Page 99 - Making things move_ DIY mechanisms for inventors, hobbyists, and artists

80 Making Things Move

All this talk of sliding boxes is great, but how does that help us design mechanisms?
Think of friction as a force that is always working against you, so it’s something you
need to compensate for when you are choosing a motor or other components for
your project. Nothing is 100% efficient. This means you’ll never get out everything
you put in. There are always losses, and many times these losses are because of
friction.

In the preceding example, where the coefficient of friction was 0.4, 40% of the input
force was lost to friction! If it seems like a lot, that’s because it is—well, at least in this
case. Friction is always relative. The combination of a box sliding on plywood might
have a lot of friction, but a roller-skate wheel turning in its bearing might have a
coefficient of friction of 0.05, for only a 5% loss.

The Coefficient of Friction
Some fancy math goes into making this simple equation to estimate the coefficient
of friction. The force arrows in Figure 4-7 are not all at perfect right angles, like
those in Figure 4-6. In order to cancel out the forces and calculate them, they need
to be pointing in the same direction. To do this, we split up the weight force (W) into
two components: one that is parallel to the plywood (opposite the force of friction)
and one that is parallel to the normal force (N).
You can see that the angle at the top of this force triangle is the same as the angle
the plywood is lifted off the floor (angle 1 on the left side of Figure 4-8). So we use
some trigonometry and figure out that the component of the weight parallel to the
plywood is = W × sin , and the component parallel to the normal force (N) is = W ×
cos . We can put these forces back in our diagram, as on the right side of Figure
4-8. Now we can start canceling out forces. We know these values:
N = W × cos and F = W × sin
f
But we also know that F = μ × N. If we substitute that into the equation on the
f
right, we get this:

μ × N = W × sin
We can also substitute what we know about N into this equation:

μ × W × cos =W × sin