Inverted Slider Crank, Coupled in Tandem to Another Four Bar, to Generate a Constant Velocity Ratio

1969 ◽  
Vol 91 (1) ◽  
pp. 37-44
Author(s):  
W. Meyer zur Capellen
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Planetary Gear ◽  
Function Generators ◽  
Scotch Yoke Mechanism

Combinations of the inverted slider-crank linkage (i.e., the Whitworth quick-return mechanism) with another of the same sort, with a scotch-yoke mechanism or with a planetary gear, are able to produce excellent function generators having a stationary value of velocity ratio. Various forms are discussed, and graphs of their characteristic motions are shown.

Characteristics of a co-flowing jet with varying lip thickness and constant velocity ratio

2020 ◽  
Vol 92 (4) ◽  
pp. 633-644
Author(s):  
Naren Shankar R. ◽  
Kevin Bennett S. ◽  
Dilip Raja N. ◽  
Sathish Kumar K.
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Critical Limit ◽  
Potential Core ◽  
Content Type ◽  
Free Jet ◽  
Current Scenario ◽  
Wake Zone ◽  
Bypass Ratio ◽  
Practical Implications

Purpose This study aims to analyze co-flowing jets (CFJs) with constant velocity ratio (VR) and varying primary nozzle lip thickness (LT) to find a critical LT in CFJs below which mixing enhances and beyond which mixing inhibits. Design/methodology/approach CFJs were characterized with a constant VR and varying LTs. A single free jet with a diameter equal to that of a primary nozzle of the CFJ was used for characteristic comparison. Numerical simulation is carried out and is validated with the experimental results. Findings The results show that within a critical limit, the mixing enhanced with an increase in LT. This was signified by a reduction in potential core length (PCL). Beyond this limit, mixing inhibited leading to the elongation of PCL. This limit was controlled by parameters such as LT and constant VR. A new region termed as influential wake zone is identified. Practical implications In this study, the VR is maintained constant and bypass ratio (BR) was varied from low value to very high values. Presently, subsonic commercial turbo fan operates under low to ultra-high BR. Hence the present study becomes vital to the current scenario. Originality/value To the best of the authors’ knowledge, this is the first effort to find the critical value of LT for a constant VR for compressible co-flow jets. The CFJs with constant VR and varying LT have not been studied in the past. The present study focuses on finding a critical LT below which mixing enhances and above which mixing inhibits.

A New Constant Velocity Coupling

1977 ◽  
Vol 99 (2) ◽  
pp. 367-372 ◽  
Author(s):  
V. Milenkovic
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Kinematic Model ◽  
Formal Proof

A constant velocity coupling has been developed that does not resemble any coupling built before. It was intended for a specialized application, with specifications that are outside the range of any existing designs. A kinematic model as well as a subscale prototype have been constructed, and the latter was successfully tested. The principles of the coupling are discussed in some detail, with emphasis on their kinematic aspects. The formal proof for the constancy of the velocity ratio of this coupling is presented.

scholarly journals Controlling the Movement of a TRR Spatial Chain With Coupled Six-Bar Function Generators for Biomimetic Motion

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Constant Velocity ◽  
Joint Angle ◽  
Synthesis Process ◽  
Function Generator ◽  
Single Degree Of Freedom ◽  
Wing Motion ◽  
Serial Chain ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Velocity Input

This paper describes a synthesis technique that constrains a spatial serial chain into a single degree-of-freedom mechanism using planar six-bar function generators. The synthesis process begins by specifying the target motion of a serial chain that is parameterized by time. The goal is to create a mechanism with a constant velocity rotary input that will achieve that motion. To do this, we solve the inverse kinematics equations to find functions of each serial joint angle with respect to time. Since a constant velocity input is desired, time is proportional to the angle of the input link, and each serial joint angle can be expressed as functions of the input angle. This poses a separate function generator problem to control each joint of the serial chain. Function generators are linkages that coordinate their input and output angles. Each function is synthesized using a technique that finds 11 position Stephenson II linkages, which are then packaged onto the serial chain. Using pulleys and the scaling capabilities of function generating linkages, the final device can be packaged compactly. We describe this synthesis procedure through the design of a biomimetic device for reproducing a flapping wing motion.

scholarly journals Controlling the Movement of a TRR Spatial Chain With Coupled Six-Bar Function Generators for Biomimetic Motion

2015 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Constant Velocity ◽  
Joint Angle ◽  
Synthesis Process ◽  
Function Generator ◽  
Single Degree Of Freedom ◽  
Wing Motion ◽  
Serial Chain ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Velocity Input

This paper describes a synthesis technique that constrains a spatial serial chain into a single degree-of-freedom mechanism using planar six-bar function generators. The synthesis process begins by specifying the target motion of a serial chain that is parameterized by time. The goal is to create a mechanism with a constant velocity rotary input that will achieve that motion. To do this we solve the inverse kinematics equations to find functions of each serial joint angle with respect to time. Since a constant velocity input is desired, time is proportional to the angle of the input link, and each serial joint angle can be expressed as functions of the input angle. This poses a separate function generator problem to control each joint of the serial chain. Function generators are linkages that coordinate their input and output angles. Each function is synthesized using a technique that finds 11 position Stephenson II linkages, which are then packaged onto the serial chain. Using pulleys and the scaling capabilities of function generating linkages, the final device can be packaged compactly. We describe this synthesis procedure through the design of a biomimetic device for reproducing a flapping wing motion.

Study of a Non-Circular Gear Infinitely Variable Transmission

2014 ◽  
Author(s):  
Kumar Hebbale ◽  
Dongxu Li ◽  
Jing Zhou ◽  
Chengwu Duan ◽  
Chi-Kuan Kao ◽  
...  
Keyword(s):  
Static Analysis ◽  
Fuel Efficiency ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Development Effort ◽  
Function Generator ◽  
Multiple Function ◽  
Variable Transmission ◽  
Infinitely Variable Transmission ◽  
Function Generators

Improving automobile fuel efficiency is an important research and development effort in the automotive industry. In the transmission area, it is generally understood that optimum fuel economy can be achieved via a combination of highly efficient power transfer (gears, for example) and an ability to transmit power at an infinite number of ratios (CVT, for example). In this paper, a geared infinitely variable transmission (IVT) is analyzed for efficiency through static analysis. This IVT is based on a non-circular gear concept described in [1, 2]. This IVT consists of multiple function generators with each function generator comprising two sets of non-circular gear sets whose outputs are combined with a summing planetary gear set. Each function generator provides the desired gear ratio for only a part of the driving rotation. So, multiple function generators are combined along with multiple one-way clutches to provide an infinitely variable transmission. This paper first explains the operating principle of the geared IVT. A static analysis of the IVT powerflow is derived and it is shown that this powerflow exhibits a torque recirculation phenomenon, which is not desired. This recirculation phenomenon is expected to be present in all similarly arranged IVTs where two inputs are combined using a planetary gear set to provide infinite gear ratio capability. The efficiency of the IVT is calculated based on assumed individual component efficiency and it is shown that, owing to torque recirculation, the efficiency of this transmission may not compare well with that of current automatic transmissions for a passenger car application.

Conceptual Design of a 16-Speed Bicycle Drive Hub

2011 ◽  
Vol 52-54 ◽  
pp. 279-284 ◽  
Author(s):  
Yi Chang Wu ◽  
Shi Liang Lin
Keyword(s):  
Conceptual Design ◽  
Kinematic Analysis ◽  
Power Transmission ◽  
Velocity Ratio ◽  
Planetary Gear ◽  
Transmission Mechanism ◽  
Gear Train ◽  
Design Approach ◽  
Schematic Diagram ◽  
Gear Mechanism

This paper presents a design approach for the conceptual design of a novel 16-speed bicycle drive hub. First, a distributed-flow type planetary gear train, which consists of two parallel- connected transmission units and one differential unit, for the power transmission mechanism of a bicycle drive hub is proposed. Based on the kinematic analysis of the presented gear mechanism, a feasible clutching sequence is synthesized to provide 16 forward speeds. Then, the numbers of teeth of all gears are determined according to the desired velocity ratio of each speed. As a result, a schematic diagram of the embodiment of the proposed 16-speed drive hub is presented.

Displacement Analysis of Spatial 7R Mechanisms Suitable for Constant-Velocity Transmission Between Parallel Shafts

1979 ◽  
Vol 101 (4) ◽  
pp. 604-613 ◽  
Author(s):  
M. J. Gilmartin ◽  
J. Duffy
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Numerical Results ◽  
Theory Method ◽  
Unified Theory ◽  
Displacement Analysis ◽  
Loop Method ◽  
Joint Coupling ◽  
Velocity Transmission ◽  
Special Case

Three types of spatial 7R mechanisms are identified as being suitable for transmitting motion with a constant velocity ratio between two parallel shafts. A displacement analysis of each type is made using a vector loop method in conjunction with the Unified Theory method. Numerical results are presented for an example of each type. It is also shown how the double Hooke joint coupling for parallel shafts is a special case of one of these three types.

Algebraic Method for Exact Synthesis of 1-DOF Linkages With Arbitrarily Prescribed Constant Velocity Ratios

2021 ◽  
pp. 1-18
Author(s):  
Kai Liu ◽  
Jingjun Yu
Keyword(s):  
Constant Velocity ◽  
High Speed ◽  
Characteristic Curve ◽  
Velocity Ratio ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Angular Motion ◽  
Open Chain ◽  
Pure Rolling ◽  
Spherical Linkages

Abstract This paper addresses the synthesis of 1-DOF linkages that can exactly transmit angular motion between coplanar axes (i.e. parallel axes or intersectant axes) with arbitrarily prescribed constant velocity ratios. According to motion polynomials over dual quaternions and pure rolling models between two circles, an algebraic approach is presented to precisely synthesize new 1-DOF linkages with arbitrarily prescribed constant velocity ratios. The approach includes four steps: (a) formulate a characteristic curve occurred by the pure rolling, (b) compute the motion polynomial of the minimal degree that can generate the curve, (c) deal with the factorization of the motion polynomial to construct an open chain, (d) convert the open chain to a 1-DOF linkage. Using this approach, several 1-DOF planar, spherical, and spatial linkages for angular motion transmission between parallel axes or intersectant ones are constructed by designating various velocity ratios. Taking the planar and spherical linkages with a constant 1:2 velocity ratio as examples, kinematics analysis is implemented to prove their motion characteristics. The result shows that the generated linkages indeed can transmit angular motion between two coplanar axes with constant velocity ratios. Meanwhile, 3D-printed prototypes of these linkages also demonstrate such a conclusion. This work provides a framework for synthesizing linkages that have great application potential to transmit motion in robotic systems that require low inertia to achieve reciprocating motion with high speed and accuracy.

On the Dynamic Gear Tooth Loading of Planetary Gearing as Affected by Bearing Clearances in High-Speed Machinery

1985 ◽  
Vol 107 (3) ◽  
pp. 430-436 ◽  
Author(s):  
B. M. Bahgat ◽  
M. O. M. Osman ◽  
R. V. Dukkipati
Keyword(s):  
High Speed ◽  
Gear Tooth ◽  
Contact Point ◽  
Velocity Ratio ◽  
Planetary Gear ◽  
Spur Gears ◽  
Governing Equations ◽  
Contact Mode ◽  
Gear Teeth ◽  
Geometrical Constraints

The paper studies the effect of bearing clearances in the dynamic analysis of planetary gear mechanisms in high-speed machinery. For this purpose, an analytical model is developed based on the interdependence between kinematics and kinetic relationships that must be satisfied when contact is maintained between the journal and its bearing. The contact mode is formulated such that the bearing eccentricity vector must align itself with bearing normal force at the point of contact. The analysis mainly relies on determining the direction of the bearing eccentricity vector defined as the clearance angles βi at the bearing revolutes for each contact mode of the gear teeth. The governing equations of the clearance angles are developed using the geometrical constraints of the contact point location and the velocity ratio. The clearance angles and their derivatives are used to systematically evaluate kinematic and dynamic quantities. A rigid planetary spur gears with two revolute clearances is analyzed to illustrate the procedure.

On the Necessary and Sufficient Conditions for Homokinetic Transmission in Chains of Cardan Joints

1993 ◽  
Vol 115 (2) ◽  
pp. 255-261 ◽  
Author(s):  
D. A. Johnson ◽  
P. Y. Willems
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Sufficient Conditions ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Flexible Design ◽  
Universal Joint ◽  
Necessary And Sufficient ◽  
Ratio Transmission

The classical double universal joint for constant velocity ratio transmission is subject to strict geometrical requirements as regards configuration, and it is generally accepted that similar constraints also prevail for longer chains of joints. This paper examines the constant velocity conditions from a necessary point of view and establishes new configuration possibilities for chains of 3 or more joints, which allow to envisage more flexible design in some applications.

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