复杂多环过约束机构是航天器天线的骨骼，模块化可重构航天器技术发展对航天器天线提出了多次平稳重复展开的重大需求，从而在机构学层面首先要解决其自由度计算、奇异分析和驱动选取三个相互关联的难题。由于复杂多环过约束机构的拓扑结构复杂，输出杆件不唯一且含有多个耦合支链，导致输入杆与输出杆之间映射规律不明，缺乏具有物理意义清晰、几何意义明确的自由度计算、奇异分析、驱动选取的普适性方法。本项申请在几何代数框架下研究复杂多环过约束机构的运动机理，建立具有解析形式、几何意义明确的自由度计算方法，提出物理意义清晰、与尺度无关的奇异接近度指标以及符合工程经验的驱动选取合理性判据，并加以实验样机验证。项目研究成果不仅将丰富、发展空间折展机构的基础理论，同时将为我国航天器天线装备的实际工程应用提供技术支持。

The complex multi-loop overconstrained mechanism is the skeleton of the spacecraft antennas. The development of modular reconfigurable spacecraft technology puts forward a major demand for the spacecraft antennas the spacecraft antenna to be repeatedly and smoothly deployed many times. Thus three interrelated difficulties need to be solved at the level of mechanism: mobility calculation, singular analysis, and actuation selection. The complex multi-loop overconstrained mechanism has complex topology and multiple coupling branches, furthermore the output link is not unique. This leads the unknown mapping rules between the input link and the output link and the lack of general method of mobility calculation, singularity analysis and actuation selection. . In the framework of geometric algebra, this application studies the motion theory of the complex multi-loop overconstrained mechanism. The method for mobility analysis with analytical form and clear geometric meaning will be established. The scale-independent and physically clear singular proximity index will be proposed. The criterion for actuation selection in accordance with engineering experience will be presented. A prototype will be built for verifying. The achievement of this project will not only enrich and develop the basic theory of the space deployable and foldable mechanism, but also provide technical support for the practical engineering application of spacecraft antenna equipment.