Multiobjective Optimization of 6-DOF Parallel Manipulator for Desired Total Orientation Workspace

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:5.34em"/><col style="width:5.35em"/><col style="width:5.46em"/><col style="width:6.64em"/><col style="width:4.58em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="3">Design variables</td><td class="align_center" colspan="2">Targets</td></tr><tr class="thead"><td class="align_center"><span style="width: 13.409ptpx;"><svg height="11.927pt" id="M156" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 13.409 11.927" width="13.409pt" 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="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 274 403 303 403C330 403 360 395 374 387Z"></path></g></svg></span></td><td class="align_center"><span style="width: 13.0802ptpx;"><svg height="11.927pt" id="M157" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 13.0802 11.927" width="13.0802pt" 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="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M460 334C460 396 434 451 378 451C330 451 241 408 148 300H146L237 679C241 697 241 710 232 710C213 710 153 684 67 675L66 646H95C141 646 145 642 134 595L39 170C23 97 31 54 46 33C64 8 100 -12 137 -12C178 -12 234 3 298 43C391 101 460 222 460 334ZM371 320C371 204 316 89 248 51C230 41 208 37 192 37C143 37 102 72 119 166C124 194 129 215 135 235C202 323 298 392 335 392C353 392 371 372 371 320Z"></path></g></svg></span></td><td class="align_center"><i>H</i></td><td class="align_center"><i>V</i></td><td class="align_center"><i>-k</i></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_center">522.71mm</td><td class="align_center">322.91mm</td><td class="align_center">853.95mm</td><td class="align_center">7.33×108mm<sup>3</sup></td><td class="align_center">-0.25917</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The set of geometric parameters for verifying the hybrid method.</div>

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Multiobjective Optimization of 6-DOF Parallel Manipulator for Desired Total Orientation Workspace 