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1. 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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2. Synthesis of Watt-Type Timed Curve Generators and Selection From Continuous Cognate Spaces

   https://doi.org/10.1115/1.4050197  

   Baskar, Aravind ; Plecnik, Mark ( October 2021 , Journal of Mechanisms and Robotics)

   Abstract Following recent work on Stephenson-type mechanisms, the synthesis equations of Watt six-bar mechanisms that act as timed curve generators are formulated and systematically solved. Four variations of the problem arise by assigning the actuator and end effector onto different links. The approach produces exact synthesis of mechanisms up to eight precision points. Polynomial systems are formulated and their maximum number of solutions is estimated using the algorithm of random monodromy loops. Certain variations of Watt timed curve generators possess free parameters that do not affect the output motion, indicating a continuous space of cognate mechanisms. Packaging compactness, clearance, and dimensional sensitivity are characterized across the cognate space to illustrate trade-offs and aid in selection of a final mechanism. 

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3. An Invariant Representation of Coupler Curves Using a Variational AutoEncoder: Application to Path Synthesis of Four-Bar Mechanisms

   https://doi.org/10.1115/1.4063726  

   Nurizada, Anar ; Purwar, Anurag ( January 2024 , Journal of Computing and Information Science in Engineering)

   This paper focuses on the representation and synthesis of coupler curves of planar mechanisms using a deep neural network. While the path synthesis of planar mechanisms is not a new problem, the effective representation of coupler curves in the context of neural networks has not been fully explored. This study compares four commonly used features or representations of four-bar coupler curves: Fourier descriptors, wavelets, point coordinates, and images. The results demonstrate that these diverse representations can be unified using a generative AI framework called variational autoencoder (VAE). This study shows that a VAE can provide a standalone representation of a coupler curve, regardless of the input representation, and that the compact latent dimensions of the VAE can be used to describe coupler curves of four-bar linkages. Additionally, a new approach that utilizes a VAE in conjunction with a fully connected neural network to generate dimensional parameters of four-bar linkage mechanisms is proposed. This research presents a novel opportunity for the automated conceptual design of mechanisms for robots and machines.

    

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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. Spatial thinning and class balancing: Key choices lead to variation in the performance of species distribution models with citizen science data

   https://doi.org/10.1111/2041-210X.13525  

   Steen, Valerie A. ; Tingley, Morgan W. ; Paton, Peter W. C. ; Elphick, Chris S. ; McPherson, ed., Jana ( December 2020 , Methods in Ecology and Evolution)

   Spatial biases are a common feature of presence–absence data from citizen scientists. Spatial thinning can mitigate errors in species distribution models (SDMs) that use these data. When detections or non‐detections are rare, however, SDMs may suffer from class imbalance or low sample size of the minority (i.e. rarer) class. Poor predictions can result, the severity of which may vary by modelling technique.

   To explore the consequences of spatial bias and class imbalance in presence–absence data, we used eBird citizen science data for 102 bird species from the northeastern USA to compare spatial thinning, class balancing and majority‐only thinning (i.e. retaining all samples of the minority class). We created SDMs using two parametric or semi‐parametric techniques (generalized linear models and generalized additive models) and two machine learning techniques (random forest and boosted regression trees). We tested the predictive abilities of these SDMs using an independent and systematically collected reference dataset with a combination of discrimination (area under the receiver operator characteristic curve; true skill statistic; area under the precision‐recall curve) and calibration (Brier score; Cohen's kappa) metrics.

   We found large variation in SDM performance depending on thinning and balancing decisions. Across all species, there was no single best approach, with the optimal choice of thinning and/or balancing depending on modelling technique, performance metric and the baseline sample prevalence of species in the data. Spatially thinning all the data was often a poor approach, especially for species with baseline sample prevalence <0.1. For most of these rare species, balancing classes improved model discrimination between presence and absence classes using machine learning techniques, but typically hindered model calibration.

   Baseline sample prevalence, sample size, modelling approach and the intended application of SDM output—whether discrimination or calibration—should guide decisions about how to thin or balance data, given the considerable influence of these methodological choices on SDM performance. For prognostic applications requiring good model calibration (vis‐à‐vis discrimination), the match between sample prevalence and true species prevalence may be the overriding feature and warrants further investigation.

    

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