A Modular Method for Mechanical Error Analysis of Planar Linkages Composed of Class II Assur Group Kinematic Chains

2021 ◽  
pp. 1-27
Author(s):  
Kuan-Lun Hsu ◽  
Jia-Yu Chung
Keyword(s):  
Error Analysis ◽  
Class Ii ◽  
Modular Approach ◽  
Numerical Examples ◽  
Kinematic Chains ◽  
Modular Method ◽  
Assur Group ◽  
Planar Linkages

Abstract This paper presents a modular method for the mechanical error analysis of complex planar linkages. The topology of the linkage under investigation is decomposed into several class II Assur group kinematic chains (AGKCs) combined in a given sequence. Therefore, the mechanical error of the whole linkage can be analyzed by investigating the error propagations of adopted AGKCs in successive order. Because class II AGKCs are first served as modules, the mechanical error equations of these AGKCs in terms of each error in link lengths and joint variables can be pre-formulated and embedded in form of subroutines in any programmable language. Once the AGKCs constituting the linkage topology is identified, the corresponding subroutines are introduced to compute the error propagations in the linkage. Therefore, the presented modular approach can facilitate the analysis by concentrating on the topology decomposition instead of the algebraic derivation. Numerical examples are provided to illustrate the advantage and flexibility of the modular approach.

A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages: Part I — Modular Structural Analysis and Modular Kinemaic Analysis

1998 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao ◽  
Ming Zhang
Keyword(s):  
Structural Analysis ◽  
Comparative Study ◽  
Type Synthesis ◽  
Dynamical Equations ◽  
Kinematic Synthesis ◽  
Automated Generation ◽  
Kinematic Chains ◽  
Analysis And Synthesis ◽  
Modular Method ◽  
Planar Linkages

Abstract This paper presents a systematical comparative study of various modular methods based on the different module types: basic kinematic chains (BKCs), single opened chains (SOCs), loops (or a tree and co-tree), links-joints, etc. for analysis and synthesis of structure, kinematics and dynamics of planar linkages. The basic idea is that any linkage can be divided into (or built up by) some modular components in sequence, and based on the component constraints and network entirty constraints of the linkage, the unified modular approaches have been used for analysis and synthesis. In the systematical comparative study, the main issues of a modular method have been discussed, such as: the topological characteristics revealed via different module types; the dimension of a set of kinematic equations; the automated generation and solution of kinematic equations; the dimension and automated generation of dynamical equations, and computation complexity for generating and solving dynamical equation; the automated generation of structural analysis and type synthesis; the generation of kinematic synthesis equations etc.. This paper gives a summary of the use of modular techniques for analyzing and synthesizing planar linkages in the recently thirty years. This comparative study includes two parts: part I — modular structural analysis and modular kinematic analysis; part II — modular dynamics analysis, modular structural synthesis and modular kinematic synthesis. This paper is the first part.

The SOCs Modular Method for Kinematic Analysis of Complicated Parallel Manipulators

2011 ◽  
Vol 52-54 ◽  
pp. 834-841
Author(s):  
Zhi Xin Shi ◽  
Mei Yan Ye ◽  
Yu Feng Luo ◽  
Ting Li Yang
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulators ◽  
Initial Guess ◽  
Modular Approach ◽  
Compatibility Conditions ◽  
Kinematic Chains ◽  
Procedural Approach ◽  
Modular Method ◽  
Parallel Kinematic

This paper presents a simple and systematic modular approach for kinematic analysis of complicated Parallel Kinematic Manipulators (in short, PKMs) which coupled degrees are more than 2. (1) Single open chains (in short, SOCs) may be regarded as the basic modules of a PKM. Any PKM can always be decomposed automatically into a set of ordered SOCs, and these SOCs can also be used to recognize the basic kinematic chains contained in it. (2) The kinematic analysis algorithms and the compatibility conditions of the SOC modules are offered. (3) Directly applying the above SOC kinematic modules, the kinematic equations of a PKM can be automatically established. (4) In order to solve kinematic equations of complicated parallel manipulators which coupled degrees are more than 2, a new searching algorithm which requires no initial guess has been presented. The procedural approach is demonstrated in parallel manipulators.

scholarly journals Extension of the Chebyshev Method of Quassi-Linear Parabolic P.D.E.S With Mixed Boundary Conditions

2009 ◽  
Vol 6 (3) ◽  
pp. 603-611
Author(s):  
Baghdad Science Journal
Keyword(s):  
Error Analysis ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Linear Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Numerical Examples ◽  
Chebyshev Method

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

A Dyad Search Algorithm for Solving Planar Linkages Using the Dyad Method

1992 ◽  
Author(s):  
Lofti Romdhane
Keyword(s):  
Search Algorithm ◽  
Class Ii ◽  
Graph Representation ◽  
Step Size ◽  
Lower Pair ◽  
Fast Solution ◽  
Complete Automation ◽  
Newton Raphson ◽  
Dyad Analysis ◽  
Planar Linkages

Abstract Based on graph representation of planar linkages, a new algorithm was developed to identify the different dyads of a mechanism. A dyad or class II group, is composed of two binary links connected by either a revolute (1) or a slider (0) pair with provision for attachment to other links by lower pair connectors located at the end of each link. There are five types of dyads: the D111, D101, D011, D001, and D010. The dyad analysis of a mechanism is predicated on the ability to construct the system from one or more of the five binary structure groups or class II groups. If the mechanism is complicated and several dyads are involved, the task of identifying these dyads by inspection could be difficult and time consuming for the user. This algorithm allows a complete automation of this task. This algorithm is based on the Dijkstra’s algorithm, for finding the shortest path in a graph, and it is used to develop a computer program, called KAMEL: Kinematic Analysis of MEchanical Linkages, and implemented on an IBM-PC PS/2 model 80. When compared to algorithmic methods, like the Newton-Raphson, the dyad method proved to be a very efficient one and requires as little as one tenth of the time needed by the method using Newton-Raphson algorithm. Moreover, the dyad method yields the exact solution of the position analysis and no initial estimates are needed to start the analysis. This method is also insensitive to the value of the step-size crank rotation, therefore, allowing a very accurate and fast solution of the mechanism at any position of the input link.

Dynamic analysis of planar elastic mechanisms using the dyad method

2003 ◽  
Vol 217 (1) ◽  
pp. 1-14 ◽  
Author(s):  
L Romdhane ◽  
H Dhuibi ◽  
H Bel Hadj Salah
Keyword(s):  
Class Ii ◽  
Graph Representation ◽  
Elastic Mechanism ◽  
Complete Automation ◽  
Newton Raphson ◽  
Set Up ◽  
Dyad Analysis ◽  
Planar Linkages ◽  
Raphson Method ◽  
Good Agreement

Based on graph representation of planar linkages, a new algorithm has been developed to identify the different dyads of a mechanism. A dyad, or class II group, is composed of two binary links connected by either a revolute (1) or a slider (0) pair, with provision for attachment of other links by lower pair connectors located at the end of each link. There are five types of dyad: D111, D101, D011, D001 and D010. The dyad analysis of a mechanism is predicated on the ability to construct the system from one or more of the five binary structure groups or class II groups. If the mechanism is complicated and several dyads are involved, the task of identifying these dyads, by inspection, can be difficult and time consuming for the user. This algorithm allows complete automation of this task. It is based on Dijkstra's algorithm for finding the shortest path in a graph. When compared with algorithmic methods, such as the Newton-Raphson method, the dyad method proved to be a very efficient one and requires as little as one-tenth of the time needed by the method using the Newton-Raphson algorithm. The second part of this work presents an extension of the dyad method to non-rigid or elastic mechanisms. Here also, this method is predicated on the ability to subdivide the elastic mechanism into elastic dyads. The solution for each type of elastic dyad is derived and can be applied to each dyad in the mechanism. Therefore, a solution of the complete elastic mechanism is possible when the mechanism is made of dyads only. This method makes a powerful and simple tool for analysing complex elastic mechanisms. Moreover, the complexity of the model does not increase as the mechanism becomes more complex. The D111 dyad is taken as an example to demonstrate this method. A finite element (FE) analysis was made for this type of dyad, and an experimental set-up was built to validate the analysis. The dyad-FE results were in good agreement with the experimental ones.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

MeKin2D: Suite for Planar Mechanism Kinematics

2016 ◽  
Author(s):  
P. A. Simionescu
Keyword(s):  
Modular Approach ◽  
Kinematic Simulation ◽  
Planar Mechanism ◽  
Involute Gear ◽  
Planar Linkages

MeKin2D is a collection of subroutines for kinematic simulation of planar linkages using a modular approach, for synthesis and analysis of disk-cam mechanisms with various types of followers, and for involute gear generation. The original set of subroutines accompanies as supplementary materials a book by this same author released in 2014. These, as well as other subroutines added since the book has been released are presented in the paper, together with examples accompanied by animations.

Kinematic Synthesis of Minimally Actuated Multi-Loop Planar Linkages With Second Order Motion Constraints for Object Grasping

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Nina Robson
Keyword(s):  
Second Order ◽  
Human Robot Interaction ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Open Problems ◽  
Kinematic Synthesis ◽  
Human Environment ◽  
Kinematic Chains ◽  
Curvature Effects ◽  
Planar Linkages

In this paper, we consider the dimensional synthesis of one degree-of-freedom multi-loop planar linkages such that they do not violate normal direction and second order curvature constraints imposed by contact with objects. Our goal is in developing minimally actuated multi-loop mechanical devices for human-robot interaction, that is, devices whose tasks will happen in a human environment. Currently no systematic method exists for the kinematic synthesis of robotic fingers that incorporate multi-loop kinematic structure with second order task constraints, related to curvature. We show how to use these contact and curvature effects to formulate the synthesis equations for the design of a planar one-degree-of-freedom six-bar linkage. An example for the design of a finger that maintains a specified contact with an object, for an anthropomorphic task, is presented at the end of the paper. It is important to note, that the theoretical foundation presented in this paper, assists in solving some of the open problems of this field, providing preliminary results on the synthesis of kinematic chains with multi-loop topology and the use of novel task specifications that incorporate curvature constraints with future applications in grasping and object manipulation.

A Modular Method for Manufacturing Error Analysis of Linkages and Manipulators

2017 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu ◽  
Long-Iong Wu ◽  
Jun Wang
Keyword(s):  
Error Analysis ◽  
Inverse Analysis ◽  
Closed Loop ◽  
Tolerance Allocation ◽  
Error Assessment ◽  
Manufacturing Error ◽  
Design And Manufacturing ◽  
Performance Error ◽  
Modular Method ◽  
And Performance

This paper presents a simple and effective methodology to address the issues on the manufacturing error analysis and the tolerance design of linkages and manipulators. It assesses the effect of the dimension tolerances to the performance error and inversely determines the required dimensional tolerances for a prescribed performance tolerance. The methodology is adaptable to assess the effect of an individual tolerance as well as any combination of tolerances. Instead of using complex closed loop equations to describe the linkage geometry, the methodology is focused on using linkage topology. Complex linkages are broken down to basic RR, PR, and RP units. The error and tolerance computation of complex linkages are reduced to repeatedly or alternatively using forward and inverse analysis of basic RR, PR, and RP units. The methodology is exemplified by simple and complex linkages. For design and manufacturing engineers, the proposed method is most useful for quick tolerance allocation and performance error assessment.

scholarly journals Solving Nonsmooth Equations Using Derivative-Free Methods

2012 ◽  
Vol 3 ◽  
pp. 37-45
Author(s):  
M.S.M. Bahgat ◽  
M.A. Hafiz
Keyword(s):  
Error Analysis ◽  
Nonlinear Equations ◽  
Divided Differences ◽  
Nonsmooth Equations ◽  
Linear Combinations ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
The Given

In this paper, a family of derivative-free methods of cubic convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442. The convergence and error analysis are given. Also, numerical examples are used to show the performance of the presented methods and to compare with other derivative-free methods. And, were applied these methods on smooth and nonsmooth equations.

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