Abstract: Coupling for transmission of torque, speed, and hydraulic thrust from a power section of a motor to a drive or output shaft. The coupling has a pair of mated hubs each with cantilevered teeth extending therefrom. The teeth are irregular in shape with an “S” curved driver side, a slanted unloaded surface, and a tooth base broader that the tooth top, which provide improved torsional and fatigue strength and wear resistance to the coupling. The coupling has utility in single and double articulation as a transmission in a mud motor for downhole directional drilling of subterranean formations. The coupling also has utility in other drilling operations employing motors requiring couplings of or for single or double articulation for minerals, geothermals, and HDD associated underground utilities. The invention further has utility with coiled tubing drilling and any power transmission equipment either with angular misalignment or direct drive.