Dead Center Identification of Two-Degrees-of-Freedom Planar Parallel Manipulator Using Graph Theory and Transmission Angle

Abstract

Parallel manipulators are widely applied for their advantages of high stiffness, load-bearing, operation speed, and precision positioning capabilities, which are required in many industrial applications. However, dead center identification is a challenging task and fundamental problem during design stage of parallel manipulators, and becomes more intractable for two-degrees-of-freedom (DOF) complex planar parallel manipulators (PPMs) design. This paper proposes a method to identify the dead center positions of two-DOF PPMs based on graph theory and transmission angle. First, these PPMs are denoted by a set of independent loops using a topological structural analysis of the kinematic chains and structural decomposition. Then, the relationship between the mobility factor and the loop factor in the same independent loop is utilized to obtain the folded or stretched operation to form the new PPMs containing the corresponding instantaneous virtual loop. Subsequently, the dead center positions can be located since the corresponding transmission angle of the new PPMs is equal to 0 deg or 180 deg. As a result, the solved dead center positions of the two-DOF three types seven-bar, nine-bar, and 11-bar PPMs will provide guidance for the proper design of these PPMs. Finally, the Jacobian method for identifying the dead center position is then used to verify the proposed method. The proposed method is systematic and programmable and can be applied to any two-DOF PPM regardless of the number of independent loops or types of joints.