Instantaneous Invariants and Curvature Analysis for Planar Mechanisms

1994 ◽  
Author(s):  
An Tzu Yang ◽  
Gordon R. Pennock ◽  
Lih-Min Hsia
Keyword(s):  
Closed Form ◽  
Analytical Procedure ◽  
Rigid Motion ◽  
Continuous Functions ◽  
Gear Train ◽  
Planar Mechanisms ◽  
Operating Cycle ◽  
Curvature Analysis ◽  
Trajectory Matching ◽  
Epicyclic Gear

Abstract This paper establishes a systematic procedure to determine the instantaneous invariants for a member in a planar mechanism and the curvature ratios of the path of a point fixed in the member. Closed-form expressions are derived for the instantaneous invariants and the curvature ratios as continuous functions of the input variable of the mechanism. The methods that are proposed in this paper can be applied to the design of planar mechanisms in general. For a given mechanism, the configuration defined by the input variable at which the member achieves the optimal approximation of a prescribed rigid motion can be determined. Alternatively, a point fixed in a member can be selected such that it will generate a trajectory matching a given curve with high precision. For purposes of illustration, the paper details the analytical procedure for a simple epicyclic gear train and a four-bar mechanism. The instantaneous invariants and the curvature ratios are generated for the complete operating cycle of each mechanism.

Instantaneous Invariants and Curvature Analysis of a Planar Four-Link Mechanism

1994 ◽  
Vol 116 (4) ◽  
pp. 1173-1176 ◽  
Author(s):  
An Tzu Yang ◽  
G. R. Pennock ◽  
Lih-Min Hsia
Keyword(s):  
Rigid Body ◽  
Fourth Order ◽  
Arbitrary Point ◽  
Canonical System ◽  
Planar Mechanisms ◽  
Operating Cycle ◽  
Curvature Analysis ◽  
Crank Angle ◽  
Moving Plane ◽  
Derivatives Of

This paper shows that the canonical system and the instantaneous invariants for a moving plane, which is connected to the fixed plane by a revolute-revolute crank, are functions of the derivatives of the crank angle. Then closed-form expressions are derived for the curvature ratios of the path generated by an arbitrary point fixed in the moving plane, in terms of the coordinates of the point and the instantaneous invariants of the plane. For illustrative purposes, numerical results are presented for the instantaneous invariants (up to the fourth-order) of the coupler of a specified crank-rocker mechanism, as a function of the input angle. In addition, the paper shows the variation in the first and second curvature ratios of an arbitrary coupler curve during the complete operating cycle of the mechanism. The authors hope that, based on the results presented here, a variety of useful tools for the kinematic design of planar mechanisms, with a rotary input, will be developed for plane rigid body guidance as well as curve generation.

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
High Velocity ◽  
Mechanical Energy ◽  
Gear Train ◽  
Recursive Method ◽  
Gear Pair ◽  
Simple Method ◽  
Epicyclic Gear ◽  
Thick Line ◽  
Gear Trains ◽  
Isomorphic Graphs

Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.

Design of an Epicyclic Transmission for Speed Control of a Turbine-Generator System

1992 ◽  
Author(s):  
Indranil Barman ◽  
Donald R. Flugrad
Keyword(s):  
Control Method ◽  
Equations Of Motion ◽  
Speed Control ◽  
Gear Train ◽  
Turbine Generator ◽  
Generator System ◽  
Epicyclic Gear ◽  
The Face ◽  
Fine Control ◽  
Parameter Values

Abstract An improved speed control method is proposed for a turbine-generator system. Whereas the present method employs a steam valve to control the flow of steam according to the desired output, the proposed system uses an epicyclic gear train to provide fine control of the speed, while coarse control is still maintained through the steam valve. The systematic design of such a gear train is the objective of this project. Two configurations are considered as suitable candidates. After the transmissions are analyzed to obtain the speed and torque relations, the dynamic equations of motion and control equations for the systems are derived for simulation purposes. The simulations are then conducted for various load cases and parameter values to determine a suitable design for application in the power industry. The final configuration allows constant generator output speeds to be reliably maintained in the face of significant load disturbances.

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.

Flow-graph techniques for epicyclic gear train analysis†

1973 ◽  
Vol 17 (2) ◽  
pp. 263-272 ◽  
Author(s):  
H. S. NAGARAJ ◽  
R. HARIHARAN
Keyword(s):  
Gear Train ◽  
Flow Graph ◽  
Epicyclic Gear

An Automated Inversion Apporach to Closed-Form Kinematic Analysis of Planar Mechanisms

1992 ◽  
Author(s):  
Arunava Biswas ◽  
Gary L. Kinzel
Keyword(s):  
Closed Form ◽  
Iterative Methods ◽  
Kinematic Analysis ◽  
Equation Approach ◽  
Planar Mechanisms ◽  
Loop Equation ◽  
Closed Form Solutions

Abstract In this paper an inversion approach is developed for the analysis of planar mechanisms using closed-form equations. The vector loop equation approach is used, and the occurrence matrices of the variables in the position equations are obtained. After the loop equations are formed, dependency checking of the unknowns is performed to determine if it is possible to solve for any two equations in two unknowns. For the cases where the closed-form solutions cannot be implemented directly, possible inversions of the mechanism are studied. If the vector loop equations for an inversion can be solved in closed-form, they are identified and solved, and the solutions are transformed back to the original linkage. The method developed in this paper eliminates the uncertainties involved, and the large number of computations required in solving the equations by iterative methods.

A step-up epicyclic gear-train and flowgraph analysis†

1973 ◽  
Vol 17 (5) ◽  
pp. 1059-1063
Author(s):  
H. S. NAGARAJ ◽  
R. HARIHARAN
Keyword(s):  
Gear Train ◽  
Epicyclic Gear

Theoretic Study of Efficiency of Two-DOFs of Epicyclic Gear Transmission via Virtual Power

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Chao Chen ◽  
Teck Teh Liang
Keyword(s):  
Design Optimization ◽  
Fundamental Form ◽  
Degrees Of Freedom ◽  
Gear Transmission ◽  
Gear Train ◽  
Mechanical Transmission ◽  
Virtual Power ◽  
Two Degrees Of Freedom ◽  
Analytical Expression ◽  
Epicyclic Gear

Epicyclic gear train is a fundamental form of mechanical transmission with broad applications. Efficiency study of these trains is critical to design, optimization, and operation. It is known that the efficiencies of these systems are highly related to the internal power flows. We apply the concept of virtual power to find analytical expression of the efficiency of a two degrees of freedom train, with associated applicable ranges. The results are verified by an example.

Cycloid Drives With Machining Tolerances

1989 ◽  
Vol 111 (3) ◽  
pp. 337-344 ◽  
Author(s):  
J. G. Blanche ◽  
D. C. H. Yang
Keyword(s):  
High Efficiency ◽  
Dynamic Instability ◽  
Torque Ripple ◽  
Gear Train ◽  
Space Applications ◽  
Input Shaft ◽  
Epicyclic Gear ◽  
Speed Reducer ◽  
Planet Gear ◽  
Gear Mechanism

The cycloidal speed reducer, or cycloid drive, is an epicyclic gear train in which the profile of the planet gear is an epitrochoid and the annular sun gear has rollers as its teeth. The cycloid drive has very high efficiency and small size, in comparison with a conventional gear mechanism, making it an attractive candidate for limited space applications. On the other hand, in this type of transmissions there exist two major drawbacks, namely, backlash and torque ripple. Backlash, the angle through which the output shaft can rotate when the input shaft is held fixed, has a degrading effect on the output accuracy. Torque ripple, the variation in mechanical advantage as the input shaft rotates, causes vibrations and could lead to dynamic instability of the machinery. If the cycloid drive were manufactured to the ideal dimensions, there would be no backlash nor torque ripple. However, in reality, there will always be some machining tolerances. In this paper an analytical model is developed which models the cycloid drive with machining tolerances. Consequently, the effect of machining tolerances on backlash and torque ripple are investigated. It is found that both the backlash and the torque ripple are inherent periodic functions of the input crank angle.

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