Pentapods with Mobility 2
This solves a long-standing problem in kinematics and robotics, offering foundational insights for mechanism design, though it is incremental in extending prior work on mobility classifications.
The paper provides a complete classification of pentapods with mobility 2, excluding cases with collinear anchor points, solving the Borel-Bricard problem for 2-dimensional motions and presenting three new types for a special case, while also listing all non-architecturally singular hexapods with 2-dimensional self-motions.
In this paper we give a full classification of all pentapods with mobility 2, where neither all platform anchor points nor all base anchor points are located on a line. Therefore this paper solves the famous Borel-Bricard problem for 2-dimensional motions beside the excluded case of five collinear points with spherical trajectories. But even for this special case we present three new types as a side-result. Based on our study of pentapods, we also give a complete list of all non-architecturally singular hexapods with 2-dimensional self-motions.