The nonlinear motion of underactuated mechanisms has drawn recent interests of researchers. Underactuated mechanical systems are often subject to so-called nonholonomic constraints which are related to many both theoretical and practical issues. We first analyze the nonlinear behavior of a two-joint planar manipulator with the second joint free, from nonlinear dynamics point of view. We then discuss the simultaneous positioning of both joints. We use a time-periodic input and propose an amplitude modulation of the feedback error. The analysis via the Poincare map shows that the behavior becomes chaotic with large amplitude. The effectiveness of the proposed positioning control is verified by experiments.

Nonholonomic system is now one of the major topics in robotics. In this paper, we discuss the nonlinear behavior of a two-joint planer manipulator with the second joint free for time-periodic inputs. First, we illustrate that when the amplitude remains small, the Poincare map of the system follows an ellipse-like closed path and it becomes chaotic with large amplitude. We then propose a control method to position the both joints via amplitude modulation of the position error. The effectiveness and robustness of the control method are verified by experiments.