This paper proposed an elastodynamic modeling method combined with independent displacement coordinates and substructure synthesis technology. Firstly, the connecting rod was discretized, and the elastodynamic control equation for each element was established. The multipoint constraint element theory, linear algebra, and singularity analysis were used to identify the globally independent displacement coordinates of the manipulator. On this basis, the elastodynamic model using the substructure synthesis for the 3-PRS parallel manipulator (PM) was developed, with its natural frequencies distribution in the regular workspace discussed. The comparison with the finite-element results showed that the maximum error of the first three-order natural frequencies was within 1.03%, which verified the correctness of the analytical model. The proposed elastodynamic model included all the kinematic constraints of the manipulator without increasing the Lagrangian multiplier. The method is computationally efficient and assesses the dynamic behaviors of the mechanism at the predesign phase.

This paper addresses the design of a 2-dof novel flexible parallel robot that maximizes the fundamental frequency of vibration under a specified total weight constraint. In order to enhance the natural frequency of the robot in the direction Z, structure modification of the robot is made based on the initial project. The proposed robot is suitable for the application that requires high-speed motion in a plane and step-by-step, or relatively low speed on the orthogonal direction.