Harmonic Synthesis Theory for Dynamic Spring Balancing

Abstract

At resonance, a small excitation force amplitude results in a relatively large amplitude system response. Although typically viewed as undesirable, operating a machine near resonance can sometimes be advantageous. A new approach to dynamic spring balancing, called harmonic synthesis, tunes a system so that the desired dynamic motion is approximated by the linear superposition of resonant mode shapes. Large amplitude machine motions are achieved with minimum energy required from system actuators. Machine motion is first approximated using a Fourier series expansion about a mean operating configuration. Equilibrators are then synthesized such that resulting machine natural frequencies and mode shapes are commensurate with the harmonics of the Fourier series expansion. Harmonic synthesis examples include one and two mode approximations to the motion of a two degree-of-freedom planar robot manipulator. Results show that equilibrator parameters are determined explicitly whether a path is specified at a number of points or described over the whole range of motion.