Pressure Angle in Parallel Mechanisms:From Planar to Spatial

• Published in: Transactions of Tianjin University Vol. 22; no. 5; pp. 411 - 418
• Main Author: 赵庆;梅江平;宋涛;刘松涛
• Format: Journal Article
• Language: English
• Published: Tianjin Tianjin University 01.10.2016; Springer Nature B.V
• Subjects: angle; Engineering; evaluation; global; Humanities and Social Sciences; index; Jacobi matrix method; Mechanical Engineering; mechanism; multidisciplinary; parallel; Parallel degrees of freedom; Performance indices; pressure; Science; performance evaluation; pressure angle; global performance index; parallel mechanism
• ISSN: 1006-4982; 1995-8196
• DOI: 10.1007/s12209-016-2887-4

This paper presents the evolution process of pressure angles from planar parallel mechanisms to spatialparallel mechanisms. Manipulability and condition number, which are frequently used in the optimum design ofThis paper presents the evolution process of pressure angles from planar parallel mechanisms to spatial parallel mechanisms. Manipulability and condition number, which are frequently used in the optimum design of parallel mechanisms, are introduced from serial robots at first. Then, both theoretical analysis and practical experiences demonstrate that these concepts seem imperfect when they are used in parallel mechanisms. For this reason,this paper introduces the pressure angles in planar 4-bar mechanisms to spatial parallel mechanisms, which include redundant parallel mechanisms. Two kinds of pressure angles extracted from the determinant of direct and indirect Jacobian matrices are investigated. Moreover, two comprehensive and visible global performance indices are defined,showing the advantages in evaluating the workspace, singularity and motion/force transmission capabilities.With a 2-DOF planar and a 3-DOF spatial parallel mechanism as examples, the application of the performance indices is investigated and compared with the condition number at last. The proposed concept can be extended to other spatial parallel mechanisms.