Kinematics-based variability of the dynamic behaviour in spatial mechanisms

The intrinsic variability of dynamic properties in spatial systems is faced in this paper by means of a kinematics-based modal approach. An effective analytical-numerical procedure is here presented to mathematically define a local linear model of a spatial mechanism, composed of rigid bodies connected by standard kinematic and lumped elastic constraints; the linearization is effective only in the closeness of the kinematically admissible position of interest and thus yields to a varying generalised eigenproblem, function of the kinematical configuration of the whole system through the working domain. An extended analysis is reported to obtain the motion equations of an unconstrained rigid body, thus linear equations of constrained motion are obtained from linearized displacements and constraint equations. The eigensystem is evaluated in every specific kinematical configuration of interest, mapping the variability of the dynamic performances across the working domain; the kinematical configuration is provided at any step of a user-defined motion law by standard non-linear kinematics. Real industrial applications, consisting in two 6 degree-of-freedom robots, are tested by means of the outlined methodology. Results are reported and discussed in detail.