spatial face rack drives: mathematical models for synthesis and software illustrations emilia...
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SPATIAL FACE RACK DRIVES: MATHEMATICAL MODELS FOR SYNTHESIS AND SOFTWARE ILLUSTRATIONS
Emilia AbadjievaInstitute of Information and Communication Technologies,
Institue of Mechanics,Bulgarian Academy of Sciences
1- INTRODUCTION
Spatial three links transmissions, transforming motions through a system of high kinematic joints, in accordance with preliminary given law (velocity ratio) and randomly oriented in the space vectors of motion of the movable links, are characterized by the biggest variety and complexity of their study. Therefore they are still insufficiently studied and thus their exploitation and technological capabilities are not realized completely (Abadjiev, 2007), (Abadjieva, 2011). This work contains special type mechanisms, belonging to transformers of rotation into translation motions (vice versa), by a system of high kinematic joints. These mechanical transmissions are known as a rack drives (Abadjieva, 2011).
In many well-known literature sources (Litvin, 1994), rack matings are treated as instrumental matings, when cylindrical involute gears are cut. Planar mechanical motion transformers – rack cylindrical gear drives are subject of study. The article (Abadjieva, 2011) is dedicated to a special rack drive, consisting of a bevel gear and a rack with straight teeth. This mechanism realizes a variable law of motion transformation. In publication (Watanabe, 2006) analysis and practical experiment of rack set of type Wildhaber-Novikov (WN-helical gear rack drive) is accomplished. The monograph (Abadjieva, 2011) should be considered as a development and improvement of the studies performed in (Abadjiev, 2007), (Kovatchev, 1990), (Abadjieva, 2009).
This study presents a mathematical model for synthesis upon mesh region of a face rack set, in which the active tooth surfaces of the rotating link - face pinion are parts of face linear helicoids and tooth surfaces of the link, performing rectilinear translation- face rack are theoretically conjugated with those of the face pinion. The rotation axis of the face pinion is orthogonal crossed with the direction of the rectilinear translation of the gear rack.
2- GENERATING OF ACTIVE TOOTH SURFACES OF THRE BASIC MOVABLE LINKS
SYNTHESIS OF FACE RACK MECHANISMS 6- CONCLUSIONSThe geometric character of the mesh region and the tooth surfaces of the movable links of spatial rack drives of type convolute, involute and Archimedean is established by kinematic and analytical studies. Algorithms for theirs synthesis are elaborated. It is developed a computer program. Based on this program a synthesis and visualization of the basic geometric elements of the upper mention types of spatial rack set is accomplished.
The discussed in this study face rack drives are one special type. Besides them, the objects of the author’s study are conic rack drives and cylindrical rack sets (Abadjieva, 2014). The study of the three types rack drives is accomplished, when the rotating link-pinion is of convolute, Archimedean and involute type.
In general they are suitable for implementation as actuators in various fields of techniques. Of particular interest is their incorporation into the constructions of bio-robots (Wenzeng, 2009), as an alternative of spatial hyperboloid gears (Abadjieva, 2013).
ACKNOWLEDGEMENT
The author gratefully acknowledges the funding by project AComIn: Advanced Computing for Innovation of the FP7 Capacity Programme, Research Potential of Convergence Regions, FP7-REGPOT-2012-2013-1
REFERENCES
Abadjiev V. Gearing theory and technical applications of hyperboloid mechanisms. D. Sc Thesis, Bulgarian Academy of Sciences, Institute of Mechanics, 2007, 309 pp, (in Bulgarian).
Watanabe M, Maki M. A study of new type WN rack and pinion. Proc of the 2nd International Conference “Power Transmissions 2006”, Balcan Associations of Power Transmission, Faculty of Technical Sciences, Novi Sad, 2006, 27-32 p.
Abadjieva E. Spatial rack drives. Mathematical modelling for synthesis. VDM Verlag Dr. Müller e.K., 2011, 72 pp.
Kovatchev G, Abadjiev V. On the synthesis of spatial rack mechanisms. 6th National Congress of Theoretical and Applied Mechanics, 1, Varna 1990, 35-38p.
Abadjieva E. Mathematical modelling oriented to kinematic synthesis of spatial rack drives. Proc. of 3rd Int. Conf. Power Transmission’09, Greece, 30.09-3.10.2009, pp. 27-34
Litvin F. Gearing geometry and applied theory. PTR Prentice Hall, A Paramount Communication Company, Englewood Eliffs, New Jersey 07632, 1994, 724 p.
Abadjieva E, Abadjiev V, Kawasaki H. On the synthesis of spatial rack mechanisms: Mathematical modelling and software teeth generating of the moving links teeth. Proc. of the Eight International Symposium KOD 2014 “Machine and Industrial Design in Mechanical Engineering”, 12-15 June, 2014 Balatonfured, Hungary, Faculty of Technical Sciences, Novi Sad, Faculty of Mechanical Engineering, Bratislava, pp. 163-170
Wenzeng, Zhang, Demeng Che, Hongbin Liu, Xiande Ma, Qiang Chen, Dong Du &Zhenguo Sun. Super Under-Actuated Multi-Fingered Mechanical Hand with Modular Self-Adaptive Gear-Rack Mechanism, Industrial Robot: An International Journal, Vol. 36 Iss: 3, 2009, pp. 255 – 262
Abadjieva E, Abadjiev, V, Kawasaki H. & Mouri T. On the synthesis of hyperboloid gears and technical applications, Proc. of ASME 2013 International Power Transmissions and Gearing Conference, IDETC/CIE 2013, Portland, Oregon, USA (published on CD)
CONTACT INFORMATION
Face convolute helicoids generation
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6th International Conference on Mechanics and Materials in DesignPonta Delgada/Azores, 26-30 July 2015
Assoc. Prof. Emilia Abadjieva, Institute Information Technologies,Bulgarian Academy of Sciences, Acad. G. Bonchev Str., block 2, 1113 Sofia, Bulgaria
E-mail: [email protected]
6th International Conference on Mechanics and Materials in DesignPonta Delgada/Azores, 26-30 July 2015
Figure 1 – Geometric scheme of face helicoids generation.
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From the above equation systems we obtain correspondingly the set of equations for involute and Archimedean helicoids generation, when we substitute and .0r0
Face convolute rack mechanism
Figure 2 – Geometric kinematic scheme of face rack mechanism
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Figure 3 – Spatial face concolute rack drive
Figure 4 – Spatial face Archimedean rack mechanism
Figure 5 – Spatial face involute rack mechanism
On the base of Figure 1 it is realized geometric synthesis of the common face linear helicoid- face convolute helicoid.