Mathematical Modeling of Walking Machines with One-Axis Body
DOI:
https://doi.org/10.14529/ctcr170206Keywords:
walking machine, plane models, dynamics equations, first task of dynamics, dynamic reactions, moving forces and force momentsAbstract
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.References
Okhotsimskiy D.E. Mekhanika i upravlenie dvizheniem avtomaticheskogo shagayushchego apparata [Mechanics and Control of Automatic Walking Machine Movement]. Moscow, Nauka Publ., 1984. 312 p.
Telegin A.I. [Structural Synthesis and Kinematic Analysis of Plane Models Walking Aids]. Bulletin of the South Ural State University. Ser. Mechanical Engineering, 2008, vol. 11, no. 10 (110), pp. 3–14. (in Russ.)
Telegin A.I. [Algorithms Prescribing Dynamics Equations at Hinge Mechanisms]. Bulletin of the South Ural State University. Ser. Mechanical engineering, 2009, no. 29 (205), pp. 4–12. (in Russ.)
Telegin V.A., Kaygorodtsev M.I. [Modeling and Animation of Plane Models Walk Walking Aids]. Bulletin of the South Ural State University. Ser. Mechanical engineering, 2008, vol. 11, no. 10, pp. 15–23. (in Russ.)
Telegin A.I. [General and Special Types of Equations of the Dynamics of Systems Absolutely Solids]. Bulletin of the South Ural State University. Ser. Mechanical engineering, 2007, vol. 9, no. 11 (83), pp. 3–13. (in Russ.)
Telegin A.I. [New Equations for the Solution of Problems of Dynamics and Synthesis of Systems of Solids]. Bulletin of the South Ural State University. Ser. Mechanical engineering, 2006, vol. 8, no. 11 (66), pp. 3–14. (in Russ.)
Telegin A.I. [New Formula for Dynamic Power Analysis of Plane Lever Mechanisms]. Bulletin of the South Ural State University. Ser. Mechanical engineering, 2007, vol. 10, no. 25(97), pp. 3–11. (in Russ.)
Ozol O.G. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines]. Moscow, Nauka Publ., 1984. 432 p.
Astashev V.K. Dinamika mashin i upravlenie mashinami: Spravochnik [Dynamics of Machines and Control Machines: Directory]. Moscow, Mechanical engineering Publ., 1988. 240 p
