Current legged landers are typical truss structures acting as one type of fundamental equipment for the close-range extraterrestrial exploration missions. Unluckily, the development process applying the current design framework always consumes a long time span searching for the final design, accompanying masses of trial and error with inefficiency and diseconomy. Its kernel reason is that the stages from concept to scheme employ the paradigm of structural-analysis-oriented redesign and untimely embed physical prototype experiments in masses of iterative design cycles. Furthermore, the current framework cannot support the creative development of future legged landers with novel functions and mechanisms. Herein, we present a complete computable design framework for speeding up the development of both current and future legged landers, highlighted by new mathematical models and new principles of forward-design paradigm and multi-mode synergistic design paradigm. It applies the numerical prototype simulation instead of the physical prototype experiment in most iterative processes. This work will facilitate the extraterrestrial exploration missions using the current legged landers (truss-based) and the future legged lander (robot-based).