Stiffness Modeling Theory And Approach Of The Spherical Coordinate Hybrid Robot

This dissertation presents a theoretical package for stiffness modeling, analysis, performance evaluation and optimization of a class of spherical coordinate parallel kinematic machines (PKM) using analytical and semi-analytical approaches. The outcome has been employed for the development of a 5-DOF hybrid robot known as the TriVariant. The following contributions have been made.By taking the Tricept and the TriVariant robots as examples, the overall deflection Jacobian of the parallel mechanisms having a properly constrained active/passive limb is formulated. In the overall deflection Jacobian, the topological characteristics in the actuations and constraints can be explicitly separated.Using the overall deflection Jacobian and linear superposition, two analytical approaches for the stiffness modeling of the PKM having a properly constrained active/passive limb are proposed by simultaneously taking into account the component compliances in both actuations and constraints. In the modeling process, the precise bending compliance of the properly constrained limb is formulated with the static condensation and loop-closure compatibility conditions. The use of the overall deflection Jacobian allows the stiffness model to be formulated in a more effective and compact manner, and the underlying relationship between the velocity and the stiffness mapping functions to be revealed.By taking the TriVariant-B robot as an example, a semi-analytical approach is developed for the stiffness modeling of the PKM having complex machine frame geometry. In this approach, the PKM is decomposed into two subsystems associated with the parallel mechanism and the machine frame by assuming one of them is rigid. The stiffness model of entire system is then achieved by linear superposition using the interface compatibility conditions. This approach enables the stiffness distributions throughout the workspace to be time-effectively examined. By means of ANSYS parametric design language (APDL), the finite element analysis model of the TriVariant-B is formulated by taking into account the compliance of machine frame. Particular attentions are placed upon: (1) precise FEA formulation of different type of joints, and (2) the development of an effective modeling strategy for the rapid rigidity estimation associated with different configurations in order to avoid FEA model re-meshing.On the basis of singular value decomposition, two global indices are proposed for evaluating the translational and rotational rigidities of the TriVariant-B robot. Utilizing these indices, the contributions of the component compliances in the parallel mechanism and the machine frame to the translational and rotational compliances of the system are investigated by sensitivity analysis. It has been found that the joints compliance has significant impact on the translational stiffness of system while the torsional compliance of the properly constrainted passive limb has significant impact on the rotational stiffness. These findings provide engineers with informative guidelines for the detailed mechanical design. In the end, the global rigidity performance indices of the TriVariant-B are also optimized using multiple-object genetic algorithm.The experimental investigation is carried out on a TriVariant-B prototype machine. It shows that the experiment results have a good match with those obtained by the FEA and theoretical analysis.The outcome of this thesis has been employed to the design of a TriVariant-B prototype machine for frame cutting and would be useful for the development of other similar parallel kinematic machines.