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Discrete Kinematic Geometry in Testing Axes of Rotation of Spindles

[+] Author Affiliations
Delun Wang, Zhi Wang, Yu Wu, Huimin Dong

Dalian University of Technology, Dalian, China

Shudong Yu

Ryerson University, Toronto, ON, Canada

Paper No. DETC2016-59495, pp. V05BT07A087; 8 pages
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5B: 40th Mechanisms and Robotics Conference
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5016-9
  • Copyright © 2016 by ASME


The accuracy of actual motion of the spindle of a machine tool, a key performance index, is measured at a series of positions, and evaluated using a discrete kinematic geometry model. The kinematic geometry model, or more precisely a novel mechanism, is presented for the first time in this paper and validated using an apparatus consisting of a spindle, an artifact with double master ball and five displacement sensors as per ASME codes and standards [1]. The six kinematic parameters of the spindle with a single rotor — three translations and three rotations are obtained using the novel mechanism and the measurements. The theory of discrete kinematic geometry is employed to reveal the intrinsic properties of the trajectories traced by the characteristic lines of the rotor. In order to avoid the influences caused by the locations and directions of the measuring coordinate systems, the invariants of a discrete line-trajectory, particularly the spherical image curve and the striction curve [2], are introduced to deal with the discrete measurements. The global invariants, the approximated moving axis and the approximated fixed axis of the rotor in the error motion, independent of the assembling position of the double master balls on the rotor, are proposed to evaluate the rotational accuracy of spindles. The discrete kinematic geometry provides a new perspective and a theoretical base for assessing the accuracy of the spindle motion.

Copyright © 2016 by ASME



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