Mathematical Modeling of Walking Machines with One-Axis Body

Abstract

The models walking machine (WM) with one-axis body are considered. Their kinematic schemes are providing the maximum carrying capacity and minimum actuators' power consumption for implementing the specified body movement. The solution of the dynamics equations (DE) for one-axis WM (OWM) are obtained. These DE contain OWM-N kinematic, geometric and simulation parameters, where N is any real number more than 5. The number of mathematical operations obtained in DE are minimal. DE are presented in two forms: first, as a system of differential-algebraic equations where differential equations contain the dynamic reaction at the support points, and algebraic equations describe the relations between the support feet and supporting plane. And secondly, as a system of N second degree differential equations with the excluded relation reactions. Formula of calculating dynamic reactions at the support points is as simple as possible. Formulas for calculating dynamic reactions at pivot points of such WM are derived. The authors also describe algorithms for solving dynamics tasks arising while studying WM walking and give examples.