Active Vibration Control of an Axially Translating Robot Arm with Rotating-Prismatic Joint Using Self-Sensing Actuator

<div>Tip trajectory of the arm when <svg height="12.0395pt" id="M148" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 112.373 12.0395" width="112.373pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,7.488,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,12.176,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,16.796,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,25.268,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,37.006,0)"><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" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,46.537,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,57.518,0)"><path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z" id="g121-113"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="367" vert-adv-y="367"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,62.49,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z" id="g121-103"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="268" vert-adv-y="268"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,66.121,0)"><path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z" id="g121-108"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="547" vert-adv-y="547"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,73.592,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,78.28,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,84.783,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,87.872,0)"><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" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,94.375,0)"><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" id="g113-238"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="591" vert-adv-y="591"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,102.655,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,107.275,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg>, <svg height="12.8011pt" id="M149" style="vertical-align:-0.2129993pt" version="1.1" viewbox="-0.0498162 -12.5881 46.6171 12.8011" width="46.6171pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,7.153,-3.699)"><path d="M-161 571C-161 600 -183 623 -212 623C-238 623 -262 600 -262 571C-262 544 -238 520 -212 520C-183 520 -161 544 -161 571Z" id="g117-11"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="0" vert-adv-y="0"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,0,0)"><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" id="g113-230"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,10.557,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,22.295,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,28.798,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,31.887,0)"><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" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,38.39,0)"><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" id="g113-238"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="591" vert-adv-y="591"></glyph.data></g></svg> rad/s.</div>

Shock and Vibration

fig8

Figure 8

Figure 8: Active Vibration Control of an Axially Translating Robot Arm with Rotating-Prismatic Joint Using Self-Sensing Actuator 