This book stems from a first graduate course taught at the University of Florida on robot geometry. It describes in detail a forward and reverse analysis for serial robot manipulators, and a displacement analysis for closed-loop spatial mechanisms.

In the forward analysis, the variable joint angles are given, together with the constant parameters that describe the geometry of the manipulator. The goal is to determine the location (position and orientation) of the robot's end effector. This problem is relatively simple. A single solution for the location of the end effector exists for a given set of joint angle parameters.

The reverse analysis is more difficult because multiple solution sets exist. Here, the desired location of the robot's end effector is specified, and the goal is to obtain all the sets of joint variables for the specified location. In other words, the manipulator has a multiple of distinct configurations for a specified location of the end effector. Here, it is required to compute all these multiple sets of joint variables that determine each distinct configuration.

One method of performing a reverse analysis is to use an iterative technique. In this approach, a multidimensional search is performed employing a minimization of some specified error function. Often, one component of the error function is the square of the distance between the end effector location for the current set of joint parameters and the desired end effector location.