<span lang="EN-US">Modeling and kinematic analysis are crucial jobs in robotics that entail identifying the position of the robot’s joints in order to accomplish particular tasks. This article uses an algebraic approach to model the kinematics of a serial link, 5 degrees of freedom (DOF) manipulator. The analytical method is compared to an optimization strategy known as sequential least squares programming (SLSQP). Using an Intel RealSense 3D camera, the colored object is picked up and placed using vision-based technology, and the pixel location of the object is translated into robot coordinates. The LOBOT LX15D serial bus servo controller was used to transmit these coordinates to the robotic arm. Python3 programming language was used throughout the entire analysis. The findings demonstrated that both analytical and optimized inverse kinematic solutions correctly identified colored objects and positioned them in their appropriate goal points.</span>