Optimization of Crank-and-Rocker Linkages with Size and Transmission Constraints

1979 ◽  
Vol 101 (1) ◽  
pp. 51-57 ◽  
Author(s):  
F. Freudenstein ◽  
Meng Sang Chew
Keyword(s):  
Logical Analysis ◽  
Direct Solution ◽  
Angle Variation ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Transmission Constraints

An algebraic procedure suitable for pocket calculators is derived for the determination of the proportions of a plane crank-and-rocker linkage in which the ratio of largest to smallest link and the transmission-angle variation are prescribed. A logical analysis of the relative lengths of the links leads to a direct solution without algorithms or iteration. The results are illustrated with tables and numerical examples.

A General Theory for Synthesizing Crank-Type Four-Bar Function Generators With Transmission Angle Control

1978 ◽  
Vol 45 (2) ◽  
pp. 415-421 ◽  
Author(s):  
Krishna C. Gupta
Keyword(s):  
General Theory ◽  
Least Square ◽  
Angle Variation ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Function Generators

In this paper, the author proposes a general theory for synthesizing crank-type (i.e., crank-rocker and double-crank) four-bar function generators in which the transmission angle variation over a full crank revolution is in a specified range. Precision point as well as least-square designs have been considered in the paper. Applications of the theory are illustrated by means of numerical examples.

Performance Criteria for High-Speed Crank-and-Rocker Linkages—Part II: Spherical Crank-and-Rocker Linkages

1979 ◽  
Vol 101 (1) ◽  
pp. 26-31 ◽  
Author(s):  
H. Funabashi ◽  
F. Freudenstein
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Performance Criteria ◽  
Link Length ◽  
Angle Variation ◽  
Numerical Examples ◽  
Transmission Angle ◽  
The Dead ◽  
Sine Functions

In Part I proportions were derived for high-speed plane crank-and-rocker mechanisms. In this part, the corresponding developments are given for spherical crank-and-rocker mechanisms. The ratios of the sine functions of the transmission angles and of the rocker accelerations—both at the dead-center positions—remain the static and dynamic performance criteria of the linkage. The results are illustrated by numerical examples, which show the influence of these ratios on the transmission-angle variation, rocker acceleration and the ratio of minimum to maximum link length.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

Determination of Singularity-Free Zones in the Workspace of Planar 3-P̱RR Parallel Mechanisms

2006 ◽  
Vol 129 (6) ◽  
pp. 649-652 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Mathematical Derivation

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P̱RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.

Mathematical Solution for the Determination of Optimal Warehouse Location and Optimal Distribution Route

2005 ◽  
Author(s):  
Jagannadha Rao Naraparaju ◽  
Raghunandan A. Karamcheti ◽  
Z. Y. Wang
Keyword(s):  
Mathematical Models ◽  
Optimal Location ◽  
Optimal Routing ◽  
Practical Case ◽  
Transport Costs ◽  
Numerical Examples ◽  
Warehouse Location ◽  
Transportation Distance

In this paper, a procedure to determine the optimal location of a distribution warehouse, from which products are sent out to a group of companies has been studied. The goal was to minimize annual transportation distance between the warehouse and the customers. Fundamentals of mathematics have been used to formulate a virtual map showing the location of the present customers. Mathematical models and equations were developed making certain assumptions and an optimal location for the warehouse has been determined. Various factors that are involved in relocating the warehouse have been considered. Also a solution is given for the optimal location of a satellite or an auxiliary warehouse in addition to the existing one. A case study has been conducted on the model with the help of various numerical examples. Based on the optimal location of the relocated warehouse and the satellite warehouse obtained, the reductions in the transport costs were estimated. Once the optimal warehouse location has been found out, the next step was to find out an optimal route (least travel distance) for a practical case in which several companies have to be supplied with necessary products from one warehouse in a single trip. For this purpose, mathematical models were created and optimal routing algorithms were developed. Case studies have been conducted with the help of numerical examples. High amounts of savings in terms of travel distances, costs and time could be observed by the implementation of these algorithms.

INVERSE ACOUSTIC SCATTERING PROBLEMS IN OCEAN ENVIRONMENTS

1999 ◽  
Vol 07 (02) ◽  
pp. 111-132 ◽  
Author(s):  
YONGZHI XU
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Stratified Medium ◽  
Computational Results ◽  
Scattering Problems ◽  
Numerical Examples ◽  
Layered Waveguide ◽  
Shape Determination

This paper presents theoretical and computational results from our research on inverse scattering problems for acoustic waves in ocean environments. In particular, we discuss the determination of a three-dimensional (3-D) distributed inhomogeneity in a two-layered waveguide from scattered sound and the shape determination of an object in a stratified medium. Numerical examples are presented.

Design of Four-Bar Function Generators With Mini-Max Transmission Angle

1977 ◽  
Vol 99 (2) ◽  
pp. 360-365 ◽  
Author(s):  
K. C. Gupta
Keyword(s):  
Extreme Values ◽  
New Method ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Function Generators ◽  
Synthesis Procedure

A new method of designing four-bar function generators with optimum transmission angle is presented. Transmission angles are considered optimum, in a mini-max sense, when their extreme values deviate equally from 90 deg. Numerical examples are given to illustrate the synthesis procedure.

scholarly journals On the Numerical Determination of Optimal Textures of Aluminium

1994 ◽  
Vol 22 (3) ◽  
pp. 177-186 ◽  
Author(s):  
P. Burgholzer ◽  
O. Scherzer
Keyword(s):  
Mathematical Model ◽  
Nonlinear Optimization ◽  
Deep Drawing ◽  
Optimization Problem ◽  
Numerical Determination ◽  
Nonlinear Optimization Problem ◽  
Numerical Examples ◽  
Mathematical Algorithm

In this paper a mathematical algorithm is studied to improve the deep-drawing quality of an aluminium sheet. The deep-drawing quality is usually expressed in terms of the normal anisotropie. In our mathematical model we use Taylor theory and ideal orientations to reformulate this problem as a nonlinear optimization problem for the normal anisotropie. Some numerical examples are presented.

scholarly journals Determination of Eccentric Anomaly for Kepler’s Satellite Orbit Using Perturbation-Based Seeded Secant Iteration Scheme

2021 ◽  
Vol 4 (1) ◽  
pp. 21-27
Author(s):  
Dike H.U. ◽  
Isaac A.E.
Keyword(s):  
Satellite Orbit ◽  
Iteration Scheme ◽  
Good Choice ◽  
Iteration Algorithm ◽  
Error Performance ◽  
Initial Value ◽  
Numerical Examples ◽  
Eccentric Anomaly

In this paper, the determination of eccentric anomaly (E) for Kepler’s satellite orbit using Perturbation-Based Seeded Secant (PBSS) iteration algorithm is presented. The solution is meant for Kepler’s orbit with the value of eccentricity (e) in the range 0 ≤ e ≤ 1. Such orbits are either circular or elliptical. The demonstration of the applicability of the PBSS iteration is presented using sample numerical examples with different values of mean anomaly (M) and eccentricity (e). The summary of the results of E for M = 30° and e in the range 0.001 ≤ e ≤1 showed that the convergence cycle (n) increases as e increases. Particularly, n increased from 2 at e = 0.01 to n = 8 at e =1. The implication is that it takes more iterations to arrive at the value of E with the desired accuracy or error performance (which in this case is set to 10^(-12)). Another implication is that a good choice of the initial value of E is essential especially as the value of e increases. As such, effort should be made to develop a means of estimating the initial value of E which will reduce the convergence cycle for higher values of e.

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