A harmonic drive assembly and fluid-powered linear motors with both axial pistons are rotary piston arrangements incorporating the harmonic drive assembly are disclosed. The motors may be used in downhole drilling applications, but the drive assembly and/or motors may be used in other applications. The assembly, motors and methods use advanced harmonic drives, advanced helical drives, and combinations thereof with 1) motors with axial pistons and reciprocating linear rings to convert reciprocative axial motion to continuous rotary motion, and 2) motors with rotary pistons and reciprocating linear rings to rectify reciprocative rotary motion to continual rotary motion to improve performance over prior configurations. Axial pistons provide a robust simple solution for generating rotation; Rotational pistons provide increased torque generation as the torque generated is proportional to motor length. Since downhole drills are long, a high-torque motor can be produced using this method.