Kinematic and Dynamic Analysis of Spatial Six Degree of Freedom ...

Chapter 4
KINEMATIC ANALYSIS
Kinematics deals with the aspects of motion without regard to the forces and/or
torques that cause it. Hence kinematics is concerned with the geometrical and time properties
of motion. The joint variables of a robot manipulator are related to the position and
orientation of the end effector by the constraints imposed by joints. These kinematic relations
are the focal points of interest in a study of the kinematics of robot manipulators.
Kinematic analysis deals with the derivation of relative motions among various links
of a given manipulator. There are two types of kinematic analysis problems: forward (or
direct) kinematics and inverse kinematics. Inverse kinematic analysis can be defined as the
problem of finding all possible sets of actuated joint variables (input variables) and possibly
their corresponding time derivatives which will bring the end effector to the set of desired
positions and orientations with the desired motion characteristics. Inverse kinematic analysis
is required to control the motion of a robot manipulator via computers, controllers and alike.
On the other hand, to find the location of the end effector using known input variables is
defined as Forward kinematic analysis. This is mainly used to calculate the actual position of
the end effector based on sensor readings of the actuators. Inverse and forward kinematic
analysis comprises displacement analysis, velocity analysis and acceleration analysis. The
scope of this study is limited to the displacement analysis.
Both direct and inverse kinematics problems can be solved by various methods of
analysis, such as geometric vector analysis, matrix algebra, screw algebra, numerical
integration and so on. In this study, two approaches are investigated: screw algebra and
numerical integration.
The main advantage of using screw algebra is that once the objective function of
platform position is obtained, one is able to solve the direct position analysis for arbitrary
input parameters. The main drawback is the accuracy limitation. On the contrary, it is possible
to define the problem as a temporal process and divide the problem into discrete intervals.
Following the methodology, it is possible to model a variety of problems using differential
equations arising from the mechanics principles. The main advantage of this approach in our
case is the availability of highly accurate solutions. Unfortunately, one can not obtain the
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