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The JSP Code
The JSP applet code given below was used to produce the diagram at right.
This applet is fairly straightforward. The image of the circle traced out by the red driver point is in fact mathematically the whole of the blue line. The reason the whole line does not appear here is a failing of the linkage method of construction.
I have chosen A and B to be 50 pixels apart, the short segments 60 pixels, and the long segments 140 pixels. The rectangle is 330 x 310 pixels.
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<APPLET codebase="jsp" CODE="GSP.class"
WIDTH=330 HEIGHT=310 ALIGN=left>
<PARAM NAME=Frame VALUE=1>
<PARAM NAME=BackRed VALUE=255>
<PARAM NAME=BackGreen VALUE=255>
<PARAM NAME=BackBlue VALUE=200>
<PARAM NAME=Construction VALUE="
{Define points and lengths etc}
{1} FixedPoint (130, 150) [label ('A')];
{2} FixedPoint (180, 150) [label ('B')];
{3} FixedPoint (270, 150) [hidden]; {C, AC = 140}
{4} Segment (1, 3) [hidden]; {length 140}
{5} Circle by radius (1,4) [red];
{6} Segment (1, 2) [hidden]; {length 60}
{7} Circle by radius (2, 6) [red];
{8} Point on object (7, 0) [label ('P')];
{9} Circle by radius (8, 6) [hidden];
{10} Intersect1 (9, 5); {R}
{11} Intersect2 (9, 5); {S}
{12} Circle by radius (10, 6) [hidden];
{13} Circle by radius (11, 6) [hidden];
{14} Intersect2 (12, 13) [blue, label ('Q')];
{Struts}
{15} Segment (1, 10) [thick, red];
{16} Segment (1, 11) [thick, red];
{17} Segment (2, 8) [thick, red];
{18} Segment (8, 10) [thick, red];
{19} Segment (8, 11) [thick, red];
{20} Segment (10, 14) [thick, red];
{21} Segment (11, 14) [thick, red];
{Locus path}
{22} FixedPoint (301, 210) [hidden];
{23} Perpendicular (4, 22) [blue];
">
</APPLET> |
Like me, you will probably adjust the window size as you go.
We define a pale yellow background.
Points A and B are the fixed pivots for the linkage.
Line {5} constructs a circle centre A and radius 140.
P will be the driving point (appears in red).
R and S are opposite vertices of the parallelogram (bottom and top).
P and Q are opposite vertices of the parallelogram (left and right). Intersect2 happens to give the right point!
This section, we draw in the struts of the linkage.
We draw in the blue locus of point Q. This in no way constrains the movement of the point. |
Exercises
1. Write a converse program in which driver point Q is constrained to lie on a line, forcing P to move around a circle..
2. In the figure, a little question makr appears in the bottom right hand corner, but no red cross. Why is this so?.
3. Can you vary the radii of the circles and the distance AB so that Q generates precisely that portion of the blue line that is showing?
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