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1. Design of Four, Six and Eight-bar Linkages for Rectilinear Movement

   Liu, Xueao; Glabe, Jeffrey; Wu, H.; Wang, C.; McCarthy, J. Michael (July 2019, Proceedings of the ASME 2019 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference)

   This paper examines the results of synthesis algorithms for four-, six-, and eight-bar linkages for rectilinear movement. Rectilinear movement is useful for applications such as suspensions that provide linear movement with out a rotation component. The algorithm yields one four-bar, seven six-bar, and 32 eightbar linkages. The synthesis strategy begins with a task guided by a multi-degree of freedom chain. The algorithm computes constraints to guide the required movement with one degree-offreedom. Each computed design is analyzed to ensure smooth movement through the specified set of task positions. Finally, we identify the design that has the least variation from a pure rectilinear movement. 

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2. Design of a Spatial Six-Bar Flapping Wing Mechanism for Combined Control of Swing and Pitch

   https://doi.org/10.1115/DETC2017-68266  

   Wang, Peter L.; McCarthy, J. Michael (August 2017, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   This paper presents a design procedure to achieve a flapping wing mechanism for a micro air vehicle that drives both the swing and pitch movement of the wing with one actuator. The mechanism combines a planar four bar linkage with a spatial RSSR attached to the input and output links forming a spatial Stephenson six-bar linkage. Function generation synthesis yields a planar four-bar that controls the wing swing profile. The pitch control is synthesized by inverting the movement of the combined system to isolate and compute the SS chain. In order to ensure the design achieves the specified task precision points, the SS chain was randomized within a prescribed tolerance zone. The result was 29 designs, one of which is presented in detail. 

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3. A General Method for Constructing Planar Cognate Mechanisms

   https://doi.org/10.1115/1.4050293  

   Sherman, Samantha N.; Hauenstein, Jonathan D.; Wampler, Charles W. (June 2021, Journal of Mechanisms and Robotics)

   null (Ed.)

   Abstract Cognate linkages are mechanisms that share the same motion, a property that can be useful in mechanical design. This article treats planar curve cognates, that is, planar mechanisms with rotational joints whose coupler points draw the same curve, as well as coupler cognates and timed curve cognates. The purpose of this article is to develop a straightforward method based solely on kinematic equations to construct cognates. The approach computes cognates that arise from permuting link rotations and is shown to reproduce all of the known results for cognates of four-bar and six-bar linkages. This approach is then used to construct a cognate of an eight-bar and a ten-bar linkage. 

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4. Design of Bio-Exoskeleton for Elbow Rehabilitation

   https://doi.org/10.1115/DMD2021-1035  

   Delgado, Pablo; Arachchige Don, Thisath Attampola; Gomez, Jesus; Miranda, Virgil; Yihun, Yimesker (May 2020, 2021 Design of Medical Devices Conference)

   null (Ed.)

   In this study, a methodology for designing a task-based exoskeleton which can recreate the end-effector trajectory of a given limb during a rehabilitation task/movement is presented. The exoskeleton provides an option to replace traditional joint-based exoskeleton joints, which often have alignment issues with the biological joint. The proper fit of the exoskeleton to the user and task are research topics to reduce pain or joint injuries as well as for the execution of the task. The proposed task-based synthesis method was successfully applied to generate the 3D motions of the elbow flexion and extensions using a one degree of freedom (DOF), spatial four-bar mechanism. The elbow joint is analyzed through motion capture system to develop the bio-exoskeleton. The resulted exoskeleton does not need to align with the corresponding limb joint to generate the desired anatomical motion. 

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5. Finding straight line generators through the approximate synthesis of symmetric four-bar coupler curves

   https://doi.org/10.1016/j.mechmachtheory.2023.105310  

   Baskar, Aravind; Plecnik, Mark; Hauenstein, Jonathan D. (October 2023, Mechanism and Machine Theory)

   The approximate path synthesis of four-bar linkages with symmetric coupler curves is presented. This includes the formulation of a polynomial optimization problem, a characterization of the maximum number of critical points, a complete numerical solution by homotopy continuation, and application to the design of straight line generators. Our approach specifies a desired curve and finds several optimal four-bar linkages with a coupler trace that approximates it. The objective posed simultaneously enforces kinematic accuracy, loop closure, and leads to polynomial first order necessary conditions with a structure that remains the same for any desired trace leading to a generalized result. Ground pivot locations are set as chosen parameters, and it is shown that the objective has a maximum of 73 critical points. The theoretical work is applied to the design of straight line paths. Parameter homotopy runs are executed for 1440 different choices of ground pivots for a thorough exploration. These computations found the expected linkages, namely, Watt, Evans, Roberts, Chebyshev, and other previously unreported linkages which are organized into a 2D atlas using the UMAP algorithm. 

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