The algebra of rotations is an alternative method for describing rigid body rotations. It can be efficiently used in the kinematic analysis of robots. One of the basic problems of the algebra of rotations is to determine the resultant sum of a number of sequential joint rotations. For this calculation, four new methods, in addition to the two methods already available in the literature, are proposed in this paper. The six methods are then compared analytically and numerically on the basis of the computational efficiency. The limitations to each of the methods are also discussed. It is found that the equivalent Rodrigues parameter method is the most efficient. However, the equivalent Euler parameter method is the preferred method for use since it is infinity free, initial vector independent and reasonably efficient.