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This paper describes the design, construction, and performance analysis of the Eclipse, a redundantly actuated six-degree-of-freedom parallel mechanism intended for rapid machining. The Eclipse is a compact mechanism capable of performing five-face machining in a single setup while retaining the advantages of high stiffness and high accuracy characteristic of parallel mechanisms. We compare numerical and algebraic algorithms for the forward and inverse kinematics of a class of the Eclipse and formalize the notion of machine tool workspace. We also develop a simple method for the first-order elasto-kinematic analysis of parallel mechanisms that is amenable to design iterations. A complete characterization of the singularities of the Eclipse is given, and redundant actuation is proposed as a solution. The Eclipse case study demonstrates how diverse analytical tools originally developed in a robotics context can be synthesized into a practical design methodology for parallel mechanisms.