Open AccessThe article proposes a technique to develop mathematical models (MM) of elements of the three-dimensional (3D) mechanical systems for universal simulation software systems that allow us automatically generate the MM of a system based on MM elements and their connections. The technique is based on the MM of 3 D body. Linear and angular velocities are used as the main phase variables (unknown in the MM of the system), linear and angular movements are used as the additional ones, the latter being defined by the normalized quaternions that have computational advantages over turning angles.
The paper has considered equations of dynamics, formulas of transition from the global coordinate system to the local one and vice versa. A spherical movable joint is presented as an example of the interaction element between the bodies. The paper shows the MM equivalent circuits of a body and a spherical joint. Such a representation, as the equivalent circuit, automatically enables us to obtain topological equations of the system. Various options to build equations of the joint and advices for their practical use are given.