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.

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.

Optimal Synthesis of Function Generators Without the Branch Defect

1984 ◽  
Vol 106 (3) ◽  
pp. 348-354 ◽  
Author(s):  
S. O. Tinubu ◽  
K. C. Gupta
Keyword(s):  
Optimal Synthesis ◽  
New Method ◽  
Numerical Examples ◽  
Design Specifications ◽  
Unlimited Number ◽  
Structural Error ◽  
Function Generators

A new method is proposed for the optimum (mini-max structural error) synthesis of function-generating mechanisms with unlimited number of design specifications, and which are free from the branch defect. This method does not require the use of explicit branching constraints. It is developed and illustrated with numerical examples for the planar four-bar and the spatial R-S-S-R mechanisms.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

Five Position Synthesis of a Slider-Crank Function Generator

2011 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Full Range ◽  
Linear Actuator ◽  
Tolerance Zone ◽  
Function Generator ◽  
Front End ◽  
Input And Output ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Branching Solutions

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Probability Distribution ◽  
Evidence Theory ◽  
Mass Function ◽  
New Method ◽  
Weighted Averaging ◽  
Minimum Entropy ◽  
Transform Method ◽  
Numerical Examples ◽  
Ordered Weighted Averaging ◽  
Open Issue

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.

scholarly journals A Two-Step Newton-Type Method for Solving System of Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lei Shi ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan
Keyword(s):  
Newton Method ◽  
New Method ◽  
Generalized Newton Method ◽  
Absolute Value Equations ◽  
Step Method ◽  
Type Method ◽  
Numerical Examples ◽  
Absolute Value ◽  
Generalized Newton

In this paper, we suggest a Newton-type method for solving the system of absolute value equations. This new method is a two-step method with the generalized Newton method as predictor. Convergence of the proposed method is proved under some suitable conditions. At the end, we take several numerical examples to show that the new method is very effective.

Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues

1995 ◽  
Vol 117 (1) ◽  
pp. 207-212 ◽  
Author(s):  
Y.-Q. Zhang ◽  
W.-L. Wang
Keyword(s):  
Recent Work ◽  
New Method ◽  
First Eigenvalue ◽  
Numerical Examples ◽  
Repeated Eigenvalues ◽  
Generalized Eigenproblem ◽  
Eigenvalue Derivatives ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector ◽  
Derivatives Of

A new method is presented for computation of eigenvalue and eigenvector derivatives associated with repeated eigenvalues of the generalized nondefective eigenproblem. This approach is an extension of recent work by Daily and by Juang et al. and is applicable to symmetric or nonsymmetric systems. The extended phases read as follows. The differentiable eigenvectors and their derivatives associated with repeated eigenvalues are determined for a generalized eigenproblem, requiring the knowledge of only those eigenvectors to be differentiated. Moreover, formulations for computing eigenvector derivatives have been presented covering the case where multigroups of repeated first eigenvalue derivatives occur. Numerical examples are given to demonstrate the effectiveness of the proposed method.

A Synthesis Procedure for Design of 3-R Planar Robotic Workcells in Which Large Rotations Are Required at the Workpiece

1992 ◽  
Vol 114 (4) ◽  
pp. 547-558 ◽  
Author(s):  
J. K. Davidson
Keyword(s):  
Motion Planning ◽  
Computer Science ◽  
New Method ◽  
Motion Trajectory ◽  
End Effector ◽  
Radial Location ◽  
Full Turn ◽  
Large Rotations ◽  
Synthesis Procedure ◽  
Planar Robots

A new method is developed for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar 3-R robots that can provide dexterous workspace. The method is an adaptation of traditional techniques of linkage synthesis, and it is particularly well-suited to applications in which the motion-trajectory requires large rotations of the end-effector. It is determined that, when the trajectory requires that the end-effector rotate a full turn at just two locations and when the critical joint in the robot is rotatable by one turn, then the radial location of the workpiece is fixed in the workcell but its angular location is not fixed. When the mounting-angle of the tool is also a variable, the method accommodates trajectories in which the tool must rotate a full turn at three locations on the workpiece. The method can be applied not only to planar robots with three hinge-joints, but also to spatial robots, each with a planar 3-R module, when the principal attitudinal excursions of the trajectory are all about a set of parallel axes. Variables are identified, for both the motion-trajectory and the workpiece itself, which strongly affect the design of the workcell and the time for it to complete a motion-trajectory. Example problems illustrate the method. The new method is suggested as an alternative to the existing methods of computer science for motion-planning.

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