Extended Rotation Matrix for Kinematics of Pointing Mechanisms

Shaoping Bai

doi:10.1007/978-3-031-08140-8_5

Extended Rotation Matrix for Kinematics of Pointing Mechanisms

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

1 Citation (Scopus)

Abstract

This paper introduces a new formation of rotation, which is developed with two non-parallel vectors. A transformation matrix, called extended rotation matrix (ERM), is thus formulated. In particular, the matrix contains two known vectors from one body and their cross product, with which all other vectors or points in the same body can be uniquely described by a set of values associated with the matrix, namely, their alternative coordinates. Using ERM and alternative coordinates, kinematic equations of pointing mechanisms can be formulated uniquely and conveniently, without any redundancy of parametrization. A case study of pointing mechanisms is included to demonstrate the advantage of the new formulation.

Original language	English
Title of host publication	Advances in Robot Kinematics 2022
Editors	Oscar Altuzarra, Andrés Kecskeméthy
Number of pages	8
Publisher	Springer Nature
Publication date	2022
Pages	39-46
ISBN (Print)	978-3-031-08139-2, 978-3-031-09403-3
ISBN (Electronic)	978-3-031-08140-8
DOIs	https://doi.org/10.1007/978-3-031-08140-8_5
Publication status	Published - 2022
Event	18th International Symposium on Advances in Robot Kinematics, ARK 2022 - Bilbao, Spain Duration: 26 Jun 2022 → 30 Jun 2022

Conference

Conference	18th International Symposium on Advances in Robot Kinematics, ARK 2022
Country/Territory	Spain
City	Bilbao
Period	26/06/2022 → 30/06/2022

Series	Springer Proceedings in Advanced Robotics
Volume	24 SPAR
ISSN	2511-1256

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Access to Document

10.1007/978-3-031-08140-8_5

AUB Link

Search for the material in Aalborg University Library's search engine

Cite this

@inproceedings{437af5a510d543bda50416366c816fb6,

title = "Extended Rotation Matrix for Kinematics of Pointing Mechanisms",

abstract = "This paper introduces a new formation of rotation, which is developed with two non-parallel vectors. A transformation matrix, called extended rotation matrix (ERM), is thus formulated. In particular, the matrix contains two known vectors from one body and their cross product, with which all other vectors or points in the same body can be uniquely described by a set of values associated with the matrix, namely, their alternative coordinates. Using ERM and alternative coordinates, kinematic equations of pointing mechanisms can be formulated uniquely and conveniently, without any redundancy of parametrization. A case study of pointing mechanisms is included to demonstrate the advantage of the new formulation.",

author = "Shaoping Bai",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 18th International Symposium on Advances in Robot Kinematics, ARK 2022 ; Conference date: 26-06-2022 Through 30-06-2022",

year = "2022",

doi = "10.1007/978-3-031-08140-8_5",

language = "English",

isbn = "978-3-031-08139-2",

series = "Springer Proceedings in Advanced Robotics",

publisher = "Springer Nature",

pages = "39--46",

editor = "Oscar Altuzarra and Andr{\'e}s Kecskem{\'e}thy",

booktitle = "Advances in Robot Kinematics 2022",

address = "United States",

}

Bai, S 2022, Extended Rotation Matrix for Kinematics of Pointing Mechanisms. in O Altuzarra & A Kecskeméthy (eds), Advances in Robot Kinematics 2022. Springer Nature, Springer Proceedings in Advanced Robotics, vol. 24 SPAR, pp. 39-46, 18th International Symposium on Advances in Robot Kinematics, ARK 2022, Bilbao, Spain, 26/06/2022. https://doi.org/10.1007/978-3-031-08140-8_5

Extended Rotation Matrix for Kinematics of Pointing Mechanisms. / Bai, Shaoping.
Advances in Robot Kinematics 2022. ed. / Oscar Altuzarra; Andrés Kecskeméthy. Springer Nature, 2022. p. 39-46 (Springer Proceedings in Advanced Robotics, Vol. 24 SPAR).

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - Extended Rotation Matrix for Kinematics of Pointing Mechanisms

AU - Bai, Shaoping

PY - 2022

Y1 - 2022

N2 - This paper introduces a new formation of rotation, which is developed with two non-parallel vectors. A transformation matrix, called extended rotation matrix (ERM), is thus formulated. In particular, the matrix contains two known vectors from one body and their cross product, with which all other vectors or points in the same body can be uniquely described by a set of values associated with the matrix, namely, their alternative coordinates. Using ERM and alternative coordinates, kinematic equations of pointing mechanisms can be formulated uniquely and conveniently, without any redundancy of parametrization. A case study of pointing mechanisms is included to demonstrate the advantage of the new formulation.

AB - This paper introduces a new formation of rotation, which is developed with two non-parallel vectors. A transformation matrix, called extended rotation matrix (ERM), is thus formulated. In particular, the matrix contains two known vectors from one body and their cross product, with which all other vectors or points in the same body can be uniquely described by a set of values associated with the matrix, namely, their alternative coordinates. Using ERM and alternative coordinates, kinematic equations of pointing mechanisms can be formulated uniquely and conveniently, without any redundancy of parametrization. A case study of pointing mechanisms is included to demonstrate the advantage of the new formulation.

UR - http://www.scopus.com/inward/record.url?scp=85133267178&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-08140-8_5

DO - 10.1007/978-3-031-08140-8_5

M3 - Article in proceeding

AN - SCOPUS:85133267178

SN - 978-3-031-08139-2

SN - 978-3-031-09403-3

T3 - Springer Proceedings in Advanced Robotics

SP - 39

EP - 46

BT - Advances in Robot Kinematics 2022

A2 - Altuzarra, Oscar

A2 - Kecskeméthy, Andrés

PB - Springer Nature

T2 - 18th International Symposium on Advances in Robot Kinematics, ARK 2022

Y2 - 26 June 2022 through 30 June 2022

ER -