Spatial Gear Research Articles

Design, analysis, and experiment of an innovative embedded compact continuously variable transmission with flexible metal V-belt

The existing deceleration systems in industrial robots often employ rotate vector (RV) or harmonic reducers to augment torque and decrease speed, yet achieving the motor’s peak power proves challenging. Given the extremely high space-size demands for reduction systems in robotic applications, an innovative compact continuously variable transmission is suggested, leveraging the transmission characteristics of spatial gear trains and metallic V-belts. The proposed system utilizes the input of an eccentric shaft to drive the planetary pulley’s rotation around the sun pulley. The pinhole, in cooperation with the eccentric shaft of the planetary pulley, achieves coaxial output of the transmission power. The article primarily explores the transmission and speed change mechanisms, then dissects the relationships between the transmission ratio and the effective radius of the pulley, the axial adjustment distance, and the factors influencing the pulley’s wrapping angle. Further, we use the Lagrange equation to derive the input equation, establishing the correlation between the planetary pulley’s rotation angle and system inertia, angular acceleration, angular velocity, and effective working radius over time. Finally, we simulate the continuously variable transmission’s motion to examine speed changes in forward, reverse, and neutral states. A continuously variable transmission prototype and a testing platform are also constructed to assess performance parameters, specifically input and output torque, and rotational speed.

Spatial motions transformers for incorporation into robot systems – review of the Bulgarian experience

This work is a review of research carried out by the author on the synthesis and design of the spatial gear mechanisms, oriented for incorporation in various technical devices, especially in robotic systems. It contains also a description of the innovative and inventive activities of the author over the years. The study illustrates the elaborated through the years, basic algorithms for the synthesis of spatial motions transformers (in particular Spiroid and Helicon gear sets), which are based on the mathematical model for synthesis upon a pitch contact point. The content of the solution of the two main tasks of the synthesis - synthesis of the pitch configurations and synthesis of the active tooth surfaces configures the mentioned above algorithm. Through it, real models of Spiroid and Helicon gear transmissions are synthesized and elaborated by 3D printing subsequently, which are designed for incorporation into robots of various purposes

Pattern Classification and Gear Design of Spatial Noncircular Gear Continuously Variable Transmission

Noncircular gear and curve face gear are collectively referred to as spatial noncircular gear. Combined with the transmission characteristics of spatial noncircular gear, a new classification design method of spatial noncircular gear continuously variable transmission (CVT) pattern was proposed, including two categories named addition type and multiplication type, with a total of five subcategories. Through the combination of the transmission ratio changing mechanism and transmission selection mechanism, it can realize the CVT. The overall transmission ratio depends on the phase angle between the spatial noncircular gear pairs and is independent of the input rotation angle. Firstly, the CVT principle and transmission ratio characteristics of each pattern were analyzed. Then the tooth profile classification design of spatial noncircular gear was carried out, and the general parametric design equations of the tooth surface with different tooth profiles were obtained. Finally, through simulation, the overall transmission ratio of each pattern was compared between theory and simulation, which verified the correctness of the CVT classification design method. The advantages and disadvantages of the two categories were analyzed. Moreover, through the transmission experiments of curve face gear pairs with different tooth profiles, the transmission ratios were compared between theory and experiment. Considering the influencing factors such as machining error, assembly error and measurement error, the experimental error is within a reasonable error range, which verified the correctness of the tooth profile classification design method. This study provides a new idea for the further research and application of spatial noncircular gear CVT.

Effects of geometric design parameters and misalignments on contact ellipse of crossed beveloid gears

Based on the meshing theory of spatial gear transmission, a calculation methodology for contact ellipse of crossed beveloid gear pair is introduced in this paper. The mathematical model of beveloid gear tooth surface is derived. After the meshing model of crossed beveloid gears with misalignments is established, the tooth contact analysis (TCA) is performed. Then, the contact ellipses are calculated and drawn on the tooth flank by mathematical software, and the effects of geometric design parameters and misalignments on contact ellipse of crossed beveloid gear pair are investigated afterwards. Results show that crossed beveloid gear pair with small FPD angle has larger contact ellipse, with the cone angles and helix angle of beveloid pinion increasing, the mean value of major axis of contact ellipse increases. Positive offset error and negative shaft angle error make the contact ellipse move from middle to heel side. Axial position errors make little effect on the mean value of contact ellipse, while axial position error of pinion has a slight effect on the location of contact ellipse on the beveloid pinion tooth flank.

Единая теория структуры, синтеза и анализа многозвенных механических систем с геометрическими, гибкими и динамическими связями звеньев. Часть 1. Базовые структурные уравнения и универсальные таблицы строения

Multibody mechanical systems (mechanisms and machine drives) are widely used in different fields of modern engineering due to their reliability and simple design. They can be found in robots, manipulators, technological and construction equipment, automatic lines, etc. This paper presents a unified theory of structure, synthesis and analysis of mechanisms and machines with geometrical (single and multiple kinematic pairs), flexible contact (friction or belt) and dynamic contactless (inertial, gravitational, etc.) connections. The theory can be used to construct planar and spatial single- and multi-loop kinematic chains of machines with a given number of closed loops and driving motors. Areas of possible existence of multibody mechanical systems with open, closed and mixed kinematic chain are determined. Based on these findings, various planar and spatial gear and linkage patentable mechanisms are developed that can be used in vibrational drives, variable structure systems requiring precise stoppage during the cycle, lever actuators of multi-axle locomotives, spatial mixers with several mixing tanks, tribometers for measuring the limiting pulling capacity of flexible belts of belt-and-pulley drives, and direct-drive devices for horizontal motion of a suspended load with a low set velocity.

In Memoriam: Veniamin I. Goldfarb

Veniamin I. Goldfarb, a well-known scholar and educator, passed away on November 12, 2019, at the age of 78. As the Director of the Institute of Mechanics of the Izhevsk State Technical University, Professor Goldfarb was a towering figure in the field of power transmission and gearing, specializing in gear geometry, kinematics, and contact mechanics.Professor Goldfarb's technical contributions included a novel classification and the study of spatial gear arrangements, rational structuring of the process of computer-aided design of worm gears, the development of a “nondifferential” method for defining surfaces formed by enveloping, and the study of a variety of spiroid gears. Professor Goldfarb was the author of more than 400 scientific publications, including seven monographs in the field of research, development, and implementation of gear transmissions. He advised nearly 40 PhD candidates and authored more than 20 patents.Professor Goldfarb was the laureate of the State Prize in the field of science and technology from the Higher Professional Education of the Russian Federation. He was awarded the Medal of Academician V.I. Vernadsky and the Medal of Academician S.P. Kapitsa by the St. George Cross of the Russian Academy of Natural Sciences for his contributions in science. He took several leadership roles in the International Federation for the Promotion of Mechanism and Machine Science (IFToMM) as the chair of the Gearing Technical Committee (1998–2005), a member of the Executive Council (2007–2011), and the Vice President (2011–2015). He was a member of the International Organization for Standardization (ISO). For three decades, he was the face of the gearing and power transmission research community in Russia.Professor Goldfarb will be remembered as a very kind and compassionate person who valued his friendship greatly. While he will be missed dearly, his legacy of mentorship, inventions, and scholarly contributions to our field will live on for many decades to come.

基于空间定轴齿轮结构与链传动的健身娱乐康复器械机构设计

基于空间定轴齿轮结构与链传动的健身娱乐康复器械机构设计

Calculation and Characteristic Analysis of Tooth Width of Eccentric Helical Curve-Face Gear

Eccentric helical curve-face gear pair is a new type of gear pair consisting of a helical non-circular gear and an eccentric helical curve-face gear, which can implement the rotation of intersected axes as well as the movement of output axes. According to the conjugate surface theory and the spatial coordinate transformation theory, the coordinate system, the meshing equation and the tooth surface equation of eccentric helical curve-face gear are obtained. Based on the spatial gear engagement theory, the undercutting and pointing phenomenon of eccentric helical curve-face gear are analyzed, and equations of tooth width of eccentric helical curve-face gear are proposed. By changing the different parameters of eccentric helical curve-face gear pair, the influencing factors and variation of undercutting radius, pointing radius and tooth width are derived. Furthermore, by building the experiment devices of the roll testing and the transmission, the correctness of the calculation method of tooth width of eccentric helical curve-face gear is verified by using the contact analysis and the experimental verification.

The kinematics and strength study of indexing bevel gear mechanism in rotating device driver

Indexing spatial gear mechanisms are widely used in automatic machines. The movement in gear mechanisms with stops is defined by complex design shapes that can lose their stiffness at critical loads. To measure the ultimate bearing stress of these mechanisms is possible by both the physical and numerical models tests results. The paper considers the numerical model for the spatial gear mechanism with driven disk indexing at a constant angular velocity of a driving disk. The presented mechanism kinematics and geometry parameters and finite element model were analyzed in the SolidWorks design environment. The structure and kinematics analysis revealed the possible reasons of mechanism failures. The numerical calculations results showing the design performance under the active area contact stresses and teeth bending stresses are represented. The maximal bend of the shaft was determined to avoid engagement failure.

Calculation and analysis of contact ratio of helical curve-face gear pair

Helical curve-face gear pair is a new type of gear pair consisting of a helical non-circular gear and a helical curve-face gear, which can transfer the movement of variable transmission ratio between intersecting axes. According to the spatial gear engagement theory and the spatial coordinate transformation theory, the transformation matrix of helical curve-face gear pair and the unit normal of helical cutter are deduced. Based on the meshing theory, the meshing equation of helical curve-face gear pair is built. Equations of instantaneous contact ratio of helical curve-face gear pair are proposed by transforming helical curve-face gear pair into helical non-circular rack and pinion. Besides, the influences of basic parameters of helical cutter and helical curve-face gear pair on contact ratio are analyzed. The tooth surface coordinate data of helical curve-face gear pair is obtained by using the gear measuring center, and the comparison findings between experimental and theoretical results are the experiment data basically agree with the theoretical calculation value, and error is within 5%, so the calculation method of contact ratio is verified.

ANALYSIS OF THE DYNAMIC BEHAVIOUR OF MULTI-MESH SPUR AND HELICAL GEARS - APPLICATION TO THE DEFINITION OF OPTIMUM PROFILE RELIEFS IN AERONAUTICAL TRANSMISSIONS

This paper is focused on the modelling and analysis of vibrations and dynamic loads in aeronautical multi-mesh gears comprising several spatial gear arrangements (idler gears, several pinions on one shaft. Optimum profile modifications are sought by applying a metaheuristic Genetic Algorithm to the local quasi-static transmission errors under load associated with each individual mesh. It is shown that the resulting linear symmetric profile modifications all lie in the vicinity of the so-called analytical Master Curves initially defined for a single pinion-gear pair. The theory is applied to a 6-mesh aeronautical transmission and it is found that the proposed profile modifications can effectively reduce dynamic overloads and improve the vibrational behaviour of complex multi-mesh gears with different power circulations. Finally, it is shown that for systems submitted to several load levels, short optimal reliefs seem preferable with regard to vibration levels.

3D Software Technology, Applicable in Elaboration of the Spatial Face Gear Drives for Incorporation into Robot Systems

The study treats a specific technological approach for the elaboration of small manufacturing series of highly precise hyperboloid gears with small module of the teeth and with not big dimensions of the gear mechanism. It is based on the application of the elaborated by authors mathematical models, algorithms and computer programs for synthesis upon a pitch contact point and upon a mesh region. A special feature of the established approach is the application of 3D software prototyping and 3D printing of the designed transmissions. The presented here models of the transmissions with crossed axes and face mated gears are indented for implementation into the driving of two type robots: bio-robot hand and walking robot with four insect-type legs.

Package of Programs for the Synthesis of Space Gear Mechanism in the MAPLE Environment

The design of any mechanism begins with the design of its scheme. Subsequent calculations for strength, structural design of links and kinematic pairs, choice of materials, and other stages of the design, as a rule cannot significantly change the basic properties of the mechanism. The design of mechanisms scheme on the specified properties is called synthesis of mechanism. In this work we considered the software package of kinematic synthesis of spatial gear lever mechanisms for five, seven, eight and nine parameters.

A Kind of Spatial Angular Magnetic Gear Transmission

Gear exciting is of vital importance in modern power transmission systems. But when the requirements of angular gear transmission are needed, the shortcomings of the current mechanical and magnetic gear transmission are even more obvious. The traditional mechanical gear boxes have the construction of direct mechanical contact, whose disadvantages are low efficiency, noisy, apt to lubricate, easy to produce vibrations to be damaged and so on. And the existing magnetic gear is coaxial which can’t meet the need of angular transmission. In this paper, the construction of a kind of spatial angular magnetic gear, which has no direct mechanical contact between the driven axis and load axis, is proposed. Besides, the principle of the gear ratio is introduced and a concrete magnetic gear is analyzed. The results show that the range of the angle of this magnetic gear can be very large.

Mathematical modelling for synthesis of spatial gears

Spatial skew axes gears are used to transform rotation between shafts with non-parallel and nonintersecting axes. Principles of mathematical modelling of a tooth contact synthesis for this general gearing case are discussed in this paper. The research presented shows that the synthesis of a skew axes gear can be realized by application of two mathematical models: a pitch contact point approach and a mesh region model. These two approaches are applied to synthesis of spatial gear sets of the Spiroid and Helicon types.

3D Dynamic Modelling of Spatial Geared Systems

In this paper, a nonlinearly dynamic model for a spatial geared systemwith intersecting-axes, which consists of bevel gears, bearings, andshafts, is proposed based on a specific finite element theory. A newtype of spatial gear element which is consistent with the specific finiteelement theory is developed and completely describes all thedeformations that exist for the spatial motions of a pair of bevel gears,the time-variant meshing stiffness, and various types of gear errors inmanufacturing and assembly. The 3D motions of the spatial geared systemin axial, lateral, and torsional directions are coupled in the model. Theproposed approach has been coded into a software system and a dynamicanalysis for the spatial geared system is carried out. The nonlinearinfluences of axial, lateral and torsional stiffnesses of the shaft onthe vibration of the spatial geared system are especially investigated.The lateral stiffness changes the resonance peak frequencies of thespatial geared system and the torsional stiffness greatly affects thesize of the dynamic load and vibration amplitude.

Signal Flow Graphs for Spatial Gear Trains

Signal flow graphs (SFG) have been applied in many areas such as circuit analysis, controls, mechanical vibrations, statistics, and operations research. They have also been applied to the analysis of planetary gear trains which are planar, i.e., where all of the gear axes are parallel. In this paper, signal flow graphs are applied to spatial planetary gear trains. Some additional terminology and rules which are needed for this important application are developed in this paper and illustrated by examples. The significance of applying SFG to a gear system is that the graph describes the interrelationship among the system variables by linking causes and effects, offers the information about the topology of system connection, and the kinematic equations of motion can be written easily by inspection. In this way, it helps use to visualize and understand spatial gear train systems better.