(rt , ρt)
P = r0(P)
rt(P)
r1(P)
T
wt
(f, λ )
w1 = f(T)
f(P) = S
(f0r1-t , ρ1-t)
Image by MIT OpenCourseWare.
1
h
c
a
b
W/2
W
l
2
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/PaperBag_OSME2006/.
Watt 1764
Peaucellier 1864
These images are in the public domain, and are available
at Project Gutenberg.
Source: Kempe, A. B. How to Draw a Straight Line.
MacMillan and Co., 1877.
Co.
3
Gutenberg edition produced by
Joshua Hutchinson, David Wilson, &
Online Distributed Proofreading Team
Created from Cinderella applet by Erik Demaine:
http://courses.csail.mit.edu/6.849/fall10/lectures/L08_applets/L08_square1.html.
4
Created from Cinderella applet by Erik Demaine:
http://courses.csail.mit.edu/6.849/fall10/lectures/L08_applets/L08_rhombus.html.
5
This image is in the public domain, and is available through Oxford Journals.
Source: Kempe, A. B. On a General Method of describing Plane Curves of
the nth degree by Linkwork, 1876.
6
Maple worksheet by Erik Demaine:
http://courses.csail.mit.edu/6.849/fall10/lectures/L08_applets/L08_trig.mws.
Created from Cinderella applet by Erik Demaine: http://courses.csail.mit.edu/
6.849/fall10/lectures/L08_applets/L08_Contraparallelogram.html.
7
This image is in the public domain, and is available through Oxford Journals.
Source: Kempe, A. B. On a General Method of describing Plane Curves of
the nth degree by Linkwork, 1876.
Created from Cinderella applet by Erik Demaine: http://courses.csail.mit.
edu/6.849/fall10/lectures/L08_applets/L08_Contraparallelogram.html.
This image is in the public domain, and is available through Oxford Journals.
Source: Kempe, A. B. On a General Method of describing Plane Curves of
8 the nth degree by Linkwork, 1876.
Created from Cinderella applet by Erik Demaine: http://courses.csail.
mit.edu/6.849/fall10/lectures/L08_applets/L08_kempeadditor.html.
.
9
This image is in the public domain, and is available through Oxford Journals.
Source: Kempe, A. B. On a General Method of describing Plane Curves of
the nth degree by Linkwork, 1876.
p
b
β
a
TRANSLATOR
α
α
0
TRANSLATOR
MULTIPLICATOR: X2
ADDITOR
β
PEAUCELLIER LINKAGE
2α
SCALE: 3a2b
2α+β
PROJECT
0
p’
3a2b cos(2α+β)
-c
Image by MIT OpenCourseWare.
10
(A)
B
A
C
x
α
D
E
α
y
(B)
(C)
A
B
A
B
C
E
D
D
E C
Image by MIT OpenCourseWare.
11
d
y
(A)
c
(B)
(C)
a2+c2
c
a+b
a
a
x
a
b
b
d
q
s
p
r
s
c
r
a
c
x
q
p
b
x
(A)
12
b
b
d
a
b2+c2
(B)
Images by MIT OpenCourseWare.
n
(A)
n
(B)
(C)
(D)
13
Image by MIT OpenCourseWare.
MIT OpenCourseWare
http://ocw.mit.edu
6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Fall 2012
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