This paper considers a system interrupted by own state and a periodic interval. We know this system has prospects of occurrence of border-collision bifurcation. To analyze properties of the dynamics, we derive a one-dimensional map explicitly. We show some theorems and the existence of regions of periodic solution within two-parameter space. Some theoretical results are verified by laboratory experiments.

Because of the size of walking machines, scaled-down models having geometrical similarity can be used instead of full-scale models to measure energetic efficiency. First, to cope with this situation, five nondimensional parameters that control energetic efficiency Of walking machines are introduced for nine physical parameters by applying dimensional analysis techniques. Next, in order to check those influences on energetic efficiency, computer simulations are performed for an n-legged walking model. In these simulations, the influence on ground reaction forces is considered to satisfy the approximate balance of forces and moments when an overall walking machine assembly is assumed as a free body. Resultantly, several new facts are acquired from the viewpoint of similarity law.

Legged locomotion over irregular terrain is composed of body-propelling motion and terrain-adapting motion. Although conventional walking machines with three degrees-of-freedom for each leg can adapt their feet on irregular ground using flexible leg freedom, such machines generally require a tremendously complex control scheme for the body-propelling motion. A walking machine with decoupled freedoms is based on the idea that body-propelling motion is realized by only one degree-of-freedom, and this freedom can be perfectly decoupled from the freedoms for terrain adaptability. As an application of such a walking machine, a hexapod walking machine using an approximate straight line mechanism was developed and several basic experiments were performed to demonstrate the properties of this type of walking machine.