Nonlinear motion analysis of a two-link arm using first integrals

In this paper we discuss the nonlinear motion of a conservative two-link arm using first integrals, which includes one integral constant. In the analysis of the motion, the constant plays important role. First, we give some discussion on the free motion by focusing on the integral constant. As the result, the free motion can be classified into two types-the one is oscillation and the other is rotation. Second, we discuss the forced motion of the arm actuated only at the second joint. We take the first integral in a more general form, and show that the forced motion of the second link can be expressed as a variation of the integral constant. Also, the characteristic of the forced motion actuated by arbitrary constant torques is discussed.