Understanding the geometry of gears with skew axes is a highly demanding task, which can be eased by invoking Study's Principle of Transference. By means of this principle, spherical geometry can be readily ported into its spatial counterpart using dual algebra. This paper is based on Martin Disteli's work and on the authors' previous results, where Camus' auxiliary curve is extended to the case of skew gears. We focus on the spatial analog of one particular case of cycloid bevel gears: When the auxiliary curve is specified as a pole tangent, we obtain “pathologic” spherical involute gears; the profiles are always interpenetrating at the meshing point because of G2-contact. The spatial analog of the pole tangent, a skew orthogonal helicoid, leads to G2-contact at a single point combined with an interpenetration of the flanks. However, when instead of a line a plane is attached to the right helicoid, the envelopes of this plane under the roll-sliding of the auxiliary surface (AS) along the axodes are developable ruled surfaces. These serve as conjugate tooth flanks with a permanent line contact. Our results show that these flanks are geometrically sound, which should lead to a generalization of octoidal bevel gears, or even of bevel gears carrying teeth designed with the exact spherical involute, to the spatial case, i.e., for gears with skew axes.
Skip Nav Destination
Article navigation
April 2016
Research-Article
A Spatial Version of Octoidal Gears Via the Generalized Camus Theorem
Giorgio Figliolini,
Giorgio Figliolini
Mem. ASME
Professor
Department of Civil and Mechanical Engineering,
University of Cassino and Southern Lazio,
Via G. Di Biasio 43,
Cassino, FR 03043, Italy
e-mail: figliolini@unicas.it
Professor
Department of Civil and Mechanical Engineering,
University of Cassino and Southern Lazio,
Via G. Di Biasio 43,
Cassino, FR 03043, Italy
e-mail: figliolini@unicas.it
Search for other works by this author on:
Hellmuth Stachel,
Hellmuth Stachel
Professor Emeritus
Institute of Discrete Mathematics and Geometry,
Vienna University of Technology,
Wiedner Hauptstrasse 8-10/104,
Wien A-1040, Austria
e-mail: stachel@dmg.tuwien.ac.at
Institute of Discrete Mathematics and Geometry,
Vienna University of Technology,
Wiedner Hauptstrasse 8-10/104,
Wien A-1040, Austria
e-mail: stachel@dmg.tuwien.ac.at
Search for other works by this author on:
Jorge Angeles
Jorge Angeles
Fellow ASME
Professor
Department of Mechanical Engineering and CIM,
McGill University,
817 Sherbrooke Street W,
Montreal, QC H3A 03C, Canada
e-mail: angeles@cim.mcgill.ca
Professor
Department of Mechanical Engineering and CIM,
McGill University,
817 Sherbrooke Street W,
Montreal, QC H3A 03C, Canada
e-mail: angeles@cim.mcgill.ca
Search for other works by this author on:
Giorgio Figliolini
Mem. ASME
Professor
Department of Civil and Mechanical Engineering,
University of Cassino and Southern Lazio,
Via G. Di Biasio 43,
Cassino, FR 03043, Italy
e-mail: figliolini@unicas.it
Professor
Department of Civil and Mechanical Engineering,
University of Cassino and Southern Lazio,
Via G. Di Biasio 43,
Cassino, FR 03043, Italy
e-mail: figliolini@unicas.it
Hellmuth Stachel
Professor Emeritus
Institute of Discrete Mathematics and Geometry,
Vienna University of Technology,
Wiedner Hauptstrasse 8-10/104,
Wien A-1040, Austria
e-mail: stachel@dmg.tuwien.ac.at
Institute of Discrete Mathematics and Geometry,
Vienna University of Technology,
Wiedner Hauptstrasse 8-10/104,
Wien A-1040, Austria
e-mail: stachel@dmg.tuwien.ac.at
Jorge Angeles
Fellow ASME
Professor
Department of Mechanical Engineering and CIM,
McGill University,
817 Sherbrooke Street W,
Montreal, QC H3A 03C, Canada
e-mail: angeles@cim.mcgill.ca
Professor
Department of Mechanical Engineering and CIM,
McGill University,
817 Sherbrooke Street W,
Montreal, QC H3A 03C, Canada
e-mail: angeles@cim.mcgill.ca
1Corresponding author.
Manuscript received March 17, 2015; final manuscript received August 28, 2015; published online November 24. Assoc. Editor: David Dooner.
J. Mechanisms Robotics. Apr 2016, 8(2): 021015 (3 pages)
Published Online: November 24, 2015
Article history
Received:
March 17, 2015
Revised:
August 28, 2015
Accepted:
September 3, 2015
Citation
Figliolini, G., Stachel, H., and Angeles, J. (November 24, 2015). "A Spatial Version of Octoidal Gears Via the Generalized Camus Theorem." ASME. J. Mechanisms Robotics. April 2016; 8(2): 021015. https://doi.org/10.1115/1.4031679
Download citation file:
Get Email Alerts
Cited By
A Proportional Control Strategy for Stiffness Tuning of Parallel Manipulators
J. Mechanisms Robotics (July 2025)
Inverse Design of Three-Dimensional Variable Curvature Pneumatic Soft Actuators
J. Mechanisms Robotics (July 2025)
Exact Solutions of the Mixed Motion and Path Synthesis Problem for Four-Bar Linkages
J. Mechanisms Robotics (July 2025)
A Systematic Procedure of Transfer Matrix Method to Analyze Compliant Mechanisms With Irregularly Connected Building Blocks
J. Mechanisms Robotics (July 2025)
Related Articles
Planar Linkage Synthesis for Mixed Motion, Path, and Function Generation Using Poles and Rotation Angles
J. Mechanisms Robotics (April,2018)
The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes
J. Mechanisms Robotics (February,2015)
MotionGen: Interactive Design and Editing of Planar Four-Bar Motions for Generating Pose and Geometric Constraints
J. Mechanisms Robotics (April,2017)
Synthesis of Six-Bar Timed Curve Generators of Stephenson-Type Using Random Monodromy Loops
J. Mechanisms Robotics (February,2021)
Related Chapters
Reduction of Voltage Harmonic in PM Wind Generator Based on Pole Width Modulation Method
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
Generators, Motors and Switch Gears
Handbook for Cogeneration and Combined Cycle Power Plants, Second Edition
Research on Land Use in Enping Industry Transfer Zone in Guangdong Province
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)