An Improved Dynamic Model and Matrix Displacement Model for Distributed-Compliance Bridge-Type Amplification Mechanism

Abstract

This paper establishes a matrix displacement model and an improved dynamic model for the static and dynamic performances analysis for a kind of bridge-type displacement amplification mechanism with distributed-compliance, which has better performances than traditional lumped-compliance bridge-type mechanisms. In the matrix displacement model, the stiffness matrix for two rigid bodies connected by flexures is first obtained by regarding the displacements and the forces on two mass centers of the rigid bodies as the node displacements and node forces. By extending and superimposing each elemental stiffness matrix, the global stiffness matrix for the flexure mechanism can be obtained to calculate the displacement amplification ratio and input stiffness of the bridge-type mechanism. In the improved dynamic model, in order to establish the Lagrangian dynamic model more accurately, the deflectional, axial, and rotational velocities of any point on the beam flexure are calculated by solving the derivatives of the deformation curves of beam flexures versus time to obtain the expression of the kinetic energy in the vibrating beams. On this basis, the three-degree-of-freedom vibration differential equation for the bridge-type mechanism is established by using the Lagrange method, and the natural frequency in the working direction is obtained accurately. The presented models are compared with the finite element analysis, and experiments for two case studies of the bridge-type distributed-compliance mechanism are presented. The comparisons results demonstrate the high prediction accuracy of the improved dynamic model.