Recent developments in 3D printing technology have opened up the prospect of selfreplication in the context of robotic in-situ resource utilization (ISRU). The focus here is on 3D printing within the context of ISRU on the Moon. 3D printing technologies can print many materials including plastics, metals and ceramics for the manufacture of structures. With a judicious choice of selected in-situ raw materials, material closure can be effected while exploiting the capabilities of 3D printing. Although advancing on multiple fronts, the true value of 3D printing lies in its potential to implement universal construction. A universal constructor is a machine capable of fabricating any physical product given an appropriate program of instructions, suitable raw materials, and a source of energy in an appropriate form. Such physical products include a copy of itself -a universal constructor is by definition a self-replicating machine. A step in this direction is represented by the RepRap 3D printer that can print copies of its own plastic components. To date, there has been little effort to attempt to 3D print actuators, sensors and/or electronics. Nevertheless, the 3D printing of actuators and associated control electronics is essential, and indeed, would represent an existence proof that an appropriately designed robotic 3D printer system would constitute a universal constructor. This is consistent with theoretical kinematic models of self-replication that characterise a self-replicating machine as a computer-controlled robotic arm. To that end, I have outlined preliminary attempts to develop self-replicating machines by addressing the 3D-printable actuator and electronics aspects within the materials limits imposed by the Moon. The design of several candidate motors and potentially 3D printable electronics through vacuum tube technology are discussed. I have adopted a neural network hardware approach based on analogue circuitry as the computational medium of choice. The use of in-situ resources offers the potential construct a complete robotic infrastructure on the Moon. To that end, the full manufacturing chain from raw material to production must be considered and lunar resources offer most of the material resources required to implement a self-replicating machine. Such universal constructors can also 3D print spacecraft including structures, mechanisms, control systems, actuators, thermal management, power generation and storage, computer-based avionics and communications chains. I conclude that physical self-replicating machines are within reach. In particular, they open the potential for a complete low-cost extraterrestrial robotic manufacturing infrastructure with hitherto unimaginable benefits to humanity. Example products from this lunar infrastructure of immediate relevance include space-based geoengineering solutions in the short term and solar power satellite solutions in the long term to our current global climate crisis. Nomenclature x = number of offspring per generation n = number of generations y i = ne...