# Maximum Tension in the Bicycle Chain

1. Oct 21, 2009

### piacere_space

Figure 1 below shows drawings of a typical bicycle chain. Consider two components of the
chain:
(i) the pin, and (ii) the link.
The chain is under tension caused by a load applied by a person pushing on one of the
pedals. Calculate the maximum tension in the chain.
Calculate the stresses in the two components, i.e., the pin, and the link. First,
derive symbolically the relationship for stresses for the two components.
Next, make numerical calculations and indicate which is the most critical part
of the chain in terms of the applied load.
The links and pins are made from the same steel material. The tensile yields strength, $$\sigma$$y,
is denoted kt. The shear yield strength is denoted ks. Assume ks = 0.5kt.
Let the safety factor be SF = 3. Then we can write for each component,
$$\sigma$$design = $$\frac{1}{SF}$$$$\times$$$$\sigma$$fail (1)
where: $$\sigma$$design is the allowed stress, $$\sigma$$fail = kt for tensile strength, and $$\sigma$$fail = ks for shear strength.

Given data:
The maximum load applied by a person to the pedal is Pmax.
The length of the pedal is L.
The diameter of the main sprocket is D.
The diameter of the minor sprocket is d.

The pin is 2.5 mm diameter. The distance between the inner links is 4.6 mm. The link
is 5.8 mm at its widest part (where the pin hole is), and 3.5 mm at its narrowest part
(between the chain holes). The thickness of the link is 1.2 mm.

Figure 1: Construction and components of a bicycle chain

Could anyone give me a clue to figure out this question?
I have no idea how and where to start....