This paper presents an improved input shaping method to eliminate vibration during circular interpolation of a flexible 2-axis positioning system. Due to the time delay introduced by input shaping, simultaneous 2-axis positioning with circular interpolation results in a certain amount of errors from the intended track or trajectory. This study investigated the track errors associated with circular interpolation caused by input shaping for a flexible 2-axis positioning system. The following three strategies for reducing such errors were proposed: velocity reduction in circular interpolation, adjustment of the time delay between 2 axes commands, and employment of a velocity profile compensation function. Simulations were performed to discuss the pros and cons of the three proposed strategies. Experiments were also performed to validate the results. Simulation and experiments showed that the track errors due to input shaping can be sufficiently reduced by combined use of the proposed strategies.

Linear roller bearings are often used for linear positioning systems due to high load-carrying capacity, precision, and durability. In this paper, guide rail deformation of linear roller bearings under vertical and horizontal loads, has been experimentally investigated. An experimental system was made to measure displacement of the carriage and guide rail deformation of a bearing with varying load. Guide rail deformation inaccessible inside the carriage, was estimated by measured carriage displacement subtracted from calculated carriage displacement from a commercial program, that does not consider flexibility of guide rail and base. In addition to estimated deformation, guide rail deformation outside the bearing carriage was measured to make a complete guide rail deformation curve due to external loads. Results revealed deformations occurring in guide rail and base are significant, as to affect bearing accuracy. Thus, deformations in guide rail and base should be considered, to estimate stiffness and motion accuracy of linear roller bearing under external loading conditions.