A new algorithm for creating diverse, irregular and physically reasonable three-dimensional linear atomic chains is described. The linear chains of atoms, or molecular graphs, are generated by solving a series of trigonometric equations within geometric constraints for a given set of atom types. The nature and number of the chains that are produced can be controlled by changing the palette of atom types, so that a chemist user could generate template suggestions that are synthetically relevant to a drug design project. Testing has shown that the method is sufficiently robust to be used in a general context. The molecular graphs could serve as useful structural templates for joining up regions in an active site where a ligand might interact strongly with the receptor. This paper is concerned with the description and proof of the methodology. The approach will form part of a larger structural tool kit for helping chemists to design novel ligands for a specified site.