{"title":"Application of instantaneous invariants to Cardan positions for two parameters complex plane motion","authors":"","doi":"10.1016/j.mechmachtheory.2024.105798","DOIUrl":null,"url":null,"abstract":"<div><div>This paper aims to represent the Cardan position in the complex plane using Bottema’s instantaneous invariants for two parameters motions. The study provides unchanging and simple quantities that simplify the analysis of complicated mechanical systems by determining complex number representations of Bottema’s instantaneous invariants for Cardan motions with two parameters. The method involves illustrating invariants based on two parameters in the complex plane, defining cycloidal and Cardan motions of two parameters, and deriving the conditions for the Cardan positions. The key results are the necessary and sufficient conditions for the Cardan position for two-parameter motions in the complex plane obtained based on these instantaneous invariants.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5000,"publicationDate":"2024-09-23","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/S0094114X24002258","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}
引用次数: 0
Abstract
This paper aims to represent the Cardan position in the complex plane using Bottema’s instantaneous invariants for two parameters motions. The study provides unchanging and simple quantities that simplify the analysis of complicated mechanical systems by determining complex number representations of Bottema’s instantaneous invariants for Cardan motions with two parameters. The method involves illustrating invariants based on two parameters in the complex plane, defining cycloidal and Cardan motions of two parameters, and deriving the conditions for the Cardan positions. The key results are the necessary and sufficient conditions for the Cardan position for two-parameter motions in the complex plane obtained based on these instantaneous invariants.
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