Mechanical power transmission with synchronized rotation is sometimes required to be achieved with high efficiency through an arbitrarily variable operating angle between an input and output shafts. Kinematically flexible shaft joints can deal with this design problem within a limited operating angle otherwise their durability would much be compromised. Two-stage right-angle bevel or spiral bevel gear arrangements are presented that allow the transmission of an appreciable power, satisfying the requirements mentioned at the outset. Their main applications are also highlighted, particularly in twin-tiltrotor aircraft that have non-tilting engines. An alternative suggestion of such an aircraft driveline is also made, which could provide additional dynamibility. Further examples of drive over highly variable operating angles are included. In addition, torus bevel gears are introduced as a single-stage solution to the same design problem. Their generating kinematics is detailed and a novel design of a dedicated gear cutting machine is accordingly presented.