Recently a methodology for closed-form modelling of non-holonomic hybrid parameter multiple body systems (HPMBS) was presented. The tool provides a means to model non-holonomic HPMBS with sets of minimal closed-form hybrid differential equations; these equations are minimal in the sense that there are no Lagrange multiplier equations required. Also provided by the method is a means to generate closed-form models of the momentum change imparted on a HPMBS when the system undergoes impulsive loads or configuration space changes. In this paper, these techniques will be merged to form an algorithm for modelling HPMBS under the influence of changes in the configuration space due to the variable presence of, or lack of, constraints. It should be noted that restitution coefficients are not needed to describe momentum transferred within the system when the configuration changes. Included in this work is the explicit minimal closed-form model of a flexible two-link planar manipulator interacting with a work-piece and the numerical simulation of this system under various conditions. The process of modelling this system will elucidate the algorithm which is applicable to higher order systems.