Accurate analytical computation of magnetic flux density of spherical permanent magnet arrays

In robotic applications, multiple one-degree of freedom electromagnetic actuators together with gearboxes are used for mimicking the multiple degree of freedom motion profiles of human limbs. However, this results in heavy and bulky robotics. A lighter alternative can be provided by the use of spherical electromagnetic actuators in directly driven human-like joints. These spherical actuators have a relative similarity to human joints and also can provide multiple degrees of freedom motion without gearboxes. Existent spherical actuator prototypes cannot deliver yet the required torques in robotic applications, therefore development of accurate and fast analytical models to replace the time-consuming finite element simulations can be a valuable tool for analysis, design and optimization of spherical actuators. As a first step in development of an analytical model of spherical actuators, this paper presents the analytical model of an array of spherical shaped permanent magnets distributed on a spherical surface. The considered structure represents in fact the rotor of a spherical actuator. It has been shown that the developed analytical model can provide fast and accurate calculation of the magnetic flux density distribution in the whole domain in view of its integration in a complete analytical model of a spherical actuator.