Singularity analysis of the kinematic chains of parallel manipulators with the linear drives

The paper considers geometric conditions of the occurring special positions in the kinematic chains that could be used to synthesize spherical parallel manipulators with the linear drives. It applies the screw calculus to analyze a general case that describes nine possible chain structures including two rotary joints which axes intersect the center of rotation and a flat dyad with the driving prismatic pair. The paper shows that from the point of view of minimizing a possibility of the mechanism getting into the special positions of different types, it is advisable to use a chain, where the dyad is connected directly to the base, and its plane does not pass through the center of rotation.
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