Solving the Kinematics of the Planar Mechanism Using Data Structures of Assur Groups

This paper presents a systematic solution of the kinematics of the planar mechanism from the aspect of Assur groups. When the planar mechanism is decomposed into Assur groups, the detailed calculating order of Assur groups is unknown. To solve this problem, first, the decomposed Assur groups are classified into three types according to their calculability, which lays the foundation for the establishment of the automatic solving algorithm for decomposed Assur groups. Second, the data structure for the Assur group is presented, which enables the automatic solving algorithm with the input and output parameters of each Assur group. All decomposed Assur groups are stored in the component stack, and all parameters of which are stored in the parameter stacks. The automatic algorithm will detect identification flags of each Assur group in the component stack and their corresponding parameters in the parameter stacks in order to decide which Assur group is calculable and which one can be solved afterward. The proposed systematic solution is able to generate an automatic solving order for all Assur groups in the planar mechanism and allows the adding, modifying, and removing of Assur groups at any time. Two planar mechanisms are given as examples to show the detailed process of the proposed systematic solution.