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阿贝原则和运动学原则是光学计量仪器设计中两个重要原则。它们不仅对量测类仪器的设计有指导意义,而且也受到了精密机械设计人员的普遍注意。在“阿贝误差”的分析计算中,过去一直沿用初等几何法,因而难以解决像“二阶误差”的存在与否、在多维测量中违反了阿贝原则所带来的影响等问题。本文从排列组合原理出发,利用坐标变换法研究了阿贝误差问题。对运动学设计原则,本文也提出了一种见解。
Abbe’s principle and kinematic principle are two important principles in the design of optical measuring instruments. They are not only instructive for the design of measuring instruments, but are also of general interest to precision machinery designers. In the Abbe error analysis and calculation, the elementary geometry has been used in the past, so it is hard to solve such problems as the existence of “second order error” and the violation of the Abe principle in multidimensional measurement. Starting from the principle of permutation and combination, this paper uses the coordinate transformation method to study the Abbe error problem. This article also presents an opinion on the design principles of kinematics.