Manufacturing Technology 2014, 14(4):561-566 | DOI: 10.21062/ujep/x.2014/a/1213-2489/MT/14/4/561

The Issue of Calculating Elliptic Trajectories

Alexander Lozhkin¹, Ivan Abramov¹, Pavol Bozek², Yuri Nikitin¹

¹ Departments "Software" and "Mechatronic Systems", M.T. Kalashnikov Izhevsk State Technical University, Studencheskaya St. 7, 426069 Izhevsk, Russia

² Institute of Applied Informatics, Automation and Mathematics, Faculty of Materials Science and Technology, Slovak University of Technology, Hajdóczyho 1, 917 24 Trnava, Slovakia

The design of elliptic trajectories of kinematic mechanisms by classical method is a challenge. New method is proposed. Theoretical tests were conducted on a method. It can not be used for scaling and rotation. Some limitations are revealed as well. Geometric modeling showed the method can be applied to arbitrary curves. It should be noted that the theoretical and modeling researches of arbitary curves is not full. Simple robot was designed for processing ellipses. The design of the stand was assembled from aluminum profiles, linear modules and fasteners RK Rose + Krieger. Experiments have shown a difference between the theoretical and actual trajectory less than 5%. The error of stationing was 8,5% before using of the direct analytical method.

Keywords: Kinematic mechanisms, Geometry, Calculation of trajectory, Arbitrary curves

Published: December 1, 2014  Show citation