Russian Engineering Research

, Volume 38, Issue 12, pp 1071–1073 | Cite as

Resultant Cutting Trajectories on Machine Tools with Raster Tool Motion

  • K. R. MuratovEmail author
  • E. A. GashevEmail author
  • T. R. AblyazEmail author
  • L. D. SirotenkoEmail author
  • E. V. MatygullinaEmail author
  • D. M. LagunovEmail author


The formation of the resultant raster trajectories in machine tools are established on the basis of Lissajous figures, taking account of additional workpiece motion for finishing purposes. Kinematic and geometric formulas are obtained for the relative tool and workpiece trajectory with strict kinematic coupling. These formulas are required in practice for abrasive lapping. They permit control of the resultant abrasive-cutting trajectory in finishing the precision planes of the workpiece.


kinematic coupling raster trajectory relative motion machine tools lapping 



Financial support was provided by the Russian Ministry of Education and Science (project 11.976.2017/BCh).


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    Muratov, K.R., Influence of rigid and frictional kinematic linkages in tool–workpiece contact on the uniformity of tool wear, Russ. Eng. Res., 2016, vol. 36, no. 4, pp. 321–323.CrossRefGoogle Scholar
  2. 2.
    Nekrasov, V.P., The study of raster finishing and patterns of formation of flat surfaces, Cand. Sci. (Eng.) Dissertation, Perm, 1971.Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Perm National Research Polytechnic UniversityPermRussia

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