2023/12/14 by Aditya Kapilavai, Kapilavai, Aditya, Georg Nawratil +1
Engineering · #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Manufacturing Process and Optimization #Robotic Mechanisms and Dynamics #Robotics (cs.RO) #Space Satellite Systems and Control
paper · pdf · doi:10.48550/arxiv.2312.09160
openalex publication_date 2023/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The kinematic/robotic community is not only interested in measuring the closeness of a given robot configuration to its next singular one but also 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 of Stewart-Gough type; namely so-called linear pentapods. Geometrically the architecture singular designs are well-understood and can be subclassified into several cases, which allows to solve the optimization problem of computing the closest architecture singular design to a given linear pentapod with algorithms from numerical algebraic geometry.