文档介绍：Mechanism and Machine Theory 44 (2009) 1223–1239
Contents lists available at ScienceDirect
Mechanism and Machine Theory
journal homepage: ate/mechmt
On the application of the curve curvature in path synthesis
Jacek Bus´kiewicz *, Roman Starosta, Tomasz Walczak
Poznan University of Technology, Institute of Applied Mechanics, Piotrowo 3, 60-965 Poznan, Poland
article info abstract
Article history: This paper presents an analysis of the applicability of the curve curvature in optimal syn-
Received 12 April 2007 thesis of mechanisms. The concept of utilizing the normalized Fourier coefficients of the
Received in revised form 10 June 2008 curvature as a curve description is known, but so far it was not applied to curves for which
Accepted 7 August 2008
the continuity of the first or second derivatives cannot be assumed. An additional discus-
Available online 17 September 2008
sion aims at pointing out that the method can be applied in synthesis of all the varieties of
the coupler curves. Special attention is put on the curves of C0 class. The numerical exper-
iments follow the analysis of how the distribution of points on the curve affects the Fourier
Keywords:
coefficients. By means of the Fourier coefficients a distance norm between two curves is
Mechanism synthesis
Four-bar linkage synthesis introduced to measure their similarity. The effect of the curve shape on convergence of
Fourier coefficients the norm is investigated on the examples of the curves generated by four-bar linkages
Curve description using ‘‘Mathematica” software. The curve description is used to formulate a goal function
ic algorithm to synthesize the coupler curve using the ic algorithm.
Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
One of the most important problems of mechanism synthesis consists in searching the dimensions of a definite linkage, a
point of which is to trace out a curve as close as possible to the required one defined by the set of points.