This work concerns the development of an algorithm that will determine the boundaries of the reachable workspace of a robot. A survey is made of some of the existing algorithms. Two approaches were taken here toward implementing such an algorithm. The First was to implement an algorithm developed by Tsai and Soni with a view to extending it. When difficulties were encountered with the algorithm that appeared to outweigh its usefulness, an alternate algorithm was developed. This algorithm is developed here for an nR robot, but it can be easily extended to robots that have prismatic joints. It can accommodate robots with limited joints, and it can find the cross-section of a robot's workspace on an arbitrary plane.