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(10) CentipedeWalking toy by Hoekens linkage.I'd like to make a high-speed bicycle from this apparatus (really). Is it possible? cf. YouTube: Walking Table --- It looks like heavy, why?, Stopohod Chebyshev Tip: For the Walking Table or the Cart (i.e. Pushing or pulling man-power cart), I'd like to introduce the slidable parallelogram frame style. (This is Hart's A-frame application. ---- Large length of stride and smooth non-heavy moving can be realized.) ----- I think "Chebyshev/ Hoekens linkage needs bigger horizontal moving power than Hart's A-frame mechanizm". (Chebyshev/ Hoekens linkage is fitted for motor driven apparatus, it's unfitted for non-motor style cart.) c. I don't know which is better Hart's A-frame or Expander-frame. c. Variable height stand (on return --- thin) ※ -- this device can be realized by CAM (2 values device. i.e. It becomes height 1 at right edge, and, becomes height 0 at left edge.) etc (--- many other alternatives are possible). ※ : Variable height stand = jack. c. I propose a hint for Hart's A-frame walking mechanism. --- this idear is 30/100 points. i.e. bad (??). bump mechanism is needed. In the below Fig., the height RT is always constant, and it depends on 5 bars and ST, that is, it depends on 6 bars, further, if we change the length ST and VZ in the same ratio, the height RT is changed, but constant property is kept. (∵ △RST ∽ △RVZ) This is good property. We can control the leg trace by controlling the ST/ZV variable. --- i.e. The bigger ST, the smaller height RT. Other 4 bar sizes doesn't need to change. (If you understand the Hart's A-frame principle, you can understand this.) Problem is How to implement. c. In below Fig. outward: stopper UP, return: stopper DOWN, is good?? c. At the start point of return stroke, decrease the height of stand. And, after middle of return stroke, increase the height, and at the just end of stroke, height is just the maximum. In outward stroke, height is all constant (= must not change).
Fumio Imai, 2014/03/21, Created with GeoGebra |
(10_a) Centipede_ A-frame Alias: Musashikoganei legThis is an answer how to implement Hart's A-frame LEG. I introduce the moderator/ auditor (like a Hoekens linkage). cf. Original document explanation. As a result, EE' is horizontal straight line (= Piston movement). This is one of keypoint. Any straight line mechanism were OK. Even piston (friction) slider is OK. c. Please consider the tuning rule. c. This implementation is somewhat degraded from original above (10) concept. ∵ foot size should be zero. c. Shorter leg size is efficient than long leg. Piston movement efficiency can be reflected. Please check the parameter leg = 5 value case.
Fumio Imai, 2014/03/31, Created with GeoGebra |
(10_b) Centipede_ A-frame 2ndAs a matter of fact, I want to make a non-motor type walking leg.c. This is not simple. Lock control is needed. bad. c. In below Fig. , One lock sample is shown. Green parts are so. ZZ', A1A'1 vertical bars are Stopper to lock the pink Leg, and provide the Sandwich style slider lock bars. Points H'1 and R'1 are slide-bar ends. This Y-axis position is y(H1) or y(R1). (Implementation is not difficult. but needs much bars.) In outward stroke, the pink Leg bar is pushing by sandwiched both green bars. and is kept/ fixed vertical style. In return stroke, pink Legs are pushing by assistant bars (--- or ---). (If green lock mechanism was applied, no need the bent pink bar part. (???)) --- Please find more simple implementation, if exist.
Fumio Imai, 2014/04/03, Created with GeoGebra |
(10_c) Walking Bicycle Alias: Musashikoganei Bicycle ™c. Please check leg = 1.5, ll = 1.5, rr = 1.5, angle = 90° case, And consider its meaning. --- I couldn't understand. Someone, Please make a real machine and check its action. Q: In this case, pedal 1 cycle round, how long the machine go ahead? which is true? --- select one. (a) 2 pedal diameter (b) 2 pedal diameter + half circle (c) half circle (d) other [ ll = 1.5 causes the shrinking in half right area of crank, F''D = F''B, so point D looks stopping all time, --- perhaps, (a) is answer (= same as other parameter values case). ex. Change to ll = 1.6 , and compare to ll = 1.5 case.] Q: I can set the point B to the middle of JJ'. How to? (my secret.)
Fumio Imai, 2014/04/04, Created with GeoGebra |
(10_d) Centipede_A-frame_crankStride size = Amplified crank diameter.(Connect the lap part of leg to the crank directly.) This system, many tuning result exist. (0) init condition: lap=2, ll=3.3, rr=1.2, leg=3.2, angle=15°, C(3.33, 4.73) [On crank 0°, 180°, points D, C, E are colinear on horizontal line.] (1) lap=1.6, ll=1.8, rr=0.9, leg=3.2, angle=33°, C(1.86, 4.73) [I intended the minimum of y(E) = y(C) condition. ---- like a toe walking. (?)] (2) lap=1.4, ll=2.3, rr=0.9, leg=3.2, angle=7°, C(2.35, 5.52) [ Almost heel only walking. The C position value changing should be rewritten by double-clicking and replacing the C address value of Point-area in the left hand algebra frame directly.] c. How to return to (0) [= init condition] stat? ----- Please click ↻ refresh mark icon at upper right corner [title message: Reset construction].
Fumio Imai, 2014/04/10, Created with GeoGebra |
(10_e) Leg by Hart's InversorExact straight line variation.At least, By using exact straight line, the (systematic) design of leg becomes so easy. Tip: In below sample, + 6 bars, parallel transformation was done. I dare indicate. + 4 implementation of course can be done, too.
Fumio Imai, 2014/04/12, Created with GeoGebra |
(10-f) Leg by Chebyshev LinkageI don't accept the green frame, because it's too complex.
Fumio Imai, 2014/04/14, Created with GeoGebra |
(10-g) 2 bars crank amplifierThis figure tells me,(1) input is not B circle motion, real input is D up/ down motion. (2) orange curve is not needed 凸 (convex) shape, any wide shape is OK. 凹 (concave) crescent moon is very enough. (3) brown ll bar angle can be replaced to green long bar angle.
Fumio Imai, 2014/04/16, Created with GeoGebra |
(11) 45 degree slider AmplifierMapping twice.
Fumio Imai, 2014/04/21, Created with GeoGebra |
(12) Ultimate Hart's A-frame LegCircle through Three Points function, P, P', P'' tuning is real tuning, Point V (center) ▲ setting is only an accessary. (I recommend "ll size , setting to O'-End' length", if so, the tuning becomes easier/ comprehensive (?!).)
Fumio Imai, 2014/04/26, Created with GeoGebra |
(12-a) inner additional information
Fumio Imai, 26 April 2014, Created with GeoGebra |
(12-b) Exact straight stroke Hart's A-frame Leg
Fumio Imai, 2014/05/07, Created with GeoGebra |
(12-c) Imai's Hart's A-frame Leg (d < d' case)(12-b) was replaced by this.This is the result of Hart's A-frame No additional techunique mode. The bare A-frame motion induces the walking stroke curve. Input is A (slidable), A' (slidable) only. cf. Leg style carrier (VTR) (© Nagoya Institute of Technology in Japan) ,,, or NITech Carrying Robot (YouTube, 2011) ∊(included in) parent page: 2009 study (Sano Lab.), ∊(included in) Sano Lab. biped division (©Nagoya Institute of Technology) --- same thing possible. i.e. Below apparatus can use for VTR work easily., Don't you think so? c. Which is Before? Left or Right? If make VTR carrier, this is the pushing type, so Left is before. Perhaps. i.e. from right to left direction, push/ proceed. ------- In this case, This is the hand pushing/ pulling driven apparatus. by Other leg driven system. Not the motor driven apparatus.
Fumio Imai, 2014/05/11, Created with GeoGebra |
(12-d) Imai's Hart's A-frame Leg (d > d' case)Input is A (slidable), A' (slidable) only.
Fumio Imai, 2014/05/11, Created with GeoGebra |
(12-e) Imai's Hart's A-frame 7.5 Leg
Fumio Imai, 2014/05/22, Created with GeoGebra |
(12-f) Imai's Hart's A-frame 5.5 Leg (vertical)
Fumio Imai, 2014/05/24, Created with GeoGebra |
(12-g) Imai's Hart's A-frame 5.5 Leg (vertical, D < D' )
Fumio Imai, 2014/05/25, Created with GeoGebra |
(12-h) How to make Vertical Leg
Fumio Imai, 2014/05/29, Created with GeoGebra |