The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased, the gaits exhibit universal period doubling bifurcations leading to chaos. Meanwhile, the phenomena of period doubling bifurcations also occur by increasing either the foot length or the mass ratio of the robot. Theory analysis and numerical simulations are given to verify our conclusion.
Many theoretical models of slender prismatic beams in a cross-wind have been developed during last decades. They mostly follow various types of the linear approach. Therefore their applicability is very limited especially for prediction of the system post-critical behavior. The subject considered in this paper represents a part of a complex theoretical background of the general nonlinear model which would enable fo predict any system reaction in the pre- and post-critical domain. In particular, the aeroelastic self-induced oscillaton of a mechanical system with generalized single degree of freedom (SDOF) is discussed. The motion is described by an ordinary differential equation of Duffing type with special generalized aero-elastic damping of Van der Pol type. A new semi-analytical approach is introduced to identify the limit cycles both stable and unstable. The latter are not possible to be identified by means of experiments nor by the numerical integration. and Obsahuje seznam literatury