On the Solution of Region-Based Straight-Line Mechanism Design Optimization

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr class="thead"><td class="align_left" colspan="2">Geometric features</td><td class="align_center">xA0</td><td class="align_center">yA0</td><td class="align_center">xB0</td><td class="align_center">yB0</td><td class="align_center">xC</td><td class="align_center">yC</td><td class="align_center">β (<svg height="7.35473pt" id="M144" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 4.94072 7.35473" width="4.94072pt" 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="M326 255C326 330 263 391 186 391S46 330 46 255S109 119 186 119S326 180 326 255ZM274 255C274 204 235 163 186 163S98 204 98 255S137 347 186 347S274 306 274 255Z"></path></g></svg>)</td></tr><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr><td class="align_left" colspan="2">General</td><td class="align_center" rowspan="3">40</td><td class="align_center">10</td><td class="align_center">80</td><td class="align_center">0</td><td class="align_center" rowspan="3">20</td><td class="align_center" rowspan="3">50</td><td class="align_center" rowspan="3">140</td></tr><tr><td class="align_left" rowspan="2">Special</td><td class="align_center"><svg height="11.927pt" id="M145" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 61.0869 11.927" width="61.0869pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.19,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.957,0)"><path d="M619 0V50H365V548H307V50H53V0H619Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.312,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,48.06,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.006,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g></svg></td><td class="align_center">—</td><td class="align_center" rowspan="2">—</td><td class="align_center" rowspan="2">—</td></tr><tr><td class="align_center">Others</td><td class="align_center">10</td></tr><tr class="table-tr"><td colspan="9"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: On the Solution of Region-Based Straight-Line Mechanism Design Optimization 