A study of the instantaneous centers of velocity for the 3-dof planar six-bar linkage

• Published in: Mechanism and machine theory 2011-09, Vol.46 (9), p.1276-1300
• Main Authors: Foster, David E., Pennock, Gordon R.
• Format: Article
• Language: English
• Subjects: 3-dof planar six-bar linkage; Analytic geometry; Applied sciences; Double points and double lines; Drives; Exact sciences and technology; Graphical and analytical techniques; Infinity; Instant centers; Kinematics; Lines at infinity; Lines of centers; Linkage mechanisms, cams; Linkages; Mathematical analysis; Mechanical engineering. Machine design; Synthesis; Theorems
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2011.04.004

This paper is a detailed study of the instantaneous centers of velocity (henceforth referred to simply as instant centers) for the three-degree-of-freedom (henceforth abbreviated as 3-dof) planar six-bar linkage. The paper focuses on graphical techniques, which only require a knowledge of elementary and analytic geometry, to locate the unknown (or secondary) instant centers. In addition, analytical techniques are provided to interpret the graphical concepts and confirm the new results. Several important theorems are proposed which relate to special cases where the secondary instant centers are either single points or infinite lines. The paper investigates points and lines at infinity and presents theorems to explain how secondary instant centers relate to each other when one, or more, are at infinity. There is an in-depth discussion of double points and double lines, that is, points and lines that map onto themselves, and several lemmas and theorems show how to obtain the number of double points and double lines for the 3-dof six-bar linkage. The results presented in this paper will prove useful in the kinematic analysis and synthesis of multi-degree-of-freedom planar linkages. ► A detailed study of the instantaneous centers of velocity for the 3-dof planar six-bar linkage. ► Graphical techniques to locate the secondary instant centers and analytical techniques to interpret the graphical concepts. ► Theorems are proposed which relate to special cases where the secondary instant centers are either single points or infinite lines and theorems are included to explain how secondary instant centers relate to each other when one, or more, are at infinity. ► An in-depth discussion of double points and double lines. ► Lemmas and theorems are proposed to obtain the number of double points and double lines for the 3-dof planar six-bar linkage.