Higher-Order Plane Motion Theories in Kinematic Synthesis

1967 ◽  
Vol 89 (2) ◽  
pp. 223-230 ◽  
Author(s):  
G. N. Sandor ◽  
F. Freudenstein
Keyword(s):  
Plane Motion ◽  
Higher Order ◽  
Conic Section ◽  
Path Generation ◽  
Kinematic Synthesis

Algebraic multiple-position theories in kinematic synthesis are classified in a manner which also suggests various extensions of classical circular theory. In the case of infinitesimally separated positions, parabolic, elliptic, hyperbolic, and general conic-section theories are developed. The results, which are generally applicable, are illustrated with reference to the synthesis of cycloidal motions involving higher-order path generation.

Kinematic Synthesis of Adjustable Mechanisms—Part 2: Path Generation

1973 ◽  
Vol 95 (2) ◽  
pp. 423-429 ◽  
Author(s):  
Joseph F. McGovern ◽  
George N. Sandor
Keyword(s):  
Closed Form ◽  
Higher Order ◽  
Complex Numbers ◽  
Path Generation ◽  
Function Generator ◽  
Kinematic Synthesis ◽  
Closed Form Solutions ◽  
Straight Line ◽  
Adjustable Mechanisms

A method utilizing complex numbers similar to that used in Part 1 for adjustable function generator synthesis is applied to the synthesis of adjustable path generators. Finitely separated path points with prescribed timing as well as higher order approximations (infinitesimally separated path points) are treated, by way of analytical and closed form solutions. Adjustment of the path generator mechanism is accomplished by moving a fixed pivot. Mechanisms adjustable for different approximate straight line motions, for various path curvatures, and path tangents as well as several arbitrary paths can be synthesized. Four-bar and geared five-bar mechanisms are considered. Examples are included describing synthesized mechanisms.

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.

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 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.

Position Analysis and Higher-Order Synthesis of the Swinging-Block Mechanism

1996 ◽  
Author(s):  
Augusto Di Benedetto ◽  
Ettore Pennestrì
Keyword(s):  
Graphical Analysis ◽  
Higher Order ◽  
Kinematic Synthesis ◽  
Position Analysis ◽  
Ideal Curve ◽  
Rigid Motions ◽  
Continuous Curves ◽  
Block Mechanism ◽  
The Ideal

Abstract Algorithms for graphical analysis and kinematic synthesis of the path generator swinging-block mechanism are proposed in this paper. In particular, through a blending of optimization procedures and higher-curvature properties of infinitesimal rigid motions, it is shown how such a mechanism may approximate symmetric continuous curves with up to two sets of four infinitesimally separated precision points. Thus the generated path has eight precision points in common with the ideal curve.

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.

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.

scholarly journals Kinematic Synthesis Using Reinforcement Learning

2018 ◽  
Author(s):  
Kaz Vermeer ◽  
Reinier Kuppens ◽  
Justus Herder
Keyword(s):  
Reinforcement Learning ◽  
Path Generation ◽  
Two Dimensional ◽  
Kinematic Synthesis ◽  
Prior Art ◽  
Straight Line ◽  
Feature Based ◽  
Kinematic Mechanisms ◽  
Straight Line Mechanism ◽  
Kinematic Simulations

The presented research demonstrates the synthesis of two-dimensional kinematic mechanisms using feature-based reinforcement learning. As a running example the classic challenge of designing a straight-line mechanism is adopted: a mechanism capable of tracing a straight line as part of its trajectory. This paper presents a basic framework, consisting of elements such as mechanism representations, kinematic simulations and learning algorithms, as well as some of the resulting mechanisms and a comparison to prior art. Series of successful mechanisms have been synthesized for path generation of a straight line and figure-eight.

Higher Order, Planar Tangent-Line Envelope Curvature Theory

1979 ◽  
Vol 101 (4) ◽  
pp. 563-568 ◽  
Author(s):  
A. H. Soni ◽  
M. N. Siddhanty ◽  
K. L. Ting
Keyword(s):  
Fourth Order ◽  
Higher Order ◽  
Tangent Line ◽  
Path Generation ◽  
Tangency Point ◽  
Characteristic Numbers ◽  
New Concepts ◽  
Synthesis Of Mechanisms ◽  
Curvature Theory ◽  
Mathematical Relationships

Following the analogy of higher order point-path generation, new concepts for tangent-line higher order envelope curvature theory are introduced. Mathematical relationships are derived to define, using the instantaneous invariants and the stretch rotation concepts, the characteristic numbers λ1 and λ2 for third and fourth-order contacts at the tangency point of a tangent-line generating an envelope. The newly developed tangent-line higher order envelope curvature theory is applied to demonstrate its application in synthesis of mechanisms. Examples involving circular, elliptic and involute are generation using a mechanism are presented.

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