"Design a crank arm for a bicycle." A bicycle crank arm is a critical component of the drive mechanism as

it transmits the force applied by the rider to the crankshaft. It also supports the rider weight. The failure

of a crank arm can cause injury to the rider's leg by contact with the broken crank or the rider can lose

control of the bike, fall and be injured. In $1997,$ Shimano American Corporation received more than $630$

reports of crank arm failures resulting in $22$ injuries, including cuts and fractures leading to a recall of

more than $1$ million crank arms installed on bicycles. Replacement of these cranks was a significant cost

burden to the company and highlights the importance of a good design. Therefore, the design of the left

crank arm of a bicycle has been assigned since it poses an interesting design problem from a number of

viewpoints.

The project is subdivided into a number of tasks:

Clear and complete free body diagram.

Internal force calculations and diagrams

Stress calculations for any point in the cross$-$section due to: axial force, bending about both

axes, shear from transverse load, torsion, and effective stress;

Plot equivalent stress as a function of crank orientation angle for $8$ points on the circumference

of the cross$-$section

Determine the critical condition, i$.$e$.,$ if effective stress is the critical quantity, for what crank

orientation angle and where in the cross$-$section does the maximum effective stress occur.

The formulae for these stress components should be in terms of the coordinates in the cross$-$

sectional plane. The rows of the spreadsheet are the crank orientation angles.

Increment the crank orientation angle by no more than $5$ degrees to get a smooth plot of stress

as a function of angle. Apply force components normal to the top of the pedal $(Fz)$ and tangent

to the top of the pedal $(Fx).$ These force components were then combined to find the resultant

force $(Fr)$ acting on the pedal.

Estimate Forces from data available on internet and bicycle testing facilities websites.