flexible coupling of the present invention in this embodiment in particular fig2 b illustrates the dimensions of the flexible coupling when viewed from the flange of the third part 205 fig2 c is a cross sectional view of the flexible coupling when cut along the line a a as indicated in fig2 b fig2 d illustrates an exploded view of a portion of the flexible coupling as indicated a in fig2 c referring to fig2 b exemplary dimensions of the flexible coupling include the outer diameter 3 625 u2033 and the inner diameter 2 324 u2033 additionally the material thickness of the flexible coupling is 0 008 inches in this embodiment table i shows working conditions during the movement of the flexible coupling an experiment has been performed to test the flexible coupling built according to the embodiment as described above the motor system embodying the present invention shows nearly the same frequency of torsional resonance as the flexible coupling previously used fig3 illustrates torsional resonance test results in a motor system built according to the present invention showing the amplitude values varying depending on the frequency the amplitude values are measured by several accelerometers 307 309 311 313 located on the surface of the encoder of the motor system as shown in fig4 the result shows that a possible mode shape occurs at the frequency range between 912 920 hz nearly identical to the other non bellows style of coupling a second experiment was performed to verify the life of the bellows coupling when operated under combined radial and axial misalignment the bellows coupling survived 113 million cycles under a 0 009 inches radial misalignment in combination with 0 012 inches radial run out with no.