Split Pin v. R-pin

Split pin or R-pin is used to secure the end of a rod or a shaft so that the shaft remains in place. Which pin is more secure? In other words, which pin requires a larger force to remove?

A diagram of split pin (Cotter pin) is shown below. A split pin usually has two flat inner surfaces, so that cross-sectionally the pin would look like a circle. The two flat inner surfaces can be individually bent so that the pin can be locked in place to prevent a shaft from moving axially, as shown in Fig. 1.

Fig. 1. Split pin is initially straight, but its two ends are bent to lock the pin in place. (http://en.wikipedia.org/wiki/Split_pin.)

The free energy per unit length of a bent rod is EI/2r², where E is Young's modulus, I is moment of inertia of the rod, and r is the radius of curvature of the bent section. The force required to bend the bent rod is equal to the derivative of the free energy with respect to r, yielding EI/r³. Assuming that the length of the bent section is one-fourth of a circle (= π R/2), where R is the rod's radius, and given that I = π R⁴/4, we get the force required equal to π²ER⁵/8r³.

When we bend the rod, it is quite reasonable to assume that the radius of curvature is equal to 10 times the rod's diameter: r = 10R (see Fig. 1). With this assumption, the required force to remove the split pin should be equal to π²ER²/8000. For a steel split pin with a rod radius of 2 mm, the force required is about 986 N. The maximum force a bare hand can deliver is about 100 N, so a tool - wrench, for example - is needed to leverage a bare hand in order to remove a split pin.

While the split pin removal relies on bending the rod, the R-pin relies on combined action of bending and friction, as shown in Fig. 2.

Fig. 2. The straight edge of an R-pin is inserted through a hole and the middle curved section will wrap around the rod to secure it. (http://en.wikipedia.org/wiki/R-clip.)

To remove an R-pin we have to push away the curved section, which effectively bends the top loop of the R-pin. The radius of curvature for this top loop is clearly several times larger than the rod's radius. The force required would be smaller than π²ER²/8000 and tools are not required since the curved section serves as a lever as well. This is an advantage for the R-pin: a human hand can remove the pin. In addition, the R-pin is reusable while the split pin is not due to fatigue stress.

Friction holds the R-pin in place. The coefficient of friction for steel on steel is quite large, about 0.75. The bending force multiplied by this friction coefficient is required to the force required to release the pin. It is smaller than the bending force for the split pin. To remove the R-pin, however, requires first bending the top loop, followed by the friction force. The friction force is perpendicular to the bending force, so this creates redundancy and can make an R-pin more difficult to remove than a split pin.

The split pin requires a larger force to remove, but it does not have increased redundancy that the R-pin has. A human hand can remove the R-pin, but the split pin requires a tool to remove it. It is a case of a clever engineering design that achieves both safety and ease of use.