A note on enveloping curves in plane. (November 2016)

• Record Type: Journal Article
• Authors: K., Ramakrishna; Sen, Dibakar
• Is Part Of: Mechanism and machine theory. Volume 105(2016:Nov.)
• Page Start: 510
• Page End: 514
• Publication Date: 2016-11
• Subjects: Envelope theory -- Euler-Savary -- Contact kinematics -- Coordinated centers -- Conjugate points; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2016.07.025
• Languages: English
• ISSNs: 0094-114X

Abstract

Abstract: This paper revisits the classical envelope theory in plane, which deals with two planar curves in a point contact moving in relative roll-slide motion. The well known result about the centers of curvature of the generating curve and the envelope curve behaving as coordinated centers, is shown to be valid even if the instantaneous relative angular velocity is zero. The analytical approach uses the contact kinematics equations and does not require the existence of finitely accessible velocity pole and polodes of the relative motion. An example of equivalent mechanisms demonstrates the extended applicability of the theorem on coordinated centers of enveloping curves. Highlights: Theorem on coordinated centers of enveloping curves valid even for T 1 -position Analytical approach uses contact kinematics alone without reference to polodes. Dwell mechanism illustrates application to equivalent mechanisms.