The Tendon-Actuated Lightweight In-Space MANipulator (TALISMAN) is a versatile long-reach robotic manipulator that is currently being tested at NASA Langley Research Center. TALISMAN is designed to be highly mass-efficient and multi-mission capable, with applications including asteroid retrieval and manipulation, in-space servicing, and astronaut and payload positioning. The manipulator uses a modular, periodic, tension-compression design that lends itself well to analytical modeling. Given the versatility of application for TALISMAN, a structural sizing methodology was developed that could rapidly assess mass and configuration sensitivities for any specified operating work space, applied loads and mission requirements. This methodology allows the systematic sizing of the key structural members of TALISMAN, which include the truss arm links, the spreaders and the tension elements. This paper summarizes the detailed analytical derivations and methodology that support the structural sizing approach and provides results from some recent TALISMAN designs developed for current and proposed mission architectures.