Constant Transmission Ratio Research Articles

A non-restrictive approach of gear geometry calculation for plastic gears

AbstractFor the unrestricted calculation of gearboxes with a constant transmission ratio, a parameter radius ratio is developed. For this purpose, a parameter radius ratio is introduced that has a piecewise continuous and differentiable domain of definition. Thus, the parameter can be used efficiently in the algorithmic implementation for the optimisation of a contact point of two gears. Furthermore, the data processing of the surface intersection is shown. Through direct surface conjugation, two paired gears can always achieve a line contact, therefore an optimal power transmission can be achieved regarding the technical properties. The procedure is demonstrated with a practical example of a planetary gear with skewed planet.

Algebraic synthesis and input-output analysis of 1-DOF multi-loop linkages with a constant transmission ratio between two adjacent parallel, intersecting or skew axes

This paper deals with the algebraic synthesis and input-output analysis of one degree-of-freedom (1-DOF) multi-loop planar, spherical, and spatial linkages for increasing or decreasing angular motion with a desired constant transmission ratio between two adjacent parallel, intersecting, and skew axes respectively. Based on the rotation scaling model and motion polynomials over dual quaternions, an algebraic synthesis method including three procedures is proposed to exactly construct novel multi-loop linkages owning arbitrarily prescribed constant transmission ratios and input/output axes. To illustrate this method, several 1-DOF multi-loop planar, spherical, and spatial linkages for rotation scaling are synthesized by designating various input and output axes as well as transmission ratios. Taking some multi-loop planar, spherical, and spatial linkages as examples, input-output analysis is carried out to verify their transmission characteristics. The results demonstrate that the generated 1-DOF multi-loop linkages can indeed transmit motion with prescribed constant transmission ratios and input/output axes. This work provides a framework for further investigation on mechanisms performing specified tasks for motion transmission.

A method for point-contact conjugate tooth surfaces with a constant instantaneous transmission ratio generated by point-contact conjugate involute helicoids

Point-contact conjugate tooth surfaces are insensitive to manufacturing errors and assembly errors and have no transmission errors. However, design conditions for the current method of generating point-contact conjugate tooth surfaces are strict or lacking. This study proposed a method for point-contact conjugate tooth surfaces with a constant instantaneous transmission ratio generated by point-contact conjugate involute helicoids. According to relative motions of single- and two-degree-of-freedom in generating, design criteria were given and a mathematical model of the method was established. The mechanism of point-contact conjugate tooth surfaces was obtained by investigating the relationship between the engagement lines/surfaces, and kinematics was studied, in which the mechanism with a constant instantaneous transmission ratio was geometrically analysed. Based on this method, four types of point-contact conjugate worm drives were studied, in which two novel types of worm drives were developed, i.e., a point-contact conjugate toroidal involute (TI) worm drive, and a point-contact conjugate involute cylindrical (ZI) worm drive. The method was validated for correctness using numerical simulations and meshing tests and the influence of adjustable parameters on the meshing performance was outlined.

Cable-Driven Parallel Robot Actuators: State of the Art and Novel Servo-Winch Concept

Cable-Driven Parallel Robots (CDPRs) use cables arranged in a parallel fashion to manipulate an end-effector (EE). They are functionally similar to several cranes that automatically collaborate in handling a shared payload. Thus, CDPRs share several types of equipment with cranes, such as winches, hoists, and pulleys. On the other hand, since CDPRs rely on model-based automatic controllers for their operations, standard crane equipment may severely limit their performance. In particular, to achieve reasonably accurate feedback control of the EE pose during the process, the length of the cable inside the workspace of the robot should be known. Cable length is usually inferred by measuring winch angular displacement, but this operation is simple and accurate only if the winch transmission ratio is constant. This problem called for the design of novel actuation schemes for CDPRs; in this paper, we analyze the existing architectures of so-called servo-winches (i.e., servo-actuators which employ a rotational motor and have a constant transmission ratio), and we propose a novel servo-winch concept and compare the state-of-the-art architectures with our design in terms of pros and cons, design requirements, and applications.

Effect of variable transmission on body-powered prosthetic grasping.

Body-powered upper-limb prostheses remain a popular option for those with limb absence due to their passive nature. These devices typically feature a constant transmission ratio between the forces input by the user and the grasp forces output by the prosthetic gripper. Work incorporating continuously variable transmissions into robotic hands has demonstrated a number of benefits in terms of their motion and forces. In this work, we use a custom prosthesis emulator to evaluate the viability of applying variable transmissions to a body-powered prosthetic context. With this haptics test bed, we measured user performance during a grasping and lift task under a variety of transmission ratio conditions and with three different test objects. Results indicate that use of a variable transmission leads to the successful manipulation of a wider variety of objects than the constant transmission ratio systems, while requiring less shoulder motion. Analysis also shows a potential tendency for users to apply higher grasp forces than necessary, when compared to constant transmission conditions. These findings suggest a multifaceted effect on grasp performance with both benefits and drawbacks when considering a variable approach that supports the continued study of variable transmissions in assisted grasping.

Basic Theory and Design Method of Variable Shaft Angle Line Gear Mechanism

In this paper, a novel line gear mechanism is proposed; it is called the variable shaft angle line gear mechanism (VSALGM). VSALGM has two rotational degrees of freedom, one is the rotation of the two gears with a constant transmission ratio, and the other is the relative swing of the two gears shafts. First, a novel contact model of VSALGM composed of one driven contact curve and one driving line teeth working surface (DLTWS) was proposed. With the concept, the basic design equations for VSALGM were derived on the basis of the space curve meshing theory of line gear. Moreover, the design criterion of pressure angle for VSALGM was analysed and proposed on the basis of the contact model. A basic design method for VSALGM was thus developed. A design example was given, and prototypes were manufactured using three-dimensional (3D) printing. Kinematic experiments and gear contact spot testing were carried out on a self-made kinematic test rig by the prototypes. The results show that the VSALGM designed in this paper can achieve a continuous, smooth and stable meshing transmission while the shaft angle is continuously changed within its setting range.

Thermodynamic Study of a Combined Power and Refrigeration System for Low-Grade Heat Energy Source

This study focuses on the thermal performance analysis of an organic Rankine cycle powered vapor compression refrigeration cycle for a set of working fluids for each cycle, also known as a dual fluid system. Both cycles are coupled using a common shaft to maintain a constant transmission ratio of one. Eight working fluids have been studied for the vapor compression refrigeration cycle, and a total of sixty-four combinations of working fluids have been analyzed for the dual fluid combined cycle system. The analysis has been performed to achieve a temperature of −16 °C for a set of condenser temperatures 34 °C, 36 °C, 38 °C, and 40 °C. For the desired temperature in the refrigeration cycle, the required work input, mass flow rate, and heat input for the organic Rankine cycle were determined systematically. Based on the manifestation of performance criteria, three working fluids (R123, R134a, and R245fa) were chosen for the refrigeration cycle and two (Propane and R245fa) were picked for the organic Rankine cycle. Further, a combination of R123 in the refrigeration cycle with propane in the Rankine cycle was scrutinized for their highest efficiency value of 16.48% with the corresponding highest coefficient of performance value of 2.85 at 40 °C.

The conjugate profile of the circular teeth of a spur gear. Part II: Problem solution

The paper aims finding the conjugate profile of a circular profile tooth from a gear mechanism with fixed parallel axes and constant transmission ratio. There are presented three manners of attaining the goal. The first two methods are based on the general methodology of gear wheel toothing by envelope machining presented in the first part of the work, considering elementary mechanisms with fixed axes and then a planetary one. The last method is based on applying the Reuleaux’s fundamental law of gearing and has the advantage of obtaining both the conjugate profile of the gear with circular profile and the line of action which is useful in the study of gearing phenomena.

The conjugate profile of the circular teeth of a spur gear. Part I: Problem statement

The paper presents the manner of finding the conjugate profile of a circular tooth of a spur gear. A synthesis of the method of enveloping applied to the cam mechanisms is presented in order to relate it the profile of the spur gears. The main argument of employing cam mechanisms is the possibility of obtaining any follower law of motion using a minimum number of parts- the cam and the follower. In the case of the mechanisms with flat face follower, the cam is obtained as an envelope of successive positions of the follower. The gear mechanisms are a particular case of cam mechanisms. The major requirement imposed to this mechanism is to transmit the rotational motion between two shafts with a constant transmission ratio. From here it results that the profile a geared wheel can be completely identified when there are known the distance between the axes, the transmission ratio and the profile of one of the wheels. The most used curve as tooth flank is the involute of a circle, due to the fact that this curve has as conjugate curve an involute, too. Although the involute profiles are common in most of the technical appliances, there are cases when they cannot satisfy the functional constraints of certain devices. As example, in the mechanical watches technology, large transmission ratios are needed and the gears with small number of teeth are used as routine. But this necessity is better fulfilled by cycloidal profiles than the involute ones. The circular profiles for the spur gear are the oldest gears due to the simple profile. The exact conjugate profile of a circular tooth obtained by enveloping by means of dedicated software is presented.

Proposed parameter for the characterization of friction in cylindrical gears teeth contact

Gear mechanisms are widely used in technical applications, mainly for transmitting rotational motion between two axes with constant transmission ratio via a higher pair. Significant friction energy loss in the pair between teeth highlights the importance of estimating the mechanical work lost by friction within this contact. In a previous study, the coefficient of rolling friction between a cylindrical body and a flat face body was found based on the decrease of oscillations amplitude of a cycloidal pendulum. The basic idea of the present paper follows the observation that in the case of a gear mechanism, the relative motion between the wheels can be taken as relative motion of their axodes. In this regard, a pendulum obtained from a mobile cylindrical gear with attached rod and a fixed corresponding rack is considered. The law of motion of the cycloidal pendulum is applied for the proposed pendulum and an “equivalent rolling friction coefficient” which characterises the friction between the teeth of the pinion and the rack is found. The differential equation modelling the motion of the pinion-rack pendulum is difficult to obtain, which is explained by the analysis of the involute gear field of a general cylindrical gear mechanism.

A perspective on gear meshing quality based on transmission error analysis

Gears are one of the most important elements in power transmission systems. Their use is present in many industries due to their various advantages. Durability, constant transmission ratio, reduced size, high efficiency, suitability for a wide range of powers are some of the benefits. But gears also feature a number of drawbacks like vibration of the gear meshing system generating an undesirable noise. The main source of such a noise is the transmission error that result from misalignment of the gear, tooth profile errors and tooth deflections. This article is a state of the art on the theory of transmission error components that influences gear meshing. The errors of static transmission in gears may have several causes. One originates in the function of the gear mechanism which transmits the rotation and torque between axes and generates forces on the teeth, thus modifying their geometry due to elastic deformation. Another undesirable consequence that would be present even if tooth deflections were insensitive is caused by manufacturing errors such as profile, eccentricity, pitch or even assembling errors. One of the best known methods of reducing transmission error of a gear pair is the profile correction. This paper describes the main differences between static and dynamic transmission errors. It will be shown the most common methods of detecting the transmission error using analytical methodology, optimization algorithms, hybrid numerical/ Finite-Element Analysis and experimental researches in order to establish the dynamic behaviour of the gear pairs under different operating conditions.

Optimization of large-scale wind-powered centrifugal pumps

A study on the optimal matching of centrifugal pumps and large-scale wind turbines is reported. The study includes mathematical modelling of the performance of high-capacity centrifugal pumps when matched with efficient high-speed low-solidity wind turbines. The dependence of the performance of wind pumps on the dimensionless parameter v/√( gh), termed the wind pump’s Froude number, was fully analysed. Similar to earlier reported results on wind-powered piston pumps, analysis is showing that the wind pump’s Froude number is the dominant independent dimensionless parameter that fully defines the system’s performance. Operation with continuous variable transmission was analysed and shown to optimize the wind pump’s performance, particularly at medium and low wind speeds. The optimum relation between the required gearbox transmission ratio and Froude number of a wind-powered centrifugal pump was analytically established for three different pumps. In addition to continuous variable transmission operation, the analysis helps in optimally sizing constant transmission ratio systems.

Potential application of power output control in the powertrain of a passenger car

The possibilities available for the control of the power output of the powertrain system in a car comprising a combustion engine with a constant transmission ratio are very limited. This results from limitations present in the traditional design of the powertrain and drivetrain systems. At the same time, when these system are coupled with a very subjective control of the passenger car’s powertrain system performed by the driver, this often leads to the conditions in which the power output delivered to the drivetrain system is not optimal, e.g. in terms of minimizing CO2 emissions to the environment. Therefore, the authors of this study have undertaken an study into the potential to vary the power output of a powertrain system by application of the digital simulation designed with the purpose of improving the power output of powertrain system in a passenger car comprising a multi-ratio mechanical gearbox.

The Moore–Penrose Dual Generalized Inverse Matrix With Application to Kinematic Synthesis of Spatial Linkages

The paper initially reports about the properties of an expression of dual generalized inverse matrix currently available in the literature. It is demonstrated that such a matrix does not fulfill all the Penrose conditions. Hence, novel and computationally efficient algorithms/formulas for the computation of the Moore–Penrose dual generalized inverse (MPDGI) are herein proposed. The paper also contains a new algorithm for the singular value decomposition (SVD) of a dual matrix. The availability of these formulas allows the simultaneous solution of overdetermined systems of dual linear equations without requiring the traditional separation in primal and dual parts. This should prove useful for the solution of many kinematic problems. The algorithms/formulas herein deduced have been also tested on the kinematic synthesis of the constant transmission ratio RCCC spatial linkage.

A Novel Cold Rotary Forging Method of Producing Multiple Racks Using One Set of Punch

When producing racks by cold rotary forging, the top punch and the rack teeth definitely intervene and thus the top punch has to be amended, which makes the technical designing processes difficult and complex (Han et al., 2016, “Cold Orbital Forging of Gear Rack,” Int. J. Mech. Sci., 117(10), pp. 227–242). In this study, a novel cold rotary forging method of producing racks is put forward to avoid the interventions between the top punch and the racks. Thus, the top punch need not be amended and the technical designing processes correspondingly become simple. In light of this presented method, a novel idea for cold rotary forging of producing multiple racks using one set of punch is motivated. The concrete researches are as follows: First, the mathematical models are developed and three kinds of key forging conditions in cold rotary forging of racks are calculated to avoid the interventions between the top punch and the racks. The first one is the condition that the top punch and the rack teeth do not intervene. The second one is the condition that the top punch and cylindrical surfaces of racks do not intervene. The third one is the condition that the top punch can be successfully constructed. On the basis of these three kinds of key forging conditions, the workpiece is optimized and the cold rotary forging processes of racks with constant and variable transmission ratio are examined using finite element (FE) simulations. The experimental researches are also conducted. The results show that for both racks with constant and variable transmission ratio, the obtained key forging conditions are effective and the presented cold rotary forging principles of producing multiple racks using one set of punch are feasible.

A novel arc-tooth-trace cycloid cylindrical gear

A novel arc-tooth-trace cycloid cylindrical gear is presented in this paper. According to the principles of gear meshing and the analysis of the basic gear geometric parameters, the profile equations of the gear tooth are deduced. The tooth trace of the gear is a segment of a circular arc, and the tooth profile is divided into two parts by the pitch circle, the first part of the tooth profile outside pitch circle is a standard arc segment; the other part, which is inside of the pitch circle, is a segment of cycloid. Two parts of the tooth profile are connected at the pitch circle with C1 continuity. An example drive in 3D model is presented and its computerized simulation is carried out. Some meshing characteristics, such as the contact ratio, instantaneous transmission ratio, and the contact and bending stresses are analyzed. The results confirm that the arc-tooth-trace cycloid cylindrical gear has constant instantaneous transmission ratio and the contact and bending stresses are reduced in comparison with the involute gear.

Parametric Design of Gear Hob Cutter

The gears are some of the most used mechanical transmission due to the advantages its provide: constant transmission ratio, high power transmitted, high efficiency, small size, silent operation, precision kinematic, etc. This causes the wheel to be one of the most valuable machine elements both in terms of accuracy and processing technology as well. From the technological point of view due to high precision and productivity, one of the most methods used is processing with gear hob cutter. Although the tool profile does not depend on the number of teeth on the wheel, but only its module, large diversity of gear requires the design of gear hob cutters tailored to existing needs. As it is known the gear hob cutters are complicated and expensive gear cutting tools, both due to the manufacturing process and in terms of design, requiring a significant amount of calculations, high effort from the designer and consequently results in a large cycle of design. For this reason, the literature and in various websites, there are many studies and research information to optimize the design process and increase accuracy of gear hob cutters.

Research on the Tension Effects on Automobile Damping Synchronous Belt Transmission System Damping and Dynamic Stiffness

because of the synchronism belts driving has the advantages of vibration absorption, noise reduction, constant transmission ratio, so it is widely used in automotive engine timing driving system, The stiffness and damping coefficients of the synchronous belt is the main factor affecting the synchronous belt transmission in the process of vibration and noise. In this paper, the model W automotive synchronous belt is simplified as a spring damper system, to solve the stiffness coefficient and damping coefficient of synchronous belt, design of a device for measuring the synchronous belt stiffness coefficient and damping coefficient, measured the belt stiffness coefficient and damping coefficient in the conditions of different tension, and the accuracy of the solution method for synchronous belt stiffness coefficient and damping coefficient was verified as well.

Novel Torus-Involute Gear Transmission

A novel torus-involute gear transmission is presented in this paper. There are two types of tooth profiles for torus-involute gears: convex tooth and concave tooth. Torus-involute gears are non-sensitive to axial misalignments and allow variable shaft angle without meshing interference. Based on revealing of essence for tooth profiles, introducing the parameter t and discretizing this type of gear into tiny linear continuous corrected gears, a design method is proposed. To testify whether the transmission ratio of torus-involute gear transmission is constant, simulation is implemented in commercial codes ADAMS. The computed results show that this novel gear drive can achieve a constant transmission ratio with variable shaft angle.

Tooth flank modification theory of dual-torus double-enveloping hourglass worm drives

In this paper, the theory of tooth flank modification is enriched and developed for a double-enveloping toroidal worm drive. The goal and significance of the modification are expounded from the point of view of changing the tooth flank configuration for the worm gear pair. It is pointed out that the constant center distance modification, the constant transmission ratio modification, and the combination of the previous two are the convenient and reasonable modification strategies. All the corrected hourglass worm pairs, attained by employing the preceding modification methodology, can be divided into two fundamental types: the type I worm pair and the type II worm pair, from the perspective of the meshing behavior. The division criterion of the worm drive type is moreover provided on the basis of the value range of the modification parameters in this study. The meshing characteristics of the two types of the modified globoidal worm drive are summarized in detail. The results indicate that the type II worm gearing with slight modification should be the preferred style for the double-enveloping toroidal worm drive.