This paper presents a comparative study of three different methods used for tracking a particular branch of solution amongst all the solutions arising from solving a set of non-linear equations. Given an initial estimate of the required root, keeping track of the branch it belongs to is a problem that commonly arises in simulating multi-body systems like a parallel manipulator or a cable-driven parallel robot (CDPR). In such cases, these roots represent feasible configurations of the manipulator. Hence, the accuracy and fast computation of the solutions are essential to ensure the safe movement of the manipulator. The primary objective of the paper is to highlight the implementation, present the comparison of three methods of tracking and discuss the context of their application. All the tracking methods are compared with the help of a simulation of the Stewart platform manipulator (SPM) following a desired path. Further, the implementation of such a method allowing a 3-3 CDPR to follow a given path is also demonstrated.