A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism
Abstract Topology and performance are the two main topics dealt in the development of robotic mechanisms. However, it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame. As the properties associated with topology and performance, fini...
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doaj-6ee3b15e83544c5ba87b5e0baac10b072020-11-25T03:25:15ZengSpringerOpenChinese Journal of Mechanical Engineering1000-93452192-82582020-09-0133111510.1186/s10033-020-00481-zA Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic MechanismXinming Huo0Shuofei Yang1Binbin Lian2Tao Sun3Yimin Song4Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin UniversityDepartment of Industrial and Systems Engineering, The Hong Kong Polytechnic UniversityKey Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin UniversityKey Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin UniversityKey Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin UniversityAbstract Topology and performance are the two main topics dealt in the development of robotic mechanisms. However, it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame. As the properties associated with topology and performance, finite motion and instantaneous motion of the robot play key roles in the procedure. On the purpose of providing a fundamental preparation for integrated modeling and design, this paper carries out a review on the existing unified mathematic frameworks for motion description and computation, involving matrix Lie group and Lie algebra, dual quaternion and pure dual quaternion, finite screw and instantaneous screw. Besides the application in robotics, the review of the work from these mathematicians concentrates on the description, composition and intersection operations of the finite and instantaneous motions, especially on the exponential-differential maps which connect the two sides. Furthermore, an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development. The presented review offers insightful investigation to the motion description and computation, and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.http://link.springer.com/article/10.1186/s10033-020-00481-zRobotic mechanismIntegrated methodMatrix Lie groupDual quaternionFinite screw |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xinming Huo Shuofei Yang Binbin Lian Tao Sun Yimin Song |
spellingShingle |
Xinming Huo Shuofei Yang Binbin Lian Tao Sun Yimin Song A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism Chinese Journal of Mechanical Engineering Robotic mechanism Integrated method Matrix Lie group Dual quaternion Finite screw |
author_facet |
Xinming Huo Shuofei Yang Binbin Lian Tao Sun Yimin Song |
author_sort |
Xinming Huo |
title |
A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism |
title_short |
A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism |
title_full |
A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism |
title_fullStr |
A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism |
title_full_unstemmed |
A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism |
title_sort |
survey of mathematical tools in topology and performance integrated modeling and design of robotic mechanism |
publisher |
SpringerOpen |
series |
Chinese Journal of Mechanical Engineering |
issn |
1000-9345 2192-8258 |
publishDate |
2020-09-01 |
description |
Abstract Topology and performance are the two main topics dealt in the development of robotic mechanisms. However, it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame. As the properties associated with topology and performance, finite motion and instantaneous motion of the robot play key roles in the procedure. On the purpose of providing a fundamental preparation for integrated modeling and design, this paper carries out a review on the existing unified mathematic frameworks for motion description and computation, involving matrix Lie group and Lie algebra, dual quaternion and pure dual quaternion, finite screw and instantaneous screw. Besides the application in robotics, the review of the work from these mathematicians concentrates on the description, composition and intersection operations of the finite and instantaneous motions, especially on the exponential-differential maps which connect the two sides. Furthermore, an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development. The presented review offers insightful investigation to the motion description and computation, and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots. |
topic |
Robotic mechanism Integrated method Matrix Lie group Dual quaternion Finite screw |
url |
http://link.springer.com/article/10.1186/s10033-020-00481-z |
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