Dynamic Analysis of a 5-DOF Flexure-Based Nanopositioning Stage

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static-preview.hindawi.com/articles/mpe/volume-2019/8501583/figures/8501583.fig.003a.svgz" name="8501583.fig.003a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Limb1</td></tr><tr class="fig-image" id="b"><td><object data="https://static-preview.hindawi.com/articles/mpe/volume-2019/8501583/figures/8501583.fig.003b.svgz" name="8501583.fig.003b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Simplified side view of limb 1</td></tr><tr class="fig-image" id="c"><td><object data="https://static-preview.hindawi.com/articles/mpe/volume-2019/8501583/figures/8501583.fig.003c.svgz" name="8501583.fig.003c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Three parallel limbs</td></tr></table>

<div>Mechanism schematic of the <svg height="14.8173pt" id="M9" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 33.0287 14.8173" width="33.0287pt" 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="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.844,0)"><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,-0.0091,17.993,3.132)"><path d="M563 395C563 428 543 451 519 451C500 451 480 438 472 423C468 415 465 403 470 394C477 381 482 368 482 347C482 272 386 136 342 74H340C334 163 323 257 312 337C302 410 290 451 257 451C214 451 160 385 127 338L145 310C169 341 203 373 209 373C219 373 225 369 232 325C249 215 269 62 271 -15C220 -80 135 -165 18 -231L26 -257L142 -230C254 -105 279 -74 342 13C394 85 484 211 526 286C553 334 563 365 563 395Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.853,0)"><path d="M669 636L663 650H260C230 650 221 652 208 675H186C177 621 162 548 144 481L173 479C195 534 211 560 226 578C248 604 266 615 373 615H544C460 511 114 112 23 16L31 0H561C577 34 611 135 622 170L594 182C566 125 544 88 515 65C481 38 416 35 319 35C249 35 197 37 152 41C270 184 542 501 669 636Z"></path></g></svg> out-of-plane stage.</div>

Mathematical Problems in Engineering

Dynamic Analysis of a 5-DOF Flexure-Based Nanopositioning Stage

Figure 3