Robot Kinematics Background
Craig (1986) describes kinematics as the science of motion, ignoring the forces which
cause the motion. Kinematics deals with the variable joint coordinates as they relate to the
position and orientation of the end-effector. Because the relationships between the joints of a
manipulator can be quite complex, the study of robot kinematics deals with the coordinate
frames that describe the kinematic relationships. Any robot manipulator is made up of links
and joints. Most joints are grouped into one of two categories with one degree-of-freedom:
revolute or hinged joints and prismatic or sliding joints. The links of the manipulator are
usually rigid and define the relationship between the joints. The common normal distance, an,
between the axes of two consecutive joints and the twist angle, an, characterize a robot link (see
Figure 3.1). The twist angle is defined as the angle between the consecutive axes in a plane
perpendicular to an. For this work, the Denavit-Hartenberg (1955) notation will be used as
applied by Paul (1981).
The relationships between coordinate frames are expressed as products of rotation and
translation transformations. Homogeneous transformations which represent rotations of one
coordinate frame about the x, y, and z axes of a reference coordinate frame by angles 0 are
represented by the following 4 x 4 matrices:
Rot(x,e) =
0 sin cose 0
Rot(y,) 0 1 0
sin 0 cos E 0
0 and (3-2)
Rot(, sine cos 0 0
Rot(z,6) =
0 0 1 0
S 0 0 1 (3-3)