Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="691464.fig.003a" src="https://static.hindawi.com/articles/mpe/volume-2014/691464/figures/691464.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Time history of and phase plane portrait of <svg height="16.3125" id="M67" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.925 16.3125" width="14.925" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M475 507q0 -83 -20 -172t-56 -167.5t-93.5 -129t-125.5 -50.5q-157 0 -157 227q0 78 21.5 164t59 161t96.5 123.5t126 48.5q79 0 114 -58t35 -147zM391 522q0 155 -81 155q-62 0 -111 -82.5t-73 -200.5h253q12 81 12 128zM373 346h-255q-12 -91 -12 -150q0 -72 20 -123
t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" id="x1D703"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.525,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="691464.fig.003b" src="https://static.hindawi.com/articles/mpe/volume-2014/691464/figures/691464.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Time history of and phase plane portrait of <svg height="16.3125" id="M68" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.925 16.3125" width="14.925" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M475 507q0 -83 -20 -172t-56 -167.5t-93.5 -129t-125.5 -50.5q-157 0 -157 227q0 78 21.5 164t59 161t96.5 123.5t126 48.5q79 0 114 -58t35 -147zM391 522q0 155 -81 155q-62 0 -111 -82.5t-73 -200.5h253q12 81 12 128zM373 346h-255q-12 -91 -12 -150q0 -72 20 -123
t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" id="x1D703"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.525,16.25)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg></td></tr></table></td></tr></table>

<table>The motion behavior of small regular swing of a 2-link manipulator.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Nonlinear Dynamics of Controlled Synchronizations of Manipulator System 