Robotic Manipulation of a Rotating Chain

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 a complex multisolutions behavior that is typical of nonlinear 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 in circular aerial manipulation with UAVs.