Structures

Structure is the stuff that holds things together. If you can look past the paint job and decals it is what you see when you look at a bicycle. It is your job as a bicycle designer to minimize structure as much as possible without increasing risk. You must recognize when enough is enough and when more is too much. Conversely, a weak structure is easily recognized by flexing, squeaks, squirrelly handling and most important, by the experienced eye.

To be successful, the structure must handle all loads without detrimental deformation. A designer must be familiar with all the steps needed to reach the final product. Loads become stresses. Stresses converted to strains. Strains become deformations and deformations cause failures. A simple example of all of these is the following.

The screw is used to hold two pieces together by tension. The nut is torqued to a specified amount. If you have an interest in things like this, then measure the overall length before and after the nut is tightened. A #10 screw one inch long will stretch .003”. Loosen the nut and the screw returns to its former length. We call this the elastic region of the stress/strain relationship. The strain depends on the mechanical properties of the steel the screw is made from. Cheap screws stretch more than good quality screws. This is why Robobike does not buy Chinese made hardware. Too much yielding going on.

Tighten the screw beyond its recommended torque value and the screw does not return to its original length when relaxed. You have reached the yield point. This deformation is permanent. Continue to tighter the nut and the screw breaks. You have reached the ultimate tensile strength of the screw(or nut if the nut strips out first).

Other kinds of deformation are important to the builder who uses the aluminum structure under discussion in this book. When tightening and screw inserted into a hole in a piece of aluminum, you can expect the hole to shrink just a bit due to material being deformed around the washers. The normal pedaling action causes the seat tube to deflect one way and then the other. The weight of the rider causes a small increase in the wheel base of the bike.

Building a bike with enough structure to control all deformation to the point where there is no deformation results in an uncomfortable, rigid and stiff bicycle. Building a bike without enough structure results in a bike that flexes to the point where it too is uncomfortable to ride.

Coordinate system and sign convention

We use the airplane coordinate system for our design work. The X axis is aligned with the direction of travel and has its origin at the front axle. Positive X is towards the rear of the bike. The Y axis is left and right with respect to the rider. If the rider holds out his right arm, she is pointing in the positive Y direction. Positive Z is up. When calculating the center of gravity, the front axle is used as the datum point and the rider’s mass adds positive moments.

We use the English system of measure at Robobike mostly because we buy steel and aluminum in that system. Our machine tools are graduated in inches, our measuring tools such as micrometers and indicators are graduated in inches, we buy acetylene by the pound and oxygen by the cubic foot. We pay for postage by the ounce, beer by the pint and sandwiches we eat at lunch time are foot longs. If I order a 30 cm long sub, the people waiting in line behind me would think that I’m a big jerk.

When drawing a bicycle layout in the airplane coordinate system, the rear wheel goes to the right