Real and complexified configuration spaces for spherical 4-bar linkages

TL;DR

This paper provides a comprehensive symbolic library and MATLAB tools for analyzing the configuration spaces of spherical 4-bar linkages, including all folding angles and diagonal relations, enhancing understanding and visualization.

Contribution

It introduces a complete symbolic parametrization of the configuration space for spherical 4-bar linkages, expanding previous work with detailed derivations and visualization tools.

Findings

Complete symbolic expressions for real and complex configuration spaces

Inclusion of all four folding angles for various linkage lengths

A MATLAB app for visualization and parametrization

Abstract

This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a spherical 4-bar linkage. Building upon the previous work from Izmestiev, (2016, Section 2), this library expands on the expressions by incorporating all four folding angles across all possible linkage length choices, along with the polynomial relation between diagonals (spherical arcs). 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.