Abstract
The device we study is made up of a movable body connected to a base by six ball-joint-ended rods. In practical manipulation linear actuators control the lengths of the rods. The question we pose is: “Given the six rod-lengths, in how many can the structure be assembled?” We succeed in answering this question for many forms of this structure, but for the two most general forms of the structure the problem remains unsolved. At the core of our study are synthetic (as distinct from analytic) methods. We draw attention to analogies between serial and in-parallel devices, and show how assembly configurations bear both on special configurations (singularities) and on controllable workspace. Some geometrical properties of certain algebraic connections are elucidated en passant.
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