Abstract Cognate linkages provide the useful property in mechanism design of having the same motion. This paper describes an approach for determining all coupler curve cognates for planar linkages with rotational joints. Although a prior compilation of six-bar cognates due to Dijksman purported to be a complete list, that analysis assumed, without proof, that cognates only arise by permuting link rotations. Our approach eliminates that assumption using arguments concerning the singular foci of the coupler curve to constrain a cognate search and then completing the analysis by solving a precision point problem. This analysis confirms that Dijksman’s list for six-bars is comprehensive. As we further demonstrate on an eight-bar and a ten-bar example, the method greatly constrains the set of permutations of link rotations that can possibly lead to cognates, thereby facilitating the discovery of all cognates that arise in that manner. However, for these higher order linkages, the further step of using a precision point test to eliminate the possibility of any other cognates is still beyond our computational capabilities.
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A General Method for Constructing Planar Cognate Mechanisms
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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- Award ID(s):
- 1812746
- NSF-PAR ID:
- 10297644
- Date Published:
- Journal Name:
- Journal of Mechanisms and Robotics
- Volume:
- 13
- Issue:
- 3
- ISSN:
- 1942-4302
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract 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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This paper presents a method to develop continuum/ compliant mechanisms based on planar bar-node linkage precursors. The method takes as inputs the initial node positions and connectivity data of a given bar-node linkage and converts it into a continuum/compliant mechanism having the same targeted motion. The line bars of the given bar-node linkage are thickened into trapezoidal planar members and the nodes are thickened by introducing fillets at each intersection of bars. The thicknesses of the bars and the shape parameters of the fillets in the continuum/compliant linkage are optimized to obtain the same targeted motion of the given bar-node linkage while keeping stresses below a maximum allowable value. Each design generated during the optimization process is evaluated using finite element analysis. The present method allows for the synthesis of mechanisms having the following advantages over conventional bar-node linkages: 1) They do not require complex ball or pin joints; 2) they can be readily 3-D printed and sizescaled, and 3) they can be optimized to decrease stresses below a maximum allowable value. Furthermore, the method uses a relatively small number of optimization variables (thicknesses of the members, shape-parameters of the fillets), making it an efficient alternative to more complex and computationally intensive methods for synthesizing compliant mechanisms such as those incorporating topology optimization.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4050293
