In the field of robotic gait rehabilitation, controlling robotic devices to follow specific human-like trajectories is often required. In recent years, various gait generator models have been proposed, providing customized gait patterns adjustable to a range of heights and gait speeds. However, these models were developed with a focus on gait rehabilitation devices designed to control the angular trajectories of the subject's joints, e.g. exoskeletons. Similar devices, e.g. end-effector robots, control the orientation and also the 3D position of the subject's joints and cannot easily implement these models. In this study, it is proposed a new individualized three-dimensional gait pattern generator for gait rehabilitation robots. The generator employs multi-variable regression models to predict the joint angular trajectories of the pelvis, hip, and ankle along the gait cycle. The 3D joints positions are then reconstructed by applying the predicted angular trajectories over a human model inspired on the inverted pendulum analogy using inverse kinematics. The generator's performance was statistically evaluated against real gait patterns from 42 participants walking at 8 different velocities. The predicted trajectories matched the measured ones with an average Root Mean Squared Error of 25.73 mm for all joints at all Cartesian axes, with better results between 3.3 - 5.4 km/h. Suggesting to be a good solution to be applied in end-effector gait robotic rehabilitation devices.