A linear pentapod is a parallel manipulator with five collinear anchor points on the motion platform (end-effector), which are connected via SPS legs to the base. This manipulator has five controllable degrees-of-freedom and the remaining one is a free rotation around the motion platform axis (which in fact is an axial spindle). In this paper we present a rational parametrization of the singularity variety of the linear pentapod. Moreover we compute the shortest distance to this rational variety with respect to a suitable metric. Kinematically this distance can be interpreted as the radius of the maximal singularity free-sphere. Moreover we compare the result with the radius of the maximal singularity free-sphere in the position workspace and the orientation workspace, respectively.

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We propose a novel design of a parallel manipulator of Stewart Gough type for virtual reality application of single individuals; i.e. an omni-directional treadmill is mounted on the motion platform in order to improve VR immersion by giving feedback to the human body. For this purpose we modify the well-known octahedral manipulator in a way that it has one degree of kinematical redundancy; namely an equiform reconfigurability of the base. The instantaneous kinematics and singularities of this mechanism are studied, where especially "unavoidable singularities" are characterized. These are poses of the motion platform, which can only be realized by singular configurations of the mechanism despite its kinematic redundancy.

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