Due to clearances in their passive joints, parallel manipulators always exhibit some unconstrained motion at the end effector. The amount of unconstrained motion depends on the pose of the manipulator and can increase significantly at or near singular configurations. This paper shows precisely how much unconstrained end effector motion exists at the end effector for a large class of parallel manipulators, namely those with passive revolute and/or spherical joints, if all the joint clearances are known. This includes the planar 3R_RR, and, in approximation the Gough-Stewart and the Hexa manipulators. For the analysis, the passive joints are assumed to be revolute or spherical because these are the simplest cases. However, the general framework also applies to other joint types, although leading to more complex calculations. For most manipulators, determining the amount of end effector motion can be transformed to a workspace generation problem. Therefore, general workspace generation techniques can be utilized.
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