The use of snake-like robots for surgery is a popular choice for intra-luminal procedures. In practice, the requirements for strength, flexibility and accuracy are difficult to be satisfied simultaneously. This paper presents a computational approach for optimizing the design of a snake-like robot using serial rolling-joints and tendons as the base architecture. The method optimizes the design in terms of joint angle range and tendon placement to prevent the tendons and joints from colliding during bending motion. The resulting optimized joints were manufactured using 3D printing. The robot was characterized in terms of workspace, dexterity, precision and manipulation forces. The results show a repeatability as low as 0.9mm and manipulation forces of up to 5.6N.