ABSTRACT
In the analysis of robotic manipulators, movement of links, tools, and workpieces in the space is very important. For many other engineering disciplines such as guidance and navigation of mobile robots, airplanes, submarines, missiles, and so on, the representation of spatial location of a rigid body is also of great importance. The ideas developed for this representation originated many years ago [45], when humans were dreaming to fly and many different representations for position and orientation of a rigid body in space were developed since then. In this chapter, some of these representations are introduced with the emphasis on some new tools and descriptions, which are more suitable for robotic manipulators. Moreover, transformation from one representation to the other is also given. It should be noted that the ideas developed for position and orientation representation will form a basis for linear and angular velocity and acceleration representations, and is also adopted to represent forces and torques applied in a robotic manipulator.
