A novel compliant robot is proposed for traversing on unstructured terrains. The robot consists of modules, each containing a link and an active wheel-pair, and neighboring modules are connected using a passive joint. This type of robots are lighter and provide high durability due to the absence of link-actuators. However, they have limited climbing ability due to tendency of tipping over while climbing big obstacles. To overcome this disadvantage, the use of compliant joints is proposed in this work. Stiffness of each compliant joint is estimated by formulating an optimization problem with an objective to minimize link joint moments while maintaining static-equilibrium. This is one of the key novelties of the proposed work. A design methodology is also proposed for developing an n-module compliant robot for climbing a given height on a known surface. The efficacy of the proposed formulation is illustrated using numerical simulations of the three and five module robots. The robot is successfully able to climb maximum heights upto three times and six times the wheel diameter using three and five modules, respectively. A working prototype was developed and the simulation results were successfully validated on it. © 2014 IEEE.