Higher-order derivatives of rigid body dynamics with application to the dynamic balance of spatial linkages

Dynamic balance eliminates the fluctuating reaction forces and moments induced by high-speed robots that would otherwise cause undesired base vibrations, noise accuracy loss. Many balancing procedures, such as addition of counter-rotating inertia wheels, increase complexity motor torques. There exist, however, a small set closed-loop linkages can be balanced specific design links' mass distribution, potentially leading to simpler cost-effective solutions. Yet, intricacy conditions hinder extension this linkages. Namely, these contain complex closed-form kinematic models express them in minimal coordinates. This paper presents an alternative approach satisfying all higher-order derivatives conditions, thus avoiding finite while providing full solution for arbitrary The resulting dynamic are linear parameters null space operation, either numeric or symbolic, yield space. concept transfer provides graphical interpretation retain intuition. A novel dynamically 3-RSR spatially moving mechanism is presented together with known examples illustrate method.