Pentapods with Mobility 2

TL;DR

This paper classifies all pentapods with mobility 2, solving a longstanding geometric problem and identifying new types, while also providing a comprehensive list of related hexapods with similar motion capabilities.

Contribution

It provides the first complete classification of pentapods with mobility 2, addressing the Borel-Bricard problem for 2D motions and introducing three new types in special cases.

Findings

Complete classification of pentapods with mobility 2

Identification of three new types in special collinear cases

List of all non-architecturally singular hexapods with 2D self-motions

Abstract

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.