This paper presents the design and analysis of a novel Discrete Modular Serpentine Tail for mobile legged robotic systems. These systems often require an inertial appendage to generate forces and moments to provide a means of improved performance in terms of stabilization, maneuvering and dynamic self-righting in addition to enhancing manipulation capabilities. The majority of existing tail designs consist of planar pendulums that limit improved performance to specific planes due to limited articulation. The proposed system consists of a modular two degree of freedom, spatial mechanism constructed from rigid segments actuated by cable tension and displacements whose curvatures are dependent on a multi-diameter pulley. Modules can be interconnected in series to achieve multiple spatial curvatures; thus, can bring about multi-planar improved performance and enhanced manipulation capabilities to the overall robotic system. First, the detailed design is presented after which the forward kinematics of the mechanism is derived to analyze both the kinematic coupling between the segments and the influence between the ratio of segment lengths and pulley diameters. The equations of motion are derived and modified due to cable tension driving segments and are used to determine torque requirements of the system to aid the design process for motor selection. Multi-objective optimal kinematic synthesis is then formulated and presented as a case study for synthesizing physical dimensions of the mechanism to achieve the best fit of user defined tail curvatures.

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