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Open AccessArticle

A Note on Equivalent Linkages of Direct-Contact Mechanisms

Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
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This paper is an extended version of our paper published in Chang, W.-T., Yang, D.-Y. A Short Note on Equivalent Four-Bar Linkages of Direct-Contact Mechanisms. In Proceedings of the IFToMM International Symposium on Robotics and Mechatronics, Taipei, Taiwan, 28–30 October 2019; pp. 51–62.
Robotics 2020, 9(2), 38; https://doi.org/10.3390/robotics9020038
Received: 31 March 2020 / Revised: 4 May 2020 / Accepted: 15 May 2020 / Published: 20 May 2020
(This article belongs to the Special Issue Theory and Practice on Robotics and Mechatronics)
In this paper, the inequivalence of the direct-contact mechanisms and their equivalent four-bar linkages in jerk analysis is discussed. Kinematic analyses for three classical types of direct-contact mechanisms consisting of: (a) higher pairs with permanently invariant curvature centers, (b) higher pairs with suddenly changed curvature, and (c) higher pairs with continuously varying curvature are performed, respectively, through their representative case studies. The analyzed results show that the equivalent four-bar linkage cannot give a correct value of jerk for most situations in the three case studies. Subsequently, the concept of “equivalent six-bar linkage” for direct-contact mechanisms is proposed in order to discuss the infeasibility of the equivalent four-bar linkage for jerk analysis. It is found that the suddenly changed or continuously varying curvature of the higher pairs is not considered in sudden or continuous link-length variations of the equivalent four-bar linkage, which further leads to inconsistency between the angular accelerations of the coupler and the contact normal, and finally results in the infeasibility of the equivalent four-bar linkage for jerk analysis of most direct-contact mechanisms. It is also found that the concept of equivalent six-bar linkage could be applied to evaluate more higher-order time derivatives for most direct-contact mechanisms. The presented case studies and discussion can give demonstrations for understanding the inequivalence of the direct-contact mechanisms and their equivalent four-bar linkages in the aspect of jerk analysis.
Keywords: direct-contact mechanisms; equivalent linkages; planar gear mechanisms; disk cam mechanisms; kinematic analysis direct-contact mechanisms; equivalent linkages; planar gear mechanisms; disk cam mechanisms; kinematic analysis
MDPI and ACS Style

Chang, W.-T.; Yang, D.-Y. A Note on Equivalent Linkages of Direct-Contact Mechanisms. Robotics 2020, 9, 38.

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