Abstract
This note describes a procedure for plane higher-curvature path analysis and synthesis. All coefficients have been written in terms of elementary instantaneous invariants. This facilitates the numerical computation of Generalized Burmester Points for a moving link of a planar mechanism in a non-symmetric position. FORTRAN subroutines have been written and a numerical example is provided.
Sommario
Si descrive una procedura di analisi e sintesi per meccanismi piani generatori di traiettoria con approssimazione del quarto ordine. Nella formulazione adottata, l'impiego degli invarianti istantanei elementari consente di valutare analiticamente i termini delle equazioni per la ricerca dei punti generalizzati di Burmester. Sono state implementate subroutines in linguaggio FORTRAN ed è stato sviluppato un esempio numerico.
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Abbreviations
- P o :
-
velocity pole
- δ :
-
inflection circle diameter
- φ :
-
angle of rotation of the moving body
- r f ,r m :
-
radii of curvature of the fixed and moving polodes, respectively
- dl :
-
infinitesimal arc length measured on the polode
- a,b :
-
coordinates ofP o , in the canonical reference system1
- a i ,b i :
-
i-th derivatives ofa andb, respectively, computed at the initial position (i.e. φ=0). These are the elementary instantaneous invariants
- h,ψ*:
-
polar coordinates of the moving point in the canonical reference system (0 ≦ψ ≦π)
- ϱ :
-
radius of curvature of the point-path trajectory
- ϱ E :
-
radius of curvature of the evolute of the point-path trajectory
- ϱ /(2) E :
-
radius of curvature of the evolute of the evolute of the point-path trajectory
References
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A canonical reference system is a rectangular right-handed cartesian system having they-axis directed toward inflexion pole, origin in the velocity pole.
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Pennestrì, E., Belfiore, N.P. On the numerical computation of Generalized Burmester Points. Meccanica 30, 147–153 (1995). https://doi.org/10.1007/BF00990453
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DOI: https://doi.org/10.1007/BF00990453