Member postings for Tony Jeffree

Duncan -

Thanks - that is very useful indeed - the evolute of a cycloid is a replica of that cycloid shifted by 180 degrees, which is what is needed for the cheeks to work. It also indicates that the generating circle for the cheeks must have the same radius as the desired cycloid's generating circle - as per previus discussions this must be half of the effective length of the pendulum. Pretty clear then that this was Huygens' intent.

Regards,

Tony

Michael

My apologies if I have offended anyone - that was not my intent.

Regards,

Tony

I'm sorry, that's absurd. What if I choose a convenient size of 0.000001mm as the radius of the generating circle?

That's the one

I don't think it is. To repeat - I may be wrong, but it seems to me that the Wiki discussion is all about demonstrating that if the pendulum bob follows a cycloidal path, then the pendulum will be isochronous, and not about how the cycloidal path is created. Where I get off the bus is the apparent assumption that the cycloidal cheeks get you there (modifying the bob's path such that it travels along acycloid). If I've missed it in the Wiki explanation, well and good, but right now I'm not seeing it.

Only if your car is up on bricks. Mind you, if it is, the wheels have probably been nicked...

Edited By Tony Jeffree on 08/09/2023 19:17:15

Plausible answer, but where's the proof?

I don't dispute that, but I haven't seen that proved, or what radius of generating circle for the cycloid is required in order for it to work.

Correct me if I am wrong, but the proofs seem to be focused on proving that if the particle (pendulum bob) follows a cycloidal path, then it will be isochronous. I couldn't see (maybe I didn't look hard enough) any discussion of how the use of cycloidal cheeks corrected the bob's path to be cycloidal, and what parameters the cheels needed to have in order for this to happen.

Michael

I certainly don't claim to have a grip on all of this! My observations above relate only to the discussion of the roller-with-attached-pendulum-suspended-under-a-(magnetic)-plane model - for that model to work you would (I believe) need the roller diameter to equal the effective pendulum length.

The Huygens approach seems to be to use cycloidal cheeks - which reduce the pendulum's effective length as the amplitude increases. I've yet to try to get my head round why he chooses 1/2 the pendulum length to generate the curves for the cheeks.

Regards,

Tony

Of course, a moment's thought about the wheels on a car would have brought you to the same conclusion. A point on the tread follows a near-enough cycloidal path (give or take the flexibility of the tyre), but you'd better hope that the wheel axle doesn't follow a cycloid, or it is going to be a rather bumpy ride!

Edited By Tony Jeffree on 07/09/2023 14:05:35

https://nathanfriend.io/inspiral-web/

Incidentally, my observation that the centre of the roller follows a straight line should tell you that the centre of mass of the bob needs to be on the circumference of the roller (earlier on there was some uncertainty as to whether the roller radius or diameter should equal the pendulum length - clearly it has to be the diameter, or the bob would travel a straight line path.)

Edited By Tony Jeffree on 07/09/2023 13:52:47

Just in case there is still any doubt about what is going on here, it might be worth digging out your old Spirograph set and playing with that. I found an online Spirograph sim that illustrates the point with a tad of imagination:

The two traces in the pic are formed by (1) using a point close to the circumference of the roller (trace near enough cycloidal), and (2) a point close to the centre of the roller (trace approaching a flat line). It will be no surprise that if you trace the path of the centre of the roller, it would actually be a straight line. What the sim doesn't allow, but which you could do with a real spirograph, is to strap a larger wheel onto the smaler one to allow you to see what happens when you trace a point that is outside the circumference of the roller - e.g., a point on the "bob". It doesn't take much to visualise what the trace looks like - apart from anything else, on each full rotation it passes through the horizontal plane, performs a retrograde loop, and then passes back through the horizontal plane.

Intriguing idea.

Just a thought - but would it help in tuning the behaviour of this setup if the coins/discs were running on a curved (rather than flat) track?

They're cheap as chips & look easy enough to set up -

https://hobbycomponents.com/wired-wireless/1054-433mhz-transmitter-receiver-modules-with-antenna

Of course, even with something like this that is on the face of it pretty simple and transparent, there will inevitably be the potential for variable delays, given that the transmitter & receiver operation isn't instantaneous, and the receiver will have some threshold for detecting the carrier. Worth a try though.

Edited By Tony Jeffree on 03/08/2023 12:01:39

Edited By Tony Jeffree on 03/08/2023 12:16:51

Peatol is the UK brand name for the Taig lathe & mill.

I have just heard from Ian Cooper that Peter passed away last week. Peter, who was the proprietor of Peatol Machine Tools, was well known to many of our community and his stall at the various UK shows was a familiar sight until recent years. I got to know him well over the years following my purchase of a Peatol lathe, and later a CNC mill, and he was kind enough to give me space on his stall at some of the shows to sell my Divisionmaster products.

He will be greatly missed.

" You are perfectly correct in saying that other clocks have been checked and adjusted by astronomical observations but these are existing events and not new technologies."

Existing events/phenomena, maybe, but in order to observe those phenomena, new technologies were required (such as optical telescopes,...). One could argue successfully that the frequency of oscillation of an atom is a similarly existing phenomenon; we just need the modern equivalent of the optical telescope to observe its frequency and make use of it.

I have little doubt that if you time travelled back to Harrison's time with an atomic clock in your back pocket and let him borrow it for a few months he would have had very few qualms making use of the opportunity, just as he did with the other techniques he invented in order to improve the way his clocks performed, none of which existed before his time.

Why use a less accurate reference when access to a world class time standard is freely available?

I entirely "get" and agree with Dave's point that the pendulum (other resonators are available) should be independent - i.e., you aren't constructing some kind of phase lock between the reference clock and your own resonator, so the resonator and its control circuitry/mechanics are truly detached from the reference, but I'm having a hard time understanding what the philosophical difference is between (e.g.,) constructing/adjusting a mechanical temperature compensation mechanism by observation/measurement relative to a reference clock and achieving the same result by constructing tables in software and using that data in an algorithm to control the frequency of the oscillator (or to correct the indicated time).

Cheers,

Tony

Either way though you are still in some sense building the reference clock(s) into your clock.

Edited By Tony Jeffree on 16/07/2023 11:19:39