Dynamic Modeling and Frequency Characteristic Analysis of a Novel 3-PSS Flexible Parallel Micro-Manipulator

Dynamic modeling and frequency characteristic analysis of a novel 3-PSS (three-prismatic-spherical-spherical) flexible parallel micro-manipulator with three translational DOF in space were investigated in this paper. Firstly, the kinematics analysis was developed based on the pseudo-rigid body model. The Jacobian matrix and the relationship between the micro angular deformation of the flexible spherical hinge and the end pose of mobile platform were respectively obtained by employing vector closed-loop method and coordinate transformation method. Then, taking into account the elastic strain energy of the flexible spherical hinge, dynamic model of this mechanism was established via Lagrange equations, and the expression of natural frequency was further derived. Combined with a set of given parameters, natural frequencies of the system were calculated by using MATLAB software. For the comparison purpose, a simulated modal analysis of the mechanism with the same parameters was also performed by employing finite element ANSYS software. Results from numerical calculation and finite element simulation indicated that maximum error of their natural frequencies was 2.71%, which verified the correctness of the theoretical dynamic model. Finally, variations of natural frequencies with changes of the basic parameters were analyzed. Analysis results show that natural frequencies increase with the increase of the bending stiffness k of flexible spherical hinge and the difference in radius E between static platform and mobile platform, while decrease with the increase of the length l of the link rod and the masses of the main components of mechanism. Besides, it can be further drawn from these obtained results that the natural frequencies increase with the increase of the angle θ between the link rod and the z axis of reference coordinate system. Considering that the increase of the stiffness k and the angle θ will reduce the scope of working space, it is recommended in designing the structure to choose a set of larger stiffness k and angle θ as much as possible under the premise of satisfying the working space.