Many surgical robots with steerable surgical instruments have been proposed for endoscopic surgery.
Surgical instruments should be small in size for insertion into the body and be able to handle large payloads such as tissue. Because the overall diameter and payload parameters are a trade-off, it
is difficult to design an instrument with a large payload while reducing its diameter. In this paper, we optimize the payload of a rolling joint mechanism by deriving the moment equilibrium equation and constraints for endoscopic surgery. A scaled-up prototype was fabricated with the design variables obtained from the optimization, and the validity of the method for calculating the payload was confirmed by the experimentally measured payload. By plotting the distribution of payloads obtained from the moment equilibrium equation, we also confirmed that the payload obtained from the optimization is the maximum. In addition, optimizations with different numbers of joints confirm that the payload tends to decrease as the number of joints increases. This payload optimization method could also be extended to minimizing the deflection of the bending section against external forces and minimizing the diameter of the surgical instrument given the minimum required payload.