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This article presents the position analysis of a new family of 3-limbed 3-dof parallel manipulators, whose output links exhibit a motion of pure translation with respect to the base. Each limb contains four passive revolute joints and an active prismatic pair, which can be mounted anywhere along the kinematic chain or replaced by a fifth revolute one. A univariate polynomial has been found that solves the direct position problem wherever the actuators are placed. The inverse analysis has been carried out in closed-form for all possible locations of the actuated joints. Finally, numerical examples are provided.
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Carricato et al. (2003) studied this question.
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