We will mainly be discusses the topic of singularities. More importantly, how the mathematical representation i.e., inverse kinematics calculations relevance to World (Cartesian) and Joint spaces. More importantly, we will understand their benefit in terms of understanding the motion of the robot. Moreover, we will delve into simulations of software RoboDK and MATLAB to utilize these kinematic advantages. Furthermore, we will compute inverse kinematic calculations by extracting the homogeneous transformation matrix from prior examples (and new examples) using a MATLAB code that was purposely created to display the individual joint angles based on the final homogeneous transformation matrix. Moreover, we will construct a singularity detection algorithm to detect the elbow and shoulder singularities. We will finally test these parameters with a few case studies of the Mitsubishi RV-2AJ 5 degree of freedom robot. All joint angles are compared to the actual, and an analysis of the accuracy will be made. Prospects include utilizing the results and the simulations made to create a trajectory.