Dynamics and Control of 6-DOF Shaking Table with Bell Crank Structure

This paper describes the kinematics, dynamics and control of a 6-DOF shaking table with a bell crank structure, which converts the direction of reciprocating movements. In this shaking table, the bell crank mechanism is used to reduce the amount of space needed to install the shaking table and create horizontal displacement of the platform. In kinematics, joint design is performed using $Gr{\ddot{u}}bler's$ formula. The inverse kinematics of the shaking table is discussed. The derivation of the Jacobian matrix is presented to evaluate singularity conditions. Considering the maximum stroke of the hydraulic actuator, collision between links and singularity, workspace is computed. In dynamics, computations are based on the Newton-Euler formulation. To derive parallel algorithms, each of the contact forces is decomposed into one acting in the direction of the leg and the other acting in the plane orthogonal to the direction of the leg. Applying the Newton-Euler approach, the solution of inverse dynamics is almost completely parallel. Only one of the steps-the application of the Newton-Euler equations to the platform-must be performed on one single processor. Finally, the efficient control scheme is proposed for the tracking control of the motion platform.