Crank Arms Case Study

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2. Crank Arms
The crank arms presented here have never been evaluated experimentally. All discussions on performances are speculative only.
Four crank arms are presented here. They all have the following characteristics.
1. Each arm comprises two bars.
2. The first bar, identified as Bar A, has a cavity to hold the second bar.
3. The second bar, Bar B, is fully or partly inside the cavity in Bar A.
The crank arms differ from each other in the shapes of Bar A, and in whether Bar B has a pin. In the bicycle, Bar A is fixed to the crank axle, and Bar B is fixed to the pedal spindle. In the figures, Bar A is colored cyan, Bar B is magenta, and the pin in Bar B is blue.

One can create more crank arms by modifying the crank arms presented here
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Bars A1 and A3 are hidden in Fig. 9, so that one can see how Bar B moves inside A2. Crank arm extension and retraction in these figures are given in detail in Figures 6B and 7, respectively.

Some remarks.
1. In the crank arm extension given by the first track and Fig. 6A, the pedal spindle initially moves up a slope with an inclination angle of 33°. This angle decreases as the crank arm rotates clockwise. One can change the dependence of this angle on arm direction by changing the shapes of the bottoms of the holes in A1 and A3.
2. There is sliding friction between the pedal spindle and the bottoms of the holes in A1 and A3 during crank arm extension. One can convert this friction to rolling friction by putting rings round the pedal spindle.
3. One can cut holes in bars A1, A2, A3, and B to facilitate cleaning and to reduce the weight of the crank arm.
4. A fully extended crank arm behaves exactly like a traditional crank arm with the maximum arm length. Here, Bar B is fixed to the pedal spindle and is parked in the maximum arm-length position. There is no friction during arm rotation, because the bars A1, A2, A3, B, and pedal spindle are fixed relative to each

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