Synthesis With Mixed Motion and Path Generation Position Specifications

1983 ◽  
Vol 105 (4) ◽  
pp. 617-623 ◽  
Author(s):  
J. C. Chuang ◽  
K. J. Waldron
Keyword(s):  
Path Generation ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Position Type

Methods are developed for solving kinematic synthesis problems using precision position type methods for mixtures of motion generation and path generation type position specifications. All possible combinations of specification types for three or four design positions are considered.

An Improved Harmony Search Algorithm for a Planar Parallel Robot Synthesis

2018 ◽  
Vol 35 ◽  
pp. 185-197
Author(s):  
Badreddine Aboulissane ◽  
Dikra El Haiek ◽  
Larbi El Bakkali
Keyword(s):  
Search Algorithm ◽  
Harmony Search ◽  
Parallel Robot ◽  
Harmony Search Algorithm ◽  
Path Generation ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Design Variables ◽  
Joint Coordinates ◽  
Improved Harmony Search

The objective of kinematic synthesis is to determine the mechanism dimensions such as link lengths, positions or joint coordinates, in order to approximate its output parameters such as link positions, trajectory points, and displacement angles. Kinematic synthesis is classified into three categories: function generation, path generation, and motion generation. This paper is dedicated only to path generation. As the number of trajectory points increases, analytical methods are limited to obtain precisely mechanism solutions. In that case, numerical methods are more efficient to solve such problems. Our study proposes an improved heuristic algorithm applied to four-bar mechanism path-generation. The objective of this work is to find optimum dimensions of the mechanism and minimize the error between the generated trajectory and the desired one, taking into consideration constraints such as: Grashof condition, transmission angle, and design variables constraints. Finally, our results are compared with those found by other evolutionary algorithms in the literature.

AN EXTENSION OF AN ALGORITHM FOR PLANAR FOUR-BAR PATH GENERATION WITH OPTIMIZATION

2009 ◽  
Vol 33 (3) ◽  
pp. 443-458 ◽  
Author(s):  
Yahia M. Al-Smadi ◽  
Kevin Russell ◽  
Wen-Tzong Lee ◽  
Raj S. Sodhi
Keyword(s):  
Static Loading ◽  
Mechanical Design ◽  
Search Algorithm ◽  
Point Load ◽  
Path Generation ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Transmission Angle ◽  
Transverse Deflection ◽  
Static Torque

This work is an extension of the authors’ published work on a planar four-bar motion generation search algorithm with Grashof, transmission angle and linkage perimeter conditions [1], This latest work considers planar four-bar path generation with a coupler point load, crank static torque, crank transverse deflection and follower buckling in a modified search algorithm. As demonstrated in the example, a conventional methodology used in kinematic path generation has been expanded to consider static loading, elastic deflection and buckling in path generation. These factors must be considered in mechanical design, but are not the focus in traditional kinematic synthesis.

Complete Solutions to Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy With M-Homogenization

1992 ◽  
Author(s):  
Anoop K. Dhingra ◽  
Jyun-Cheng Cheng ◽  
Dilip Kohli
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Numerical Results ◽  
Path Generation ◽  
Link Function ◽  
Homotopy Methods ◽  
Motion Generation ◽  
The Matrix ◽  
Function Generators ◽  
Complete Solutions

Abstract This paper presents complete solutions to the function, motion and path generation problems of Watt’s and Stephenson six-link, slider-crank and four-link mechanisms using homotopy methods with m-homogenization. It is shown that using the matrix method for synthesis, applying m-homogeneous group theory, and by defining compatibility equations in addition to the synthesis equations, the number of homotopy paths to be tracked can be drastically reduced. For Watt’s six-link function generators with 6 thru 11 precision positions, the number of homotopy paths to be tracked in obtaining all possible solutions range from 640 to 55,050,240. For Stephenson-II and -III mechanisms these numbers vary from 640 to 412,876,800. For 6, 7 and 8 point slider-crank path generation problems, the number of paths to be tracked are 320, 3840 and 17,920, respectively, whereas for four-link path generators with 6 thru 8 positions these numbers range from 640 to 71,680. It is also shown that for body guidance problems of slider-crank and four-link mechanisms, the number of homotopy paths to be tracked is exactly same as the maximum number of possible solutions given by the Burmester-Ball theories. Numerical results of synthesis of slider-crank path generators for 8 precision positions and six-link Watt and Stephenson-III function generators for 9 prescribed positions are also presented.

Real Continuation Method and its Application in Kinematic Synthesis

2000 ◽  
Author(s):  
Liu Anxin ◽  
Yang Tingli
Keyword(s):  
High Efficiency ◽  
Continuation Method ◽  
Linear Equations ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Real Solutions ◽  
Non Linear ◽  
Four Bar Linkage ◽  
Non Linear Equations

Abstract Real continuation method for finding real solutions to non-linear equations is proposed. Synthesis of planar four-bar linkage for path generation with nine precision points is studied using this method. The proposed method has high efficiency and can best be used for solving synthesis problems.

OPTIMIZATION OF MODIFIED WATT’S LINKAGE FOR AN APPROXIMATELY LONG STRAIGHT PATH WITHIN LIMITED DIMENSION

2016 ◽  
Vol 40 (3) ◽  
pp. 399-417
Author(s):  
Jun Wu ◽  
Shaowei Fan ◽  
Minghe Jin ◽  
Hong Liu
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Synthesis Process ◽  
Path Generation ◽  
Practical Application ◽  
Optimal Method ◽  
Kinematic Synthesis ◽  
Straight Path ◽  
Limited Dimension

This paper presents an optimal method of aiming for an approximately straight path of the Modified Watt’s Linkage (MWL) within limited dimension. A modification to the Watt’s linkage and the corresponding condition are introduced, followed by the kinematic synthesis. The path generation based on the modification considering constraints from practical application is provided. Genetic algorithm is utilized to perform the constrained optimization. The centrosymmetric property of the MWL is considered in the synthesis process. Ideal parameters of the mechanism are achieved to demonstrate the effectiveness of the proposed method.

On Adjustable Planar Four-Bar Motion Generation With Order, Branch and Circuit Defect Rectification

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Qiong Shen ◽  
Wen-Tzong Lee ◽  
Kevin Russell
Keyword(s):  
Nonlinear Equation ◽  
Objective Function ◽  
Inequality Constraints ◽  
Equation System ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Order Branch ◽  
Circuit Defects ◽  
Displacement Model ◽  
Defect Elimination

This work is an incremental extension of adjustable planar four-bar kinematic synthesis theory to consider not only synthesis, but also the elimination of the defects inherent in synthesis. A nonlinear equation system for moving pivot-adjustable planar four-bar motion generation that includes constraints for order defect, branch defect and circuit defect elimination is presented in this work. In the objective function of the equation system, the error between the prescribed and achieved precision positions is minimized. The equation system includes inequality constraints to eliminate order defects and branch defects. The equation system also includes a complete planar four-bar displacement model to eliminate circuit defects.

On a General Method of Spatial Kinematic Synthesis by Means of a Stretch-Rotation Tensor

1969 ◽  
Vol 91 (1) ◽  
pp. 115-121 ◽  
Author(s):  
G. N. Sandor ◽  
K. E. Bisshopp
Keyword(s):  
Mathematical Model ◽  
Kinematic Chain ◽  
Higher Order ◽  
Motion Generation ◽  
Rotation Tensor ◽  
Kinematic Synthesis ◽  
Rotation Operator ◽  
Key Concepts ◽  
The Mathematical Model ◽  
General Method

One of the key concepts in a general method of spatial kinematic synthesis is a stretch-rotation operator applied to members of a general spatial kinematic chain. The latter consists of one or more interconnected loops of successively ball-jointed bar-slideball members. Each member is represented by a vector free to stretch-rotate with the motion of the chain. In the mathematical model of the general chain, displacement is simulated by means of stretch-rotation tensors operating on each member vector. Appropriate mathematical constraints render the general chain and its mathematical model equivalent to a particular mechanism. With this approach and by taking derivatives, first, second, and higher-order loop equations can be developed which form the basis for a general method of spatial kinematic synthesis, applicable to path, function and motion generation (body guidance) with first, second, and higher-order as well as for combined “point-order” approximations.

Principles of a General Quaternion-Operator Method of Spatial Kinematic Synthesis

1968 ◽  
Vol 35 (1) ◽  
pp. 40-46 ◽  
Author(s):  
George N. Sandor
Keyword(s):  
Operator Method ◽  
Kinematic Chain ◽  
Point Theory ◽  
System Of Equations ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Special Cases ◽  
General Complex ◽  
Spatial Method ◽  
Space Mechanisms

The basic concepts of a general method of kinematic synthesis of space mechanisms are developed by means of vectors and quaternion operators applicable to path, function, and motion generation (body guidance) for finite and infinitesimal displacements (point, order, and combined point-order approximations). For writing the position equations, space mechanisms are represented by one or more loops of a general kinematic chain of ball-jointed bar-slideball members. Appropriate mathematical constraints on the relative freedom of these members render the general chain equivalent to the represented mechanism. The method leads to a system of equations of canonical simplicity, uniform for all tasks of finite spatial synthesis, often yielding closed-form linear solutions for small numbers of precision conditions. The same system of equations is then used to refine the solution for greater precision by numerical methods. Typical applications are indicated, some involving the use of a spatial finite circlepoint-center point theory, which includes classical planar Burmester theory as one of its special cases. An earlier general complex-number method of planar synthesis is shown to be a special case of the general spatial method introduced here.

Finding All Solutions to Approximate Synthesis of Planar Linkages for Function Generation, Rigid-Body Guidance and Path Generation

1996 ◽  
Author(s):  
An-Xin Liu ◽  
Ting-Li Yang
Keyword(s):  
Rigid Body ◽  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Optimum Solution

Abstract Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and 3 examples are given to illustrate the advantages of the proposed method.

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