Forward kinematics is used to describe the static position and orientation of the manipulator
linkages. There are two different ways to express the position of any link: using the
Cartesian space, which consists of position (x,y,z), and orientation, which can be
represented by a 
matrix called the rotation matrix; or using the joint space, by
representing the position by the angles of the manipulator's links. Forward kinematics is the
transformation from joint space to Cartesian space.
This transformation depends on the configuration of the robot (i.e., link lengths, joint
positions, type of each joint, etc.). In order to describe the location of each link relative to its
neighbor, a frame is attached to each link, then we specify a set of parameters that
characterize this frame. This representation is called the Denavit-Hartenberg notation.
Figure 2: A physical six-link robot manipulator
Figure 2 shows a physical six-link robot manipulator.
The Denavit-Hartenberg parameters are [1]:
from 
to the intersection of the
and 
axes.
from 
to the intersection of the
and axes. is variable if joint i is prismatic.
and 
measured about
.
and measured about . is variable if joint i is revolute.
The Denavit-Hartenberg parameters for our prototype robot are shown in Table
1. The parameters for the last 3 links are constants with the exception of
's, the joint
variables and 
the offset parameter which represents the offset distance between
and the center of the wrist O. 
and 
are zeros because the distance
along from to the intersection of and is zero.
Table 1: Symbolic DH parameters for the robot.
The corresponding Transformation matrix is
where
