3D inertia transfer concept and symbolic determination of the base inertial parameters

A new and simple symbolic/geometric procedure to obtain the base inertial parameters of general mechanisms is presented. The procedure is based on: 1) the concept of low mobility of bodies with respect to the Inertial Reference frame (IR), which allows one to determine the inertial parameters that do not have an effect on the motion dynamics; and 2) a generalisation of the mass transfer method introduced in [1,2] in such a way that first and second moments of inertia can also be transferred. The concepts of monopole, dipole and quadrupole mass distributions (multipoles) are introduced as means to visualise the inertia transfers and cancellations geometrically, greatly simplifying the application of the method. Criteria that simplify the symbolic expressions of base inertial parameters and of the equations of motion are given for the selection of optimal frames to define inertial properties. The proposed method is illustrated with a 3RPS parallel manipulator, demonstrating how expressions for the base parameters can be obtained in symbolic form.