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1. A Unified Real-Time Motion Generation Algorithm for Approximate Position Analysis of Planar N-Bar Mechanisms

   https://doi.org/10.1115/1.4064132  

   Lyu, Zhijie; Purwar, Anurag; Liao, Wei (June 2024, Journal of Mechanical Design)

   Abstract This paper presents a novel real-time kinematic simulation algorithm for planar N-bar linkage mechanisms, both single- and multi-degrees-of-freedom, comprising revolute and/or prismatic joints and actuators. A key feature of this algorithm is a reinterpretation technique that transforms prismatic elements into a combination of revolute joint and links. This gives rise to a unified system of geometric constraints and a general-purpose solver which adapts to the complexity of the mechanism. The solver requires only two types of methods—fast dyadic decomposition and relatively slower optimization-based—to simulate all types of planar mechanisms. From an implementation point of view, this algorithm simplifies programming without requiring handling of different types of mechanisms. This versatile algorithm can handle serial, parallel, and hybrid planar mechanisms with varying degrees-of-freedom and joint types. Additionally, this paper presents an estimation of simulation time and structural complexity, shedding light on computational demands. Demonstrative examples showcase the practicality of this method. 

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2. A compliant metastructure design with reconfigurability up to six degrees of freedom

   https://doi.org/10.1038/s41467-024-55591-2  

   Yang, Humphrey; Patel, Dinesh_K; Johnson, Tate; Zhong, Ke; Olson, Gina; Majidi, Carmel; Islam, Mohammad_F; Zhang, Teng; Yao, Lining (January 2025, Nature Communications)

   Abstract Compliant mechanisms with reconfigurable degrees of freedom are gaining attention in the development of kinesthetic haptic devices, robotic systems, and mechanical metamaterials. However, available devices exhibit limited programmability and form-customizability, restricting their versatility. To address this gap, we propose a metastructure concept featuring reconfigurable motional freedom and tunable stiffness, adaptable to various form factors and applications. These devices incorporate passive flexures and actively stiffness-changing rods to modify kinematic freedom. A rational design pipeline informs the flexures’ topological arrangements, geometric parameters, and control signals based on targeted mobilities, enabling the creation of unitary joints with up to six degrees of freedom. Our demonstrative application examples include a wrist device that has an effective stiffness of 0.370 Nm/deg (unlocked state, 5% displacement) to 2.278 Nm/deg (locked state, 1% displacement) to enable dynamic joint mobility control, a haptic thimble device (2.27-52.815 Nmm⁻¹at 1% displacement) that mimics the sensation of touching physical materials ranging from soft gel to metal surfaces, and a wearable device composed of multiple joints tailored for the arm and hand to augment haptic experiences or facilitate muscle training. We believe the presented method can help democratize compliant metastructures development and expand their versatility for broader contexts. 

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3. Locomotion of a Multi-link Nonholonomic Snake Robot

   Dear, T; Kelly, S; Travers, M; Choset, H. (July 2017, Proceedings of the ASME Dynamic Systems and Control Conference)

   Robot system models often have difficulty allowing for direct command over all input degrees of freedom if the system has a large number of imposed constraints. A snake robot with more than three links and a nonholonomic wheel on each link cannot achieve arbitrary configurations in all of its joints simultaneously. For such a system, we assume partial command over a subset of the joints, and allow the rest to evolve according to kinematic chained and dynamic models. Different combinations of commanded and passive joints, as well as the presence of dynamic elements such as torsional springs, can drastically change the coupling interactions and stable oscillations of the joints. We use the oscillation modes that emerge to inform feedback controllers that achieve desired overall locomotion of the robot. 

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4. Locomotion of a multi-link non-holonomic snake robot with passive joints

   Dear, T; Buchanan, B; Abrajan-Guerrero, R; Kelly, SD; Travers, M; Choset, H (April 2020, The international journal of robotics research)

   Abstract Conventional approaches in prescribing controls for locomoting robots assume control over all input degrees of freedom (DOFs). Many robots, such as those with non-holonomic constraints, may not require or even allow for direct command over all DOFs. In particular, a snake robot with more than three links with non-holonomic constraints cannot achieve arbitrary configurations in all of its joints while simultaneously locomoting. For such a system, we assume partial command over a subset of the joints, and allow the rest to evolve according to kinematic chained and dynamic models. Different combinations of actuated and passive joints, as well as joints with dynamic elements such as torsional springs, can drastically change the coupling interactions and stable oscillations of joints. We use tools from nonlinear analysis to understand emergent oscillation modes of various robot configurations and connect them to overall locomotion using geometric mechanics and feedback control for robots that may not fully utilize all available inputs. We also experimentally verify observations and motion planning results on a physical non-holonomic snake robot 

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5. Point-Based Models: A Unified Approach for Geometric Constraint Analysis of Planar n -Bar Mechanisms With Rotary, Sliding, and Rolling Joints

   https://doi.org/10.1115/1.4066963  

   Lyu, Zhijie; Purwar, Anurag (April 2025, Journal of Mechanisms and Robotics)

   Abstract Kinematic simulation of planar n-bar mechanisms has been an intense topic of study for several decades now. However, a large majority of efforts have focused on position analysis of such mechanisms with limited links and joint types. This article presents a novel, unified approach to the analysis of geometric constraints of planar n-bar mechanisms with revolute joint (R-joint), prismatic joint (P-joint), and rolling joint. This work is motivated by a need to create and program a system of constraint equations that deal with different types of joints in a unified way. A key feature of this work is that the rolling joint constraints are represented by four-point models, which enables us to use the well-established undirected graph rigidity analysis algorithms. As a result, mechanisms with an arbitrary combination of revolute-, prismatic joints, and wheel/gear/wheel-belt chains without any limitations on their actuation scheme can be analyzed and simulated efficiently for potential implementation in interactive computer software and large-scale data generation. 

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