250000 0.250000
687 | vt 0.250000 0.250000
688 | vt 0.250000 0.250000
689 | vt 0.250000 0.250000
690 | vt 0.250000 0.250000
691 | vt 0.250000 0.250000
692 | vt 0.250000 0.250000
693 | vt 0.250000 0.250000
694 | vt 0.250000 0.250000
695 | vt 0.250000 0.250000
696 | vt 0.250000 0.250000
697 | vt 0.250000 0.250000
698 | vt 0.250000 0.250000
699 | vt 0.250000 0.250000
700 | vt 0.250000 0.250000
701 | vt 0.250000 0.250000
702 | vt 0.250000 0.250000
703 | vt 0.250000 0.250000
704 | vt 0.250000 0.250000
705 | vt 0.250000 0.250000
706 | vt 0.250000 0.250000
707 | vt 0.250000 0.250000
708 | vt 0.250000 0.250000
709 | vt 0.250000 0.250000
710 | vt 0.250000 0.250000
711 | vt 0.250000 0.250000
712 | vt 0.250000 0.250000
713 | vt 0.250000 0.250000
714 | vt 0.250000 0.250000
715 | vt 0.250000 0.250000
716 | vt 0.250000 0.250000
717 | vt 0.250000 0.250000
718 | vt 0.250000 0.250000
719 | vt 0.250000 0.250000
720 | vt 0.250000 0.250000
721 | vt 0.250000 0.250000
722 | vt 0.250000 0.250000
723 | vt 0.250000 0.250000
724 | vt 0.250000 0.250000
725 | vt 0.250000 0.250000
726 | vt 0.250000 0.250000
727 | vt 0.250000 0.250000
728 | vt 0.250000 0.250000
729 | vt 0.250000 0.250000
730 | vt 0.250000 0.250000
731 | vt 0.250000 0.250000
732 | vt 0.250000 0.250000
733 | vt 0.250000 0.250000
734 | vt 0.250000 0.250000
735 | vt 0.250000 0.250000
736 | vt 0.250000 0.250000
737 | vt 0.250000 0.250000
738 | vt 0.250000 0.250000
739 | vt 0.250000 0.250000
740 | vt 0.250000 0.250000
741 | vt 0.250000 0.250000
742 | vt 0.250000 0.250000
743 | vt 0.250000 0.250000
744 | vt 0.250000 0.250000
745 | vt 0.250000 0.250000
746 | vt 0.250000 0.250000
747 | vt 0.250000 0.250000
748 | vt 0.250000 0.250000
749 | vt 0.250000 0.250000
750 | vt 0.250000 0.250000
751 | vt 0.250000 0.250000
752 | vn -0.0000 1.0000 0.0000
753 | vn 0.0133 0.9994 0.0323
754 | vn 0.0163 0.9995 0.0269
755 | vn 0.1023 0.9457 -0.3084
756 | vn 0.0003 1.0000 0.0007
757 | vn -0.0000 1.0000 0.0050
758 | vn 0.0585 0.9776 -0.2023
759 | vn 0.0029 1.0000 -0.0047
760 | vn 0.0106 0.9999 -0.0055
761 | vn -0.0008 1.0000 0.0006
762 | vn 0.0001 1.0000 -0.0000
763 | vn 0.0953 0.9421 0.3215
764 | vn 0.0134 0.9991 0.0410
765 | vn -0.0087 1.0000 0.0009
766 | vn 0.0034 0.9999 0.0095
767 | vn 0.0003 1.0000 -0.0002
768 | vn 0.0042 1.0000 -0.0068
769 | vn 0.0005 1.0000 -0.0008
770 | vn 0.0032 1.0000 0.0039
771 | vn 0.0006 1.0000 0.0003
772 | vn 0.0135 0.9999 -0.0064
773 | vn 0.0084 0.9999 -0.0087
774 | vn -0.0158 0.9975 -0.0689
775 | vn -0.0048 0.9997 -0.0219
776 | vn -0.0154 0.9972 -0.0732
777 | vn -0.0172 0.9998 -0.0096
778 | vn -0.0080 0.9995 -0.0314
779 | vn -0.0017 1.0000 0.0055
780 | vn -0.0206 0.9997 0.0104
781 | vn -0.0492 0.9977 -0.0472
782 | vn -0.1517 0.8571 0.4923
783 | vn 0.0113 0.9999 -0.0022
784 | vn 0.0113 0.9999 0.0039
785 | vn 0.0054 0.9999 -0.0117
786 | vn -0.0079 0.9996 -0.0281
787 | vn -0.0001 1.0000 0.0004
788 | vn -0.0211 0.9998 0.0044
789 | vn 0.0023 1.0000 0.0088
790 | vn 0.0028 1.0000 0.0012
791 | vn 0.0047 1.0000 0.0045
792 | vn -0.0995 0.9747 0.2003
793 | vn 0.0013 1.0000 -0.0058
794 | vn -0.2691 0.9495 0.1612
795 | vn -0.1872 0.9735 0.1316
796 | vn -0.2987 0.8284 0.4738
797 | vn -0.0227 0.9670 0.2539
798 | vn 0.0112 0.9126 0.4087
799 | vn 0.0010 1.0000 -0.0077
800 | vn -0.0009 0.9997 -0.0241
801 | vn -0.0034 0.9993 -0.0360
802 | vn -0.0652 -0.9975 -0.0275
803 | vn -0.0860 -0.9958 0.0326
804 | vn -0.0701 -0.9956 -0.0629
805 | vn 0.0028 -0.9990 -0.0451
806 | vn 0.0114 -0.9979 -0.0639
807 | vn -0.0338 -0.9972 0.0664
808 | vn -0.0334 -0.9934 0.1098
809 | vn 0.0476 -0.9979 0.0447
810 | vn 0.0383 -0.9969 0.0683
811 | vn 0.0763 -0.9968 -0.0246
812 | vn 0.1017 -0.9948 0.0089
813 | vn -0.2313 -0.9667 0.1093
814 | vn -0.0200 -0.9995 -0.0261
815 | vn -0.0192 -0.9996 -0.0206
816 | vn -0.0122 -0.9999 -0.0056
817 | vn -0.1251 -0.9921 0.0029
818 | vn -0.0058 -1.0000 0.0046
819 | vn -0.0058 -1.0000 0.0063
820 | vn -0.1416 -0.9889 -0.0454
821 | vn 0.3765 -0.0186 0.9262
822 | vn 0.2747 0.1182 0.9542
823 | vn 0.3395 0.0010 0.9406
824 | vn 0.5827 -0.0077 0.8126
825 | vn 0.6021 0.0609 0.7961
826 | vn 0.9195 -0.0705 0.3866
827 | vn 0.9180 -0.0799 0.3885
828 | vn 0.9262 -0.0226 0.3764
829 | vn 0.9276 -0.0098 0.3735
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1406 | vn -0.0756 0.2441 0.9668
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1408 | vn 0.1183 0.0476 0.9918
1409 | vn 0.2672 -0.1126 0.9570
1410 | vn 0.9940 0.0817 0.0730
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1412 | vn 0.9941 0.0693 0.0832
1413 | vn 0.9917 0.0141 0.1279
1414 | vn 0.6694 0.6722 0.3162
1415 | vn 0.3826 -0.4294 0.8181
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1421 | vn 0.0160 0.9984 0.0544
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1423 | vn -0.0368 -0.9955 -0.0871
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1446 | vn 0.9765 0.1039 -0.1887
1447 | vn 0.9154 0.3986 0.0567
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1449 | vn 0.2443 0.8371 0.4895
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1452 | vn -0.2437 0.6112 -0.7530
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1454 | vn -0.3070 0.7263 -0.6151
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1469 | vn -0.9411 0.0406 -0.3357
1470 | vn -0.9553 0.1027 -0.2772
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1472 | vn -0.9206 -0.0199 -0.3901
1473 | vn -0.7855 -0.1753 0.5935
1474 | vn -0.4930 0.1741 0.8524
1475 | vn 0.4582 0.0351 0.8882
1476 | vn 0.3041 -0.0814 0.9492
1477 | vn 0.4523 0.0305 0.8913
1478 | vn 0.5891 0.1462 0.7947
1479 | vn 0.9963 -0.0515 -0.0694
1480 | vn 0.9850 -0.1647 0.0513
1481 | vn 0.9962 -0.0479 -0.0731
1482 | vn 0.9716 0.0923 -0.2179
1483 | vn 0.2484 0.1016 -0.9633
1484 | vn 0.8710 0.4255 -0.2456
1485 | vn 0.9625 -0.2582 0.0831
1486 | vn -0.2183 0.4841 0.8473
1487 | vn -0.8325 0.4182 -0.3634
1488 | vn -0.7663 0.6109 -0.1991
1489 | vn -0.8024 0.5300 -0.2742
1490 | vn -0.6759 0.7347 -0.0583
1491 | vn 0.0027 0.9994 -0.0334
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1493 | vn -0.2458 -0.9587 0.1434
1494 | vn -0.0386 -0.9869 0.1569
1495 | vn -0.1308 -0.9905 -0.0433
1496 | vn -0.0158 -0.9888 -0.1484
1497 | vn 0.0306 -0.9876 -0.1541
1498 | vn 0.1219 -0.9907 0.0602
1499 | vn 0.1336 -0.9906 0.0291
1500 | vn -0.6164 0.0131 -0.7873
1501 | vn -0.5931 -0.0235 -0.8048
1502 | vn -0.6238 0.0252 -0.7812
1503 | vn -0.6452 0.0616 -0.7615
1504 | vn -0.9135 -0.0076 0.4069
1505 | vn -0.9039 0.0189 0.4272
1506 | vn -0.9158 -0.0147 0.4014
1507 | vn -0.9248 -0.0442 0.3779
1508 | vn 0.1410 0.0570 0.9884
1509 | vn 0.2940 -0.0814 0.9523
1510 | vn 0.3165 -0.1025 0.9430
1511 | vn 0.4198 -0.2020 0.8849
1512 | vn 0.8833 0.2515 0.3957
1513 | vn 0.7713 -0.0891 -0.6302
1514 | vn 0.7996 -0.1514 -0.5812
1515 | vn 0.7559 -0.0592 -0.6521
1516 | vn 0.7100 0.0191 -0.7039
1517 | vn 0.4870 0.4710 -0.7355
1518 | vn 0.4867 0.4714 -0.7355
1519 | vn 0.4869 0.4712 -0.7355
1520 | vn 0.4865 0.4716 -0.7354
1521 | vn -0.0174 -0.1439 0.9894
1522 | vn -0.3908 0.7059 0.5908
1523 | vn -0.8395 0.3891 -0.3793
1524 | vn -0.0218 0.9996 0.0202
1525 | vn -0.0022 0.9995 -0.0319
1526 | vn -0.1882 -0.9817 -0.0290
1527 | vn -0.2216 -0.9749 -0.0191
1528 | vn -0.1140 -0.9897 -0.0872
1529 | vn -0.0266 -0.9812 -0.1909
1530 | vn 0.0618 -0.9869 -0.1493
1531 | vn 0.1586 -0.9841 0.0806
1532 | vn 0.1489 -0.9887 -0.0145
1533 | vn 0.0298 -0.9940 0.1056
1534 | vn -0.0041 -0.9959 0.0904
1535 | vn -0.9807 0.0327 0.1929
1536 | vn -0.9948 -0.0969 0.0318
1537 | vn -0.9758 0.0494 0.2131
1538 | vn -0.9209 0.1666 0.3523
1539 | vn -0.3463 -0.2135 0.9135
1540 | vn 0.1376 0.1153 0.9837
1541 | vn 0.8552 0.0441 0.5164
1542 | vn 0.7845 -0.0679 0.6164
1543 | vn 0.8607 0.0547 0.5061
1544 | vn 0.9073 0.1713 0.3839
1545 | vn 0.7532 0.0227 -0.6574
1546 | vn 0.7904 -0.0328 -0.6117
1547 | vn 0.7458 0.0329 -0.6653
1548 | vn 0.7012 0.0901 -0.7072
1549 | vn -0.4694 0.0132 -0.8829
1550 | vn -0.3297 -0.1287 -0.9353
1551 | vn -0.4877 0.0333 -0.8724
1552 | vn -0.5990 0.1672 -0.7831
1553 | vn -0.8491 0.3870 -0.3597
1554 | vn 0.0390 0.7675 -0.6398
1555 | vn 0.6230 0.0679 -0.7793
1556 | vn -0.0494 0.3577 0.9325
1557 | vn -0.0538 0.3496 0.9353
1558 | vn -0.0511 0.3546 0.9336
1559 | vn -0.0571 0.3433 0.9375
1560 | vn 0.0049 -1.0000 -0.0051
1561 | vn 0.0145 -0.9999 -0.0059
1562 | vn 0.0184 -0.9996 -0.0216
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1565 | vn 0.0002 -1.0000 -0.0049
1566 | vn 0.0198 -0.9996 -0.0212
1567 | vn -0.0036 -0.9997 -0.0256
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1570 | vn -0.0061 -1.0000 0.0078
1571 | vn -0.3669 0.0239 0.9299
1572 | vn -0.3725 0.0132 0.9280
1573 | vn -0.3615 0.0343 0.9317
1574 | vn -0.3571 0.0427 0.9331
1575 | vn 0.7546 -0.0694 0.6525
1576 | vn 0.7148 -0.1533 0.6823
1577 | vn 0.7954 0.0400 0.6048
1578 | vn 0.8167 0.1175 0.5649
1579 | vn 0.8639 -0.0668 -0.4992
1580 | vn 0.8855 -0.1798 -0.4285
1581 | vn 0.8142 0.0776 -0.5754
1582 | vn 0.7638 0.1800 -0.6198
1583 | vn 0.0280 -0.2334 -0.9720
1584 | vn -0.3914 0.1892 -0.9005
1585 | vn -0.7125 -0.1737 -0.6799
1586 | vn -0.9905 0.1361 -0.0175
1587 | vn -0.9977 0.0440 0.0516
1588 | vn -0.9931 -0.0372 0.1115
1589 | vn -0.9713 -0.1443 0.1893
1590 | vn -0.3702 0.0299 0.9285
1591 | vn -0.0851 -0.0271 0.9960
1592 | vn -0.3117 0.0178 0.9500
1593 | vn -0.0371 -0.0363 0.9987
1594 | vn 0.5520 0.0410 0.8328
1595 | vn 0.9996 -0.0193 -0.0216
1596 | vn 0.9997 -0.0244 -0.0008
1597 | vn 0.9997 -0.0237 -0.0039
1598 | vn 0.9995 -0.0181 -0.0265
1599 | vn 0.6172 0.0359 -0.7860
1600 | vn -0.3117 0.0202 -0.9500
1601 | vn 0.0371 -0.0476 -0.9982
1602 | vn -0.0160 -0.0376 -0.9992
1603 | vn -0.3837 0.0349 -0.9228
1604 | vn -0.9930 0.0069 -0.1179
1605 | vn -0.9996 -0.0207 -0.0168
1606 | vn -0.9954 0.0007 -0.0955
1607 | vn -0.9997 -0.0255 0.0010
1608 | vn 0.0014 1.0000 -0.0012
1609 | vn 0.0003 0.9994 -0.0341
1610 | vn 0.0044 1.0000 -0.0073
1611 | vn 0.0053 1.0000 -0.0009
1612 | vn 0.0090 0.9999 -0.0064
1613 | vn 0.0104 0.9997 -0.0200
1614 | vn 0.5829 -0.7738 -0.2479
1615 | vn -0.5831 -0.7736 0.2479
1616 | vn -0.6051 -0.6796 0.4146
1617 | vn -0.6023 -0.7021 0.3799
1618 | vn 0.5178 -0.2137 -0.8284
1619 | vn 0.9284 -0.3187 0.1910
1620 | vn 0.2828 0.1856 0.9410
1621 | vn -0.5943 -0.4820 0.6438
1622 | vn -0.8731 0.1447 -0.4656
1623 | s 1
1624 | f 1/1/1 2/2/1 3/3/1
1625 | f 1/1/1 3/3/1 4/4/1
1626 | f 5/5/2 6/6/3 7/7/4
1627 | f 8/8/5 9/9/6 10/10/7
1628 | f 10/10/7 9/9/6 11/11/8
1629 | f 12/12/9 13/13/10 14/14/11
1630 | f 15/15/12 16/16/13 17/17/14
1631 | f 18/18/1 19/19/1 20/20/1
1632 | f 21/21/15 20/20/1 22/22/16
1633 | f 23/23/17 24/24/18 25/25/19
1634 | f 25/25/19 24/24/18 19/19/1
1635 | f 21/21/15 26/26/1 14/14/11
1636 | f 21/21/15 27/27/20 26/26/1
1637 | f 14/14/11 26/26/1 12/12/9
1638 | f 28/28/21 12/12/9 29/29/22
1639 | f 28/28/21 29/29/22 23/23/17
1640 | f 29/29/22 27/27/20 23/23/17
1641 | f 30/30/23 31/31/24 32/32/25
1642 | f 8/8/5 33/33/26 31/31/24
1643 | f 8/8/5 31/31/24 34/34/27
1644 | f 10/10/7 35/35/28 8/8/5
1645 | f 35/35/28 33/33/26 8/8/5
1646 | f 34/34/27 31/31/24 30/30/23
1647 | f 33/33/26 35/35/28 36/36/29
1648 | f 36/36/29 37/37/30 33/33/26
1649 | f 11/11/31 38/38/31 39/39/31
1650 | f 11/11/32 13/13/10 12/12/9
1651 | f 11/11/32 12/12/9 28/28/21
1652 | f 11/11/32 28/28/21 38/38/33
1653 | f 7/7/4 39/39/34 5/5/2
1654 | f 5/5/2 40/40/35 16/16/13
1655 | f 18/18/1 16/16/13 19/19/1
1656 | f 19/19/1 16/16/13 25/25/19
1657 | f 25/25/19 16/16/13 40/40/35
1658 | f 17/17/14 41/41/36 15/15/12
1659 | f 42/42/37 41/41/36 43/43/38
1660 | f 41/41/36 44/44/39 45/45/40
1661 | f 41/41/36 45/45/40 15/15/12
1662 | f 42/42/37 46/46/41 47/47/42
1663 | f 48/48/43 49/49/44 43/43/38
1664 | f 42/42/37 47/47/42 41/41/36
1665 | f 47/47/42 44/44/39 41/41/36
1666 | f 46/46/41 42/42/37 50/50/45
1667 | f 44/44/39 47/47/42 51/51/46
1668 | f 44/44/39 51/51/46 52/52/47
1669 | f 43/43/38 41/41/36 48/48/43
1670 | f 14/14/11 53/53/48 21/21/15
1671 | f 34/34/27 54/54/49 14/14/11
1672 | f 14/14/11 54/54/49 53/53/48
1673 | f 53/53/48 54/54/49 55/55/50
1674 | f 21/21/15 18/18/1 20/20/1
1675 | f 8/8/5 34/34/27 14/14/11
1676 | f 27/27/20 21/21/15 22/22/16
1677 | f 27/27/20 22/22/16 23/23/17
1678 | f 23/23/17 22/22/16 24/24/18
1679 | f 56/56/51 57/57/52 58/58/53
1680 | f 56/56/51 58/58/53 59/59/54
1681 | f 59/59/54 58/58/53 60/60/55
1682 | f 61/61/56 62/62/57 57/57/52
1683 | f 61/61/56 57/57/52 56/56/51
1684 | f 63/63/58 64/64/59 61/61/56
1685 | f 61/61/56 64/64/59 62/62/57
1686 | f 65/65/60 66/66/61 63/63/58
1687 | f 63/63/58 66/66/61 64/64/59
1688 | f 65/65/60 60/60/55 66/66/61
1689 | f 59/59/54 60/60/55 65/65/60
1690 | f 67/67/62 68/68/63 69/69/64
1691 | f 67/67/62 70/70/65 71/71/66
1692 | f 67/67/62 69/69/64 70/70/65
1693 | f 72/72/67 73/73/68 74/74/69
1694 | f 72/72/67 74/74/69 70/70/65
1695 | f 70/70/65 74/74/69 71/71/66
1696 | f 68/68/70 75/75/71 76/76/72
1697 | f 68/68/70 76/76/72 77/77/73
1698 | f 68/68/70 77/77/73 69/69/74
1699 | f 69/69/75 77/77/76 78/78/77
1700 | f 69/69/75 78/78/77 70/70/78
1701 | f 70/70/79 78/78/80 72/72/81
1702 | f 72/72/81 78/78/80 79/79/82
1703 | f 72/72/83 79/79/83 73/73/83
1704 | f 73/73/84 79/79/85 80/80/86
1705 | f 80/80/86 81/81/87 73/73/84
1706 | f 76/76/88 75/75/89 82/82/90
1707 | f 76/76/88 82/82/90 83/83/91
1708 | f 84/84/92 83/83/91 82/82/90
1709 | f 85/85/93 83/83/91 84/84/92
1710 | f 83/83/91 85/85/93 86/86/94
1711 | f 87/87/95 86/86/94 85/85/93
1712 | f 88/88/96 89/89/97 90/90/98
1713 | f 88/88/96 90/90/98 91/91/99
1714 | f 88/88/96 91/91/99 92/92/100
1715 | f 93/93/101 92/92/100 91/91/99
1716 | f 92/92/100 93/93/101 80/80/86
1717 | f 80/80/86 93/93/101 81/81/87
1718 | f 48/48/102 94/94/103 95/95/104
1719 | f 95/95/104 94/94/103 96/96/105
1720 | f 95/95/106 96/96/107 97/97/108
1721 | f 95/95/106 97/97/108 98/98/109
1722 | f 94/94/110 48/48/111 99/99/112
1723 | f 99/99/112 48/48/111 100/100/113
1724 | f 99/99/114 100/100/115 101/101/116
1725 | f 101/101/116 100/100/115 102/102/117
1726 | f 101/101/118 102/102/119 97/97/120
1727 | f 97/97/120 102/102/119 98/98/121
1728 | f 103/103/122 84/84/122 50/50/122
1729 | f 84/84/123 103/103/123 104/104/123
1730 | f 84/84/124 104/104/124 49/49/124
1731 | f 103/103/125 50/50/126 105/105/127
1732 | f 105/105/127 50/50/126 42/42/128
1733 | f 105/105/129 42/42/130 43/43/131
1734 | f 105/105/129 43/43/131 106/106/132
1735 | f 106/106/133 43/43/133 49/49/133
1736 | f 106/106/134 49/49/134 104/104/134
1737 | f 51/51/135 107/107/136 108/108/137
1738 | f 109/109/138 108/108/137 107/107/136
1739 | f 108/108/139 109/109/140 46/46/141
1740 | f 46/46/141 109/109/140 110/110/142
1741 | f 107/107/143 51/51/144 47/47/145
1742 | f 107/107/143 47/47/145 111/111/146
1743 | f 111/111/147 47/47/147 110/110/147
1744 | f 110/110/148 47/47/148 46/46/148
1745 | f 15/15/149 112/112/149 113/113/149
1746 | f 113/113/150 112/112/150 114/114/150
1747 | f 114/114/151 52/52/151 113/113/151
1748 | f 115/115/152 52/52/152 114/114/152
1749 | f 112/112/153 15/15/154 116/116/155
1750 | f 116/116/155 15/15/154 45/45/156
1751 | f 116/116/157 45/45/158 117/117/159
1752 | f 117/117/159 45/45/158 44/44/160
1753 | f 117/117/161 44/44/161 115/115/161
1754 | f 115/115/162 44/44/162 52/52/162
1755 | f 118/118/163 18/18/164 41/41/165
1756 | f 118/118/166 41/41/167 119/119/168
1757 | f 119/119/168 41/41/167 17/17/169
1758 | f 119/119/170 17/17/171 16/16/172
1759 | f 119/119/170 16/16/172 120/120/173
1760 | f 120/120/174 16/16/175 18/18/176
1761 | f 120/120/174 18/18/176 121/121/177
1762 | f 121/121/178 18/18/164 118/118/163
1763 | f 122/122/179 19/19/180 123/123/181
1764 | f 123/123/181 19/19/180 24/24/182
1765 | f 123/123/183 24/24/184 22/22/185
1766 | f 123/123/183 22/22/185 124/124/186
1767 | f 124/124/187 22/22/188 20/20/189
1768 | f 124/124/187 20/20/189 125/125/190
1769 | f 125/125/191 20/20/192 122/122/193
1770 | f 122/122/193 20/20/192 19/19/194
1771 | f 126/126/195 27/27/196 127/127/197
1772 | f 127/127/197 27/27/196 29/29/198
1773 | f 127/127/199 29/29/199 128/128/199
1774 | f 128/128/200 29/29/200 12/12/200
1775 | f 128/128/201 12/12/202 129/129/203
1776 | f 129/129/203 12/12/202 26/26/204
1777 | f 129/129/205 26/26/206 126/126/207
1778 | f 126/126/207 26/26/206 27/27/208
1779 | f 4/4/209 9/9/210 1/1/211
1780 | f 9/9/210 8/8/212 1/1/211
1781 | f 1/1/213 8/8/214 14/14/215
1782 | f 1/1/213 14/14/215 2/2/216
1783 | f 2/2/217 14/14/217 13/13/217
1784 | f 2/2/218 13/13/219 3/3/220
1785 | f 13/13/219 11/11/221 3/3/220
1786 | f 3/3/222 11/11/223 4/4/224
1787 | f 4/4/224 11/11/223 9/9/225
1788 | f 36/36/226 130/130/226 131/131/226
1789 | f 36/36/227 131/131/227 132/132/227
1790 | f 133/133/228 132/132/229 131/131/230
1791 | f 133/133/228 10/10/231 132/132/229
1792 | f 130/130/232 36/36/233 134/134/234
1793 | f 134/134/234 36/36/233 35/35/235
1794 | f 134/134/236 35/35/237 10/10/238
1795 | f 134/134/236 10/10/238 133/133/239
1796 | f 135/135/240 32/32/241 136/136/242
1797 | f 37/37/243 32/32/241 135/135/240
1798 | f 137/137/244 37/37/245 135/135/246
1799 | f 136/136/247 32/32/248 31/31/249
1800 | f 136/136/247 31/31/249 138/138/250
1801 | f 138/138/251 31/31/252 33/33/253
1802 | f 138/138/251 33/33/253 137/137/254
1803 | f 137/137/244 33/33/255 37/37/245
1804 | f 139/139/256 140/140/257 55/55/258
1805 | f 141/141/259 140/140/257 139/139/256
1806 | f 141/141/260 30/30/260 140/140/260
1807 | f 142/142/261 30/30/262 141/141/263
1808 | f 139/139/264 55/55/265 54/54/266
1809 | f 139/139/264 54/54/266 143/143/267
1810 | f 143/143/268 54/54/269 142/142/270
1811 | f 142/142/270 54/54/269 34/34/271
1812 | f 142/142/261 34/34/272 30/30/262
1813 | f 134/134/1 133/133/1 130/130/1
1814 | f 144/144/273 145/145/274 146/146/275
1815 | f 144/144/273 146/146/275 89/89/276
1816 | f 147/147/277 89/89/278 146/146/279
1817 | f 147/147/277 53/53/280 89/89/278
1818 | f 145/145/274 144/144/273 148/148/281
1819 | f 145/145/282 148/148/283 149/149/284
1820 | f 149/149/284 148/148/283 21/21/285
1821 | f 149/149/286 21/21/286 147/147/286
1822 | f 147/147/287 21/21/287 53/53/287
1823 | f 67/67/288 150/150/289 75/75/71
1824 | f 67/67/288 75/75/71 68/68/70
1825 | f 150/150/289 67/67/288 151/151/290
1826 | f 60/60/291 150/150/289 151/151/290
1827 | f 152/152/292 74/74/293 153/153/294
1828 | f 73/73/84 81/81/87 74/74/293
1829 | f 74/74/293 81/81/87 153/153/294
1830 | f 152/152/292 153/153/294 62/62/295
1831 | f 62/62/295 153/153/294 57/57/296
1832 | f 57/57/296 153/153/294 154/154/297
1833 | f 57/57/298 154/154/299 155/155/300
1834 | f 57/57/298 155/155/300 58/58/301
1835 | f 58/58/302 155/155/303 150/150/289
1836 | f 58/58/302 150/150/289 60/60/291
1837 | f 152/152/304 62/62/304 64/64/304
1838 | f 74/74/69 152/152/305 156/156/306
1839 | f 74/74/69 156/156/306 71/71/66
1840 | f 71/71/66 156/156/306 67/67/62
1841 | f 152/152/305 157/157/307 156/156/306
1842 | f 156/156/306 157/157/308 151/151/309
1843 | f 156/156/306 151/151/309 67/67/62
1844 | f 152/152/305 64/64/310 157/157/307
1845 | f 64/64/310 66/66/311 157/157/307
1846 | f 157/157/308 66/66/312 151/151/309
1847 | f 151/151/309 66/66/312 60/60/313
1848 | f 158/158/314 159/159/315 160/160/316
1849 | f 160/160/316 159/159/315 161/161/317
1850 | f 161/161/317 159/159/315 162/162/318
1851 | f 5/5/319 159/159/320 163/163/321
1852 | f 5/5/319 39/39/322 164/164/323
1853 | f 5/5/319 164/164/323 159/159/320
1854 | f 164/164/323 162/162/324 159/159/320
1855 | f 40/40/325 5/5/326 163/163/327
1856 | f 165/165/328 40/40/325 163/163/327
1857 | f 165/165/329 163/163/330 158/158/331
1858 | f 158/158/331 163/163/330 159/159/332
1859 | f 39/39/322 162/162/324 164/164/323
1860 | f 25/25/333 40/40/334 166/166/335
1861 | f 40/40/334 165/165/336 166/166/335
1862 | f 166/166/335 165/165/336 158/158/337
1863 | f 161/161/317 162/162/318 167/167/338
1864 | f 167/167/339 162/162/340 38/38/341
1865 | f 38/38/341 162/162/340 39/39/342
1866 | f 23/23/343 25/25/344 166/166/335
1867 | f 28/28/345 23/23/343 161/161/346
1868 | f 23/23/343 160/160/347 161/161/346
1869 | f 23/23/343 166/166/335 160/160/347
1870 | f 166/166/335 158/158/337 160/160/347
1871 | f 38/38/348 28/28/349 167/167/350
1872 | f 28/28/349 161/161/351 167/167/350
1873 | f 104/104/1 103/103/1 105/105/1
1874 | f 107/107/1 111/111/1 110/110/1
1875 | f 110/110/1 109/109/1 107/107/1
1876 | f 114/114/1 112/112/1 115/115/1
1877 | f 115/115/1 112/112/1 116/116/1
1878 | f 117/117/1 115/115/1 116/116/1
1879 | f 120/120/1 118/118/1 119/119/1
1880 | f 120/120/1 121/121/1 118/118/1
1881 | f 125/125/1 122/122/1 123/123/1
1882 | f 123/123/1 124/124/1 125/125/1
1883 | f 129/129/1 127/127/1 128/128/1
1884 | f 126/126/1 127/127/1 129/129/1
1885 | f 56/56/51 65/65/60 61/61/56
1886 | f 61/61/56 65/65/60 63/63/58
1887 | f 59/59/54 65/65/60 56/56/51
1888 | f 150/150/289 155/155/303 6/6/352
1889 | f 7/7/353 6/6/354 154/154/355
1890 | f 154/154/355 6/6/354 155/155/356
1891 | f 154/154/357 153/153/357 7/7/357
1892 | f 10/10/7 11/11/8 7/7/4
1893 | f 11/11/8 39/39/34 7/7/4
1894 | f 7/7/4 132/132/358 10/10/7
1895 | f 132/132/358 7/7/4 153/153/294
1896 | f 132/132/358 153/153/294 81/81/87
1897 | f 6/6/3 15/15/12 113/113/359
1898 | f 6/6/3 5/5/2 16/16/13
1899 | f 6/6/3 16/16/13 15/15/12
1900 | f 113/113/360 75/75/361 6/6/352
1901 | f 6/6/352 75/75/361 150/150/289
1902 | f 87/87/95 89/89/97 86/86/94
1903 | f 88/88/96 86/86/94 89/89/97
1904 | f 98/98/362 87/87/95 95/95/363
1905 | f 52/52/47 51/51/46 108/108/364
1906 | f 37/37/365 93/93/101 32/32/366
1907 | f 91/91/99 90/90/98 140/140/367
1908 | f 87/87/95 85/85/93 95/95/363
1909 | f 82/82/90 75/75/89 108/108/368
1910 | f 81/81/369 93/93/101 37/37/365
1911 | f 93/93/101 91/91/99 32/32/366
1912 | f 32/32/366 91/91/99 140/140/367
1913 | f 140/140/370 90/90/371 55/55/372
1914 | f 132/132/373 81/81/369 36/36/374
1915 | f 84/84/375 82/82/376 50/50/45
1916 | f 52/52/47 75/75/377 113/113/378
1917 | f 90/90/371 89/89/379 53/53/380
1918 | f 89/89/381 87/87/95 144/144/382
1919 | f 144/144/382 87/87/95 98/98/362
1920 | f 95/95/383 85/85/384 48/48/43
1921 | f 81/81/369 37/37/365 36/36/374
1922 | f 32/32/366 140/140/367 30/30/385
1923 | f 55/55/372 90/90/371 53/53/380
1924 | f 144/144/386 98/98/387 148/148/388
1925 | f 48/48/43 85/85/384 84/84/389
1926 | f 48/48/43 84/84/389 49/49/44
1927 | f 82/82/376 108/108/390 50/50/45
1928 | f 50/50/45 108/108/390 46/46/41
1929 | f 108/108/364 75/75/377 52/52/47
1930 | f 130/130/1 133/133/1 131/131/1
1931 | f 138/138/1 137/137/1 136/136/1
1932 | f 136/136/1 137/137/1 135/135/1
1933 | f 143/143/1 142/142/1 139/139/1
1934 | f 141/141/1 139/139/1 142/142/1
1935 | f 146/146/1 149/149/1 147/147/1
1936 | f 145/145/1 149/149/1 146/146/1
1937 | f 96/96/1 94/94/1 99/99/1
1938 | f 96/96/1 99/99/1 97/97/1
1939 | f 99/99/1 101/101/1 97/97/1
1940 | f 104/104/1 105/105/1 106/106/1
1941 | f 21/21/15 102/102/391 100/100/392
1942 | f 41/41/36 100/100/392 48/48/43
1943 | f 18/18/1 21/21/15 41/41/36
1944 | f 102/102/391 148/148/388 98/98/387
1945 | f 148/148/388 102/102/391 21/21/15
1946 | f 41/41/36 21/21/15 100/100/392
1947 | f 168/168/393 169/169/393 170/170/393
1948 | f 170/170/394 171/171/394 172/172/394
1949 | f 173/173/395 174/174/396 175/175/397
1950 | f 173/173/395 175/175/397 176/176/398
1951 | f 176/176/398 175/175/397 177/177/399
1952 | f 176/176/400 177/177/401 178/178/402
1953 | f 178/178/402 177/177/401 179/179/403
1954 | f 178/178/402 179/179/403 174/174/404
1955 | f 168/168/405 177/177/406 175/175/407
1956 | f 168/168/408 175/175/408 169/169/408
1957 | f 169/169/409 175/175/409 174/174/409
1958 | f 169/169/410 174/174/410 170/170/410
1959 | f 170/170/411 174/174/412 179/179/413
1960 | f 170/170/411 179/179/413 171/171/414
1961 | f 171/171/415 179/179/416 177/177/417
1962 | f 171/171/415 177/177/417 172/172/418
1963 | f 172/172/419 177/177/406 168/168/405
1964 | f 168/168/420 170/170/421 180/180/422
1965 | f 180/180/422 170/170/421 181/181/423
1966 | f 172/172/424 168/168/424 180/180/424
1967 | f 170/170/425 172/172/425 181/181/425
1968 | f 181/181/426 172/172/426 180/180/426
1969 | f 182/182/427 183/183/428 184/184/429
1970 | f 184/184/429 183/183/428 185/185/430
1971 | f 184/184/429 186/186/431 182/182/427
1972 | f 185/185/432 187/187/432 186/186/432
1973 | f 188/188/433 189/189/433 190/190/433
1974 | f 188/188/434 190/190/435 191/191/436
1975 | f 191/191/436 190/190/435 192/192/437
1976 | f 192/192/438 193/193/438 194/194/438
1977 | f 194/194/439 193/193/440 189/189/441
1978 | f 194/194/439 189/189/441 188/188/442
1979 | f 182/182/443 190/190/443 183/183/443
1980 | f 183/183/444 190/190/444 189/189/444
1981 | f 183/183/445 189/189/445 185/185/445
1982 | f 185/185/446 189/189/447 193/193/448
1983 | f 185/185/446 193/193/448 187/187/449
1984 | f 187/187/450 193/193/451 186/186/452
1985 | f 186/186/452 193/193/451 192/192/453
1986 | f 186/186/454 192/192/454 182/182/454
1987 | f 182/182/455 192/192/455 190/190/455
1988 | f 185/185/456 186/186/456 195/195/456
1989 | f 184/184/457 185/185/457 195/195/457
1990 | f 186/186/458 184/184/458 195/195/458
1991 | f 196/196/459 197/197/460 198/198/460
1992 | f 198/198/460 197/197/460 199/199/460
1993 | f 200/200/461 201/201/462 202/202/463
1994 | f 202/202/463 201/201/462 203/203/464
1995 | f 202/202/463 203/203/464 204/204/465
1996 | f 204/204/465 203/203/464 205/205/466
1997 | f 204/204/465 205/205/466 206/206/467
1998 | f 206/206/467 205/205/466 207/207/468
1999 | f 206/206/467 207/207/468 200/200/461
2000 | f 200/200/461 207/207/468 201/201/462
2001 | f 196/196/469 203/203/470 201/201/471
2002 | f 196/196/469 201/201/471 197/197/472
2003 | f 197/197/473 201/201/474 199/199/475
2004 | f 199/199/475 201/201/474 207/207/476
2005 | f 199/199/477 207/207/477 208/208/477
2006 | f 208/208/478 207/207/478 205/205/478
2007 | f 208/208/479 205/205/479 198/198/479
2008 | f 198/198/480 205/205/481 203/203/482
2009 | f 198/198/480 203/203/482 196/196/483
2010 | f 199/199/484 208/208/484 209/209/484
2011 | f 198/198/485 199/199/485 210/210/485
2012 | f 210/210/486 199/199/486 209/209/486
2013 | f 208/208/487 198/198/488 209/209/489
2014 | f 209/209/489 198/198/488 210/210/490
2015 | f 211/211/491 212/212/492 213/213/493
2016 | f 214/214/494 215/215/494 216/216/494
2017 | f 216/216/495 217/217/496 211/211/491
2018 | f 216/216/495 211/211/491 213/213/493
2019 | f 213/213/493 212/212/492 214/214/497
2020 | f 218/218/498 219/219/499 220/220/500
2021 | f 220/220/500 219/219/499 221/221/501
2022 | f 220/220/500 221/221/501 222/222/502
2023 | f 222/222/502 221/221/501 223/223/503
2024 | f 222/222/502 223/223/503 224/224/504
2025 | f 222/222/502 224/224/504 218/218/498
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/README.md:
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1 | # Legolas - An Open Source Bipedal Robot
2 |
3 | Legolas is a mini bipedal robot inspired by the Cassie by Agility Robotics. The project aims to provide an open-source platform for learning and applying reinforcement learning in robotics.
4 |
5 |
6 | 
7 | 
8 |
9 |
10 |
11 | 
12 |
13 |
14 | ## Repository Contents
15 |
16 | This repository contains CAD files and 3D printing files for Legolas.
17 |
18 | The code for the robot is available at [Legolas Controller](https://github.com/daviddoo02/Legolas_Controller).
19 |
20 | ## Getting Started
21 |
22 | 1. **Clone this repository:**
23 |
24 | ```bash
25 | git clone https://github.com/daviddoo02/Legolas-an-open-source-biped/
26 | ```
27 |
28 | 2. **Modify the CAD files:**
29 |
30 | Modify the CAD files to fit your specific needs using Solidworks.
31 |
32 | 3. **3D Print your own robot:**
33 |
34 | Alternatively, use the provided STL files located in `CAD/Legolas/V2/STLs` to 3D print your own robot.
35 |
36 | 4. **Assemble the robot and have fun!**
37 |
38 | ## Required Materials
39 |
40 | Materials and components used are listed and linked below.
41 |
42 | ### Main Body
43 |
44 | 1. [3D printing filament x 1 kg](https://www.amazon.com/dp/B089S1HB8K)
45 | 2. [Metric Nuts and Bolts](https://www.amazon.com/Assortment-M2-M3-M4-M5/dp/B0CBMMPPKF)
46 | 3. [Metric Locknuts](https://www.amazon.com/dp/B0CHVTYLWC)
47 | 4. [Thrust Bearings](https://www.amazon.com/gp/product/B08FHTD8VT)
48 | 5. [Ball joint rod end](https://www.amazon.com/gp/product/B0828T1NNW)
49 | 6. [M4 threaded rod](https://www.amazon.com/gp/product/B01MAYQ12S)
50 |
51 | ### Electronics
52 |
53 | 1. [Raspberry Pi 4](https://www.amazon.com/Raspberry-Model-2019-Quad-Bluetooth/dp/B07TC2BK1X)
54 | 2. [PCA9685 Servo Driver Board](https://www.amazon.com/gp/product/B07BRS249H)
55 | 3. [40 kg Hobby Servos x 8](https://www.amazon.com/Servo-Torque-Waterproof-Degree-Compatible/dp/B0C95YMMQS)
56 | 4. [80 kg Hobby Servos x 2](https://www.amazon.com/GoolRC-Digital-Torque-Waterproof-Replacements/dp/B0B5H4MWZG/ref=sr_1_2?crid=1JM9GBMY97KTM&keywords=80%2Bkg%2Bservo&qid=1705472455&sprefix=80%2Bkg%2Bservo%2Caps%2C98&sr=8-2&th=1)
57 | 5. [MPU6050 IMU](https://www.amazon.com/Acceleration-Sensors-Accelerometer-Three-Axis-Quadcopter/dp/B07V67DQ5N)
58 | 6. [ADS1115 ADC](https://www.amazon.com/gp/product/B07VPFLSMX)
59 | 7. [Jumper Wires](https://www.amazon.com/Elegoo-EL-CP-004-Multicolored-Breadboard-arduino/dp/B01EV70C78)
60 | 8. [Power DIY Connector](https://www.amazon.com/dp/B09S3S6RYC)
61 | 9. [USB C Connector](https://www.amazon.com/dp/B0CCJRWKC5)
62 | 10. [4 to 1 Wire Connector](https://www.amazon.com/dp/B0B28GNVGZ)
63 |
64 | ## Assembly Instruction
65 |
66 | Instructions and examples for assembling Legolas will be added in future updates.
67 |
68 | ## License
69 |
70 | This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.
71 |
72 | ## Acknowledgments
73 |
74 | - Inspired by the Cassie robot by Agility Robotics.
75 | - Solidworks was used for the physical design of the robot.
76 |
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/static_analysis/Leg_Static_Analysis.ipynb:
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1 | {
2 | "cells": [
3 | {
4 | "cell_type": "code",
5 | "execution_count": 2,
6 | "metadata": {},
7 | "outputs": [],
8 | "source": [
9 | "from anastruct import SystemElements\n",
10 | "import numpy as np\n",
11 | "import matplotlib.pyplot as plt\n",
12 | "from scipy.optimize import least_squares\n",
13 | "from ipywidgets import interact, widgets\n",
14 | "from typing import Tuple\n",
15 | "import matplotlib.pyplot as plt\n",
16 | "from mpl_toolkits.mplot3d import Axes3D"
17 | ]
18 | },
19 | {
20 | "cell_type": "markdown",
21 | "metadata": {},
22 | "source": [
23 | "Initializing parameters"
24 | ]
25 | },
26 | {
27 | "cell_type": "code",
28 | "execution_count": 3,
29 | "metadata": {},
30 | "outputs": [],
31 | "source": [
32 | "def pol2cart(l : float, th: float, phi: float):\n",
33 | " \"\"\"\n",
34 | " Convert polar information to cartesian translation\n",
35 | "\n",
36 | " Parameters:\n",
37 | " l (float): linkage's length in mm\n",
38 | " th (float): angle in degrees\n",
39 | "\n",
40 | " Returns:\n",
41 | " Tuple[float, float]: Converted cartesian translation\n",
42 | " \"\"\"\n",
43 | "\n",
44 | " th = np.deg2rad(th)\n",
45 | " phi = np.deg2rad(phi)\n",
46 | "\n",
47 | " # Calculate Cartesian coordinates\n",
48 | " x = l * np.sin(th) * np.cos(phi)\n",
49 | " y = l * np.sin(th) * np.sin(phi)\n",
50 | " z = l * np.cos(th)\n",
51 | " return np.array([x, y, z], dtype=float)"
52 | ]
53 | },
54 | {
55 | "cell_type": "code",
56 | "execution_count": 4,
57 | "metadata": {},
58 | "outputs": [],
59 | "source": [
60 | "# Function to update the plot\n",
61 | "class Create_Plot():\n",
62 | " def __init__(self):\n",
63 | " # Create sliders for joint angles\n",
64 | " self.th1_slider = widgets.FloatSlider(value=60, min=-180, max=180, step=1, description='Theta1 (degrees)', orientation='horizontal', layout=widgets.Layout(width='auto', height='auto'))\n",
65 | " self.th2_slider = widgets.FloatSlider(value=85, min=-180, max=180, step=1, description='Theta2 (degrees)', orientation='horizontal', layout=widgets.Layout(width='auto', height='auto'))\n",
66 | "\n",
67 | " self.prev_th1 = self.th1_slider.value\n",
68 | " self.prev_th2 = self.th2_slider.value\n",
69 | "\n",
70 | " # Create interactive plot with additional constant variables\n",
71 | " interact(self.update_plot, th1=self.th1_slider, th2=self.th2_slider)\n",
72 | "\n",
73 | " def update_plot(self, th1, th2):\n",
74 | "\n",
75 | " j1, j2, j3, j4, j5 = forward_kinematics(th1, th2)\n",
76 | " \n",
77 | " plt.figure(figsize=(10, 8))\n",
78 | " \n",
79 | " plt.plot([j1[0], j2[0], j3[0], j4[0], j3[0], j5[0], j1[0]], [j1[1], j2[1], j3[1], j4[1], j3[1], j5[1], j1[1]], marker='o', linestyle='-', color='b')\n",
80 | " plt.title(\"Biped Robot Forward Kinematics\")\n",
81 | " plt.xlabel('X-axis (m)')\n",
82 | " plt.ylabel('Y-axis (m)')\n",
83 | " plt.grid(True)\n",
84 | " \n",
85 | " # Set aspect ratio to be equal\n",
86 | " plt.axis('equal')\n",
87 | " \n",
88 | " # Set specific axis limits\n",
89 | " plt.xlim([-0.3, 0.3]) # Set your desired X-axis limits\n",
90 | " plt.ylim([-0.5, 0.1]) # Set your desired Y-axis limits\n",
91 | " \n",
92 | " # plt.show()\n",
93 | "\n",
94 | "# Create_Plot()"
95 | ]
96 | },
97 | {
98 | "cell_type": "code",
99 | "execution_count": 5,
100 | "metadata": {},
101 | "outputs": [],
102 | "source": [
103 | "# Circle Equations and Find Intersection to close the loop\n",
104 | "\n",
105 | "def circle_equations(params: Tuple[float, float], center1: np.ndarray, r1: float, center2: np.ndarray, r2: float) -> Tuple[float, float]:\n",
106 | " \"\"\"\n",
107 | " System of equations representing the circles.\n",
108 | "\n",
109 | " Parameters:\n",
110 | " params (Tuple[float, float]): Coordinates (x, y) of the point to evaluate.\n",
111 | " center1 (np.ndarray): Center of the first circle.\n",
112 | " r1 (float): Radius of the first circle.\n",
113 | " center2 (np.ndarray): Center of the second circle.\n",
114 | " r2 (float): Radius of the second circle.\n",
115 | "\n",
116 | " Returns:\n",
117 | " Tuple[float, float]: Residuals for the system of equations.\n",
118 | " \"\"\"\n",
119 | " x, y = params\n",
120 | " eq1 = (x - center1[0])**2 + (y - center1[1])**2 - r1**2\n",
121 | " eq2 = (x - center2[0])**2 + (y - center2[1])**2 - r2**2\n",
122 | " return np.array([eq1, eq2], dtype=float)\n",
123 | "\n",
124 | "def find_circle_intersection(center1: np.ndarray, r1: float, center2: np.ndarray, r2: float) -> np.ndarray:\n",
125 | " \"\"\"\n",
126 | " Find the intersection points of two circles using the Levenberg-Marquardt algorithm.\n",
127 | "\n",
128 | " Parameters:\n",
129 | " center1 (np.ndarray): Center of the first circle.\n",
130 | " r1 (float): Radius of the first circle.\n",
131 | " center2 (np.ndarray): Center of the second circle.\n",
132 | " r2 (float): Radius of the second circle.\n",
133 | "\n",
134 | " Returns:\n",
135 | " np.ndarray: Coordinates of the intersection points.\n",
136 | " \"\"\"\n",
137 | " # Find the rightmost point among the two circles\n",
138 | " rightmost_point = max(center1[0] + r1, center2[0] + r2)\n",
139 | "\n",
140 | " # Initial guess (to the right of each circle center)\n",
141 | " current = np.array([rightmost_point, 0.0])\n",
142 | "\n",
143 | " # Use Levenberg-Marquardt to find the roots\n",
144 | " result = least_squares(circle_equations, current, args=(center1, r1, center2, r2))\n",
145 | "\n",
146 | " return result.x\n",
147 | "\n",
148 | "def angle_between_vectors(v1, v2):\n",
149 | " \"\"\"\n",
150 | " Find the angle (in degrees) between two vectors.\n",
151 | "\n",
152 | " Parameters:\n",
153 | " v1 (numpy.ndarray): First vector.\n",
154 | " v2 (numpy.ndarray): Second vector.\n",
155 | "\n",
156 | " Returns:\n",
157 | " float: Angle between the two vectors in degrees.\n",
158 | " \"\"\"\n",
159 | " dot_product = np.dot(v1, v2)\n",
160 | " norm_v1 = np.linalg.norm(v1)\n",
161 | " norm_v2 = np.linalg.norm(v2)\n",
162 | "\n",
163 | " cosine_angle = dot_product / (norm_v1 * norm_v2)\n",
164 | " angle_in_radians = np.arccos(np.clip(cosine_angle, -1.0, 1.0))\n",
165 | " angle_in_degrees = np.degrees(angle_in_radians)\n",
166 | "\n",
167 | " # Calculate the cross product to determine the direction\n",
168 | " cross_product = np.cross(v1, v2)\n",
169 | "\n",
170 | " # If the cross product is positive --> clockwise\n",
171 | " if cross_product > 0:\n",
172 | " angle_in_degrees *= -1\n",
173 | "\n",
174 | " return angle_in_degrees\n"
175 | ]
176 | },
177 | {
178 | "cell_type": "code",
179 | "execution_count": 6,
180 | "metadata": {},
181 | "outputs": [],
182 | "source": [
183 | "def forward_kinematics(th1: float, th2: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]:\n",
184 | " \"\"\"\n",
185 | " Perform forward kinematics for the biped\n",
186 | "\n",
187 | " Parameters:\n",
188 | " th1 (float): Joint angle 1 in radians.\n",
189 | " th2 (float): Joint angle 2 in radians.\n",
190 | "\n",
191 | " Returns:\n",
192 | " Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]: Joint coordinates (j1, j2, j3, j4, j5).\n",
193 | " \"\"\"\n",
194 | "\n",
195 | " th1 = th1 + 180\n",
196 | "\n",
197 | " th_s = 180 # Theta shin\n",
198 | "\n",
199 | " s = 1 # Scale\n",
200 | "\n",
201 | " l1 = 55.34 / 1000 * s\n",
202 | " l2 = 105 / 1000 * s\n",
203 | " l3 = 105 / 1000 * s\n",
204 | " l4 = 105 / 1000 * s\n",
205 | " l5 = 55.34 / 1000 * s\n",
206 | "\n",
207 | " j1 = np.array([0, 0])\n",
208 | " j2 = j1 + pol2cart(l1, th1)\n",
209 | " j3 = j2 + pol2cart(l2, th1 + th2)\n",
210 | "\n",
211 | " j5 = find_circle_intersection(j1, l4, j3, l5) # Closing the loop\n",
212 | "\n",
213 | " j4 = j3 + pol2cart(l3, (th_s + np.rad2deg(np.arctan2(j5[1] - j3[1], j5[0] - j3[0])))) # end-effector position\n",
214 | "\n",
215 | " return j1, j2, j3, j4, j5"
216 | ]
217 | },
218 | {
219 | "cell_type": "code",
220 | "execution_count": 13,
221 | "metadata": {},
222 | "outputs": [
223 | {
224 | "data": {
225 | "image/png": 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",
226 | "text/plain": [
227 | ""
228 | ]
229 | },
230 | "metadata": {},
231 | "output_type": "display_data"
232 | }
233 | ],
234 | "source": [
235 | "j1,j2,j3,j4,j5 = forward_kinematics(60, 120)\n",
236 | "\n",
237 | "# Create 3D plot\n",
238 | "fig = plt.figure()\n",
239 | "ax = fig.add_subplot()\n",
240 | "\n",
241 | "# Plot joints\n",
242 | "ax.scatter(*zip(j1, j2, j3, j4, j5), marker='o', label='Joints')\n",
243 | "\n",
244 | "# Connect joints with lines\n",
245 | "ax.plot([j1[0], j2[0]], [j1[1], j2[1]], color='b')\n",
246 | "ax.plot([j2[0], j3[0]], [j2[1], j3[1]], color='b')\n",
247 | "ax.plot([j3[0], j4[0]], [j3[1], j4[1]], color='b')\n",
248 | "ax.plot([j4[0], j5[0]], [j4[1], j5[1]], color='b')\n",
249 | "ax.plot([j5[0], j1[0]], [j5[1], j1[1]], color='b')\n",
250 | "\n",
251 | "# Set labels\n",
252 | "ax.set_xlabel('X-axis')\n",
253 | "ax.set_ylabel('Y-axis')\n",
254 | "# ax.set_zlabel('Z-axis')\n",
255 | "\n",
256 | "# Show plot\n",
257 | "plt.show()"
258 | ]
259 | },
260 | {
261 | "cell_type": "code",
262 | "execution_count": 8,
263 | "metadata": {},
264 | "outputs": [],
265 | "source": [
266 | "# Gradient Descent\n",
267 | "def error_function(desired_pos: np.ndarray, current: np.ndarray) -> float:\n",
268 | " th1, th2 = current\n",
269 | " current_pos = forward_kinematics(th1, th2)[3]\n",
270 | " error = np.linalg.norm(current_pos - desired_pos)\n",
271 | " # print(th1, th2)\n",
272 | " # print(error)\n",
273 | " return error\n",
274 | "\n",
275 | "def inverse_kinematics(desired: np.ndarray, angles_guess: Tuple[float, float], max_iterations: int = 50, learning_rate: int = 10000) -> Tuple[float, float]:\n",
276 | " \"\"\"\n",
277 | " Perform inverse kinematics using gradient descent.\n",
278 | "\n",
279 | " Parameters:\n",
280 | " desired (np.ndarray): Target end-effector position [x, y].\n",
281 | " angles_guess (Tuple[float, float]): current joint angles.\n",
282 | " max_iterations (int): Maximum number of iterations for gradient descent.\n",
283 | " learning_rate (float): Learning rate for gradient descent.\n",
284 | "\n",
285 | " Returns:\n",
286 | " Tuple[float, float]: Joint angles (th1, th2).\n",
287 | " \"\"\"\n",
288 | " angle1, angle2 = angles_guess\n",
289 | "\n",
290 | " step1 = 0.5\n",
291 | " step2 = 0.5\n",
292 | "\n",
293 | " tolerance = 0.001 # stop when the error is less than this or when weve done max_iterations\n",
294 | " iter = 0\n",
295 | "\n",
296 | " for _ in range(max_iterations):\n",
297 | " # error is the distance between the desired point and our current point. We want to minimize this.\n",
298 | " error = error_function(desired, np.array([angle1, angle2]))\n",
299 | " \n",
300 | " # step in a direction to find the error of the 2 angles\n",
301 | " error_angle1 = error_function(desired, np.array([angle1+step1, angle2]))\n",
302 | " error_angle2 = error_function(desired, np.array([angle1, angle2+step2]))\n",
303 | "\n",
304 | " # this is the gradient\n",
305 | " grad1 = (error_angle1 - error) / step1\n",
306 | " grad2 = (error_angle2 - error) / step2\n",
307 | "\n",
308 | " # step in the direction of the gradient. grad is the slope (rate of change), error is the distance, so in theory grad*error is the distance we want to step to get to the desired point in one step, but lmao no, multiply by really small fraction. 0.00001 is the largest that doesnt overshoot.\n",
309 | " angle1 -= grad1 * error * learning_rate\n",
310 | " angle2 -= grad2 * error * learning_rate\n",
311 | "\n",
312 | " iter += 1\n",
313 | "\n",
314 | " # print(grad1, grad2)\n",
315 | " # print(iter)\n",
316 | " \n",
317 | " # every other iteration, step in the opposite direction. When the leg is up against 2 of the 4 walls, the gradient descent will get stuck trying to step into the wall and getting a gradient of 0.\n",
318 | " step1 *= -1\n",
319 | " step2 *= -1\n",
320 | "\n",
321 | " if abs(error) < tolerance:\n",
322 | " break\n",
323 | " \n",
324 | " return angle1, angle2"
325 | ]
326 | },
327 | {
328 | "cell_type": "markdown",
329 | "metadata": {},
330 | "source": [
331 | "Building Trusses"
332 | ]
333 | },
334 | {
335 | "cell_type": "code",
336 | "execution_count": null,
337 | "metadata": {},
338 | "outputs": [],
339 | "source": [
340 | "desired_pos = np.array([0, -0.3])\n",
341 | "guess = np.array([56, 120])\n",
342 | "theta1, theta2 = inverse_kinematics(desired_pos, guess)"
343 | ]
344 | },
345 | {
346 | "cell_type": "code",
347 | "execution_count": null,
348 | "metadata": {},
349 | "outputs": [],
350 | "source": [
351 | "n1, n2, n3, n4, n5 = forward_kinematics(theta1, theta2)\n",
352 | "\n",
353 | "\n",
354 | "ss = SystemElements()\n",
355 | "\n",
356 | "ss.add_truss_element(location=[n1, n2])\n",
357 | "ss.add_truss_element(location=[n1, n5])\n",
358 | "ss.add_truss_element(location=[n2, n3])\n",
359 | "ss.add_truss_element(location=[n5, n3])\n",
360 | "ss.add_truss_element(location=[n3, n4])\n",
361 | "\n",
362 | "# Motor Torques:\n",
363 | "T1 = 40 * 9.8/100 # Convert 40 kgcm to Nm\n",
364 | "T2 = 80 * 9.8/100\n",
365 | "\n",
366 | "ss.moment_load(node_id=[1], Ty=T1)\n",
367 | "ss.moment_load(node_id=[2], Ty=-T2)\n",
368 | "\n",
369 | "# Main body's weight:\n",
370 | "Wt = 0 * 9.8 # Convert kg to N\n",
371 | "# ss.point_load(node_id=[1], Fx=Wt, rotation=90)\n",
372 | "\n",
373 | "ss.add_support_hinged(node_id=[5,1])\n",
374 | "\n",
375 | "ss.solve()\n",
376 | "ss.show_structure()\n",
377 | "ss.show_reaction_force()"
378 | ]
379 | },
380 | {
381 | "cell_type": "code",
382 | "execution_count": null,
383 | "metadata": {},
384 | "outputs": [],
385 | "source": [
386 | "print(ss.get_node_results_system(node_id=5)['Fy'] * -1 / 9.8)"
387 | ]
388 | },
389 | {
390 | "cell_type": "code",
391 | "execution_count": null,
392 | "metadata": {},
393 | "outputs": [],
394 | "source": []
395 | }
396 | ],
397 | "metadata": {
398 | "kernelspec": {
399 | "display_name": "Python 3",
400 | "language": "python",
401 | "name": "python3"
402 | },
403 | "language_info": {
404 | "codemirror_mode": {
405 | "name": "ipython",
406 | "version": 3
407 | },
408 | "file_extension": ".py",
409 | "mimetype": "text/x-python",
410 | "name": "python",
411 | "nbconvert_exporter": "python",
412 | "pygments_lexer": "ipython3",
413 | "version": "3.10.11"
414 | }
415 | },
416 | "nbformat": 4,
417 | "nbformat_minor": 2
418 | }
419 |
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