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On the Synthesis of Cycloidal and Involute Gears with Skew Axes

Giorgio Figliolini
Department of Civil and Mechanical Engineering University of Cassino and Southern Lazio

July 31, 2015 at  9:00 AM
McConnell Engineering Room 437


The formulation of a unified framework for the synthesis of spatial cycloidal and involute gears is the focus of this seminar. Our approach is based on the fundamentals of kinematics, as required in the synthesis of a pair of conjugate surfaces, to produce either constant or variable transmission ratios, between two parallel, intersecting or skew axes for cylindrical (C), bevel (B) or spatial (S) gears, respectively. A general algorithm, still under development, should impact not only the gear-manufacturing sector, but also the CAD/CAE industry, which at the moment lacks capabilities to produce gears more general than cylindrical. The well-established synthesis technique aimed at the conjugate profiles of C gears is extended to spatial gears, as intended to determine the position of the instant screw axis (ISA) of the relative motion between gear and pinion. The axodes swept by the ISA on each of the meshing elements, namely, hyperboloids, play then the role of the pitch cylinders (commonly referred to as their projections, the pitch circles) for C gears, and of the pitch cones for B gears. In the case of S gears, the pitch surfaces become hyperboloids. The synthesis of the conjugate surfaces of S gears with cycloidal or involute teeth is quite challenging. Indeed, these surfaces are synthesized via an extension of the Camus Theorem, known for the generation of C gears, as the theorem calls for the use of the Pl├╝cker conoid of the relative motion between the meshing gears. The choice of a suitable auxiliary surface is thus a key issue in the synthesis of S gears with cycloidal and involute teeth. The synthesis of these gears is described, while outlining the role of the orthogonal helicoid in the generation of the tooth flanks of involute-gear pairs with skew axes. These concepts are illustrated with animations.


Giorgio Figliolini is Professor of Mechanics of Machines at the University of Cassino and Southern Lazio (UCSL), where he started his academic career in 1992. At the same university, Figliolini obtained his Master's degree in Mechanical Engineering with honours. In 1998-99, he spent six months as Visiting Scholar at the Centre for Intelligent Machines (CIM), McGill University, where he started a long-term research project on Innovative Mechanical Transmission Systems. In 2000, he took a specialization on Hydraulic Systems at the Centre for Fluid Power Transmission and Motion Control of the University of Bath, U.K. Figliolini's main research interests lie in the fields of the theory of machines and mechanisms (TMM), robotics and mechatronics. Currently, Figliolini teaches Mechanics of Machines and Mechanism Design at the UCSL, along with Kinematics and Dynamics of Mechanisms at the University of Rome-Tor Vergata. Figliolini's research recognitions, shared with his local and international teams, include the AIMETA (Italian Association of Theoretical and Applied Mechanics) Ettore Funaioli Prize in 2009; the Best Paper Award in Theoretical Kinematics at the ASME 2012 IDETC-CIE; and the Best Paper Award-Honorable Mention at the ASME 2014 IDETC-CIE.