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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. Design of an Articulated Modular Caterpillar Using Spherical Linkages

   https://doi.org/10.1109/ICRA55743.2025.11127993  

   O'Connor, Sam; Plecnik, Mark (May 2025, IEEE Xplore)

   Articulation between body segments of small insects and animals is a three degree-of-freedom (DOF) motion. Implementing this kind of motion in a compact robot is usually not tractable due to limitations in small actuator technologies. In this work, we concede full 3-DOF control and instead select a one degree-of-freedom curve in SO(3) to articulate segments of a caterpillar robot. The curve is approximated with a spherical four-bar, which is synthesized through optimal rigid body guidance. We specify the desired SO(3) motion using discrete task positions, then solve for candidate mechanisms by computing all roots of the stationary conditions using numerical homotopy continuation. A caterpillar robot prototype demonstrates the utility of this approach. This synthesis procedure is also used to design prolegs for the caterpillar robot. Each segment contains two DC motors and a shape memory alloy, which is used for latching and unlatching between segments. The caterpillar robot is capable of walking, steering, object manipulation, body articulation, and climbing. 

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