基于蛇形魔方机构分析的模块化可重构机构理论

Reconfiguration Theory of Modular Reconfigurable Mechanism Based on Analysis of Snake Cube

蛇形魔方是一种由相同的27个正方体模块串接组成的模块化机构,在对该机构综合分析的基础上,着重于研究模块的几何描述、运动干涉检测、正逆运动学的计算以及机构的等价变化等重构理论问题。应用Clifford代数对正方体模块进行几何描述。建立机构运动过程中的约束关系,并通过逆运动学计算获得到达目标构型的转角序列。针对运动模块的特殊几何形状,采用柔性关节等价替换的方法,实现机构到达目标构型的运动。为了有效检测机构在运动过程中存在的干涉,提出一种基于Clifford代数的模块运动干涉检测算法。进而提出一种新的机构离散运动的表达方式——运动变化序列,并与指数积公式结合实现机构的正运动学计算。通过仿真试验验证所提出理论的正确性,并在仿真结果分析的基础上实现了面向特定目标构型的机构等价简化。

Snake cube is a kind of modular mechanism composed of 27 identical cube modules connected in series.Based on the comprehensive analysis of the modular reconfigurable mechanism-snake cube,the study of geometry description,interference detection,kinematics calculation and equivalent variation of mechanism are emphatically studied.The geometry description of cube module is accomplished by employing the Clifford algebra.The angle sequence of target configuration is obtained from inverse kinematics according to the constraint relationship among modules during the movement.Due to the special geometric shape of modules,flexible-joint equivalent replacement is used to implement the movement of achieving the target configuration.An interference detection algorithm on the basis of Clifford algebra is proposed to effectively detect the modular interference during the movement.A new expression of discrete movement-motion sequence combined with exponential formula for kinematics calculation is presented.Simulations are performed to verify the validity of our reconfiguration theory,and the equivalent simplification of mechanism for special configuration is achieved based on the analysis of simulation results.