A Math and Mechanism problem

[Paul Alciatore]

Yea, the other favorite my math professors used was, "It is obvious that ...". That usually meant you had two or three hours of effort in store that night. And an embarrassing question at the next session of that class. Marv, I guess your professors were higher class than mine and had further refined that statement.

I know my statement above is true. I also know it is going to take a bunch of math to prove it. And I really do not have time for that now. Take my word for it or do the math and post it, your choice.

[Stepside]

Paul

Thank you for the input. The vernier scale information will be of use for future projects or to answer a question on Jeopardy. My learning style is closely coupled to having to have a use for the knowledge before really learning it. My math teachers all thought you should be thrilled with the answer and usually did not know how to apply the knowledge to an actual problem.

What I am making is a rotary valve with adjustable timing for a compressed air engine.

Thanks again
Pete

[oldtiffie]

I do appreciate the maths as provided by our two resident Physicists and others here.

But.

From the application of the indexing/vernier application the degrees accuracy of the manufacturing will determine the usefulness of the discs.

This will include the accuracy of the location of the discs and (guessing here) the location pin on the pitch circle as well as the diameter of every hole and the diameter of the locating pin (to be inserted into both discs).

Perhaps the "pinned" disc and pin as a set will need to be allocated by the same pin in a fixed block (as on a "Spindex").

The OP will need to determine his allowable tolerances - including the circular pitches.

Various tolerances (and their limits) at various points will be either/and accumulative (+ve or -ve) - ie additive or subtractive.

It all depends on the output accuracy that the OP requires - as well as the machines and measuring tools that the OP has available.

This may well be heading toward some serious metrology applications - including ambient temperature/s.

Having the design in say a good CAD system is one ting but the quality of the output (finished job) may not live up to the design parameters.

I hope it does.

[Barrington]

As I do not need the entire 360 degrees I will just drill the holes lie in one quadrant.

Pete, I don't know how much adjustment your application will require, but if you just drill holes in one quadrant, that will only provide a 'continuous' range of 36°.

If that's o.k. then please ignore the following...

If you do need more, then the table below might be useful to work out how many holes are needed. The box covers the available settings using only one quadrant - the green area shows the 342°->18° available without gaps; 341° and 19° cannot be set.

(Columns are 10° steps, rows 9°, table is simply the difference of the two.)



Cheers

.

[Lew Hartswick]

Paul

Thank you for the input. The vernier scale information will be of use for future projects or to answer a question on Jeopardy. My learning style is closely coupled to having to have a use for the knowledge before really learning it. My math teachers all thought you should be thrilled with the answer and usually did not know how to apply the knowledge to an actual problem.

Thanks again
Pete

Re - Teachers: That is what made for the best math teacher I ever had. Math 55 in college, the teacher was a lady who had worked at MIT during WWII on some military projects
and she REALLY could make the point of the relation between the stuff in the book and real life work.
...lew...

[Stepside]

Barrington

That is a great chart and will give me information for future projects. The quadrant should give me more than enough adjustment. If my workmanship is of any quality whatsoever, I should need only a degree or two of adjustment. The rest of the adjustment would be there to cover "foggy thinking" as well as some "outside the box" ideas.

Thank you for taking your time to work up the chart.

Pete

[A.K. Boomer]

I cannot remember the number of holes in the cam or the cam sprockets but this is how your set up your valve timing on the older porsche 911's and in fact is just a great system esp. on DOHC engines as you can separate the cams and retard the intakes and advance the exhausts for higher end (RPM) power...

of course now with VVT this system is becoming obsolete - still - for back in the day it was all they had to personally tune an engine to your particular needs...

[mklotz]

" My learning style is closely coupled to having to have a use for the knowledge before really learning it."

While I fully understand this attitude, I'm of the opinion that a good student should, as part of his learning process, determine why his teachers think it's important to teach him the subject at hand. One has to presume that, given a decent school, the curriculum has been chosen with the eventual benefit to the student as primary consideration.

"My math teachers all thought you should be thrilled with the answer and usually did not know how to apply the knowledge to an actual problem."

It depends on the problem. If one is studying multiplication, then the answer is everything. If one is learning to prove geometric theorems then the process is everything.

Put yourself in the position of the teacher. The students have only very limited experience and seldom do much of anything involving math beyond simple arithmetic in their everyday life. If you teach the Pythagorean theorem to twelve year-olds, what sort of application is going to resonate with them?

What they really need to teach is an expansion of what I said in my first paragraph - a course that shows them HOW to learn and explains, as much as possible, WHY they need to learn even if no immediate application of the subject occurs to their immature minds.