This paper presents a new open-source mechanical design of a 6-DOF anthropomorphic ALARIS robotic hand that can serve as a low-cost design platform for further customization and utilization for research and educational purposes. The presented hand design employs linkage-based three-phalange finger and two-phalange adaptive thumb designs with non-backdrivable worm-and-rack transmission mechanisms. Combination of design improvements and solutions, discussed in the paper, are implemented in a functional robotic hand prototype with powerful grasping capabilities, which utilizes off-the-shelf inexpensive components and 3D printing technology ensuring the hand low manufacturing cost and replicability. The open-source mechanical design of the presented ALARIS robotic hand is freely available for downloading from the authors’ research lab web-site https://www.alaris.kz and https://github.com/alarisnu/alaris_hand.