Physically balancing multi-articulated objects

In many fields of computer science and other engineering areas, we often need to balance multi-articulated structures. In this paper, we formalize this kind of balancing problem from a more physical and theoretical point of view. Through describing details of all the solution steps, we finally represent a set of algorithms to automatically balance multi-articulated objects with tree topologies. Given the geometric configurations and masses at the leaf nodes of target multi-articulated objects, our algorithms achieve their balanced state through adjusting the mass of each node. To minimize the mass changes from the initial configuration, we use constraints of minimizing the norms of the mass differences between the initial masses and the final balanced masses. Actually, we use three different metrics, l ₁, l ₂ and l _∞ norms. These norms show slightly different behaviors in the minimization process, and users can select one of them according to their preferences and application purposes. We show all the details of algorithms, their time complexity analyses, and experimental results.