2016/04/06 by Pham, Hung, Pham, Quang-Cuong · 1 citation
#FOS: Computer and information sciences #I.2.9 #Robotics (cs.RO)
paper · doi:10.48550/arxiv.1604.01507
This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are slow enough for the chain to be always in "rotational" equilibrium. The curve traced by the chain in a rotating plane -- its shape function -- can be determined by a simple force analysis, yet it possesses complex multi-solutions behavior typical of non-linear systems. We prove that the configuration space of the uniformly rotating chain is homeomorphic to a two-dimensional surface embedded in ℝ3. Using that representation, we devise a manipulation strategy for transiting between different rotation modes in a stable and controlled manner. We demonstrate the strategy on a physical robotic arm manipulating a rotating chain. Finally, we discuss how the ideas developed here might find fruitful applications in the study of other flexible objects, such as elastic rods or concentric tubes.