Torque-transmitting steering mechanism for a steerable tool

A steerable tool comprising:

• a mechanical transmission system comprising:
• at least four longitudinal members each having a proximal and distal end, arranged in a longitudinal direction around a geometric shape that is a tube,
• a transmission shaft region, transmission bendable proximal part that is omnidirectionally moveable and bendable along a curve, and transmission bendable distal part that is omnidirectionally moveable and bendable along a curve,
• wherein the longitudinal members transmit longitudinal forces to bend the transmission bendable distal part responsive to movement of the transmission bendable proximal part,
• wherein a plane section of at least one longitudinal member has an anisotropic area moment of inertia,
• wherein a majority of the longitudinal members are each constrained at one or more constraining points along the transmission bendable distal part or along the transmission shaft region,
• wherein, at the constraining point, rotation around a longitudinal axis of the longitudinal member is constrained,
• wherein the longitudinal members are longitudinally slidable with respect to each discrete constraining point, and
• wherein the mechanical transmission system is configured such that a transmission bendable distal part tip is axially rotatable in a bent position by a complementary rotation of the transmission bendable proximal part.