Host: The Japan Society of Mechanical Engineers
Name : [in Japanese]
Date : August 07, 2016 - August 10, 2016
Although more than 55 years have been passed, we have not known posicast shaped function (PSF) is a unique input command for one rapid rest-to-rest motion in one natural period and if there are more generalized expressions or not. Recently, we have deduced a feedforward formula, termed vibration manipulation function (VMF), to manipulate a 1DOF linear undamped floating oscillator from the dynamics of three-vibro-impact oscillators under Grover algorithm. Since VMF is a linear combination of half-integer trigonometric functions, it can express general input command to transfer the oscillator from arbitral initial position and velocity to arbitral aimed ones. As a special case of VMF, we can define an input command for rest-to-rest motion in one natural period, termed roVMF. In this study we have proved any PSF for the undamped 1DOF oscillator (uPSF) can be expressed by roVMF. Moreover, since uPSF has more strict symmetrical property than roVMF, we conclude the set of uPSF, Uup, is contained in the set of roVMF, UroV. Hence roVMF is more general expression of uPSF.
