The recent era of Industry 4.0 extensively utilizes manipulators for various critical automation tasks. Handling a manipulator robot is a complex task. This research employs a 3-R (revolute) manipulator robot to achieve optimal joint trajectories for drawing different alphabets and shapes. The solution to inverse kinematics (IK) is essential; therefore, an artificial neural network (ANN) based model is used. The forward and backward reaching inverse kinematics (FABRIK) technique provides stability, though it is computationally intensive and time-consuming. To design a low-cost hybrid model, ANN combined with FABRIK is proposed to compute IK. Using the proposed model, coordinates for different alphabets and shapes within the confined workspace were calculated. We have developed a 3R (revolute) manipulator that utilizes deep learning (DL) and IK. The ANN automatically obtains specific end-effector coordinates. Due to the non-linear characteristics of IK’s mathematical model, inverse kinematics is a time-consuming procedure, making it difficult to provide a mathematical solution. Our primary goal is to reduce processing costs by using ANN and FABRIK with the IK model to solve IK problems and obtain coordinates for any form or alphabet within a given workspace. To ensure a safe region is selected, this model combines the control barrier function (CBF) with the Lyapunov function. The accuracy of the model exceeds 99.5 percent. We have calculated the mean square error (MSE) as 1.66, the root mean square error (RMSE) as 1.25, and the mean absolute error (MAE) as 0.96 for our model. The error between the model’s predicted and actual coordinates also demonstrates letter coordinates and shapes drawn using a physical 3R manipulator model. As a result, this approach can be used to accurately estimate the angles in complex 3DoF inverse kinematics models.