It is well known that the inverse kinematics problem for the spherical serial manipulator has been solved in the past by diverse methods; but this problem for a generalized architecture based on the Denavit-Hartenberg parameters has not been treated. Therefore, this paper considers such treatment in a geometric analysis to derive a closed-form solution of the inverse kinematics problem, whose algorithm is validated by simulating pick and place operations. With the code implementation of a novel linear tracking algorithm introduced here, this application is accomplished in real time with the aid of a development software devoted to simulate robotic applications in real time, allowing the visualization of the performance of all possible architectures including the eight types defined in this paper; It is also shown that the Stanford arm is comprised within this classification. In order to demonstrate the great potential offered by combining the algorithms released here in simulations for industrial applications requiring a quick response, a case study is presented by taking as examples, the Stanford manipulator and a spherical manipulator with generalized architecture.