There are two main types of screws used on woodwind instruments to secure the keys in place; one is the rod or hinge screw and the other is the point or pivot screw.
This article deals with point screws and discusses how they work and the various pros and cons of the different types you're likely to see.

Basic principles:

Point screws allow for keys to be securely mounted to the body of the instrument whilst still allowing them to move in an appropriate fashion. Typically you'll find them used on long single keys where a rod screw would be impractical or undesirable. In most cases a point screw can be recognised by its large head (usually much larger than that of rod screws), though a more reliable way of spotting them is to look at the pillars at each end of a key - if you can see a screw head with a slot in it in each pillar then it's very likely the key is pivoted on such screws.

Here we see a typical setup in which a pillar is fitted with a point screw, which in turn supports a key barrel. Attached to the barrel would be various key arms or key cups.
This diagram represent the best-case scenario; the slotted head of the point screw fits flush into the pillar (so there are no edges sticking out on which to catch your fingers) and the tapered point of the screw exactly fits a corresponding hole in the pillar.
There is a very tiny gap between the end of the key barrel and the opposing face of the pillar. This keeps friction to a minimum and by preventing the key barrel from rubbing against the pillar also reduces wear to both components.

When suitably lubricated, this arrangement allows the key to rotate quite freely and smoothly, and because everything is a snug fit there's no free play in the mechanism. The key cannot move in any other fashion.

Point screw types:

These are the six most common types of point screws in use.
They're divided into two sections; proper points and parallel points.
From the top down we have:

The parts of the screw are broken down as follows:

The head - the largest diameter of the screw, which also houses the slot...where the screwdriver goes.
The thread - the section that screws into the pillar.
The tip - the 'business' end of the screw, which sits inside the key barrel.

Screws can vary in size - small ones would be found on flutes, oboes and clarinets - larger ones on saxophones.
These too will vary in size, shape and design - the threads will be different between manufacturers, the diameter and thickness of the heads vary, the length of the tips too.
This is an important consideration - if you happen to lose a screw (they do sometimes drop out of of their own accord) you can't just bung any old thing back in the pillar as there's a very slim chance that it will fit...or even if it appears to fit, it very probably won't be of the correct dimensions. Forcing a screw with a different thread into a pillar may damage it severely - and if it gets so tight that it breaks, you'll end up with a hefty bill for putting it right. It's not uncommon to find that someone has gone to all the trouble of forcing a point screw into a pillar (and thus 'crossing' the thread) only to find that the tip is too small for the job.

Incidentally, if you do happen to lose a point screw (and it happens to the best of us from time to time) poke a matchstick into the pillar. It's strictly a temporary measure, but it'll get you through a gig or two.

The pros and cons:

I referred the the proper point screw as the 'King' of screws earlier, and here's why.

On the left is a diagram of what happens to the setup shown in the opening diagram after the instrument has seen a good few years use.
The pillar and screw haven't moved - but now there's a noticeable gap between the tip of the point screw and the key barrel. This will mean that the barrel is able to wobble on its pivot screws, and when that happens it leads to a rattly action that feels sloppy and imprecise. It also means that any key cups and arms attached to the barrel won't move with as much accuracy - so a pad might leak or a connection with another key won't be spot on (this can lead to what's known as a regulation leak...a leak caused by the mechanism rather than a pad).
It also means that any lubrication between the screw tip and the barrel will get pumped out...and grit can get in...so the wear gets ever worse.
You can see too that the gap between the pillar's face and the key barrel has increased because the point screw can no longer hold the barrel off - so it can now rub against the pillar and wear itself down.

Here's the clever thing though - because the tip of the screw is a proper taper, if there were a means of allowing it to push deeper into the key barrel it would once again fit snugly and all would be well.
And there is such a means - by reaming the pillar. This simply involves removing a small amount of metal from the head end of the pillar, which then allows the screw to be driven further into the pillar...thus pushing the tip further out from the face. The section of the pillar that would be removed is indicated in red. The actual amount removed would be far smaller than shown, and such a job would need doing maybe two or three times in an instrument's life - assuming it was kept well lubricated inbetween-times.

This is half of the job known as tightening the action - the other half being that which deals with free play on keys mounted on rod screws.

Here's a slight variation on the theme.
In this instance the barrel has been drilled out with a cylindrical hole.
This is far more likely to to be the case than finding a barrel that's been properly reamed with a tapered hole to match the screw tip. It's a lot harder to get a tapered hole exactly right - one tiny fraction too big and the key will never sit snugly...and the manufacturer would have to throw it away and start again. Very costly indeed.
That's why I said 'in an ideal world', because this diagram shows what you're more likely to encounter.

It's our good old proper point screw again, but note how almost all of the tip is sitting in air.
The part of the tip that's actually in contact with the barrel is marked in red. As with most of these diagrams it's slightly exaggerated in order to make it clearer, so you could reasonably expect rather more of the tip to be doing some work.
I've shown the point of contact as being near the base of the tip, but it could quite easily be near the end of the tip. It doesn't really matter that much (although you might have realised that there won't be much more room for adjustment with this particular setup) as long as there's a single point of contact that holds the key barrel snugly.

The variations on the proper point screw (the elliptical and the shoulderless) deal with the wear in exactly the same way - though because the shoulderless screw has no head it does not require the pillar to be reamed...you simply screw it in further. This is simple and efficient way of dealing with wear but it does, however, require a means of locking the screw in place - and this can be in the form of a small grub screw, a lock-nut, a nylon insert or a drop of threadlocking fluid.

So this explains how and why proper point screws work, and what makes them such a desirable feature. Let's look now at why the parallel types fare less well.

As you can see it's much the same setup as the proper point screw.
The diagram show the 'ideal world' scenario, with the cylindrical tip of the screw nestling snugly inside the key barrel, which has been drilled so as to perfectly accommodate it.
Unfortunately it seldom works out that way. What's more likely to be the case is that the hole extends some way into the barrel - as marked by the dotted lines.

When this occurs it allows for the barrel to move back and forth along the screw tip - so the only thing preventing it from doing so is having the ends of the key barrel rub up against the pillar face.
We already know that's not a good idea as it adds friction and leads to wear...and when that happens it leads to yet more wear.

However, as long as the diameter of the hole in the barrel is a close fit to that of the screw tip the key will at least be unable to wobble.
This means that the setup is unlikely to lead to regulation problems but could, just about, lead to slight leaks in pads. At least until the hole wears...and then it all gets a bit nasty.

And here it is, a classic example of wear in a key pivoted on a parallel point screw.
As per the wear with a proper point screw, you can see that the key barrel has worn around the diameter of the hole. so the tip is now floating in free air.
When this happened with the proper point screw setup it was able to be taken up by means of driving the whole screw deeper into the pillar. But that's not going to work here.

If we assume this diagram accurately represents the state of wear in a typical key barrel you can see that driving the screw in deeper would allow for the end of the tip to meet the bottom of the hole. But that wouldn't be of much use - the best that it would do would be to prevent the ends of the barrel rubbing against the pillar face...the key would still wobble. Besides, as we saw just above, the hole is often very much deeper.

It should be quite clear then that's there's very little that can be done to take up the wear.
Well, there is one method - which involves swedging (pronounced sway-jing) the key barrel. This technique compresses the barrel and thus decreases the size of the hole. It's a technique that's used to take up the wear in keys mounted on rod screws. It's hard work, and therefore expensive, and it often leaves visible marks on the key barrels.
It's also the case that it's not always possible to swedge a key barrel. The one shown in the diagram is conveniently bare, but many of the will have a key arm attached at precisely the place where you'd need to swedge the key.
In such cases rather more drastic measures are called for - such as filling up the hole with silver-solder and re-drilling it.

Here's the same problem, but this time with a pseudo or bullet point screw.
Remember, the definition of a parallel point screw is that its tip doesn't get increasingly larger in diameter - so it's prone to exactly the same problems as the cylindrical point screw.

It does, however, have a slight advantage - it has a tapered tip. In effect it's half a proper point screw.
The diagram show the screw fitted to a barrel that has some wear - note the gap above and below the tip - but the coloured sections are where it gets interesting.
The green section represents that portion of the key barrel that the end of the tip is in contact with. As long as this remains the case this type of screw will function as a proper point screw...i.e. perfectly well.
When it wears it can be driven further into the pillar...but only as far as the green portion extends. Once it gets much beyond this you will have driven the head of the screw so far into the pillar that there won't be much thread left in it - and that's not at all good.
At this point the tip enters the red section...and with the end now floating in free space the screw reverts to being nothing more than a fancy cylindrical screw...with all the disadvantages that come with it.
The spear-headed point screw would work in exactly the same fashion...though why anyone would go to all the trouble of making such a screw I have no idea - it seems utterly (and I've been waiting for this bit) pointless.

All this assumes that the hole in the key isn't already too deep - and unfortunately it usually is. The easy way to check this is to remove the point screw from the pillar and poke the tip into the hole in the barrel. If the screw goes in right up to the thread then the hole is too deep. As it happens, this is one way in which parallel point screws can be 'botched' to take up free play...they're driven into the pillar until the threaded portion of the screw comes out from the pillar face - the barrel then rubs up against the thread, giving the appearance of being nice and snug. And it is, but only for as long as it takes the rough thread to chew away the metal of the barrel...which won't take very long at all.

A fascinating variation is this system found on modern Selmer saxophones.
These instruments use a unique method to automatically adjust for any wear in the action by means of a sprung cylinder inserted into the bore of the key barrel.

As the tip of the screw wears away the contact point in the cylinder, the spring pushes the cylinder forward to close the gap (obviously this wear happens at an extremely slow rate). This ensures that the business end of the pseudo point screw is always in contact with the key barrel - and this means that you should never need to ream the pillars to take up wear in the action.

Sounds ideal, but there are one or two drawbacks.

Because the system requires that there's a bit of a gap between the end of the key barrel and pillar face (otherwise the sprung cylinder would simply butt up against the pillar and you'd be back to square one once the point screw tip starts to wear the barrel), and because there's a spring in the barrel...or one at each end actually...you can never adjust the action so that it's really tight.
By tight I don't mean stiff...but if you've ever wiggled a key properly fitted between two proper point screws you'll know exactly what I mean. The key can move up and down freely but there's no lateral movement.

The other drawback is that it's possible for the cylinder to wear in the key barrel...and then you're in trouble.

Technically speaking you can replace the cylinder...but if the barrel's worn then there's little point. It could get very messy!

In the review section you'll often see comments like "I was disappointed to find pseudo point screws had been used..." and perhaps this article explains why I feel that way about them. Wear and tear is part of a woodwind instrument's life, and if you've coughed up well into four figures for a nice sax or clarinet etc. it's a bit disheartening to find that, sooner or later, you're going to run into problems when it comes to tightening the action.
The worst of it is, the part that's responsible for the problem isn't even replaceable. Putting a new point screw in when a key has worn isn't going to change anything - you'd have to change the key itself.
There is an option though - changing the type of point screw fitted. In theory you could take out the pseudo or parallel points screws and replace them with proper points - but this upgrade rather relies on being able to find point screws of a suitable size and shape. It's tricky, admittedly, but not always impossible. If all else fails there's always the option of having them custom made. This won't be a particularly cheap option, but it will be a one-time fix and you'll be able to have the wear and tear in the keywork adjusted out for at least as long as your playing life.

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