Generalized high-speed vibration-damping transfer cam curve with arbitrary rise time in point symmetry consisting of half-odd-integer trigonometric functions

In the present investigation, we have proposed universal formulas for point symmetrical high-speed vibration-damping transport cams for a 1DOF undamped follower vibrator in an arbitral rise time. These formulas, composed of half-odd integer trigonometric functions, are deduced as solutions to a two-point boundary value problem. We evaluated the behavior of non-dwell and two-dwell cam profiles with low wavenumbers through simulations. Also, we show infinite linear sums of these formulas can express smooth and practical cam profiles comprising elementary and non-elementary functions. These formulations facilitate various expressions of the cam function, thereby broadening its potential.