A mechanism is constructed by twelve-axis geometry and controlled by spherical coordinate, so that all torques in twelve axes can be parallelly integrated. Timing belts, pulleys, hollow shafts, and spur gears onto four arc-link sets are included. Via these transmission components, base arc-links can be indirectly but synchronously rotated by base driving modules and terminal arc-links can be indirectly but synchronously rotated by terminal driving modules. The final output torque can be integrated via serial linking and parallel cooperating by the twelve rotating modules. Therefore, four arc-link sets work cooperatively and effectively in group but bear no burden each other. The mechanism can be applied to a multi-axis composite machining center machine or a multi-time element detection measuring bed and shoulder joints or hip joints corresponding to robots.