Kinematic Transmission Research Articles

Implementation of an exact completing method of generation for face-milled spiral bevel gears with uniform depth taper

AbstractThis paper proposes an exact completing method of generation of face-milled spiral bevel gears with uniform depth taper. This method ensures localized bearing contact without kinematic transmission errors in both directions of rotation. Both sides of the tooth are generated simultaneously using the same set of basic machine tool settings. A tip relief on the tooth surfaces is the only required microgeometry modification to achieve a smooth transition of load between consecutive pairs of teeth. An analytical approach to determine the basic machine tool settings and select the grinding cutter parameters has been also developed. The selection of the nominal cutter radius follows the recommendations of Information Sheet AGMA 22849-A12. The basis for alignment error compensation has been also established. Tooth contact and stress analyses demonstrate the advantages and limitations of the proposed method, making it suitable for applications with higher power demands for the drive side than for the coast side.

РАЗРАБОТКА ДИНАМИЧЕСКОЙ МОДЕЛИ ДЛЯ РАСЧЕТА КИНЕМАТИЧЕСКОЙ ПОГРЕШНОСТИ И ОЦЕНКИ ЕЕ ВЛИЯНИЯ НА КПД ПЛАНЕТАРНЫХ МЕХАНИЗМОВ С ТЕЛАМИ КАЧЕНИЯ

When studying the characteristics of the mechanisms of small-sized drives, an important task is to develop ways to increase the efficiency of the mechanism. The article discusses theoretical issues related to the influence assessment of kinematic error on the efficiency of gears with rolling bodies. As a result of the research, a generalized dynamic model of planetary ball and roller mechanisms is obtained, taking into account kinematic errors, linking manufacturing errors or elastic deformations and kinematic transmission error. Mathematical dependences of the dynamic model of mechanisms with rolling bodies are derived. The model was tested on the example of calculating the kinematic error of a single-stage planetary ball transmission. Polynomial equations with constant coefficients are obtained for determining kinematic errors from the influence of manufacturing errors of transmission links. It is established that for different kinematic schemes, gear ratios and angular velocities of planetary mechanisms with rolling bodies, the transmission efficiency can vary significantly depending on its kinematic error. For gear ratios from 1.5 to 5, drive shaft rotation speeds from 1,500 to 3,000 rpm, depending on the highest values of the kinematic error from 0.00175 to 0.0349 radians, the transmission efficiency within the driven shaft rotation can decrease from 0.93 to 11 %. At the same time, transmissions constructed according to the sixth kinematic scheme have the highest efficiency values. The average efficiency value per revolution of the driven shaft from the influence of kinematic errors can decrease up to 5 %. Graphs of the dependences of transmission efficiency on their kinematic errors are given.

The contributions regarding to the behavior of bearings in wind turbines

With the growth of the wind industry in the world and the commissioning of turbines with powers higher than 1 MW, higher loads and increased stresses have a strong effect on the durability of the bearings that equip the main shaft and the kinematic transmission of wind turbine gears. As a result, the wind industry is demanding greater durability of the bearings that equip the main shaft and the kinematic transmission with gears, and manufacturers are striving to come up with solutions for these requirements. The novelty in this work consists in the identification of some solutions, as well as improvements of the existing solutions for the construction of some mechanical systems for the existing wind turbines. We present below some constructive bearing solutions that are effective in the wind turbine industry. The research in the paper consists of: stress analysis of the load- bearing structure for the axial radial bearing with straight rollers with single ring, some aspects about lubrication of blade bearing in wind turbine and defects in blade bearings.

Organismal form constrains the evolution of complex lever systems in Neotropical cichlid four-bar linkages.

The diversification of functional traits may be limited by the intrinsic constraints of organismal form (i.e., constructional constraints), owing to the differential investment in different anatomical structures. In this study, we test whether overall organismal form impacts the evolution of shape and function in complex lever systems. We examined the relationship between four-bar shape and overall head shape in two four-bar linkage systems: the oral-jaw and hyoid-neurocranium systems in Neotropical cichlids. We also investigated the strength of form-function mapping in these four-bar linkages and the impact of constraining head shape on these correlations. We quantified the shape of the head and two four-bar linkages using geometric morphometrics and compared these with the kinematic transmission coefficient of each linkage system. The shapes of both linkages were strongly correlated with their mechanical properties, and head shape appears to constrain the shape of both four-bar linkages. Head shape induced greater integration between the two linkages, was associated with stronger form-function correlations and higher rates of evolution in biomechanically important features. Head shape constraints may also contribute to a weak but significant trade-off in linkage kinematics. Elongation of the head and body, in particular, appears to minimize the impact of this trade-off, possibly through maximizing anterior-posterior space availability. However, the strength of relationships between shape and function, and the impact of head shape differed between the two linkages, with the hyoid four-bar in general showing stronger form-function relationships despite being more independent from head shape constraints.

A comprehensive evaluation framework for kinematic performance of parallel mechanisms based on joint transmissibility and multi-attribute decision making methods

The evaluation of kinematic transmission performance is one of the key elements of mechanism analysis and the foundation of optimal design, where performance indices related to motion and force transmission provide evaluation criteria for parallel mechanisms. The paper will focus on the two significant and challenging aspects of performance evaluation of parallel mechanisms: (1) presenting the generalized angle to evaluate the joint transmissibility and (2) establishing a systematic and complete multi-index comprehensive evaluation method (MICEM). Utilizing the transmission vector involving the transmissibility of all inputs and outputs, the general approaches to establishing multiple indices are further proposed to reveal performance presentations limited by a single index. Combing multiple indices and multi-attribute decision making (MADM) methods, the procedures including determining reasonable weights of the indices, screening appropriate indices, and aggregating those indices into a composite index are further developed to address the comprehensive evaluation problem. Moreover, the results of the comprehensive evaluation for a 3-RUU parallel mechanism verify the effectiveness and rationality of the new method. This work can also provide references for evaluation analysis and optimal design of different performance.

Flexure Variable Stiffness Actuators

Series elastic actuators (SEAs) and variable elastic actuators (VSAs) provide shock resistance, energy storage, and stable force control. However, they usually require extra springs, mechanical parts, and transmissions, increasing size, weight, number of moving parts, and reducing the mechanical efficiency. In particular, this mechanical complexity is one of the significant challenges in the design of wearable and scalable force feedback devices. In this article, flexure variable stiffness actuators (F‐VSAs), which combine kinematic transmission, elasticity, and stiffness modulation via a network of folding patterns using flexure hinges, are presented. Thus, F‐VSAs allow the creation of robots benefiting from the advantages of SEAs and VSAs without hindering form factor or mechanical efficiency. To illustrate the design strategy of F‐VSAs, a 4‐design‐of‐freedom (DoF) robot that provides stiffness and force output is presented. An analytical model that estimates the inherent stiffness and the end‐effector force output for any given configuration of the folding pattern is proposed. Finally, stiffness modulation and force control of the robot are implemented and good agreement with the predictions from the model is observed. Thus, this novel design strategy allows the creation of compact and scalable robots with stiffness and force output for wearable, rehabilitation, and haptic applications.

Design, Analysis, and Experiment of an Underactuated Robotic Gripper Actuated by Linear Series Elastic Actuator

Abstract The primary motivation of this study is to develop a cost-effective, safe, easily controlled, and passively adaptive robotic gripper. A novel linear series elastic actuated robotic gripper (LSEA-RG) is proposed to accomplish the aforementioned goals. The LSEA-RG has the ability to adaptively grasp objects with different shapes and sizes by grasping force control. First, the mechanical design, including the transmission scheme, the finger mechanism, and the actuating mechanism is presented. Subsequently, the kinematic analysis is performed to explore the transmission characteristic of the actuating displacement and force. Then a model-free control method based on the lookup functions of the kinematic transmission characteristics is presented to achieve the grasping range and force control. Finally, several grasping experiments are carried out based on the LSEA-RG prototype to evaluate the grasping performance. The results demonstrate that the presented grasping control method which based on the lookup functions is valid. The LSEA-RG could estimate the grasping force without the help of a fingertip force sensor and grasp objects with different shapes and hardness adaptively.

INVESTIGATION OF THE PHYSICAL PROCESSES OF POWER TRANSMISSION IN FRICTION BELT DRIVES

The physical regularities of power transmission by a flexible friction-type coupling (belt) by means of the friction force arising on the arcs of the transmission pulleys girth are considered. Theoretical dependences of stresses and deformations of belt elements on the basic geometric and kinematic transmission parameters are obtained, allowing to proceed to the prediction of belt durability.

Control of the servo drive in the presence of a backlash in the kinematic transmission with high stiffness

Control of the servo drive in the presence of a backlash in the kinematic transmission with high stiffness

Generation of Artificial Learning Data to Train Functional Meta-Models of Micro Gears

The complexity of products increases considerably and key functions can often only be realized by using high-precision components. As a result, the requirements of high-precision components reach technological manufacturing limits. This is of particular importance for micro components, such as micro gears, where the manufacturing deviations are relatively large compared to the component size and therefore have a large influence on the functional characteristics of the assembled product. A potential solution is to develop a meta-model with machine learning (ML) methods, which enables the real-time prediction of functional characteristics of micro gears in terms of kinematic transmission error (KTE), based on optical in-line measurements of the entire topography of the gear. To train a suitable ML model large amounts of data are needed. This poses a challenge because real measurements cannot cover the entire spectrum of all deviations and also require a large amount of resources in terms of time, material and costs. In this paper, an approach for the generation of learning data on the basis of virtual and deviated gear models is developed with the help of Skin Model Shapes. The objective is to generate gear data that reflects the nominal shape as well as the process-related manufacturing deviations and the random scatter. For validation, the artificially generated gears are compared with a reference dataset both geometrically and functionally. Therefore, both the standard deviations and the KTE are calculated for both data sets.

Trophic divergence of Lake Kivu cichlid fishes along a pelagic versus littoral habitat axis.

Local adaptation to the littoral and pelagic zones in two cichlid haplochromine fish species from Lake Kivu was investigated using morphometrics. Cranial variation and inferred jaw mechanics in both sexes of the two species across the two habitat types were quantified and compared. Comparisons of littoral versus pelagic populations revealed habitat‐specific differences in the shape of the feeding apparatus. Also, kinematic transmission of the anterior jaw four‐bar linkage that promotes greater jaw protrusion was higher in the pelagic zone than in the littoral zone for both species. Inferred bite force was likewise higher in pelagic zone fish. There were also sex‐specific differences in craniofacial morphology as males exhibited longer heads than females in both habitats. As has been described for other cichlids in the East African Great Lakes, local adaptation to trophic resources in the littoral and pelagic habitats characterizes these two Lake Kivu cichlids. Similar studies involving other types of the Lake Kivu fishes are recommended to test the evidence of the observed trophic patterns and their genetic basis of divergences.

Energy Flow in Multibody Limb Models: A Case Study in Frogs.

A frog jump is both simple and difficult to comprehend. The center-of-mass (COM) follows a two-dimensional (2D) path; it accelerates diagonally upward, then traces a predictable arc in flight. Despite this simplicity, the leg segments trace intricate trajectories to drive the COM both upwards and forwards. Because the frog sits crouched with sprawled legs, segments must pivot, tilt, and twist; they solve a long-recognized problem of converting non-linear 3D motion of the leg segments to linear 2D motion of the COM. I use mathematical approaches borrowed from robotics to address: How do frogs manipulate the flow of kinetic energy through their body to influence jump trajectory? I address (1) transfer of motion through kinematic transmission and (2) transfer of motion through dynamic coupling of segment mass-inertia properties. Using a multi-body simulation, I explore how segment acceleration induces rotations at neighboring segments (even without accounting for bi-articular muscles). During jumps, this inertial coupling mechanism is likely crucial for modulating the direction of travel. The frog case study highlights a useful computational framework for studying how limb joints produce coordinated motion.

The Evolutionary Dynamics of Mechanically Complex Systems

Animals use a diverse array of motion to feed, escape predators, and reproduce. Linking morphology, performance, and fitness is a foundational paradigm in organismal biology and evolution. Yet, the influence of mechanical relationships on evolutionary diversity remains unresolved. Here, I focus on the many-to-one mapping of form to function, a widespread, emergent property of many mechanical systems in nature, and discuss how mechanical redundancy influences the tempo and mode of phenotypic evolution. By supplying many possible morphological pathways for functional adaptation, many-to-one mapping can release morphology from selection on performance. Consequently, many-to-one mapping decouples morphological and functional diversification. In fish, for example, parallel morphological evolution is weaker for traits that contribute to mechanically redundant motions, like suction feeding performance, than for systems with one-to-one form–function relationships, like lower jaw lever ratios. As mechanical complexity increases, historical factors play a stronger role in shaping evolutionary trajectories. Many-to-one mapping, however, does not always result in equal freedom of morphological evolution. The kinematics of complex systems can often be reduced to variation in a few traits of high mechanical effect. In various different four-bar linkage systems, for example, mechanical output (kinematic transmission) is highly sensitive to size variation in one or two links, and insensitive to variation in the others. In four-bar linkage systems, faster rates of evolution are biased to traits of high mechanical effect. Mechanical sensitivity also results in stronger parallel evolution—evolutionary transitions in mechanical output are coupled with transition in linkages of high mechanical effect. In other words, the evolutionary dynamics of complex systems can actually approximate that of simpler, one-to-one systems when mechanical sensitivity is strong. When examined in a macroevolutionary framework, the same mechanical system may experience distinct selective pressures in different groups of organisms. For example, performance tradeoffs are stronger for organisms that use the same mechanical structure for more functions. In general, stronger performance tradeoffs result in less phenotypic diversity in the system and, sometimes, a slower rate of evolution. These macroevolutionary trends can contribute to unevenness in functional and lineage diversity across the tree of life. Finally, I discuss how the evolution of mechanical systems informs our understanding of the relative roles of determinism and contingency in evolution.

Mathematical Model of Speeds Change Device on the Basis of Switched Differential Mechanisms

The geometry and kinematics of a dynamic system with several degrees of freedom and controllable friction clutches are considered. The necessary kinematic transmission ratio between the input and output links is obtained using the friction clutches. The model uses a smooth approximation of the discontinuous function of the moment of friction. This allows continuous numerical integration of the equations of motion without changing their structure, i.e., preserving their number. The switching from one speed of rotation of the output link to another is controlled by specifying time functions that implement the pressure of the clutch discs. An example of a numerical study of such a mechanism consisting of three differentials and four clutches is considered. Dynamic processes for this system are analyzed.

Two methods of determining the kinematic transmission ratio of coupled circulatory gears with bevel wheels

The paper will present an analysis of kinematics of coupled circulatory gears with cylindrical and bevel wheels with the use of contour graphs method. This method has already been used to analyze the kinematics of lever mechanisms and toothed planetary gears and planetary gears coupled with cylindrical wheels. A formula for kinematic gearing was also derived using Willis' formula, thanks to which it is possible to verify the metadata of contour graphs.

Система управления взаимосвязанными электроприводами с электромеханическим распором и распределением нагрузки

The article presents the results from the development of a double-motor electromechanical system, in which the automatic control of interconnected electric drives ensures the formation of electromechanical torsion to maintain the closed state of backlash in the kinematic transmission within the specified load torque variation range. When the load torque escapes from the preset range, it is automatically distributed equally among the electric drives. The aims of this technical solution are to form a torsion when it is needed in accordance with the peculiarities of the load acting on the mechanism, and to prevent the installed capacity of electric drives from being exceeded in comparison with the power required for moving the mechanism. The application of the development results for controlling the motion of the antenna installation lifting axis is illustrated. The peculiarity of this system is that the load torque of this mechanism is active, sign- variable and depends on the lifting angle. When crossing the vertical position, it changes direction, which facilitates the opening of backlash in the kinematic transmission and the occurrence of self-oscillations. At lifting angles close to the horizontal position, the load torque has its maximum value, and the backlash is closed under its action. In addition, when the mechanism is near the vertical position, the wind load facilitates opening of the backlash. The system for controlling the electromechanical systems coordinates includes torque control loops, which are individual for each of the electric drives, and a loop that is common for control of their position. Recommendations for synthesizing these loops are given. The specified torsion torque is calculated by a nonlinear element with a trapezoidal I/O characteristic depending on the mismatch between the specified and actual angular position of the driving mechanism axis processed by the position controller, which makes it possible to indirectly estimate the load torque value. The control system software and hardware have been developed. In developing the microprocessor control system software, model-oriented development tools were used. A prototype replicating the antenna installation lifting mechanism design has been made. The proposed control system made it possible to reduce the influence of backlash at lifting angles close to the vertical position and to distribute the load torque between the electric drives at lifting angles close to the horizontal position, when torsion is not required, as well as when exposed to wind load. Experimental oscillograms of electromechanical system coordinates are presented, confirming the declared results.

Why the long face? Static allometry in the sexually dimorphic phenotypes of Neotropical electric fishes

Abstract The evolution of sexually dimorphic traits is thought to have marked effects on underlying patterns of static allometry. These traits can negatively affect organismal survivability by creating trade-offs between trait size and performance. Here we use three-dimensional geometric morphometrics to study the static allometry of two species of sexually dimorphic electric fishes (Apteronotus rostratus and Compsaraia samueli) in which mature males grow elongate jaws used in agonistic male–male interactions. We also estimate jaw-closing performance between the sexes of both species to track changes in kinematic transmission associated with the development of sexual weaponry. We find significantly different patterns of static allometry between the sexes of both species, with males exhibiting more positive allometric slopes relative to females. We also find a negative relationship between skull shape and mandibular kinematic transmission in C. samueli, suggesting a trade-off where males with longer faces exhibit lower mechanical advantages, suggesting weaker jaw leverage. In contrast, males and females of A. rostratus exhibit no difference between sexes in mechanical advantage associated with facial elongation.

Finding the weakest link: mechanical sensitivity in a fish cranial linkage system.

Understanding the physical mechanics behind morphological systems can offer insights into their evolution. Recent work on linkage systems in fish and crustaceans has suggested that the evolution of such systems may depend on mechanical sensitivity, where geometrical changes to different parts of a biomechanical system have variable influence on mechanical outputs. While examined at the evolutionary level, no study has directly explored this idea at the level of the mechanism. We analyse the mechanical sensitivity of a fish cranial linkage to identify the influence of linkage geometry on the kinematic transmission (KT) of the suspensorium, hyoid and lower jaw. Specifically, we answer two questions about the sensitivity of this linkage system: (i) What changes in linkage geometry affect one KT while keeping the other KTs constant? (ii) Which geometry changes result in the largest and smallest changes to KT? Our results show that there are ways to alter the morphology that change each KT individually, and that there are multiple ways to alter a single link that have variable influence on KT. These results provide insight into the morphological evolution of the fish skull and highlight which structural features in the system may have more freedom to evolve than others.

EFFECT OF A TORSEN DIFFERENTIAL MECHANISM ON CAR TYRE WEAR

4WD systems include various constructions aimed at optimal distribution of torque between drive axles. In these systems, it is necessary to apply mechanisms separating the power provided from the engine to drive wheels. Many systems operate on the basis of wet multi-disc clutch or/and dog clutch control with the use of mechatronic devices. However, in view of their reliability and construction simplicity, the most valuable 4WD systems under field conditions are mechanical solutions. Torsen is an inter-axle differential mechanism, where the emerging internal friction moment of this mechanism causes that all kinematic discrepancies between transmission shafts of the front and rear axle of a vehicle produce a change in the distribution of torque, helping to level the rotational speeds of transmission shafts of the front and rear axles. As a result of the phenomenon described, the drive wheels of both axles of the vehicle move with different peripheral speeds, which causes energy losses and wear of tyres on both vehicle axles. This paper presents an analysis of the results obtained in tests on a vehicle with the Torsen system and describes phenomena occurring in the examined system as a result of emerging kinematic discrepancies, which may be caused by such factors as vertical force acting on the wheels of individual drive axles and tyre pressure.

The measurement of Gear Transmission Error as an NVH indicator: Theoretical discussion and industrial application via low-cost digital encoders to an all-electric vehicle gearbox

Abstract Gear Transmission Error (TE) is often considered as the main cause of gear whine. TE represents the difference between the perfectly kinematic transmission of motion and the one actually achieved. TE vibrations are extremely small and pose significant measurement challenges. This article demonstrates how low-cost digital encoders can be successfully used together with the Elapsed Time Method to simplify TE measurement with respect to the traditional Direct Method. A precision gear pair test rig is exploited to compare the two methods from a theoretical and an experimental point of view. Following the observations drawn from such comparison, a measuring chain is set up to validate the proposed procedure on a real case all-electric vehicle gearbox. It is shown how TE represents a useful gearbox NVH indicator and how it can be used to support gear microgeometry design.