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.