Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

1997 ◽  
Vol 119 (2) ◽  
pp. 284-291 ◽  
Author(s):  
S. Kota ◽  
S. Bidare
Keyword(s):  
Degrees Of Freedom ◽  
Building Blocks ◽  
Degree Of Freedom ◽  
Differential Systems ◽  
Epicyclic Gear ◽  
Wheel Drive ◽  
Differential Mechanism ◽  
Long Time ◽  
Gear Trains ◽  
Drive Systems

A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and a four output differential systems and their applications including all-wheel drive vehicles, universal robotic grippers and multi-spindle nut runners.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

1992 ◽  
Author(s):  
Sridhar Kota ◽  
Srinivas Bidare
Keyword(s):  
Degrees Of Freedom ◽  
Building Blocks ◽  
Degree Of Freedom ◽  
Differential Systems ◽  
Practical Applications ◽  
Epicyclic Gear ◽  
Differential Mechanism ◽  
Long Time ◽  
Gear Trains ◽  
Drive Systems

Abstract A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and four output differential systems and some of their practical applications.

Meshing Efficiency Analysis of Two Degree-of-Freedom Epicyclic Gear Trains

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Essam Lauibi Esmail
Keyword(s):  
Reference Frame ◽  
Power Efficiency ◽  
Power Flow ◽  
Flow Direction ◽  
Efficiency Analysis ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Two Degree Of Freedom

The concept of potential power efficiency is introduced as the efficiency of an epicyclic gear train (EGT) measured in any moving reference frame. The conventional efficiency can be computed in a carrier-moving reference frame in which the gear carrier appears relatively fixed. In principle, by attaching the reference frame to an appropriate link, torques can be calculated with respect to each input, output, or (relatively) fixed link in the EGT. Once the power flow direction is obtained from the potential power ratio, the torque ratios are obtained from the potential power efficiencies, the particular expression of the efficiency of the EGT is found in a simple manner. A systematic methodology for the efficiency analysis of one and two degree-of-freedom (DOF) EGTs is described, and 14 ready-to-use efficiency formulas are derived for 2DOF gear pair entities (GPEs). This paper includes also a discussion on the redundancy of the efficiency formulas used for 1DOF GPEs. An incomplete in the efficiency formulas in previous literature, which make them susceptible to wrong application, is brought to light.

Innovation Synthesis of Basic Configurationof Epicyclic Gear Trains with Three-Degrees of Freedom

2011 ◽  
Vol 199-200 ◽  
pp. 358-364
Author(s):  
Heng Bin Ren ◽  
Mao Lin Huang
Keyword(s):  
Degrees Of Freedom ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Practical Application ◽  
New Approach ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Train System ◽  
Three Degrees Of Freedom ◽  
Basic Configuration

Epicyclical gear trains with three-degrees of freedom have found its wide application as the development of new technique. Currently, nearly all domestic researches on epicyclical gear trains with three or more degrees of freedom are aimed at the practical application, and scare works systematically investigate basic configuration and synthesis of the train system. An innovation synthesis method is proposed based on the compound joint kinematic chain and the substitution of low pair with high pair for epicyclical gear trains with three-degrees of freedom, and the possible independent basic configurations of epicyclical gear trains with three-degrees of freedom are obtained by applying the proposed method and the utilization of the method is also discussed. The method provides not only a new approach for innovation synthesis of epicyclical gear trains but also a few basic configurations of epicyclical gear trains with three-degrees of freedom for practice design.

Generation of Epicyclic Gear Trains of One Degree of Freedom

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Y. V. D. Rao ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Hamming Matrix

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

A GEAR-SHIFTING MECHANISM WITH A ROTARY CONFIGURATION FOR APPLICATIONS IN A 16-SPEED BICYCLE TRANSMISSION HUB

2016 ◽  
Vol 40 (4) ◽  
pp. 597-606
Author(s):  
Yi-Chang Wu ◽  
Li-An Chen
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Systematic Design ◽  
Embodiment Design ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Mechanism ◽  
Gear Trains ◽  
To Come ◽  
Gear Differential

A multi-speed bicycle transmission hub includes a geared speed-changing mechanism for providing different speed ratios and a gear-shifting mechanism for controlling the gear stage. This paper focuses on the embodiment design of a mechanical gear-shifting mechanism with a rotary configuration used in a 16-speed transmission hub for bicycles. A 16-link, five-degrees of freedom (DOF) split-power epicyclic gear mechanism, which consists of a gear differential and four sets of parallel-connected basic planetary gear trains, is introduced. Based on the clutching sequence table, a systematic design process is developed to come up with the embodiment design of the gear-shifting mechanism. A feasible and compact 16-speed rear transmission hub for bicycles is presented.

Application of Matroid Method in Kinematic Analysis of Parallel Axes Epicyclic Gear Trains

2006 ◽  
Vol 128 (6) ◽  
pp. 1307-1314 ◽  
Author(s):  
Ilie Talpasanu ◽  
T. C. Yih ◽  
P. A. Simionescu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Oriented Graph ◽  
General Applicability ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Trains ◽  
Transfer Method ◽  
Cycle Matroid ◽  
Mobile Links

A novel method for kinematic analysis of parallel-axes epicyclic gear trains is presented, called the incidence and transfer method, which uses the incidence matrices associated with the edge-oriented graph associated to the mechanism and the transfer joints (teeth contact joints). Relative to such joints, a set of independent equations can be generated for calculating the angular positions, velocities, and accelerations. Complete kinematic equations are obtained in matrix form using a base of circuits from a cycle matroid. The analysis uses the relationships between the number of mobile links, number of joints, and number of circuits in the base of circuits, together with the Latin matrix (whose entries are function of the absolute values of the partial gear ratios of the transmission). Calculating the rank of the Latin matrix can identify singularities, like groups of gears that rotate as a whole. Relationships between the output and input angular velocities and accelerations are then determined in a matrix-based approach without using any derivative operations. The proposed method has general applicability and can be employed for systems with any number of gears and degrees of freedom, as illustrated by the numerical examples presented.

scholarly journals Islands with gravitating baths: towards ER = EPR

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Louise Anderson ◽  
Onkar Parrikar ◽  
Ronak M. Soni
Keyword(s):  
Black Holes ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Degree Of Freedom ◽  
Thermal Bath ◽  
Island Rule ◽  
The Third ◽  
The World ◽  
Long Time ◽  
Internal Degrees Of Freedom

Abstract We study the Page curve and the island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection with the ER=EPR proposal. We consider several models of two entangled 2d black holes in Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first, “doubled PSSY,” model is one in which the black holes have end-of-the-world (ETW) branes with a flavour degree of freedom. We study highly entangled states of this flavour degree of freedom and find an entanglement-induced Hawking-Page-like transition from a geometry with two disconnected black holes to one with a pair of black holes connected by a wormhole, thus realising the ER = EPR proposal. The second model is a dynamical one in which the ETW branes do not have internal degrees of freedom but the JT gravity is coupled to a 2d CFT, and we entangle the black holes by coupling the two CFTs at the AdS boundary and evolving for a long time. We study the entanglement entropy between the two black holes and find that the story is substantially similar to that with a non-gravitating thermal bath. In the third model, we couple the two ends of a two-sided eternal black hole and evolve for a long time. Finally, we discuss the possibility of a Hawking-Page-like transition induced by real-time evolution that realises the ER = EPR proposal in this dynamical setting.

scholarly journals An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains

1987 ◽  
Vol 109 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Characteristic Polynomial ◽  
Random Number ◽  
Degree Of Freedom ◽  
Characteristic Polynomials ◽  
Systematic Procedure ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Isomorphic Graphs ◽  
Topological Synthesis

In this paper, a random number technique for computing the value of a linkage characteristic polynomial is shown to be an effective method for identifying isomorphic graphs. The technique has been applied to the topological synthesis of one-degree-of-freedon, epicyclic gear trains with up to six links. All the permissible graphs of epicyclic gear trains were generated by a systematic procedure, and the isomorphic graphs were identified by comparing the values of their corresponding linkage characteristic polynomials. It is shown that there are 26 nonisomorphic rotation graphs and 80 displacement nonisomorphic graphs from which all the six-link, one-degree-of-freedom, epicyclic gear trains can be derived.

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