Self-motions of pentapods with linear platform

TL;DR

This paper classifies pentapods with linear platforms that have non-trivial self-motions, updating classical results with modern bond theory and kinematic analysis to aid in designing simpler direct kinematics.

Contribution

It provides a comprehensive classification of self-motions in pentapods with linear platforms, incorporating platform point coincidences and modern mathematical tools.

Findings

Complete classification of pentapods with self-motions

Design of pentapods with simplified direct kinematics

Updated analysis of classical results using bond theory

Abstract

We give a full classification of all pentapods with linear platform possessing a self-motion beside the trivial rotation about the platform. Recent research necessitates a contemporary and accurate re-examination of old results on this topic given by Darboux, Mannheim, Duporcq and Bricard, which also takes the coincidence of platform anchor points into account. For our study we use bond theory with respect to a novel kinematic mapping for pentapods with linear platform, beside the method of singular-invariant leg-rearrangements. Based on our results we design pentapods with linear platform, which have a simplified direct kinematics concerning their number of (real) solutions.