Type Synthesis and Typical Application of 1T2R-Type Parallel Robotic Mechanisms

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left"><img alt="206181.table.005a" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005a.jpg"/></td><td align="center">
									Constraint-space atlas of each limb</td><td align="center">
									Freedom-space atlas</td><td align="center">
									Model and kinematic joints of each limb</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">1st limb</td><td align="center"><img alt="206181.table.005b" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005b.jpg"/></td><td align="center"><img alt="206181.table.005c" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005c.jpg"/></td><td align="center"><img alt="206181.table.005d" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005d.jpg"/></td></tr><tr><td align="left">2nd limb</td><td align="center"><img alt="206181.table.005e" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005e.jpg"/></td><td align="center"><img alt="206181.table.005f" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005f.jpg"/></td><td align="center"><img alt="206181.table.005g" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005g.jpg"/></td></tr><tr><td align="left">3rd limb</td><td align="center"><svg height="11.3125" id="M6" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.9375 11.3125" width="12.9375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.25)"><path d="M488 658v-28q-47 -3 -58.5 -12t-11.5 -39q49 -2 97 -15t93.5 -39.5t73.5 -75t28 -112.5q0 -53 -19.5 -96.5t-50 -71t-70 -47t-77.5 -27.5t-75 -9q0 -36 11.5 -45.5t58.5 -12.5v-28h-223v28q47 3 58.5 12.5t11.5 45.5q-47 1 -94.5 14t-93 39.5t-74.5 76t-29 114.5
q0 51 19 93.5t49 70t69.5 47t77.5 28t76 10.5q0 30 -11 39t-54 12v28h218zM335 118v429q-34 -2 -67 -13.5t-63.5 -35t-49.5 -65.5t-19 -96q0 -56 18.5 -99t49 -67.5t63.5 -37.5t68 -15zM418 547v-429q35 2 67.5 14t63.5 35.5t50 66.5t19 99t-19 99t-50 66.5t-64 35t-67 13.5
z" id="x3A6"></path></g>
</svg>No constraint</td><td align="center"><img alt="206181.table.005h" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005h.jpg"/></td><td align="center"><img alt="206181.table.005i" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005i.jpg"/></td></tr><tr><td align="left">Synthesis result</td><td align="center"> </td><td align="center"><img alt="206181.table.005j" src="https://static.hindawi.com/articles/mpe/volume-2013/206181/figures/206181.table.005j.jpg"/></td><td align="center"> </td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Type synthesis based on the subspace presented in Figure <a href="../fig3/#b">3(b)</a>.

Mathematical Problems in Engineering

tab5

Table 5

Table 5: Type Synthesis and Typical Application of 1T2R-Type Parallel Robotic Mechanisms 