Periodic locomotion of a two‐body crawling system along a straight line on a rough inclined plane. Issue 11 (24th August 2018)

• Record Type: Journal Article
• Authors: Bolotnik, N.; Schorr, P.; Zeidis, I.; Zimmermann, K.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 98:Issue 11(2018)
• Page Start: 1930
• Page End: 1946
• Publication Date: 2018-08-24
• Subjects: dry friction -- inclined plane -- limbless locomotion -- two‐body system; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201800107
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: The motion of a two‐body limbless crawler along a line of maximum slope on an inclined plane is considered. Dry friction (anisotropic in the general case) acts between the system's bodies and the underlying plane. The motion is excited and controlled by a periodic change in the distance between the bodies. Of most interest is the periodic upward motion of the system, when the velocity of the system's center of mass changes periodically with a period coinciding with that of the excitation. A mathematical model of the crawler is presented. An upper bound for the inclination angles of the plane at which the system can move upward is estimated. This estimate is based on the averaged model, which implies smallness of the coefficient of friction. Numerical and physical simulation is performed to verify the theoretical results and define an applicability area for them. Abstract : The motion of a two‐body limbless crawler along a line of maximum slope on an inclined plane is considered. Dry friction (anisotropic in the general case) acts between the system's bodies and the underlying plane. The motion is excited and controlled by a periodic change in the distance between the bodies. Of most interest is the periodic upward motion of the system, when the velocity of the system's center of mass changes periodically with a period coinciding with that of the excitation. A mathematical model of the crawler is presented. An upper bound for the inclination angles of the plane at which the system can move upward is estimated. This estimate is based on the averaged model, which implies smallness of the coefficient of friction. Numerical and physical simulation is performed to verify the theoretical results and define an applicability area for them.