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1. Design, Analysis, and Optimization of a New Two-DOF Articulated Multi-Link Robotic Tail

   https://doi.org/10.1115/DETC2019-97537  

   Liu, Yujiong; Ben-Tzvi, Pinhas (August 2019, Proceedings of the ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE), 43rd Mechanisms & Robotics Conference)

   Based on observations from nature, tails are believed to help animals achieve highly agile motions. Traditional single-link robotic tails serve as a good simplification for both modeling and implementation purposes. However, this approach cannot explain the complicated tail behaviors exhibited in nature where multi-link structures are more commonly observed. Unlike its single-link counterpart, articulated multi-link tails essentially belong to the serial manipulator family which possesses special transmission design challenges. To address this challenge, a cable driven hyper-redundant design becomes the most used approach. Limited by cable strength and elastic components, this approach suffers from low frequency responses, inadequate generated inertial loading, and fragile hardware, which are all critical drawbacks for robotic tails design. To solve these structure related shortcomings, a multi-link robotic tail made up of rigid links is proposed in this paper. The new structure takes advantage of the traditional hybrid mechanism architecture, but utilizes rigid mechanisms to couple the motions between ith link and i + 1th link rather than using cable actuation. By doing so, the overall tail becomes a rigid mechanism which achieves quasi-uniform spatial bending for each segment and allows performing highly dynamic motions. The mechanism and detailed design for this new tail are synthesized. The kinematic model was developed and an optimization process was conducted to minimize the bending non-uniformity for the rigid tail. 

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2. Complex In Vivo Motion of the Bovine Tail Provides Unique Insights Into Intervertebral Disc Adaptation

   https://doi.org/10.1002/jsp2.70084  

   Michalek, Arthur J; Wood, Isabelle M; Gonzalez_Carranza, Daniela; Ferlito, Lindsay (June 2025, JOR SPINE)

   ABSTRACT IntroductionThe intervertebral disc (IVD) of the bovine tail is a commonly used research analogue for the human disc at the organ, tissue, and cellular levels. While these tails are subjected to thousands of dynamic motion events daily, little is known about how these motions might induce tissue remodeling, particularly in the outer annulus fibrosus (AF) of IVDs connecting adjacent vertebrae. This study hypothesized that despite the similarities in geometry and biochemical composition of IVDs in the bovine tail, level‐wise variations in repetitive in‐vivo motion would be associated with tissue level adaptations. MethodsIn‐vivo active range of motion (RoM) was measured by placing inertial measurement unit sensors on the tails of adult cows and using a multi‐segment rigid body model to calculate level‐wise flexion‐extension and lateral bending angles. Level‐wise passive RoM was measured from cadaveric adult bovine tails in flexion, extension, and lateral bending with skin and muscles removed. IVDs were extracted for measurement of height, diameters, AF radial thicknesses, and AF fiber crimp periods. ResultsIn‐vivo joint RoM was found to vary drastically by level, largely due to a prominent second order mode with inflection point at the fourth joint. Joint levels near this inflection point were found to have the highest passive RoMs. In the proximal tail, decreased RoM was associated with an increased fiber crimp period in the outer AF, while in the distal tail it was associated with increased AF thickness. DiscussionTaken together, these findings suggest that IVDs in the bovine tail respond to repeated complex dynamic motions through a process of adaptation at the mesoscale (AF thickening during growth) and microscale (residual strain accumulation in the mature state). The bovine tail thus provides a powerful tool for modeling how the human lumbar intervertebral disc may remodel in response to changes in exposure to repetitive motions. 

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3. A Cable Length Invariant Robotic Tail Using a Circular Shape Universal Joint Mechanism

   https://doi.org/10.1115/1.4044067  

   Liu, Yujiong; Wang, Jiamin; Ben-Tzvi, Pinhas (October 2019, Journal of Mechanisms and Robotics)

   This paper presents the development of a new robotic tail based on a novel cable-driven universal joint mechanism. The novel joint mechanism is synthesized by geometric reasoning to achieve the desired cable length invariance property, wherein the mechanism maintains a constant length for the driving cables under universal rotation. This feature is preferable because it allows for the bidirectional pulling of the cables which reduces the requisite number of actuators. After obtaining this new joint mechanism, a serpentine robotic tail with fewer actuators, simpler controls, and a more robust structure is designed and integrated. The new tail includes two independent macro segments (2 degrees of freedom each) to generate more complex shapes (4 degrees of freedom total), which helps with improving the dexterity and versatility of the robot. In addition, the pitch bending and yaw bending of the tail are decoupled due to the perpendicular joint axes. The kinematic modeling, dynamic modeling, and workspace analysis are then explained for the new robotic tail. Three experiments focusing on statics, dynamics, and dexterity are conducted to validate the mechanism and evaluate the new robotic tail's performance. 

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4. Robots with Tails

   https://doi.org/10.1115/1.2021-NOV2  

   Ben-Tzvi, Pinhas; Liu, Yujiong (November 2021, Mechanical Engineering)

   Abstract Until recently, most four-legged robots have lacked a feature that is found again and again in nature—a tail. Studies of animal locomotion and robots in the laboratory indicate that leaving out tails has been a design drawback. In fact, research conducted by our lab at Virginia Tech has shown that an articulated robotic tail can effectively maneuver and stabilize a quadruped both for static and dynamic locomotion. 

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5. Feedback Control of the Locomotion of a Tailed Quadruped Robot

   https://doi.org/10.1115/DETC2021-71611  

   Liu, Yujiong; Ben-Tzvi, Pinhas (August 2021, ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 45TH MECHANISMS AND ROBOTICS CONFERENCE (MR))

   The traditional locomotion paradigm of quadruped robots is to use dexterous (multi degrees of freedom) legs and dynamically optimized footholds to balance the body and achieve stable locomotion. With the introduction of a robotic tail, a new locomotion paradigm becomes possible as the balancing is achieved by the tail and the legs are only responsible for propulsion. Since the burden on the leg is reduced, leg complexity can be also reduced. This paper explores this new paradigm by tackling the dynamic locomotion control problem of a reduced complexity quadruped (RCQ) with a pendulum tail. For this specific control task, a new control strategy is proposed in a manner that the legs are planned to execute the open-loop gait motion in advance, while the tail is controlled in a closed-loop to prepare the quadruped body in the desired orientation. With these two parts working cooperatively, the quadruped achieves dynamic locomotion. Partial feedback linearization (PFL) controller is used for the closed-loop tail control. Pronking, bounding, and maneuvering are tested to evaluate the controller’s performance. The results validate the proposed controller and demonstrate the feasibility and potential of the new locomotion paradigm. 

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