Inspired by the Black Ghost Knifefish: Bionic Design of Undulatory Fin with 2-DOF Rays and Its Propulsion Performance

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Joints</td><td class="align_center" colspan="4">Parameters</td></tr><tr class="thead"><td class="align_center"><span style="width: 18.515ptpx;"><svg height="9.36162pt" id="M5" style="vertical-align:-3.40071pt" version="1.1" viewbox="-0.0498162 -5.96091 18.515 9.36162" width="18.515pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 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396 265 404 297 404S372 390 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M294 607C294 643 272 671 230 671C172 671 143 618 143 593C143 548 173 524 215 524C261 524 294 565 294 607ZM285 104L263 135C232 107 205 93 193 93C185 93 184 106 191 135L247 358C259 406 254 457 224 457C184 457 113 420 28 348L47 315C76 336 101 349 109 349S115 337 109 314L58 109C33 10 61 -12 96 -12C128 -12 209 18 285 104Z"></path></g></svg></span></td><td class="align_center"><span style="width: 9.71099ptpx;"><svg height="12.5794pt" id="M8" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 9.71099 12.5794" width="9.71099pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M294 607C294 643 272 671 230 671C172 671 143 618 143 593C143 548 173 524 215 524C261 524 294 565 294 607ZM285 104L263 135C232 107 205 93 193 93C185 93 184 106 191 135L247 358C259 406 254 457 224 457C184 457 113 420 28 348L47 315C76 336 101 349 109 349S115 337 109 314L58 109C33 10 61 -12 96 -12C128 -12 209 18 285 104Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center"><span style="width: 42.6559ptpx;"><svg height="11.5564pt" id="M9" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 42.6559 11.5564" width="42.6559pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.93,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.466,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.706,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.204,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g></svg></span></td><td class="align_center"><span style="width: 26.0536ptpx;"><svg height="9.3838pt" id="M10" style="vertical-align:-0.6304598pt" version="1.1" viewbox="-0.0498162 -8.75334 26.0536 9.3838" width="26.0536pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.631,0)"><path d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.315,0)"><path d="M298 665H241L25 -44H81L298 665Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.634,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg></span></td><td class="align_center">0</td><td class="align_center"><span style="width: 12.5426ptpx;"><svg height="9.39034pt" id="M11" 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<div>Transformation parameters of coordinate system.</div>

Applied Bionics and Biomechanics

tab3

Table 3

Table 3: Inspired by the Black Ghost Knifefish: Bionic Design of Undulatory Fin with 2-DOF Rays and Its Propulsion Performance 