Design and Analysis of a Novel Speed-Changing Wheel Hub with an Integrated Electric Motor for Electric Bicycles

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Case</td><td align="center">Fixed link</td><td align="center">Input link</td><td align="center">Output link</td><td align="center">SR formula</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">I</td><td align="center">1</td><td align="center">2</td><td align="center">3</td><td align="center"><span style="width: 126.8375px;"><svg height="17.225" id="M38" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 126.8375 17.225" width="126.8375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,50.85,12.138)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,64.585,12.138)"><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><g transform="matrix(.017,-0,0,-.017,72.744,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g><g transform="matrix(.017,-0,0,-.017,78.626,12.138)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,85.629,12.138)"><path d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5
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</svg></span></td></tr><tr><td align="left">II</td><td align="center">1</td><td align="center">3</td><td align="center">2</td><td align="center"><span style="width: 126.8375px;"><svg height="17.225" id="M39" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 126.8375 17.225" width="126.8375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td></tr><tr><td align="left">III</td><td align="center">1</td><td align="center">2 (3)</td><td align="center">2 (3)</td><td align="center">1</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Speed ratio at each speed of the three-speed wheel hub.

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Design and Analysis of a Novel Speed-Changing Wheel Hub with an Integrated Electric Motor for Electric Bicycles 