Optimal structural design of a planar parallel platform for machining

Parallel manipulators have many advantages over traditional serial manipulators. These advantages include high accuracy, high stiffness and high load-to-weight ratio, which make parallel manipulators ideal for machining operations where high accuracy is required to meet the requirements that modern standards demand. Recently, the finite element method has been used by some workers to determine the stiffness of spatial manipulators. These models are mainly used to verify stiffness predicted using kinematic equations, and are restricted to relatively simple truss-like models. In this study, state-of-the-art finite elements are used to determine the out of plane stiffness for parallel manipulators. Euler-Bernoulli beam elements and flat shell elements with drilling degrees of freedom are used to model the platform assembly. The main objective of this study is to quantify the stiffness, particularly the out of plane stiffness, of a planar parallel platform to be used for machining operations. The aim is to obtain a design that is able to carry out machining operations to an accuracy of 10 mum for a given tool force. Reducing the weight of a parallel manipulator used in machining applications has many advantages, e.g. increased maneuverability, resulting in faster material removal rates. Therefore the resulting proposed design is optimized with respect to weight, subject to displacement and stress constraints to ensure feasible stiffness and structural integrity. The optimization is carried out by means of two gradient-based methods, namely LFOPC and Dynamic-Q. (C) 2003 Elsevier Inc. All rights reserved.