4. CHEBYSHEV LINKAGE – JSP
The JSP Code

The JSP applet code given below was used to produce the diagram at right.

You should be getting proficient at producing these programs by now! However, I expect you will still be getting some incomprehensible JSP alerts from time to time.

       
<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.

Exercises

1. In your program, add a ‘traced’ command in line 16. You will find that this portion of the path of P is very close to straight.

2. Compare the Chebyshev linkage with the Watt linkage. What are the similarities? What are the differences?

3. Try programming the Chebyshev linkage with different ratios of lengths for the links. Does this affect the final outcome? In what ways?