---
abstract: 'This paper deals with the old and classical problem of determining necessary conditions for the overconstrained mobility of some mechanical device. In particular, we show that the mobility of pentapods/hexapods implies either a collinearity condition on the anchor points, or a geometric condition on the normal projections of base and platform points. The method is based on a specific compactification of the group of direct isometries of ${\mathbb{R}}^3$.'
address:
- |
     Research Institute for Symbolic Computation\
    Johannes Kepler University\
    Altenberger Strasse 69\
    4040 Linz, Austria.
- |
     Institute of Discrete Mathematics and Geometry\
    Vienna University of Technology\
    Wiedner Hauptstrasse 8-10/104\
    1040 Vienna, Austria.
- |
     Research Institute for Symbolic Computation\
    Johannes Kepler University\
    Altenberger Strasse 69\
    4040 Linz, Austria.
author:
- Matteo Gallet
- Georg Nawratil
- Josef Schicho
title: Bond Theory for pentapods and hexapods
---

Introduction
============

The objects we will focus on in this paper are the so–called *$n$–pods*. For $n=5$ they are referred as pentapods and for $n = 6$ as hexapods, which are also known as *Stewart Gough platforms*. As described in [@Nawratil2014], the geometry of this kind of mechanical manipulators is defined by the coordinates of the $n$ platform anchor points $p_i 