Bicycle Frame Geometry II - Frame Angles

Use the geometry generator applet below to help you with the exercises on this page.

Once again you are allowed to design your own bicycle frame geometry by moving the joints. However in this activity you will be looking at how adjusting the joint positions affects the angles between the tube members. As you will see later, it is actually these angles that greatly affect member loading.

Create a rectangular shape of the four outer members with the seat tube (connecting the seat and the pedals) forming the diagonal. Estimate visually each of the angles formed by the members. Check your answers with the applet. Were your estimates close?

Modify the design of the frame again. Perhaps try to make it a more realistic shape. Now try visually estimating the angles and checking them with the applet. Were you as close as before?

While visual inspection may provide you with a good approximation in some cases, it is often necessary to know the angle precisely. Just given the coordinates of joints, how can you calculate the angles? You may want to consult the Vector Dot Product concept page for some ideas.

Using the dot product calculate each of the frame angles. Check your calculations with the applet. Hopefully your calculations will be an improvement over your estimates.

Once you have finished calculating the frame angles for the current frame shape, you can change modes and get immediate angle updates while dragging the joints. Try this and see if you can appreciate how changing the joint coordinates changes the frame angles.


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