{"title":"分析确定指定方向工作空间的 6-6 斯图尔特平台机械手的最佳有效规则工作空间","authors":"","doi":"10.1016/j.mechmachtheory.2024.105791","DOIUrl":null,"url":null,"abstract":"<div><div>This article presents an analytical method to identify the largest <em>effective regular workspaces</em> (ERWs) of a class of 6-6 Stewart platform manipulators for a given orientation workspace. The ERWs are modelled as spheres. The orientation workspace is specified in terms of ranges of Euler angles, as is the standard practice in the parallel robot industry. The radius of the said sphere is maximised through an optimisation problem, which is solved analytically. Consequently, the results obtained are <em>exact</em> in nature. The analytical formulation of the problem and its exact solutions constitute the novel theoretical contributions of this article. Moreover, since the results hold good over a given subset of <span><math><mrow><mi>SO</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>, the proposed method obviates the need for numerical scanning of the orientation workspaces in design-related computations, thus improving the accuracy, robustness, as well as computational efficiency. Finally, the significance of the <em>neutral height</em> in harnessing the desired extents of position and orientation workspaces has been established through parametric studies. The formulations are illustrated via applications to Stewart platform manipulators of three distinct platform dimensions.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical determination of the optimal effective regular workspace of a 6-6 Stewart platform manipulator for a specified orientation workspace\",\"authors\":\"\",\"doi\":\"10.1016/j.mechmachtheory.2024.105791\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This article presents an analytical method to identify the largest <em>effective regular workspaces</em> (ERWs) of a class of 6-6 Stewart platform manipulators for a given orientation workspace. The ERWs are modelled as spheres. The orientation workspace is specified in terms of ranges of Euler angles, as is the standard practice in the parallel robot industry. The radius of the said sphere is maximised through an optimisation problem, which is solved analytically. Consequently, the results obtained are <em>exact</em> in nature. The analytical formulation of the problem and its exact solutions constitute the novel theoretical contributions of this article. Moreover, since the results hold good over a given subset of <span><math><mrow><mi>SO</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>, the proposed method obviates the need for numerical scanning of the orientation workspaces in design-related computations, thus improving the accuracy, robustness, as well as computational efficiency. Finally, the significance of the <em>neutral height</em> in harnessing the desired extents of position and orientation workspaces has been established through parametric studies. The formulations are illustrated via applications to Stewart platform manipulators of three distinct platform dimensions.</div></div>\",\"PeriodicalId\":49845,\"journal\":{\"name\":\"Mechanism and Machine Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.5000,\"publicationDate\":\"2024-09-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanism and Machine Theory\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0094114X24002180\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanism and Machine Theory","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0094114X24002180","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Analytical determination of the optimal effective regular workspace of a 6-6 Stewart platform manipulator for a specified orientation workspace
This article presents an analytical method to identify the largest effective regular workspaces (ERWs) of a class of 6-6 Stewart platform manipulators for a given orientation workspace. The ERWs are modelled as spheres. The orientation workspace is specified in terms of ranges of Euler angles, as is the standard practice in the parallel robot industry. The radius of the said sphere is maximised through an optimisation problem, which is solved analytically. Consequently, the results obtained are exact in nature. The analytical formulation of the problem and its exact solutions constitute the novel theoretical contributions of this article. Moreover, since the results hold good over a given subset of , the proposed method obviates the need for numerical scanning of the orientation workspaces in design-related computations, thus improving the accuracy, robustness, as well as computational efficiency. Finally, the significance of the neutral height in harnessing the desired extents of position and orientation workspaces has been established through parametric studies. The formulations are illustrated via applications to Stewart platform manipulators of three distinct platform dimensions.
期刊介绍:
Mechanism and Machine Theory provides a medium of communication between engineers and scientists engaged in research and development within the fields of knowledge embraced by IFToMM, the International Federation for the Promotion of Mechanism and Machine Science, therefore affiliated with IFToMM as its official research journal.
The main topics are:
Design Theory and Methodology;
Haptics and Human-Machine-Interfaces;
Robotics, Mechatronics and Micro-Machines;
Mechanisms, Mechanical Transmissions and Machines;
Kinematics, Dynamics, and Control of Mechanical Systems;
Applications to Bioengineering and Molecular Chemistry