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This paper presents a technique, known as the Pure Condition, which has found use in analysing the rigidity of truss-like structures. The analysis is applied to the Stewart Platform where it can be used to identify special configurations. The conditions that produce special configurations in the octahedral manipulator are compared to previously known conditions and the associated geometry is seen to be more revealing with this method than was the case previously. The results lead to a simple and clear method for identifying special configurations in the octahedral manipulator and other specializations of the Stewart Platform.

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