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：本文档构建了一个完整的符号参数化表达式库，涵盖了球面四连杆机构的实与复构型空间。基于 Izmestiev (2016, Section 2) 的前期工作，本库扩展了相关表达式，纳入了所有可能连杆长度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。此外，库中提供了一个完整的 MATLAB 应用程序脚本，支持构型的可视化与参数化。推导过程以详尽的方式呈现，以确保跨学科研究者的可理解性。