This paper presents a new method for kinematic error analysis of planar complex mechanisms, i.e., the ordered single -opened -chains method. This approach is based on the ordered single-opened chains (namely, series binary links, in short, SOCs)and makes use of the properties of SOCs and the network constraint relationships between SOCs. Its mathematical model harmonizes with the structure, kinematics, and dynamics model of mechanisms. The kinematic error analysis equations with few unknown variables can be automatically generated and easily solved. Therefore, any planar complex mechanism can be automatically decomposed into a series of the ordered single-opened-chains and then its kinematic error analysis can be easily completed through this method. Perhaps, the most attractive features of this method are its high automation and convergence in computer implementations.

This work describes the principle of the ordered SOC method, introduces its computer automatic generation and compiles the corresponding computer program KEAPL. Two Examples are given at the end of the paper.

The proposed method can be easily extended to the kinematic error analysis of the spatial mechanisms.

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