Trajectory-based synthesis of a three-mass vibratory system excited by a dual phase-controlled crank-slider mechanism

This paper addresses trajectory-oriented excitation of a vibration machine working body by using a planar three-mass oscillatory system driven by a dual, phase-controlled crank-slider mechanism. The working body is assumed to undergo purely translational motion along two orthogonal axes, while two auxiliary masses move along inclined guides and transmit excitation through linear viscoelastic links. An exact kinematic description of the crank-slider base motions is combined with the derived 4-DOF dynamic model to relate the controlled phase shift between the excitation channels to the resulting vibration orbit of the working body. The proposed synthesis framework is formulated in terms of steady-state amplitude and phase relations, enabling intentional generation of rectilinear, elliptical, and circular trajectories. Numerical simulations performed in Wolfram Mathematica demonstrate trajectory switching and continuous steering by adjusting the crank-pin phase offset, the guide orientation angles, and the relative stroke amplitudes of the two excitation branches. The results confirm that phase control provides the primary trajectory-control parameter, while geometric settings rotate the orbit and tune its aspect ratio, with minor deviations from ideal ellipses (circles) attributable to higher harmonics of the crank-slider kinematics.