<APPLET CODE="GSP.class"
WIDTH=300 HEIGHT=300 ALIGN=left>
<PARAM NAME=Frame VALUE=1>
<PARAM NAME=BackRed VALUE=200>
<PARAM NAME=BackGreen VALUE=255>
<PARAM NAME=BackBlue VALUE=200>
<PARAM NAME=Construction VALUE="
{Fixed points A and D, 200 apart}
{1} FixedPoint (50, 280) [black, label('A')];
{2} FixedPoint (250, 280) [black, label('D')];
{3} Segment (1, 2) [hidden];
{Defining distances 100, 250}
{4} Midpoint (3) [hidden];
{5} Segment (1, 4) [hidden]; {length 100}
{6} FixedPoint (300, 280) [hidden];
{7} Segment (1, 6) [hidden]; {length 250}
{Point B}
{8} Circle by radius (1, 7) [hidden];
{9} Point on object (8, -0.927) [label ('B')]; {arccos 3/5}
{10} Segment (1, 9) [red, thick];
{Point C}
{11} Circle by radius (2, 7) [hidden];
{12} Circle by radius (9, 5) [hidden];
{13} Intersect1 (11, 12) [black, label ('C')];
{14} Segment (2, 13) [red, thick];
{Point P}
{15} Segment (9, 13) [red, thick];
{16} Midpoint (15) [blue, label('P')];
{Horizontal path}
{17} Point (50, 80) [hidden];
{18} Point (250, 80) [hidden];
{19} Segment (17, 18) [blue];
">
</APPLET> |
This defines the two fixed pivots A and D.
We don’t specifically need this midpoint (M), but we use it to define AM which has length 100.
This is an arbitrary point distant 250 from A to define the length 250.
As indicated, this second number is arccos 3/5 expressed in radians. The angle is chosen to centre P in the initial position. Here point B is 150 right of A and AB = 250, giving cos A = 3/5. The minus gives the required direction.
Point C lies on circles centre D and B, due to the rigid links.
P is the midpoint of BC.
We just draw in the locus of P. This has no constraining effect on the movement of P. |