Parent page "Musashikoganei Square Wheel"

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http://www.java.com/en/download/help/jcp_security.xml
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I apology for this inconvenience. (Java environment is foolish, I think so.)

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or,
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Apologize to this inconvenience. ---- (∵ geogebra.org is safe, and me, too.)

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Index
(1) Oval Chebyshev wheel (Cassini oval like wheel)
(1_a) Cassini 4 legs structure
(1_b) Cassini 4 legs structure (Enhanced version)
    Alias: Cassini Square wheel
(1_c) Cassini Wheel (8 legs)
(2) Chebyshev egg-crank wheel
(3) Chebyshev Crescent Moon Crank (/Peaucellier linkage leg)
(4) Chebyshev Crescent Crank Variation
(5) Circle-Ellipse hybrid crank Standard
(6) Unexpected foot trace (Good accident)
(7) Chebyshev Butterfly Crank
(8) Typical Hart's A-frame
(9) How to Square Wheel (Rhombus)
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Decomposition from 2014/05/06
Above is moved/ remained to Chebyshev_oval page. (Chebyshev_oval.html)
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(10) Centipede apparatus (Hoekens linkage)
(10-a) Centipede_A-frame (Hart's A-frame leg)
    Alias: Musashikoganei leg
(10-b) Centipede_A-frame 2nd (Hart's A-frame leg)
    Alias: Musashikoganei leg 2nd
(10-c) Centipede_bicycle
    Alias: Musashikoganei Bicycle
(10-d) Centipede_A-frame_crank +4 bars
(10-e) Leg by Hart's Inversor
(10-f) Leg by Chebyshev Linkage
(10-g) 2 bars crank amplifier
(11) 45 degree slider Amplifier
(12) Ultimate Hart's A-frame Leg
(12-a) inner additional information
(12-b) Exact straight stroke Hart's A-frame Leg
(12-c) Imai's Hart's A-frame Leg (d < d' case) --- This is great.
(12-d) Imai's Hart's A-frame Leg (d > d' case)
(12-e) Imai's Hart's A-frame 7.5 Leg (vertical leg, d < d' case)
(12-f) Imai's Hart's A-frame 5.5 Leg (vertical)
(12-g) Imai's Hart's A-frame 5.5 Leg (vertical, D < D')
 -----------------------
Decomposition from 2014/05/25
Above is moved/ remained to centipede_part1 page. (Chebyshev_centipede.html)
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(13) 5 bars Chebyshev Leg (best)
(13-a) 5 bars Chebyshev Leg (small span)
(13-b) 5 bars Chebyshev Leg (big span)
(13-c) 5 bars Chebyshev Leg (quasi-linear)
(13-d) Variety of output (big type, circle slider)
(13-e) Imai's linkage (alias, Crescent mapping leg)
(13-f) Imai's Linkage equivalent frame
(13-g) Imai's Linkage (tri-pedal) (alias: walking easel)
(13-h) Imai's linkage ( arm3, arm4 rule )
(13-i) Imai's Linkage (bi-pedal with foot)
(13-j) Imai's Watt's linkage Leg (3 bars/ Leg)
subtitle: -- Why exists Arches of the foot? --
(13-k) Imai's Watt's linkage Leg walking Toy on the slope
(13-l) Imai's Watt's linkage Vertical Leg (5 bars/ leg)
(13-m) Imai's Watt's linkage Vertical Leg (180° cycle)
(13-n) Imai's Watt's linkage Leg (180° cycle) Judge
(13-o) Imai's Watt's Linkage curve
(14) Imai's Inversor Leg (+4, +3, +2 included)
(14-a) Imai's Inversor +2 Leg (+2 bar type, +3)
(14-b) Imai's Inversor out-crank Leg (+4 bars, +5)
(14-c) Imai's hiccup sector Leg
(14-d) Hart's Inversor DEMO
(14-e) Hart's A-frame hiccup Leg sample
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Decomposition from 2014/05/25
Above is moved/ remained to centipede_part2 page. (Chebyshev_centipede_2.html)
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(15) Imai's Watt's linkage vertical Leg walking Toy on the slope
 -----------------------
Decomposition from 2014/07/02
Above is moved/ remained to centipede_part3 page. (Chebyshev_centipede_3.html)
 -----------------------

c. I got the GeoGebra fabicon.ico from Faviconer.com site. Thank you to Author (University of Salzburg).

(13) 5 bars Chebyshev Leg (best)

Now restriction: When P (target,slidable) position is in left side of D position, Q' (2nd leg) trace tells a lie. Pardon me.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Fumio Imai, 2014/04/28, Created with GeoGebra

(13-a) 5 bars Chebyshev Leg (small span)

This is the material for Understanding the mechanism of 5 bars Leg, and tuning application of its bar size estimation.

Drag the red bullet ● Crank.
Leg frame moving is as if a human walking. --- It's interesting to see.
i.e. The man who is walking on the Belt conveyor.

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Fumio Imai, 2014/04/28, Created with GeoGebra

(13-b) 5 bars Chebyshev Leg (big span)

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Fumio Imai, 2014/04/28, Created with GeoGebra

(13-c) 5 bars Chebyshev Leg (quasi-linear)

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Fumio Imai, 2014/04/30, Created with GeoGebra

(13-d) Variety of output (big type, circle slider)

Like a Klann Leg shape, but the same crank rotation direction.

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Fumio Imai, 2014/05/03, Created with GeoGebra

(13-e) Imai's linkage (alias, Crescent mapping leg)

Green curve, what is this?
, where, point N = middle of segment IJ, length of NQ = 0.5 IJ.

c. Perhaps, ideal arm4 = 7 [=Integer] (Please chck by yourself. Slide the point J (1st leg) [= this is slidable] position tuning. and set FJ = 7.00. Please compare to default FJ = 6.41 --- which curve is more straight?)
FJ=6.41 is better. 0.5(arm4 + FJ) radius draws the circle in the complele middle of crescent moon. so, arm4 < FJ is true.
----- latest information; FJ = 6.00 is better than 6.41

I think " this works is ART.", don't you think so?


c. long = 2, M = (-0.53, 9.51) case, pink trace is almost the same as the long = ∞ case (violet color trace).
i.e. long is not necessary long. short is OK.
------ why? this is able to explain theoretically.
--- See, my parent material. "(quasi) Vertical straight line slider doesn't need long long bar."

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Fumio Imai, 2014/05/04, Created with GeoGebra

(13-f) Imai's Linkage equivalent frame

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Fumio Imai, 2014/05/27, Created with GeoGebra

(13-g) Imai's linkage (tri-pedal) (alias: walking easel)

I want to locate the point C to (-1, 0) by mouse dragging. but I couldn't/ failed.
Can't set precise position. How to? GeoGebra is foolish.

Alternately, define T=0 to 2 pi (and specify slider function), and, C = (cos(T), sin(T)) , then slide T.
trace is discrete type. At last, by input box, Type "T=pi". --- if necessary please do.

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Fumio Imai, 2014/05/30, Created with GeoGebra

(13-h) Imai's linkage ( arm3, arm4 rule )

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Fumio Imai, 2014/06/11, Created with GeoGebra

(13-i) Imai's Linkage (bi-pedal with foot)

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Fumio Imai, 2014/06/12, Created with GeoGebra

(13-j) Imai's Watt's linkage Leg (3 bars/ leg)

subtitle: -- Why exists Arches of the foot? --


Number slider: leg ---- C'F' length. leg' ---- C'I length.
Point F'', tF, B▲ (circle center) is slidable.
tF is large circle tangent point. I'' is mirror point of I', tF' is it's middle point. Pink arc I'-tF-I'' is made by Circumcircular Arc through Three Points function.
this Arc radius size is calclated by rr = (I'tF)2/(2tFtF').

Now, Point A'' (straight foward stroke end crank angle point) is fixed by Object Properties function specifying " ☑ Fix Object", so if you want to move A'' , remove this specifying mark ✓.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Fumio Imai, 2014/06/16, Created with GeoGebra

(13-k) Imai's Watt's linkage Leg walking Toy on the slope

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Fumio Imai, 2014/06/16, Created with GeoGebra

(13-l) Imai's Watt's linkage Vertical Leg (5 bars/ leg)

Please check, B = (0, 1.64) [ or B(-1.64, 0) ] case ------ This is Chebyshev linkage case.
(Chebyshev linkage and Watt's linkage are the same family.)

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Fumio Imai, 2014/06/20, Created with GeoGebra

(13-m) Imai's Watt's linkage Vertical Leg (180° cycle)

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Fumio Imai, 2014/06/24, Created with GeoGebra

(13-n) Imai's Watt's linkage Leg (180 deg cycle) Judge

Please try: r=3, u=1, ε = 0.1, XC = 12.84
This shape is allowable. more symmetric form. ( Please consider the meaning of U, U' position. )

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Fumio Imai, 2014/06/25, Created with GeoGebra

(13-o) Imai's Watt's Linkage curve

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Fumio Imai, 2014/06/29, Created with GeoGebra


(14) Imai's Inversor Leg

I think + 2 bars method is so simple, so good.

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Fumio Imai, 2014/05/13, Created with GeoGebra

(14-a) Imai's Inversor +2 Leg

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Fumio Imai, 2014/05/18, Created with GeoGebra

(14-b) Imai's Inversor out-crank Leg

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Fumio Imai, 2014/05/20, Created with GeoGebra

(14-c) Imai's hiccup sector Leg

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Fumio Imai, 2014/06/02, Created with GeoGebra

(14-d) Hart's Inversor DEMO


For your reference: This information is a review.
Q: What is Hart's Inversor ? --------- A: See below my DEMO.

qq is internal division point/ external division point RATIO.
qq > 1 is OK, too. i.e. External division.

(In general, 0 < qq < 1, is well known. but qq > 1 is OK, and this is better /more useful than qq < 1 case.
The shape of qq > 1 case is near the shape of manipulator/ arm/ leg. --- is not a inner point, but end-point node. So, not crowded space. no nuisance bars.)

This DEMO was brought from below URL java applet.
http://www5d.biglobe.ne.jp/~the_imai/etymology/G_A-frame.html

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Fumio Imai, 2014/01/29, Created with GeoGebra

(14-e) Hart's A-frame hiccup leg sample

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Fumio Imai, 2014/06/07, Created with GeoGebra



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