Dead Center Identification of Single-DOF Multi-Loop Planar Manipulator and Linkage Based on Graph Theory and Transmission Angle

• Main Authors: Liangyi Nie, Huafeng Ding, Jinqiang Gan
• Format: Article
• Language: English
• Published: IEEE 2019-01-01
• Series: IEEE Access
• Subjects: Dead center position; independent loop; mobility factor; planar manipulator and linkage; topological graph
• Online Access: https://ieeexplore.ieee.org/document/8731917/

The dead center position (or singular position) is an important kinematic characteristic in mechanical design. However, its identification is a challenging task and becomes even more complex in multi-loop planar linkages (or manipulators). According to graph theory and transmission angle, this paper proposes a method to identify the dead center positions of single-degree-of-freedom (DOF) planar linkages. The planar linkages can be denoted by a set of independent loops based on topological structural analysis of the kinematic chains and a structural decomposition. According to the relationship between the mobility factor w_i and loop factor f_i in the same independent loop, the dead center positions can be located when the new planar linkages containing the corresponding instantaneous virtual loop are formed by adjusting f_i to equal to w_i or (w_i -1), in which the corresponding transmission angle is equal to 0° and 180°. The Jacobian method for identifying the dead center position is then used to verify the proposed method. Furthermore, the dead center positions of the single-DOF 10-bar and 12-bar planar linkages are solved. The proposed method is systematic and programmable and can be applied to any single-DOF multi-loop linkage regardless of the number of independent loops or types of joints.