First integral approach to non-linear motion analysis of a two-link system

In this paper we discuss the non-linear motion of a conservative two-link system based on first integrals. In the analysis of the motion, the constant of the first integral plays an important role. First, we show that the free motion can be classified into two types by investigating the integral constant. The one is oscillation and the other is rotation. We also show that the forced motion actuated at the second joint can be expressed schematically as a variation of the integral constant. Also, the dynamic characteristics of the forced motion are presented based on the proposed analytic approach. This analytic approach may be applied to similar non-linear dynamical systems which have the first integrals.