Page 81 - Concise Encyclopedia of Robotics

Degrees of Rotation
You can use your own arm to get an idea of the degrees of freedom that
a robot arm might have.Extend your right arm straight out toward the hori-
zon. Extend your index finger so it is pointing. Keeping your arm straight,
move it from the shoulder. You can move your arm three ways. Up-and-
down movement is called pitch. Movement to the right and left is yaw. You
can also rotate your whole arm as if you were using it as a screwdriver; this
is roll. Your shoulder has three degrees of freedom: pitch, yaw, and roll.
Now move your arm from the elbow only.If you hold your shoulder and
upper arm in the same position constantly,you can see that your elbow joint
has the equivalent of pitch in your shoulder joint. But that is all (unless
your elbow is dislocated). The human elbow has one degree of freedom.
Extend your arm toward the horizon, straighten it out, and move
only your wrist. Keep the arm above the wrist straight and motionless.
Your wrist can bend up and down and can also move side to side. The
human hand has two degrees of freedom with respect to the arm above
it: pitch and yaw. Thus, in total, your shoulder/elbow/wrist system has
six degrees of freedom: three in the shoulder, one in the elbow, and two
in the wrist. A certain amount of roll is also possible in the arm below
the elbow; this does not occur in either the elbow joint or the wrist joint,
but in the lower arm itself. This makes for a seventh degree of freedom.
Three degrees of freedom are sufficient to bring the end of a robot arm
to any point within its work envelope, or work space, in three dimensions.
Thus, in theory, it might seem that a robot should never need more than
three degrees of freedom. But the extra possible motions, provided by
multiple joints, give robot arms versatility that they could not have with
only three degrees of freedom.
See also ARTICULATED GEOMETRY, CARTESIAN COORDINATE GEOMETRY, CYLINDRICAL COORDI-
NATE GEOMETRY, DEGREES OF ROTATION, POLAR COORDINATE GEOMETRY, REVOLUTE GEOMETRY,
ROBOT ARM, SPHERICAL COORDINATE GEOMETRY, and WORK ENVELOPE.
DEGREES OF ROTATION
Degrees of rotation are a measure of the extent to which a robot joint, or a
set of robot joints, is turned. Some reference point is always used, and the
angles are specified in degrees or radians with respect to that joint.
Rotation in one direction (usually clockwise) is represented by positive
angles; rotation in the opposite direction is specified by negative angles.
Thus, if angle X = 58°,it refers to a rotation of 58° clockwise with respect to
the reference axis. If angle Y = 74°, it refers to a rotation of 74° counter-
clockwise.
The illustration shows a robot arm with three joints. The reference
axes are J1, J2, and J3, for rotation angles X, Y, and Z. The individual angles
add together.

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