Calculating joint angles for sequential manipulators consists of studying the correlation between Cartesian and joint variables. The problem-solving technique encounters two main hurdles described as direct and inverse kinematics. Matrix multiplications usually simplify the direct kinematic problem. However, inverse kinematic problems are harder as they require solving many nonlinear equations and eliminating variables a lot. In our work, we introduce two new methods of handling the complicated inverse kinematic problem for robotic manipulator arms; Poor and Rich Optimization Algorithm and Clonal Selection Algorithm (CSA). These advanced techniques enhance greatly the estimation of various joints in the arm which makes the solution more precise and efficient. To demonstrate the effectiveness, robustness, and potential benefits of these approaches for complicated kinematic problems we present extensive simulation results thereby enabling better performance of robots.