A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages

Robotics

Juan Ignacio Valderrama-Rodríguez¹  J. Jesús Cervantes-Sánchez²  Ricardo García-García²  José M. Rico² 

[1] Independent Researcher, Ciudad de Duitama 150461, Colombia;Mechanical Engineering Department, División de Ingenierías, Campus Irapuato-Salamanca, Universidad de Guanajuato, Guanajuato 36885, Mexico;

关键词: planar linkages;    indeterminate linkages;    screw theory;   

DOI  :  10.3390/robotics11010006

来源: DOAJ

【 摘 要 】

This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, $se\left(3\right)$, of the Euclidean group, $SE\left(3\right)$, and the invariant symmetric bilinear forms defined on $se\left(3\right)$.

【 授权许可】

Unknown