LOW-HARMONIC RATIONAL BEZIER CURVES FOR TRAJECTORY GENERATION OF HIGH-SPEED MACHINERY

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.