Modularized Analysis of Kinematic and Mechanical Error for Planar Linkages Composed of Class 3 and Order 3 Assur Groups

This paper presents a modular approach for analyzing kinematics and mechanical error for planar linkages or manipulators composed of class 3 and order 3 Assur groups (AGs). Since a planar multi-link mechanism or manipulator can be decomposed into several AGs, it is only necessary to individually analyze the modules that constitute the whole linkage or manipulator. Then, an overall analysis can be obtained by combining analyses of each module. To this end, analytical expressions for kinematic and mechanical error analysis of the class 3 and order 3 AGs kinematic chains are first derived. Derived algorithms can be programmed into user subroutines in advance. Established subroutines can be further used to cope with computations necessary for the analysis by substituting known parameters. This modular approach enables users to perform kinematic and mechanical error analysis by concentrating on topology decompositions of planar linkages or manipulators. The strength of the presented method is that there is no need to re-derive closed-loop equations and perform tedious solutions to the mechanism under investigation. This paper provides three numerical examples to demonstrate the presented algorithms.