Real and complexified configuration spaces for planar 4-bar linkages

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.