Generating the Isocurve Representation for Configuration Space of Mechanisms

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/3085930/figures/3085930.fig.0014a.svgz" name="3085930.fig.0014a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Direction representation</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/3085930/figures/3085930.fig.0014b.svgz" name="3085930.fig.0014b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Finite motion directions marked on the<i> q</i><sub>34 </sub>surface</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/3085930/figures/3085930.fig.0014c.svgz" name="3085930.fig.0014c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Contours of <svg height="11.5564pt" id="M333" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 23.5874 11.5564" width="23.5874pt" 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="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></g><g transform="matrix(.013,0,0,-0.013,7.185,0)"><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></g><g transform="matrix(.013,0,0,-0.013,11.683,0)"><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" id="g113-101"></path></g><g transform="matrix(.013,0,0,-0.013,18.898,0)"><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></g></svg></td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/3085930/figures/3085930.fig.0014d.svgz" name="3085930.fig.0014d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Surface of <svg height="11.5564pt" id="M334" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 23.5874 11.5564" width="23.5874pt" 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="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></g><g transform="matrix(.013,0,0,-0.013,7.185,0)"><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></g><g transform="matrix(.013,0,0,-0.013,11.683,0)"><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" id="g113-101"></path></g><g transform="matrix(.013,0,0,-0.013,18.898,0)"><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></g></svg></td></tr></table>

<div>The directions in which all the second-order derivatives are zero at the singular point.</div>

Mathematical Problems in Engineering

fig14

Figure 14

Figure 14: Generating the Isocurve Representation for Configuration Space of Mechanisms 