Rational Parametrization of Linear Pentapod's Singularity Variety and the Distance to it
This work addresses a specific problem in robotics for manipulator design, focusing on singularity analysis, and appears incremental as it builds on existing knowledge of parallel manipulators.
The paper tackled the problem of characterizing and measuring the singularity variety of a linear pentapod parallel manipulator, resulting in a rational parametrization and computation of the shortest distance to this variety, interpreted as the radius of the maximal singularity-free sphere.
A linear pentapod is a parallel manipulator with five collinear anchor points on the motion platform (end-effector), which are connected via extendible 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.