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.

翻译：本笔记提供了球面四杆机构实与复形配置空间的完整符号参数化表达式库。基于Izmestiev先前工作(2016, 第2节)，该库通过纳入所有可能杆长选择下的四个折叠角，以及对角线(球面弧)之间的多项式关系，扩充了原有表达式。此外，附带了完整的MATLAB应用程序脚本，支持可视化与参数化。推导过程以详尽方式呈现，确保跨学科研究人员均能理解。