On the theory and methodology of systematic analysis of positions, singular configurations, branches and circuits, and ranges of motion for planar complex linkages

Abstract Complex linkages refer to the linkages composed of 4-bar or more than 4-bar Assur Groups (AG). This paper presents a hybrid position analysis method for complex AG. Firstly, position solutions of an external link in AG are obtained by solving the position analysis polynomial, then all configurations of the AG corresponding to the solutions can be determined through solving 2-bar AG. Above is the position analysis process at a single input condition. With the increasement of the input angle, a series of discrete position solutions can be obtained. How to connect these solutions to form different branches and circuits, and determine the movement range of the linkage are the other problems to be solved. This paper presents an effective methodology to determine the branches and circuits as well as the movement range of the linkage and gives a novel discriminant for identifying singular configurations of complex AG. Finally, several numerical examples are presented to demonstrate the correctness, effectiveness and universality of the proposed methods and the practicability of the program compiled based on the formulations and methodology.