Architecture Singularity Distance Computations for Linear Pentapods

Abstract

The kinematic/robotic community is not only interested in measuring the closeness of a given robot configuration to its next singular one but also interested in a geometric meaningful index evaluating how far the robot design is away from being architecturally singular. Such an architecture singularity distance, which can be used by engineers as a criterion within the design process, is presented for a certain class of parallel manipulators called linear pentapods. Geometrically the architecture singular designs are well-understood and can be sub-classified into several cases, which allows for solving the optimization problem of computing the closest architecture singular design to a given linear pentapod with algorithms from numerical algebraic geometry.