Real and complexified configuration spaces for planar 4-bar linkages

TL;DR

This paper provides a comprehensive symbolic library and visualization tools for the configuration spaces of planar 4-bar linkages, including real and complex cases, expanding previous work with complete angle and diagonal relations.

Contribution

It introduces a complete symbolic library and MATLAB visualization app for the configuration spaces of planar 4-bar linkages, covering all angles and length choices.

Findings

Complete symbolic expressions for real and complex configuration spaces.

Inclusion of all four rotational angles and diagonal polynomial relations.

Accessible derivations and visualization tools for researchers.

Abstract

This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a planar 4-bar linkage. Building upon the previous work from Izmestiev (2015), this library expands on the expressions by incorporating all four rotational angles across all possible linkage length choices, along with the polynomial relation between diagonals. Furthermore, a complete MATLAB app script is included, enabling visualization and parametrization. The derivations are presented in a detailed manner, ensuring accessibility for researchers across diverse disciplines.