This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.
This paper aims to develop a new computationally efficient method for the dynamic modelling of a Planar Parallel Manipulator (PPM) based on the Discrete Time Transfer Matrix Method (DT-TMM). In this preliminary work, we use a 3-PRR PPM as a study case to demonstrate the major procedures and principles of employing the DT-TMM for the dynamic modelling of a PPM. The major focus of this work is to present the basic principles of the DT-TMM for the dynamic modelling of a PPM: decomposing the whole parallel manipulator to the individual components, establishing the dynamics of each component/link, linearizing the component/element dynamics to obtain the transfer matrix of each component/link, and assembling the component dynamics into the system dynamics of the PPM using the transfer matrices of all components/elements. To make the work more readable, the brief introduction of the inverse kinematics and the inverse dynamics is also included. The numerical simulations are conducted based on the 3-PRR PPM with rigid links in this preliminary research effort. The simulation results are compared with those from the model using the principle virtual work method and ADAMS software. The numerical simulation results and comparison demonstrate the effectiveness of the dynamic modelling method using DT-TMM for the PPM.
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