Modeling of a Fully Flexible 3PRS Manipulator for Vibration Analysis

In this paper we provide a vibration analysis model and the modeling method for a fully flexible 3-Parallel-Revolute-joint-and-Spherical-joint (3PRS) manipulator-a sliding-leg tripod with flexible links and joints. A series of tripod configurations are set by rigid kinematics for simulation and experiment. All the links are modeled by finite elements: triangular membranes combined with bending plates for the moving platform and spatial beams for the legs. The joint complication is overcome by modeling the joint constraints as virtual springs. The nodal coordinates are statically condensed in order to validate the model. Using eigenvalue sensitivity analysis in terms of the condensed coordinates, the stiffness parameters of the joint virtual springs are adjusted in the experimental configurations until the acceleration frequency response functions (FRFs) from the calculation agree with the ones from the impact tests. The adjusted joint parameters are interpolated linearly into a series of configurations in simulation. The analysis shows that the model with the modified joints proposed in this paper is more effective than the conventional model with ideal joints for predicting the system natural frequencies and their variations against different tripod configurations. The good agreement between the simulation and the experiment at resonant peaks of the FRFs indicates the effectiveness of the modeling method.