11/8/06

齒輪組構成之五連桿分析

下面為利用MATLAB撰寫之程式函式f5link_int(),以計算一組齒輪構成之五連桿(參閱機動學範例7.1),其齒輪2與4之直徑分別為6、7cm。其他桿之相關尺寸為r1=8cm,r5=6cm。齒輪2為驅動輪。在初始位置時ABC正好成一直線,設桿2角度之初始值為零。當桿2旋轉60度角時,其他相關之θ3、θ4、θ5值之變化可由f5link_int()程式求得,其呼叫型式為:

function [th3,th4,th5]=f5link_int(r)


其輸入項為r。其中包括五桿之長度,其中第二桿為驅動齒輪之半徑r2。

function [th3,th4,th5]=f5link_int(r1,R2,R4,r5)
% Program 7.1 solving eqs 7.11-7.17
% The 5 link system consists of 2 gears with one
% holding link(r5), except the ground(r1)
% Find the intial positions of the 5-link system
% Input:
% r1,r5: the length of ground and the 5th links.
% R2,R4: radius of the gear pair
%
% Output:
% th3,th4,th5: angles of link 3,4 & 5, degrees
% Example: [th3,th4,th5]=f5link_int(8, 3, 3.5, 6)
d2r=pi/180;
r3=R2+R4;
r34=r3+R4;
cos5=(r34*r34-r5*r5-r1*r1)/(2*r1*r5);
cos3=(r1+r5*cos5)/r34;
th50=acos(cos5);
th30=acos(cos3);
th3=th30/d2r;th4=th3;th5=th50/d2r;

執行例:

>> [th3,th4,th5]=f5link_int(8, 3, 3.5, 6)
th3 = 36.8699
th4 = 36.8699
th5 = 90

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