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

   Liu, X.; Glabe, J.; Wu, H.; Wang, C.; McCarthy, J. M. (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. Rec- tilinear 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 eight- bar 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-of- freedom. 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 recti- linear movement. 

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2. Design of a Continuum Mechanism that Matches the Movement of an Eight-bar Linkage

   https://doi.org/10.1115/1.4047439  

   Liu, Xueao; McCarthy, J. Michael (December 2020, Journal of Mechanisms and Robotics)

   Abstract This paper presents a design methodology for mechanisms consisting of a single continuous structure, continuum mechanisms, that blends the kinematic synthesis of rigid-body mechanisms with topology optimization for compliant mechanisms. Rather than start with a generic structure that is shaped to achieve a required force deflection task for a compliant mechanism, our approach shapes the initial structure based on kinematic synthesis of a rigid body mechanism for the required movement, then the structure is shaped using Finite Element Analysis to achieve the required force deflection relationship. The result of this approach is a continuum mechanism with the same workpiece movement as the rigid link mechanism when actuated. An example illustrates the design process to obtain an eight-bar linkage that guides its workpiece in straight-line rectilinear movement. We show that the resulting continuum mechanism provides the desired rectilinear movement. A 210 mm physical model machined from Nylon-6 is shown to achieve 21.5mm rectilinear movement with no perceived deviation from a straight-line. 

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3. 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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4. 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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5. Design of Wearable Lower Leg Orthotic Based on Six-Bar Linkage

   https://doi.org/10.1115/DETC2017-67837  

   Ghosh, Shramana; Robson, Nina; McCarthy, J. M. (August 2017, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   The paper presents the design of a lower leg orthotic device based on dimensional synthesis of multi-loop six-bar linkages. The wearable device is comprised of a 2R serial chain, termed the backbone, sized according to the wearer’s limb anthropometric dimensions. The paper is a result of our current efforts in proposing a systematic process for the development of 3D printed customized assistive devices for patients with reduced limb mobility, based on anthropometric data and physiological task. To design the wearable device, the physiological task of the limb is obtained using an optical motion capture system and its dimensions are set such that it matched the lower leg kinematics as closely as possible. As a next step a six-bar linkage is synthesized and ensured that its motion is as close as possible to the physiological task. Next, the 2R backbone is replaced by the wearer’s limb to provide the skeletal structure for the multiloop wearable device. During the final stage of the process the 2R backbone is relocated to parallel the human’s limb on one side, providing support and stability. The designed device can be secured to the thigh of the user to guide the lower leg without causing any discomfort and to ensure a natural physiological gait trajectory. This results in orthotic device for assisting people with lower leg injuries with compact size and better wearability. 

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