In this paper, we present the 3-D analysis of the torque transmitted to a small permanent magnet that is embedded in a capsule robot to achieve targeted drug delivery. This analysis is carried out by using analytical models and experimental results for the magnetic field created by multiple arc-shaped permanent magnets (ASMs), and the torque imparted to a magnetic capsule robot that has an arbitrary position and orientation. Our experimental results, which are in agreement with the analytical results, show that the on-board drug release mechanism can be actuated at any position and with large inclinations of the capsule robot without having to make positional adjustments in the external magnetic system. We have established analytical expressions describing the relationship between the rotating magnetic field created by the ASMs and the transmitted torque. Such relationships are essential to establish real-time control strategies for the actuation of magnetically articulated devices such as drug delivery in capsule robots.