Assur Groups with up to 16 links

Published: 19 December 2022| Version 1 | DOI: 10.17632/7g6yggnnjt.1
Fernando Vinícius Morlin,


The following zipped file contains supplementary material for the manuscript “Synthesis of Assur groups via group and matroid theory”, written by Morlin, Carboni and Martins and submitted for publication in Mechanism and Machine Theory.


Steps to reproduce

The supplementary files are distributed in 8 folders, referring to the number of independent circuits of the kinematic chains. The list of kinematic chains is classified according to the number of links and link assortments. Each chain is represented by the corresponding .g6 string. The format graph6 is suitable for both small or large dense graphs. It encodes the upper triangle of the adjacency matrix as a concatenation of printable ASCII characters. Detailed information about the format is available online at Each line of each file is composed of the graph6 string of a Baranov chain and the list of representative vertices of each orbit of the corresponding graph, this information is separated by a hyphen. Therefore, the total number of Baranov chains is equivalent to the sum of the number of lines in all the files. On the other hand, the total number of Assur groups is equivalent to the sum of the number of orbits in each graph.


Universidade Federal de Santa Catarina


Graph Theory, Robotics Theory, Machine Design