| Driven by the exhaustive needs from the large-diameter aspheric numerical control polishing equipment, this thesis deals with the issues on kinematics analysis, workspace analysis, semi-analytical stiffness modeling, finite element analysis of stiffness and dynamic characteristics of a 6-DOF hybrid robot---Tricept. The following contributions have been made:According to process requirement, the layout of the large-diameter aspheric polishing equipment using the Tricept robot is proposed. The inverse and forward kinematics analysed are carried out by means of vector method. On the basis of forward kinematics, a method to determine the boundary of reachable workspace is proposed by taking into account the actuated limb lengthes and joint constraints, leading to a prescribed cylindrical task space.On the basis of force analysis using the wrenches of actuations and constraints imposed upon the platform, a semi-analytical stiffness model of 3-UPS-UP parallel mechanism with in the Tricept is formulated that accounts for the compliances of all limb components and joints. This model can be used to evaluate the stiffness of the mechanism over its entire task workspace in a very quick manner and its validity has been proved by SAMCEF at typical configurations.With the aid of powerful geometric modeling capability of SolidWorks and finite element analysis capability of SAMCEF, the static and dynamic behaviours of the Tricept robot over the entire task workspace are also evaluated in terms of static rigidity, natiral frequencies and mode shapes by considering the compliances of the 3D rotating head as well as the end-effector for polishing. The results show that the stiffness of the 3D rotating head, the torsional stiffness of the gear reducer of the C axis in particular, has significant bearings on static and dynamics compliances of the hybrid robot as a whole.Based on the outcome of this thesis, a prototype machine for large-diameter aspheric polishing is being designed and developed. |
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