Grasshopper Lego Clock Escapement W21

Grasshopper Lego Clock Escapement W21

Single pivot grasshopper escapement (John Harrison, ca 1722)

Here, the pivot is situated IN the pendulum (rather than in an arm perpendicular to the p). This arrangement assures that force-components IN the pendulum are not pressing sideways on the p-arbor, which should be avoided in delicate p-suspensions (spring, knife-edge).
Each pallet is made of a 2x2 tile #3068, sandwiched between two 1x4 liftarms #32449 that are pressed together by two axles in the axle-holes.
No buffers to absorb recoil forces have been installed. Actually, they are necessary, because now the p-support is pressed slightly to the left when the lower pallet causes recoil.
(The usual arrangement is different from this: the wheel axis is at the same height as the pendulum axis (which makes the pallets-wheel arrangement asymmetric, and, in fact, more complicated). Then the whole thing is rotated 90 deg. clockwise, and the pendulum is attached perpendicular to the red box at the p.arbor)

Geometry: The single pivot and the scapewheel axis are at the same height. R1 is the height of the p-axis above the pivot. The angle subtended by the sw-axis and the impact points of the pallets is ALFA. When, at contact, the pallet arms are tangent to the sw circumference (radius R2), the distance r between the common pivot and the sw-axis is R2/cos(ALFA/2). The length of the pallet arms is R2*tan(ALFA/2). The (full) swing angle BETA of the p can now be approximated by BETA = (R2/R1) * (360/N) * sin(ALFA/2)




where N is the number of teeth of the sw.
Here, ALFA = 120 deg (90 deg. might be a better choice; however, decreasing ALFA reduces the impuls-component perpendicular to the p).
R1=5, R2=4.5, and N=14, which gives BETA=20 deg., in good agreement with the actual value.
To reduce this value, it seems appropriate (apart from increasing N) to increase R1 (with R2 given by the sw). However, this would severely affect the tangent geometry, making the pallets approach the sw at a small angle (they rotate with the p about the p-axis), causing unwanted contacts with neighboring teeth.

A more involved analysis, by Peter Hastings bhi, (N=120, R1 ~ 0.9, R2 = 5.625/2 in., ALFA ~ 50 deg.) can be found here: www.bhi.co.uk/update/Grasshopper.pdf




NB: Only after I uploaded this video, I realized that the driving weight was too heavy.
This is obvious from the bending of the lower pallet arm and it's banking pallet. After
correction, the weight, 55g, drops 13 cm/min (still too much), and no bending is observed. Nevertheless, I think at least one composer will be necessary to minimize the significant domination of the escapement.

Category:

Science & Technology

Tags:

• grasshopper
• single
• pivot
• lego
• clock
• escapement
• John
• Harrison
• pendulum

[Rallynumanair]

It looks like you used two 2x2 smooth plates. Why these instead of two 2x2 round plates with the hole for an axle in the center?

[BenVanDeWaal]

@Rallynumanair The pallets must have the shape of a hook, in which the toothpoints can rotate; an axle would be unreliable for that purpose. Moreover, for each pallet I use 2 axles, wide apart for one pallet, close apart for the other one. In this way the pallet arms can have the same pivot, in the middle of the pendulum and the pressure points are in the centerline of the pendulum.

[Lewissnicholls]

I really like your mechinisums, but are they ever accurate?

[BenVanDeWaal]

@Lewissnicholls I don't think so. The Lego wheel I use has only 14 teeth (rather than, e.g., in the Harrison clock, 120), which makes the swing angle too large. Moreover, the escapement dominates the pendulum, which results in a non-harmonic motion. For precision (at least with Lego) you should go to the gravity escapements.

[vinesthemonkey]

When the video loads, it says the video is 1:01, then it changes to 1:00

[KEvronista]

ah! much better. the design is so....simple!

KEvron

[Lewissnicholls]

@BenVanDeWaal Okay cool, thanks for the reply. I'm going to give this ago.