Page 42 - Making things move_ DIY mechanisms for inventors, hobbyists, and artists

Chapter 1 Introduction to Mechanisms and Machines 23

Degrees of Freedom FIGURE 1-24 Coordinate system of axes and
planes
Every object has six different ways it
can move: three straight line motions,
called translations, and three
rotations. This is usually shown on a
coordinate system, as in Figure 1-24.

If you stand straight up and picture
the origin (the middle where all the
lines meet) of this coordinate system
at your belly button, it will be easier
to understand the movement. You
can jump up and down (translation
along the Z axis), shuffle side to side
(translation along the Y axis), or walk
forward and backward (translation along the X axis). Every linear movement is a
combination of X, Y, and Z translations.

For example, if you walk forward diagonally, you are moving in X and Y. Remember
the Etch A Sketch? It has two knobs: one that controls horizontal, or X motion, and
one that controls vertical, or Y motion. To make a diagonal line, you spin both knobs
at once. You could say that you are drawing in the XY plane, because your motion is
part X and part Y movement. You can do this with your body if you walk forward and
to the right diagonally. The axes in Figure 1-24 also define three planes: the XY plane,
YZ plane, and XZ plane. Can you think of a way to move in the XZ plane?

In addition to these three translations, any object can spin around any of these three
axes. If you spin around in place, you are rotating about the Z axis. If you bend
forward and backward at your waist, you’re rotating your body about the Y axis.
And if you bend to the side, you are rotating about the X axis.

Rotations may be easier to picture on an airplane, where they have more specific
names, as shown in Figure 1-25. When a plane tilts its wings with respect to the