Qj. Ge et al., LOW-HARMONIC RATIONAL BEZIER CURVES FOR TRAJECTORY GENERATION OF HIGH-SPEED MACHINERY, Computer aided geometric design, 14(3), 1997, pp. 251-271
For a given high-speed machinery, a significant source of the internal
ly induced vibrational excitation is the presence of high frequency ha
rmonics in the trajectories that the system is forced to follow. In th
is paper a special class of rational Bezier curves is presented that c
orrespond to low-harmonic trajectory patterns. Harmonic Bernstein poly
nomials and harmonic deCasteljau algorithm are also introduced as two
major tools for generating the harmonic rational Bezier curves. These
curves can be used to synthesize trajectories within the dynamic respo
nse limitations of the actuators while avoiding the excitation of the
natural modes of vibration of the system.