Abstract
The dynamic model of 4-SPS/PS parallel mechanism with a flexible actuated rod and clearance spherical joint is established based on the equation of motion. Firstly, the flexible actuated rod is modeled using finite element (FE) 3D beam based on the floating frame of reference (FFR) formulation since small deformation occurs in the rod. In order to build the actual dynamic model, some rigid joints are introduced to connect the related components in 4-SPS/PS parallel mechanism. Secondly, two different sets of reference conditions are imposed at the FE analysis stage for the 3D beam to obtain the free-free modes and fixed-fixed modes based on the normal mode approach, which circumvents the fact that the free-free modes are not suitable for some instances. Further, the dimension of the whole dynamic model is reduced by the normal mode approach as well. Besides, clearance is introduced to one of the spherical joints in this parallel mechanism. The normal and tangential contact forces are estimated based on the Lankarani–Nikravesh contact force model and a modified Coulomb friction model, respectively. Finally, the effects of the free-free modes and fixed-fixed modes from the flexible actuated rod on the dynamic responses of the parallel mechanism with clearance spherical joint are firstly discussed in this investigation. The comparative analysis between considering flexible actuated rod (FAR model), considering clearance spherical joint (CSJ model) and simultaneously considering flexible actuated rod and clearance spherical joint (FAR-CSJ model) has been carried out. The simulation results showed that a reliable and comprehensive solution requires both appropriate reference conditions, and taking the clearance spherical joint and the flexible moving platform into consideration.
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