空间变胞机构运动及误差的全构态四元数模型

Kinematics and error modeling based on configuration-complete quaternion for spatial metamorphic mechanisms

空间变胞机构的拓扑结构可变特性使得建立全构态模型是其运动及误差研究的一个难题,而现有欧拉参数运动模型中存在数学奇异和非奇异退化等问题,因此提出了采用罗德里格-哈密顿参数建立空间变胞机构的全构态模型。基于四元数理论建立了任意构态的运动模型,推导了相邻构态广义运动变量的递推关系。研究了结构误差、运动变量误差及运动副间隙对理想模型的扰动,构建了统一的范式表示机构的全构态四元数模型。通过典型实例的理论计算和仿真分析对比结果表明,所建模型的有效性,它既可分析空间变胞机构的全构态运动特性,也可研究构态变换前后的运动特性变化,为变胞机构的工程应用提供了理论基础。

The variable topology characteristics of spatial metamorphic mechanisms make the establishment of a configuration-complete model a thorny problem for studying the kinematics and kinematic error of spatial metamorphic mechanisms. Current models with Euler parameters appear to bring in mathematical singularity with degeneration in non-singular situations. Therefore,configuration-complete models with Rodriguez-Hamilton parameters were proposed. The kinematic model of sample configurations was constructed using quaternion theory,and recurrence relations were derived for the generalized state variables of adjacent structures. The perturbations caused by structure errors,joint variable errors,and joint clearances,using the kinematic model in an ideal state were researched,then configuration-complete models were established with unified paradigms. Theoretical calculations and physical simulations were carried out for a typical example,comparing the results shows that the established configuration-complete models are effective. The models can be used not only to analyze the configuration-complete kinematic characteristics,but also to study the change of kinematic characteristics during configuration transformation of spatial metamorphic mechanisms. This provides a theoretical basis for engineering applications of metamorphic mechanisms.