Robotics has become an essential component of virtually every industry sector, including modern assembly, manufacturing, agricultural processes, and even retail operations. Ensuring the safety of human collaborators working alongside robots is of utmost importance, and accurate estimation of the robot's end-effector pose is critical for achieving this goal. In this paper, we present a method to estimate the end-effector pose of an industrial serial manipulator without relying on the robot's encoders. Our method uses depth cameras in the robot workspace, feeding a convolutional neural network and a cascade estimator to determine the 3D coordinates of every joint sequentially. We studied three variations of the method, with the first estimating all joints independently, the second estimating every joint based on the estimation of the previous joint, and the third using all the previous joints. Our experimental setup employed a UR5 6DOF robot arm in the ROS-Gazebo simulation ecosystem. The results show that the third variation exhibits the best performance, demonstrating the effectiveness of this methodology in predicting the pose of a manipulator using only computer vision. This approach is an enabling technology for many Industry 4.0 applications, improving both human safety and manufacturing efficiency.