Here is linkage to simulate a real folding chair. Click right picture to see the animation. The following is a detailed construction process.
1. Start with an arbitrary point A on z-axis. Draw a circle in yz-plane centered on A through the origin O and take a movable point M on this circle.
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2. Draw a line parallel y-axis through point A.
This line intersects previous circle on D. Point E is on this line such
that
=
(1/8)
.
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3. Project point M into this line to obtain point B. Point C is on this line such that
=
(1/8)
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4. Draw a line through O and C. Rotate this
line around x-axis mapping A towards E to obtain line
.
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5. Take an arbitrary point F on.
6. Hide previous objects expect line
and
point O, A, M, F.
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7. Point G on
such
that
= 
.
Translate point M mapping A to G to obtain point H.
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8. Draw a line in yz-plane through point G
perpendicular .
Project point H into this line to obtain point I.
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9. Draw a line through F and I. Rotate this line around the line parallel x-axis and through point F 51 degrees counterclockwise to obtain line
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10. Hide previous objects expect point F and
lines
,
.
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11. Take a point J on
such
that
=
0.211
.
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12. Draw three circles in yz-plane: circle
centered
on F with radius 0.233
,
circle
centered
on J with radius 0.311
,
and
centered
on K with radius 0.133
where
point K is the intersection line
and
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13. Hide previous circles and line
.
Draw line
through
K, L and line
through
J, L.
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14. Create a convex polygon FKLJ.
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15. Point N on
such
that
=
0.335
.
Point S on
such
that
=
0.804
.
Point P, Q, and R on
such
that
=
0.889
,
=
0.511
,
and
=
0.769
.
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16. Connect segments ON, JS, and PR.¡@
17. Hide yz-plane and lines
,
,
.
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18. Take a point on x-axis such that distance between this point and O is.
Translate previous points and segments mapping O to this point.
19. Draw rectangles PP'Q'Q and JJ'S'S where J', S', P', and Q' are corresponding points of J, S, P, and Q.
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20. Add two suitable segments parallel x-axis.¡@
