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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 <inline-formula> <tex-math notation="LaTeX">$\text{w}_{\mathrm {i}}$ </tex-math></inline-formula> and loop factor <inline-formula> <tex-math notation="LaTeX">$\text{f}_{\mathrm {i}}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$\text{f}_{\mathrm {i}}$ </tex-math></inline-formula> to equal to <inline-formula> <tex-math notation="LaTeX">$\text{w}_{\mathrm {i}}$ </tex-math></inline-formula> or (<inline-formula> <tex-math notation="LaTeX">$\text{w}_{\mathrm {i}}$ </tex-math></inline-formula> -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.

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